Subgroups — #13066590

Order 1408.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622313	C₂	1	1	yes	maximal, characteristic
2	C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622101	C₂	1	1	yes	maximal, characteristic, complemented
4	#66957	C₄	1	1	yes	characteristic
5	#66954	—	2	1	no	—
6	C₄×C₈×C₁₁	—	2	1	no	—
7	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#66883	C₄	1	1	yes	characteristic
9	#66876	—	2	1	no	—
10	#66869	—	2	1	no	—
11	#4339	—	2	1	no	—
12	C₂×C₈×C₁₁	—	2	2	no	—
13	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
15	C₄²×C₁₁	D₄	1	1	yes	characteristic
16	#4318	—	2	1	no	—
17	Dic₄₄	C₈	1	1	yes	characteristic, complemented
18	D₈₈	C₈	1	1	yes	characteristic, complemented
19	#4314	—	2	1	no	—
20	#4313	—	4	1	no	—
21	C₈×D₁₁	—	4	1	no	—
22	C₁₁⋊C₁₆	—	4	1	no	—
23	#1335	—	11	1	no	maximal, Sylow
24	C₂×C₄×C₁₁	—	2	1	no	—
25	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²⋊D₁₁	—	4	1	no	—
27	D₄₄	—	2	1	no	—
28	C₄×D₁₁	—	4	1	no	—
29	Dic₂₂	—	2	1	no	—
30	C₈×C₁₁	—	2	4	no	—
31	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₁	M₁₆	1	1	yes	characteristic
33	C₈×C₁₁	D₈	1	1	yes	characteristic
34	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
35	C₁₁⋊C₈	—	4	1	no	—
36	#443	—	11	1	no	—
37	#364	—	11	1	no	—
38	C₈²	D₁₁	1	1	yes	characteristic, complemented
39	C₂²×C₁₁	#104	1	1	yes	characteristic
40	C₂×D₁₁	—	4	1	no	—
41	C₄×C₁₁	—	2	2	no	—
42	C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₁₁	#102	1	1	yes	characteristic
44	Dic₁₁	—	4	1	no	—
45	#135	—	11	1	no	—
46	#131	—	22	1	no	—
47	M₃₂	—	22	1	no	—
48	#108	—	11	1	no	—
49	#104	—	22	1	no	—
50	C₄×C₈	—	2	1	no	—
51	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
52	C₂×C₁₁	—	2	1	no	—
53	C₂×C₁₁	D₄⋊C₈	1	1	yes	characteristic
54	D₁₁	—	8	1	no	—
55	#41	—	22	1	no	—
56	Q₁₆	—	11	1	no	—
57	SD₁₆	—	22	1	no	—
58	D₈	—	11	1	no	—
59	M₁₆	—	22	1	no	—
60	M₁₆	—	44	1	no	—
61	C₂×C₈	—	2	2	no	—
62	C₂×C₈	—	44	1	no	—
63	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
64	C₂×C₈	D₄₄	1	1	yes	characteristic
65	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
66	C₁₆	—	44	1	no	—
67	C₁₁	#1335	1	1	yes	characteristic, complemented, Sylow
68	Q₈	—	22	1	no	—
69	D₄	—	22	1	no	—
70	D₄	—	44	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	44	1	no	—
73	C₂×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
74	C₈	—	2	4	no	—
75	C₈	—	44	1	no	—
76	C₈	C₈×D₁₁	1	1	yes	characteristic
77	C₈	#4313	1	1	yes	characteristic
78	C₈	#4314	1	1	yes	characteristic
79	C₈	D₈₈	1	1	yes	characteristic
80	C₂²	—	44	1	no	—
81	C₂²	#66869	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	44	1	no	—
84	C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
85	C₄	#66885	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	88	1	no	—
88	C₂	#10622097	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈₈
commutator	C₈×C₁₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₈²×C₁₁	C₂
socle	C₂×C₁₁	D₄⋊C₈
prime radical	#66957	C₄
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₈²	D₁₁
hypocenter	C₁₁	#1335
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. C₈²×C₁₁	C₂	semidirect
3. #10622101	C₂	semidirect
17. Dic₄₄	C₈	semidirect
18. D₈₈	C₈	semidirect
38. C₈²	D₁₁	semidirect
67. C₁₁	#1335	semidirect

Maximal subgroups

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

subgroup	index
#10622313	2
C₈²×C₁₁	2
#10622101	2
#1335	11