Subgroups — #20299645

Order 7232.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813709	C₂	1	2	yes	maximal, complemented
2	#16813692	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813686	C₂	1	2	yes	maximal, complemented
4	#16813676	C₂	1	1	yes	maximal, characteristic, complemented
5	#16813641	C₂	1	1	yes	maximal, characteristic
6	#14268657	C₂²	1	2	yes	—
7	#14268656	—	2	2	no	—
8	#14268655	C₂²	1	1	yes	characteristic
9	C₂×#11744753	—	2	2	no	—
10	C₄×#90673	C₂²	1	1	yes	characteristic
11	#14268646	C₂²	1	2	yes	—
12	Dic₄₅₂	C₄	1	1	yes	characteristic, complemented
13	#14268635	C₄	1	2	yes	complemented
14	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
15	D₈×C₁₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#90673	—	2	1	no	—
17	D₄×C₁₁₃	C₂×C₄	1	2	yes	—
18	C₂²⋊D₁₁₃	—	2	2	no	—
19	C₂×Dic₁₁₃	—	2	2	no	—
20	C₄×D₁₁₃	C₂³	1	1	yes	characteristic
21	Dic₂₂₆	C₂×C₄	1	2	yes	—
22	#11744753	—	2	2	no	—
23	#11744753	D₄	1	2	yes	—
24	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
25	#11744751	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₁₃	—	2	2	no	—
27	C₂×D₁₁₃	#41	1	1	yes	characteristic
28	#90673	—	4	1	no	—
29	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₁₃	—	2	2	no	—
31	Dic₁₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₁₁₃	—	4	2	no	—
33	C₂×C₁₁₃	C₄×D₄	1	1	yes	characteristic
34	D₁₁₃	—	2	1	no	—
35	C₁₁₃	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	113	1	no	maximal, Sylow
37	#135	—	113	1	no	—
38	#131	—	113	2	no	—
39	#108	—	113	1	no	—
40	#104	—	113	2	no	—
41	#97	—	113	1	no	—
42	#41	—	113	2	no	—
43	Q₁₆	—	113	1	no	—
44	SD₁₆	—	113	2	no	—
45	D₈	#90673	1	1	yes	characteristic, complemented
46	M₁₆	—	113	2	no	—
47	M₁₆	—	226	2	no	—
48	C₂×C₈	—	113	1	no	—
49	C₂×C₈	—	113	1	no	—
50	C₂×C₈	—	226	2	no	—
51	C₄²	—	113	1	no	—
52	Q₈	—	113	2	no	—
53	D₄	—	226	2	no	—
54	D₄	C₂×#90673	1	2	yes	—
55	C₂×C₄	—	113	1	no	—
56	C₂×C₄	—	226	2	no	—
57	C₂×C₄	—	226	1	no	—
58	C₈	—	113	2	no	—
59	C₈	—	113	1	no	—
60	C₈	—	226	2	no	—
61	C₈	C₂×#90673	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	113	1	no	—
64	C₄	—	113	1	no	—
65	C₄	—	452	1	no	—
66	C₄	—	226	2	no	—
67	C₄	C₂²×#90673	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	226	1	no	—
70	C₂	D₄×#90673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#90673
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₄	C₂²×#90673
Fitting	D₈×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₄×D₄
hypercenter	D₈	#90673
hypocenter	C₁₁₃	#444
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #16813709	C₂	semidirect
2. #16813692	C₂	semidirect
3. #16813686	C₂	semidirect
4. #16813676	C₂	semidirect
12. Dic₄₅₂	C₄	semidirect
13. #14268635	C₄	semidirect
15. D₈×C₁₁₃	C₄	semidirect
35. C₁₁₃	#444	semidirect
45. D₈	#90673	semidirect