Fixing the regex
You've got to let the regex engine know exactly how many preceding groups there will be. On top of that, you'll need to use the .keyword field because the standard analyzer that's applied on text fields by default will have split the original string by whitespace and converted each token to lowercase -- both of which should be prevented if you aim to work with capture groups.
Having said that, here's a working regexp query:
GET /test/_search
{
  "query": {
    "regexp": {
      "info_list.keyword": "( ?[a-zA-Z0-9]+){2} 5678 .*"
    }
  }
}
Extracting the groups before ingestion
Should I change the mapping of the field?
I'd say go for it. When you know which group you'll be targeting, you should, ideally, extract the groups before you ingest the documents.
See, what I'd do in your case is the following:
- Preserve the original info_listas a keyword for consistency
- Extract the groups in the programming language of your choice, annotate them with keys atoi(analogously to the way you naturally think about said groups).
- Store store them inside a nestedfield in order to guarantee that the connections between the keys and the values aren't lost due to array flattening.
In concrete terms:
- Set up a mapping
PUT extracted-groups-index
{
  "mappings": {
    "properties": {
      "info_list": {
        "type": "keyword"
      }, 
      "info_list_groups": {
        "type": "nested",
        "properties": {
          "group_key": {
            "type": "keyword"
          },
          "value": {
            "type": "keyword"
          }
        }
      }
    }
  }
}
- Ingest the doc(s)
POST extracted-groups-index/_doc
{
  "info_list": "1234 2D 5678 8765 5678 1111 2222 3333 1",
  "info_list_groups": [
    {
      "group_key": "a",
      "value": "1234"
    },
    {
      "group_key": "b",
      "value": "2D"
    },
    {
      "group_key": "c",
      "value": "5678"
    },
    { ... } // omitted for brevity
  ]
}
- Leverage a pair of nestedtermqueries:
POST extracted-groups-index/_search
{
  "query": {
    "nested": {
      "path": "info_list_groups",
      "query": {
        "bool": {
          "must": [
            {
              "term": {
                "info_list_groups.group_key": "c"
              }
            },
            {
              "term": {
                "info_list_groups.value": "5678"
              }
            }
          ]
        }
      }
    }
  }
}
Harnessing the full power of Elasticsearch 
The downside of the nested approach is that it'll increase your index size. Plus, the queries tend to get quite verbose and confusing. If you don't want to go that route, you can leverage what's called a custom analyzer.
Such an analyzer is typically composed of:
- a tokenizer(which receives character streams and outputs a stream of tokens -- usually words)
- and a few token filterswhose role it is to mold the tokens into the desired form.
In concrete terms, the aim here is to:
- Take in the string - 1234 2D 5678 8765 5678 1111 2222 3333 1as a whole
 
- Locate the individual groups separated by whitespace - --> - (1234) (2D) (5678) (8765) (5678) (1111) (2222) (3333) (1)
 
- Annotate each group with its alphabetical index - --> - a:1234 b:2D c:5678 d:8765 e:5678 f:1111 g:2222 h:3333 i:1
 
- And finally split the resulting string by whitespace in order to use queries like - a:1234and- c:5678
 
All of this can be achieved through a combination of the "noop" keyword tokenizer, and pattern_replace + pattern_capture filters:
PUT power-of-patterns
{
  "mappings": {
    "properties": {
      "info_list": {
        "type": "text",
        "fields": {
          "annotated_groups": {
            "type": "text",
            "analyzer": "info_list_analyzer"
          }
        }
      }
    }
  },
  "settings": {
    "analysis": {
      "analyzer": {
        "info_list_analyzer": {
          "type": "custom",
          "tokenizer": "keyword",
          "filter": ["pattern_grouper", "pattern_splitter"]
        }
      },
      "filter": {
        "pattern_grouper": {
          "type": "pattern_replace",
          "pattern": "((?<a>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<b>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<c>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<d>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<e>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<f>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<g>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<h>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))((?<i>(?:\b ?[a-zA-Z0-9]+){0}.*?([a-zA-Z0-9]+) ?))",
          "replacement": "a:${a}b:${b}c:${c}d:${d}e:${e}f:${f}g:${g}h:${h}i:${i}"
        },
        "pattern_splitter": {
          "type" : "pattern_capture",
           "preserve_original" : true,
           "patterns" : [
              "([a-i]\\:[a-zA-Z0-9]+)"
           ]
        }
      }
    }
  }
}
Note that the friendly-looking regex from above is nothing more than a repetitive named group catcher.
After setting up the mapping, you can ingest the document(s):
POST power-of-patterns/_doc
{
  "info_list": [
    "1234 2D 5678 8765 5678 1111 2222 3333 1"
  ]
}
And then search for the desired segment in a nice, human-readable form:
POST power-of-patterns/_search
{
  "query": {
    "term": {
      "info_list.annotated_groups": "c:5678"
    }
  }
}