Subgroups — #20299717

Order 7232.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813719	C₂	1	2	yes	maximal, complemented
2	#16813718	C₂	1	2	yes	maximal, complemented
3	#16813717	C₂	1	2	yes	maximal, complemented
4	C₂×#14268655	C₂	1	1	yes	maximal, characteristic
5	#14268659	C₂²	1	4	yes	complemented
6	#14268655	C₄	1	1	yes	characteristic
7	#14268655	C₄	1	1	yes	characteristic
8	#14268655	C₂²	1	1	yes	characteristic
9	#14268655	C₂²	1	1	yes	characteristic
10	C₂×#11744753	C₄	1	1	yes	characteristic
11	C₂×#11744753	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₁₁₃	C₄	1	1	yes	characteristic
13	C₂²×D₁₁₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₈	1	1	yes	characteristic
15	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₁₃	C₈	1	1	yes	characteristic
17	C₄×D₁₁₃	C₈	1	1	yes	characteristic
18	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
20	#11744753	C₂×C₄	1	1	yes	characteristic
21	#11744753	C₂×C₄	1	1	yes	characteristic
22	#11744753	C₂×C₄	1	1	yes	characteristic
23	#11744753	C₂³	1	1	yes	characteristic
24	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×D₁₁₃	—	2	2	no	—
26	C₂×D₁₁₃	C₂×C₈	1	1	yes	characteristic
27	C₂×D₁₁₃	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
30	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
31	Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₁₁₃	—	2	1	no	—
33	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
34	D₁₁₃	—	2	1	no	—
35	D₁₁₃	M₃₂	1	2	yes	complemented
36	C₁₁₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×M₃₂	—	113	1	no	maximal, Sylow
38	C₂²×C₈	—	113	1	no	—
39	M₃₂	—	113	2	no	—
40	M₃₂	—	113	2	no	—
41	C₂×C₁₆	—	113	2	no	—
42	C₂²×C₄	—	113	1	no	—
43	C₂×C₈	—	113	1	no	—
44	C₂×C₈	—	113	1	no	—
45	C₂×C₈	—	113	1	no	—
46	C₂×C₈	—	113	1	no	—
47	C₂×C₈	—	113	1	no	—
48	C₂×C₈	—	113	1	no	—
49	C₁₆	—	113	4	no	—
50	C₂³	—	113	1	no	—
51	C₂×C₄	—	113	1	no	—
52	C₂×C₄	—	113	1	no	—
53	C₂×C₄	—	113	1	no	—
54	C₂×C₄	—	113	1	no	—
55	C₂×C₄	—	113	1	no	—
56	C₂×C₄	#11744762	1	1	yes	characteristic
57	C₈	—	113	1	no	—
58	C₈	—	113	1	no	—
59	C₈	—	113	1	no	—
60	C₈	—	113	1	no	—
61	C₂²	—	113	1	no	—
62	C₂²	—	113	1	no	—
63	C₂²	—	226	2	no	—
64	C₂²	C₂×#11744762	1	1	yes	characteristic
65	C₄	—	113	1	no	—
66	C₄	—	113	1	no	—
67	C₄	C₂×#11744762	1	1	yes	characteristic
68	C₄	C₂×#11744762	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	113	2	no	—
71	C₂	—	226	1	no	—
72	C₂	C₂²×#11744762	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#11744762
commutator, socle	C₂×C₁₁₃	C₂²×C₈
Frattini	C₂	C₂²×#11744762
Fitting	C₂×C₄×C₁₁₃	C₈
hypercenter	C₂×C₄	#11744762
hypocenter	C₁₁₃	C₂×M₃₂
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #16813719	C₂	semidirect
2. #16813718	C₂	semidirect
3. #16813717	C₂	semidirect
5. #14268659	C₂²	semidirect
35. D₁₁₃	M₃₂	semidirect
36. C₁₁₃	C₂×M₃₂	semidirect