Subgroups — #13066652

Order 1408.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622308	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈₈	—	2	1	no	—
5	C₂×D₈₈	—	2	1	no	—
6	#66927	C₄	1	2	yes	—
7	C₁₁×M₃₂	—	2	1	no	—
8	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	#66876	—	2	1	no	—
10	C₂×D₄₄	—	2	2	no	—
11	C₂×D₄₄	—	4	2	no	—
12	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
15	D₈₈	—	4	1	no	—
16	D₈₈	—	4	1	no	—
17	D₈₈	—	4	1	no	—
18	D₈₈	—	4	1	no	—
19	C₁₁×C₁₆	—	4	1	no	—
20	C₁₁⋊C₁₆	—	4	1	no	—
21	#1357	—	11	1	no	maximal, Sylow
22	C₂²×D₁₁	—	4	2	no	—
23	C₂×C₄×C₁₁	—	2	1	no	—
24	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
25	D₄₄	—	4	2	no	—
26	D₄₄	—	4	2	no	—
27	D₄₄	—	8	4	no	—
28	C₈×C₁₁	D₈	1	1	yes	characteristic
29	C₈×C₁₁	D₈	1	1	yes	characteristic
30	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
31	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
32	#493	—	11	1	no	—
33	#364	—	11	1	no	—
34	#364	D₁₁	1	1	yes	characteristic, complemented
35	C₂²×C₁₁	#100	1	1	yes	characteristic
36	C₂×D₁₁	—	8	4	no	—
37	C₂×D₁₁	—	8	2	no	—
38	C₄×C₁₁	—	2	2	no	—
39	C₄×C₁₁	#102	1	1	yes	characteristic
40	C₄×C₁₁	#102	1	1	yes	characteristic
41	C₂×D₈	—	22	1	no	—
42	C₂×D₈	—	22	1	no	—
43	#127	—	11	2	no	—
44	M₃₂	—	2	1	no	—
45	M₃₂	—	22	1	no	—
46	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
47	C₂×C₁₁	—	2	1	no	—
48	C₂×C₁₁	#331	1	1	yes	characteristic
49	D₁₁	—	16	2	no	—
50	C₂×D₄	—	22	2	no	—
51	C₂×D₄	—	44	2	no	—
52	D₈	—	44	1	no	—
53	D₈	—	44	1	no	—
54	D₈	—	44	1	no	—
55	D₈	—	44	1	no	—
56	C₂×C₈	D₄₄	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₄²	C₄×D₁₁	1	1	yes	characteristic
59	C₁₆	—	4	1	no	—
60	C₁₆	—	44	1	no	—
61	C₁₁	#1357	1	1	yes	characteristic, complemented, Sylow
62	C₂³	—	44	2	no	—
63	D₄	—	44	2	no	—
64	D₄	—	44	2	no	—
65	D₄	—	88	4	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
68	C₈	#4314	1	1	yes	characteristic
69	C₈	D₈₈	1	1	yes	characteristic
70	C₈	#4323	1	1	yes	characteristic
71	C₈	#4325	1	1	yes	characteristic
72	C₂²	—	88	4	no	—
73	C₂²	—	88	2	no	—
74	C₂²	#66887	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#66873	1	1	yes	characteristic
77	C₄	#66885	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	176	2	no	—
80	C₂	#10622123	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10622123
commutator	C₄²×C₁₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₁₁×#364	C₂
socle	C₂×C₁₁	#331
prime radical	#10622308	C₂
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	#364	D₁₁
hypocenter	C₁₁	#1357
LCS	G ▷ C₄²×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₁₁×#364	C₂	semidirect
3. #10622101	C₂	semidirect
34. #364	D₁₁	semidirect
61. C₁₁	#1357	semidirect

Maximal subgroups

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

subgroup	index
#10622308	2
C₁₁×#364	2
#10622101	2
#1357	11