Subgroups — C₂²×Dic₃×D₁₁ #11761404

Order 1056.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₁₁
commutator, hypocenter	C₃×C₁₁	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₁₁
Fitting, socle	C₂³×C₃×C₁₁	C₂²
prime radical	C₂³×C₃×D₁₁	C₂
cosocle	C₂×C₃×C₁₁	C₂⁴
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃₃	C₂	semidirect
3. C₂²×C₁₁×Dic₃	C₂	semidirect
4. C₂×Dic₃×D₁₁	C₂	direct (N × H)
7. C₂²×C₃×D₁₁	C₄	semidirect
9. C₂×Dic₃₃	C₂²	semidirect
10. C₂×C₁₁×Dic₃	C₂²	semidirect
11. Dic₃×D₁₁	C₂²	direct (N × H)
16. C₂²×C₃×C₁₁	C₂×C₄	semidirect
18. C₂×C₃×D₁₁	C₂×C₄	semidirect
20. Dic₃₃	C₂³	semidirect
21. C₁₁×Dic₃	C₂³	semidirect
24. C₂²×D₁₁	Dic₃	direct (N × H)
29. C₂×C₃×C₁₁	C₂²×C₄	semidirect
31. C₃×D₁₁	C₂²×C₄	semidirect
35. C₂²×Dic₃	D₁₁	direct (N × H)
36. C₂²×C₁₁	C₂×Dic₃	semidirect
38. C₂×D₁₁	C₂×Dic₃	direct (N × H)
42. C₃×C₁₁	C₂³×C₄	semidirect
49. C₂×Dic₃	C₂×D₁₁	direct (N × H)
50. C₂×C₁₁	C₂²×Dic₃	semidirect
52. D₁₁	C₂²×Dic₃	direct (N × H)
59. C₂²×C₃	C₄×D₁₁	semidirect
62. Dic₃	C₂²×D₁₁	direct (N × H)
63. C₁₁	C₂³×Dic₃	semidirect
71. C₂×C₃	C₂×C₄×D₁₁	semidirect
75. C₂²	Dic₃×D₁₁	direct (N × H)
79. C₃	C₂²×C₄×D₁₁	semidirect
81. C₂	C₂×Dic₃×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₁₁	2
C₂²×Dic₃₃	2
C₂²×C₁₁×Dic₃	2
C₂×Dic₃×D₁₁	2
C₂²×C₄×D₁₁	3
C₂³×Dic₃	11

Subgroups — C22×Dic3×D11 #11761404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₃×D₁₁ #11761404