Subgroups — C₁₁×#237 #10587271

Order 528.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₁×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₄×D₃×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#41	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₁₁	C₂²	1	2	yes	—
8	C₂×D₃×C₁₁	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×Dic₃	C₂²	1	2	yes	—
11	C₁₁×Dic₃	C₂²	1	1	yes	characteristic
12	Q₈×C₁₁	—	3	1	no	—
13	D₄×C₁₁	—	3	2	no	—
14	D₄×C₁₁	D₃	1	1	yes	characteristic, complemented
15	C₂×C₄×C₁₁	—	3	2	no	—
16	C₂×C₄×C₁₁	—	3	1	no	—
17	C₂×C₃×C₁₁	—	2	2	no	—
18	C₂×C₃×C₁₁	C₂³	1	1	yes	characteristic
19	D₃×C₁₁	—	2	1	no	—
20	#237	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₁₁	—	3	1	no	—
22	C₂²×C₁₁	C₂×D₃	1	2	yes	—
23	C₄×C₁₁	—	3	1	no	—
24	C₄×C₁₁	—	3	2	no	—
25	C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
26	C₃×C₁₁	#41	1	1	yes	characteristic, complemented, Hall
27	C₃×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
28	#67	C₂×C₁₁	1	2	yes	complemented
29	C₂×Dic₃	C₂×C₁₁	1	2	yes	complemented
30	C₄×D₃	C₂×C₁₁	1	1	yes	characteristic, complemented
31	Dic₆	C₂×C₁₁	1	1	yes	characteristic, complemented
32	C₂×C₁₁	—	2	2	no	—
33	C₂×C₁₁	—	6	1	no	—
34	C₂×C₁₁	C₂²×D₃	1	1	yes	characteristic
35	#41	—	3	1	no	Sylow
36	C₂²×C₃	C₂²×C₁₁	1	2	yes	—
37	C₂×D₃	C₂²×C₁₁	1	1	yes	characteristic
38	C₃×C₄	C₂²×C₁₁	1	1	yes	characteristic
39	Dic₃	C₂²×C₁₁	1	2	yes	—
40	Dic₃	C₂²×C₁₁	1	1	yes	characteristic
41	C₁₁	#237	1	1	yes	characteristic, direct product factor, Sylow
42	Q₈	—	3	1	no	—
43	D₄	—	3	2	no	—
44	D₄	D₃×C₁₁	1	1	yes	characteristic, complemented
45	C₂×C₄	—	3	2	no	—
46	C₂×C₄	—	3	1	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	C₂³×C₁₁	1	1	yes	characteristic
49	D₃	—	2	1	no	—
50	C₂²	—	3	1	no	—
51	C₂²	C₂×D₃×C₁₁	1	2	yes	—
52	C₄	—	3	1	no	—
53	C₄	—	3	2	no	—
54	C₄	C₂×D₃×C₁₁	1	1	yes	characteristic
55	C₃	C₁₁×#41	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2	2	no	—
57	C₂	—	6	1	no	—
58	C₂	C₂²×D₃×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₁₁
Frattini	C₂	C₂²×D₃×C₁₁
Fitting	C₃×D₄×C₁₁	C₂
socle	C₂×C₃×C₁₁	C₂³
hypercenter	D₄×C₁₁	D₃
hypocenter	C₃	C₁₁×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₁ ◁ D₄×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₁₁	C₂	semidirect
2. C₁₁×#67	C₂	semidirect
3. C₂×C₁₁×Dic₃	C₂	semidirect
4. C₄×D₃×C₁₁	C₂	semidirect
5. C₁₁×Dic₆	C₂	semidirect
14. D₄×C₁₁	D₃	semidirect
20. #237	C₁₁	direct (N × H)
26. C₃×C₁₁	#41	semidirect
27. C₃×D₄	C₂×C₁₁	semidirect
28. #67	C₂×C₁₁	semidirect
29. C₂×Dic₃	C₂×C₁₁	semidirect
30. C₄×D₃	C₂×C₁₁	semidirect
31. Dic₆	C₂×C₁₁	semidirect
41. C₁₁	#237	direct (N × H)
44. D₄	D₃×C₁₁	semidirect
55. C₃	C₁₁×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₄×C₁₁	2
C₁₁×#67	2
C₂×C₁₁×Dic₃	2
C₄×D₃×C₁₁	2
C₁₁×Dic₆	2
C₁₁×#41	3
#237	11

Subgroups — C11×#237 #10587271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#237 #10587271