Subgroups — #20298953

Order 7232.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813614	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813610	C₂	1	1	yes	maximal, characteristic
3	#16813547	C₂	1	2	yes	maximal, complemented
4	#16813544	C₂	1	2	yes	maximal
5	C₄×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₂₆	C₂²	1	1	yes	characteristic
7	C₂×D₄₅₂	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
9	#14268626	—	2	2	no	—
10	#14268624	—	2	2	no	—
11	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
12	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₂²×D₁₁₃	—	2	1	no	—
14	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
15	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
16	C₂×Dic₁₁₃	—	2	1	no	—
17	C₂×Dic₁₁₃	—	2	2	no	—
18	D₄₅₂	—	2	2	no	—
19	Dic₂₂₆	—	2	2	no	—
20	C₈×C₁₁₃	—	2	2	no	—
21	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×D₁₁₃	—	4	1	no	—
23	C₂×D₁₁₃	—	4	2	no	—
24	C₄×C₁₁₃	—	2	2	no	—
25	C₄×C₁₁₃	#41	1	2	yes	—
26	Dic₁₁₃	—	4	1	no	—
27	Dic₁₁₃	—	4	2	no	—
28	C₂×C₁₁₃	#124	1	1	yes	characteristic
29	C₂×C₁₁₃	#135	1	2	yes	—
30	D₁₁₃	—	8	1	no	—
31	C₁₁₃	#488	1	1	yes	characteristic, complemented, Sylow
32	#488	—	113	1	no	maximal, Sylow
33	#125	—	113	1	no	—
34	#124	—	113	1	no	—
35	#103	—	113	2	no	—
36	#102	—	113	2	no	—
37	C₄×C₈	D₁₁₃	1	1	yes	characteristic, complemented
38	C₂×Q₈	—	113	1	no	—
39	C₂×D₄	—	113	1	no	—
40	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
41	C₄⋊C₄	—	113	2	no	—
42	C₄⋊C₄	—	226	2	no	—
43	C₂²⋊C₄	—	226	2	no	—
44	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
45	C₂³	—	226	1	no	—
46	Q₈	—	226	2	no	—
47	D₄	—	226	2	no	—
48	C₂×C₄	—	226	1	no	—
49	C₂×C₄	—	226	2	no	—
50	C₂×C₄	D₄₅₂	1	2	yes	—
51	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₂²	—	452	1	no	—
54	C₂²	—	452	2	no	—
55	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	452	1	no	—
58	C₄	—	452	2	no	—
59	C₄	#14268647	1	2	yes	—
60	C₂	—	904	1	no	—
61	C₂	#16813610	1	1	yes	characteristic
62	C₂	#16813644	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₅₂
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄×C₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄×C₈	D₁₁₃
hypocenter	C₁₁₃	#488
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #16813614	C₂	semidirect
3. #16813547	C₂	semidirect
5. C₄×C₈×C₁₁₃	C₂	semidirect
31. C₁₁₃	#488	semidirect
37. C₄×C₈	D₁₁₃	semidirect