Subgroups — C₂²×#63143 #11761413

Order 1056.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#63143	C₂	1	12	yes	maximal, direct product factor
5	C₂²×Dic₂₂	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₃	C₂²	1	6	yes	—
8	C₂×C₁₁×Dic₃	C₂²	1	6	yes	—
9	C₂×C₃×Dic₁₁	C₂²	1	6	yes	—
10	#63143	C₂²	1	16	yes	direct product factor
11	C₂²×C₄×C₁₁	—	3	1	no	—
12	C₂²×Dic₁₁	—	3	1	no	—
13	C₂²×Dic₁₁	D₃	1	1	yes	characteristic
14	C₂×Dic₂₂	—	3	12	no	—
15	C₂²×C₃×C₁₁	Q₈	1	4	yes	complemented
16	C₂²×C₃×C₁₁	C₂³	1	3	yes	—
17	Dic₃₃	C₂³	1	4	yes	—
18	C₃×Dic₁₁	C₂³	1	4	yes	—
19	C₁₁×Dic₃	C₂³	1	4	yes	—
20	C₂²×Dic₆	—	11	1	no	maximal, Hall
21	C₂³×C₁₁	C₂×D₃	1	1	yes	characteristic
22	C₂×C₄×C₁₁	—	3	6	no	—
23	C₂×Dic₁₁	—	3	6	no	—
24	C₂×Dic₁₁	C₂×D₃	1	6	yes	—
25	Dic₂₂	—	3	16	no	—
26	C₂×C₃×C₁₁	C₂×Q₈	1	6	yes	complemented
27	C₂×C₃×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₂²×C₃×C₄	—	11	1	no	—
29	C₂²×Dic₃	—	11	1	no	—
30	C₂²×Dic₃	D₁₁	1	1	yes	characteristic
31	C₂×Dic₆	—	11	12	no	—
32	C₂²×C₁₁	Dic₆	1	4	yes	complemented
33	C₂²×C₁₁	C₂²×D₃	1	3	yes	—
34	C₄×C₁₁	—	3	4	no	—
35	Dic₁₁	—	3	4	no	—
36	Dic₁₁	C₂²×D₃	1	4	yes	—
37	C₃×C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
38	C₂²×Q₈	—	33	1	no	Sylow
39	C₂³×C₃	C₂×D₁₁	1	1	yes	characteristic
40	C₂×C₃×C₄	—	11	6	no	—
41	C₂×Dic₃	—	11	6	no	—
42	C₂×Dic₃	C₂×D₁₁	1	6	yes	—
43	Dic₆	—	11	16	no	—
44	C₂×C₁₁	C₂×Dic₆	1	6	yes	complemented
45	C₂×C₁₁	C₂³×D₃	1	1	yes	characteristic
46	C₂×Q₈	—	33	12	no	—
47	C₂²×C₄	—	3	1	no	—
48	C₂²×C₄	—	11	1	no	—
49	C₂²×C₄	—	33	1	no	—
50	C₂²×C₃	Dic₂₂	1	4	yes	complemented
51	C₂²×C₃	C₂²×D₁₁	1	3	yes	—
52	C₃×C₄	—	11	4	no	—
53	Dic₃	—	11	4	no	—
54	Dic₃	C₂²×D₁₁	1	4	yes	—
55	C₁₁	C₂²×Dic₆	1	1	yes	characteristic, complemented, Sylow
56	C₂³	D₃×D₁₁	1	1	yes	characteristic
57	Q₈	—	33	16	no	—
58	C₂×C₄	—	3	6	no	—
59	C₂×C₄	—	11	6	no	—
60	C₂×C₄	—	33	6	no	—
61	C₂×C₃	C₂×Dic₂₂	1	6	yes	complemented
62	C₂×C₃	C₂³×D₁₁	1	1	yes	characteristic
63	C₂²	#63143	1	4	yes	direct product factor
64	C₂²	C₂×D₃×D₁₁	1	3	yes	—
65	C₄	—	3	4	no	—
66	C₄	—	11	4	no	—
67	C₄	—	33	4	no	—
68	C₃	C₂²×Dic₂₂	1	1	yes	characteristic, complemented, Sylow
69	C₂	C₂×#63143	1	6	yes	direct product factor
70	C₂	C₂²×D₃×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₁₁
commutator, cosocle	C₂×C₃×C₁₁	C₂⁴
Frattini	C₂	C₂²×D₃×D₁₁
Fitting, socle, prime radical	C₂³×C₃×C₁₁	C₂²
hypocenter	C₃×C₁₁	C₂²×Q₈
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂×#63143	C₂	direct (N × H)
10. #63143	C₂²	direct (N × H)
15. C₂²×C₃×C₁₁	Q₈	semidirect
26. C₂×C₃×C₁₁	C₂×Q₈	semidirect
32. C₂²×C₁₁	Dic₆	semidirect
37. C₃×C₁₁	C₂²×Q₈	semidirect
44. C₂×C₁₁	C₂×Dic₆	semidirect
50. C₂²×C₃	Dic₂₂	semidirect
55. C₁₁	C₂²×Dic₆	semidirect
61. C₂×C₃	C₂×Dic₂₂	semidirect
63. C₂²	#63143	direct (N × H)
68. C₃	C₂²×Dic₂₂	semidirect
69. C₂	C₂×#63143	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×Dic₃₃	2
C₂²×C₁₁×Dic₃	2
C₂²×C₃×Dic₁₁	2
C₂×#63143	2
C₂²×Dic₂₂	3
C₂²×Dic₆	11

Subgroups — C22×#63143 #11761413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#63143 #11761413