Subgroups — #13066670

Order 1408.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622295	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#10622096	C₂	1	1	yes	maximal, characteristic
4	#66922	—	2	1	no	—
5	C₂×C₁₁×C₁₆	—	2	1	no	—
6	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	#66882	—	2	1	no	—
8	#66882	C₄	1	2	yes	—
9	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
10	C₂×Dic₂₂	—	4	1	no	—
11	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
13	C₄²×C₁₁	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₁	—	2	2	no	—
15	C₄⋊Dic₁₁	—	4	1	no	—
16	C₂×C₁₁⋊C₈	—	4	1	no	—
17	C₁₁×C₁₆	—	4	1	no	—
18	#1364	—	11	1	no	maximal, Sylow
19	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
21	C₂×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
22	C₂×Dic₁₁	—	4	2	no	—
23	Dic₂₂	—	8	1	no	—
24	Dic₂₂	—	8	1	no	—
25	C₈×C₁₁	—	2	1	no	—
26	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
27	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
28	C₁₁⋊C₈	—	8	1	no	—
29	#500	—	11	1	no	—
30	C₄⋊C₁₆	D₁₁	1	1	yes	characteristic
31	#335	—	11	1	no	—
32	C₂²×C₁₁	#102	1	1	yes	characteristic
33	C₄×C₁₁	—	2	1	no	—
34	C₄×C₁₁	#101	1	1	yes	characteristic
35	C₄×C₁₁	#103	1	1	yes	characteristic
36	C₄×C₁₁	D₁₆	1	1	yes	characteristic
37	C₄×C₁₁	SD₃₂	1	1	yes	characteristic
38	Dic₁₁	—	8	2	no	—
39	C₄⋊Q₈	—	22	1	no	—
40	C₂×C₁₆	—	2	1	no	—
41	#107	—	11	2	no	—
42	#107	—	22	1	no	—
43	C₄⋊C₈	—	22	1	no	—
44	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
45	C₂×C₁₁	#332	1	1	yes	characteristic
46	C₂×C₁₁	#357	1	1	yes	characteristic
47	C₂×C₁₁	#362	1	1	yes	characteristic
48	C₂×Q₈	—	44	1	no	—
49	C₂×C₈	—	44	1	no	—
50	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
52	C₄⋊C₄	—	22	2	no	—
53	C₄⋊C₄	—	44	1	no	—
54	C₄²	D₄₄	1	1	yes	characteristic
55	C₁₆	—	4	1	no	—
56	C₁₁	#1364	1	1	yes	characteristic, complemented, Sylow
57	Q₈	—	88	1	no	—
58	Q₈	—	88	1	no	—
59	C₂×C₄	—	44	2	no	—
60	C₂×C₄	#4314	1	1	yes	characteristic
61	C₂×C₄	D₈₈	1	1	yes	characteristic
62	C₂×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	88	1	no	—
65	C₈	#4324	1	1	yes	characteristic
66	C₈	#4326	1	1	yes	characteristic
67	C₂²	#66885	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	88	2	no	—
70	C₄	D₁₇₆	1	1	yes	characteristic
71	C₄	#66864	1	1	yes	characteristic
72	C₄	#66874	1	1	yes	characteristic
73	C₄	#66888	1	1	yes	characteristic
74	C₂	#10622124	1	1	yes	characteristic
75	C₂	#10622147	1	1	yes	characteristic
76	C₂	#10622155	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#66885
commutator	C₂×C₈×C₁₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₁₁×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₄⋊C₁₆	D₁₁
hypocenter	C₁₁	#1364
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
56. C₁₁	#1364	semidirect

Maximal subgroups

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

subgroup	index
#10622295	2
C₁₁×C₄⋊C₁₆	2
#10622096	2
#1364	11