Subgroups — #13070892

Order 1408.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#499	C₂	1	1	yes	maximal, characteristic
2	#10622296	C₂	1	1	yes	maximal, characteristic
3	#10622128	C₂	1	2	yes	maximal
4	#10622127	C₂	1	2	yes	maximal
5	C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#125	—	2	1	no	—
7	#66923	—	2	1	no	—
8	C₁₁×#107	C₂²	1	2	yes	—
9	C₁₁×#106	—	2	1	no	—
10	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#66882	C₂²	1	2	yes	—
12	#66881	—	2	1	no	—
13	C₂×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₁₁×C₄⋊C₄	—	2	2	no	—
18	C₁₁×C₄⋊C₄	—	4	2	no	—
19	C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₁	—	2	2	no	—
21	Dic₁₁⋊C₄	—	4	2	no	—
22	C₁₁⋊C₁₆	Q₈	1	2	yes	—
23	C₁₁⋊C₁₆	Q₈	1	2	yes	—
24	#2253	—	11	1	no	maximal, Sylow
25	C₂×C₄×C₁₁	—	4	2	no	—
26	C₂×C₄×C₁₁	D₈	1	2	yes	—
27	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₁	—	4	2	no	—
29	C₈×C₁₁	Q₁₆	1	2	yes	—
30	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
31	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
32	#499	—	11	1	no	—
33	#499	D₁₁	1	1	yes	characteristic
34	#367	—	11	2	no	—
35	#366	—	11	2	no	—
36	C₄×C₁₆	—	11	1	no	—
37	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
38	C₄×C₁₁	—	2	2	no	—
39	C₄×C₁₁	—	8	2	no	—
40	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
41	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
42	Dic₁₁	—	8	2	no	—
43	#125	—	2	1	no	—
44	#125	—	22	1	no	—
45	C₂×C₁₆	—	11	1	no	—
46	C₂×C₁₆	—	11	1	no	—
47	#107	—	11	2	no	—
48	#107	C₂×D₁₁	1	2	yes	—
49	#106	—	2	1	no	—
50	#106	—	22	1	no	—
51	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
52	C₂×C₁₁	#500	1	1	yes	characteristic
53	C₂×C₁₁	#508	1	2	yes	—
54	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
55	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
56	C₄⋊C₄	—	2	2	no	—
57	C₄⋊C₄	—	4	2	no	—
58	C₄⋊C₄	—	22	2	no	—
59	C₄⋊C₄	—	44	2	no	—
60	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
61	C₁₆	—	11	2	no	—
62	C₁₆	—	11	2	no	—
63	C₁₁	#2253	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	44	2	no	—
66	C₂×C₄	#4323	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
68	C₈	#4326	1	2	yes	—
69	C₈	Q₈×D₁₁	1	1	yes	characteristic
70	C₈	Q₈×D₁₁	1	1	yes	characteristic
71	C₂²	C₂×#4323	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	88	2	no	—
75	C₄	C₂×#4326	1	1	yes	characteristic
76	C₄	#66997	1	1	yes	characteristic
77	C₂	#10622691	1	1	yes	characteristic
78	C₂	#10622807	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#499	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
hypercenter	#499	D₁₁
hypocenter	C₁₁	#2253
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
63. C₁₁	#2253	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#499	2
#10622296	2
#10622128	2
#10622127	2
C₄×C₁₁⋊C₁₆	2
#2253	11