Subgroups — #20299642

Order 7232.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813710	C₂	1	2	yes	maximal, complemented
2	#16813693	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813687	C₂	1	2	yes	maximal, complemented
4	C₈×#90673	C₂	1	1	yes	maximal, characteristic, complemented
5	#16813645	C₂	1	1	yes	maximal, characteristic
6	#14268657	—	2	2	no	—
7	#14268657	C₂²	1	2	yes	—
8	#14268655	—	2	2	no	—
9	#14268655	C₂²	1	1	yes	characteristic
10	C₄×#90673	C₂²	1	1	yes	characteristic
11	#14268648	C₂²	1	2	yes	—
12	#14268634	C₄	1	2	yes	complemented
13	D₉₀₄	C₄	1	1	yes	characteristic, complemented
14	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
15	Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#90673	—	2	1	no	—
17	Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
18	D₄₅₂	—	2	2	no	—
19	D₄₅₂	C₂×C₄	1	2	yes	—
20	C₄×D₁₁₃	—	2	2	no	—
21	C₄×D₁₁₃	C₂³	1	1	yes	characteristic
22	#11744753	—	2	2	no	—
23	#11744753	D₄	1	1	yes	characteristic
24	#11744753	D₄	1	1	yes	characteristic
25	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
26	#11744751	C₂×C₄	1	1	yes	characteristic
27	C₂×D₁₁₃	—	2	2	no	—
28	C₂×D₁₁₃	#41	1	1	yes	characteristic
29	#90673	—	2	2	no	—
30	C₄×C₁₁₃	—	2	2	no	—
31	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
32	Dic₁₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₁₃	C₄×D₄	1	1	yes	characteristic
34	D₁₁₃	—	2	1	no	—
35	D₁₁₃	—	4	2	no	—
36	C₁₁₃	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	113	1	no	maximal, Sylow
38	#135	—	113	1	no	—
39	#131	—	113	2	no	—
40	#108	—	113	1	no	—
41	#104	—	113	2	no	—
42	C₄×C₈	—	113	1	no	—
43	#41	—	113	2	no	—
44	Q₁₆	#90673	1	1	yes	characteristic, complemented
45	SD₁₆	—	113	2	no	—
46	D₈	—	113	1	no	—
47	M₁₆	—	113	2	no	—
48	M₁₆	—	226	2	no	—
49	C₂×C₈	—	113	1	no	—
50	C₂×C₈	—	113	1	no	—
51	C₂×C₈	—	226	2	no	—
52	C₄²	—	113	1	no	—
53	Q₈	C₂×#90673	1	2	yes	—
54	D₄	—	113	2	no	—
55	D₄	—	226	2	no	—
56	C₂×C₄	—	113	1	no	—
57	C₂×C₄	—	226	2	no	—
58	C₂×C₄	—	226	1	no	—
59	C₈	—	113	1	no	—
60	C₈	—	113	1	no	—
61	C₈	—	113	1	no	—
62	C₈	—	226	2	no	—
63	C₈	C₂×#90673	1	1	yes	characteristic
64	C₂²	—	113	1	no	—
65	C₂²	—	226	2	no	—
66	C₄	—	2	2	no	—
67	C₄	—	113	1	no	—
68	C₄	—	226	2	no	—
69	C₄	C₂²×#90673	1	1	yes	characteristic
70	C₂	—	452	2	no	—
71	C₂	—	226	1	no	—
72	C₂	D₄×#90673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#90673
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₄	C₂²×#90673
Fitting	Q₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₄×D₄
hypercenter	Q₁₆	#90673
hypocenter	C₁₁₃	#443
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #16813710	C₂	semidirect
2. #16813693	C₂	semidirect
3. #16813687	C₂	semidirect
4. C₈×#90673	C₂	semidirect
12. #14268634	C₄	semidirect
13. D₉₀₄	C₄	semidirect
15. Q₁₆×C₁₁₃	C₄	semidirect
36. C₁₁₃	#443	semidirect
44. Q₁₆	#90673	semidirect