Subgroups — #20299516

Order 7232.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813697	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813692	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268657	—	2	1	no	—
5	#14268650	—	2	1	no	—
6	D₄×D₁₁₃	—	2	1	no	—
7	D₉₀₄	C₄	1	1	yes	characteristic
8	#14268632	—	2	1	no	—
9	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
10	D₈×C₁₁₃	C₄	1	1	yes	characteristic
11	C₂²×D₁₁₃	—	4	1	no	—
12	D₄×C₁₁₃	—	2	1	no	—
13	C₂²⋊D₁₁₃	—	4	1	no	—
14	D₄₅₂	—	2	1	no	—
15	C₄×D₁₁₃	D₄	1	1	yes	characteristic
16	#11744753	—	4	1	no	—
17	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	#11744751	D₄	1	1	yes	characteristic
19	C₂²×C₁₁₃	—	4	1	no	—
20	C₂×D₁₁₃	—	4	1	no	—
21	C₂×D₁₁₃	—	8	2	no	—
22	C₂×D₁₁₃	SD₁₆	1	1	yes	characteristic
23	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₁₃	D₈	1	1	yes	characteristic
25	C₂×C₁₁₃	—	8	1	no	—
26	C₂×C₁₁₃	#102	1	1	yes	characteristic
27	D₁₁₃	—	2	1	no	—
28	D₁₁₃	—	8	1	no	—
29	C₁₁₃	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	113	1	no	maximal, Sylow
31	C₂×D₈	—	113	1	no	—
32	M₃₂	—	113	1	no	—
33	#108	—	113	1	no	—
34	C₂×D₄	—	226	1	no	—
35	D₈	—	113	1	no	—
36	D₈	—	226	1	no	—
37	D₈	#90673	1	1	yes	characteristic
38	M₁₆	—	226	1	no	—
39	C₂×C₈	—	113	1	no	—
40	C₁₆	—	226	1	no	—
41	C₂³	—	452	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	452	1	no	—
44	D₄	—	226	1	no	—
45	C₂×C₄	—	113	1	no	—
46	C₈	—	113	1	no	—
47	C₈	—	452	1	no	—
48	C₈	C₂×#90673	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	113	1	no	—
51	C₂²	—	904	2	no	—
52	C₂²	—	452	1	no	—
53	C₄	—	113	1	no	—
54	C₄	C₂²⋊#90673	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	904	1	no	—
57	C₂	—	226	1	no	—
58	C₂	#16813684	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16813684
commutator	C₈×C₁₁₃	C₂×C₄
Frattini	C₈	C₂×#90673
Fitting	D₈×C₁₁₃	C₄
socle	C₂×C₁₁₃	#102
hypercenter	D₈	#90673
hypocenter	C₁₁₃	#361
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #16813697	C₂	semidirect
2. #16813692	C₂	semidirect
29. C₁₁₃	#361	semidirect