Subgroups — C₁₁×#462 #10622949

Order 704.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Q₁₆	C₂	1	2	yes	maximal
2	C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#103	C₂	1	2	yes	maximal
6	C₂×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₂×Q₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×Q₁₆	—	2	4	no	—
9	C₂×C₈×C₁₁	C₂²	1	2	yes	—
10	C₁₁×C₄⋊C₄	—	2	1	no	—
11	C₁₁×C₄⋊C₄	—	2	1	no	—
12	C₁₁×C₄⋊C₄	—	2	1	no	—
13	C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₄²×C₁₁	—	2	1	no	—
15	C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	Q₈×C₁₁	—	2	1	no	—
17	Q₈×C₁₁	—	2	2	no	—
18	Q₈×C₁₁	—	2	2	no	—
19	Q₈×C₁₁	D₄	1	2	yes	—
20	C₂×C₄×C₁₁	—	2	1	no	—
21	C₂×C₄×C₁₁	—	2	1	no	—
22	C₂×C₄×C₁₁	—	2	2	no	—
23	C₂×C₄×C₁₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₈×C₁₁	—	2	2	no	—
27	#462	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₁₁	C₂×D₄	1	1	yes	characteristic
29	C₄×C₁₁	—	2	2	no	—
30	C₄×C₁₁	—	2	1	no	—
31	C₄×C₁₁	—	4	2	no	—
32	C₄×C₁₁	—	4	1	no	—
33	C₄×C₁₁	Q₁₆	1	2	yes	complemented
34	C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₁	#41	1	1	yes	characteristic
36	C₂×Q₁₆	C₂×C₁₁	1	2	yes	—
37	C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
38	C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic
39	C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
40	#103	C₂×C₁₁	1	2	yes	—
41	C₂×C₁₁	#121	1	1	yes	characteristic
42	C₂×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₁₁	#137	1	1	yes	characteristic
44	C₂×Q₈	C₂²×C₁₁	1	2	yes	—
45	C₂×Q₈	C₂²×C₁₁	1	1	yes	characteristic
46	Q₁₆	—	2	4	no	—
47	C₂×C₈	C₂²×C₁₁	1	2	yes	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
52	C₄²	—	2	1	no	—
53	C₄²	C₂²×C₁₁	1	1	yes	characteristic
54	C₁₁	#462	1	1	yes	characteristic, direct product factor, Sylow
55	Q₈	—	2	1	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	D₄×C₁₁	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	D₄×C₁₁	1	1	yes	characteristic
63	C₂×C₄	D₄×C₁₁	1	1	yes	characteristic
64	C₂×C₄	C₂³×C₁₁	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₄×C₁₁	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	4	1	no	—
71	C₄	C₁₁×Q₁₆	1	2	yes	complemented
72	C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
73	C₄	C₁₁×#41	1	1	yes	characteristic
74	C₂	C₁₁×#121	1	1	yes	characteristic
75	C₂	C₂×C₁₁×Q₁₆	1	1	yes	characteristic
76	C₂	C₁₁×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
27. #462	C₁₁	direct (N × H)
33. C₄×C₁₁	Q₁₆	semidirect
54. C₁₁	#462	direct (N × H)
71. C₄	C₁₁×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×Q₁₆	2
C₁₁×C₄⋊Q₈	2
C₄×Q₈×C₁₁	2
C₁₁×C₄⋊C₈	2
C₁₁×#103	2
#462	11

Subgroups — C11×#462 #10622949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#462 #10622949