Subgroups — #20299657

Order 7232.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813697	C₂	1	2	yes	maximal, complemented
2	#16813696	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813695	C₂	1	2	yes	maximal, complemented
4	C₂×#14268650	C₂	1	1	yes	maximal, characteristic, complemented
5	#16813630	C₂	1	1	yes	maximal, characteristic
6	#14268650	C₂²	1	1	yes	characteristic
7	#14268650	C₂²	1	1	yes	characteristic
8	#14268650	C₂²	1	2	yes	—
9	#14268647	C₄	1	1	yes	characteristic
10	#14268630	C₄	1	2	yes	—
11	C₂×#11744751	C₂²	1	1	yes	characteristic
12	C₈×D₁₁₃	C₂²	1	2	yes	—
13	M₁₆×C₁₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₁₁₃	C₈	1	2	yes	—
16	D₄₅₂	C₈	1	1	yes	characteristic
17	C₄×D₁₁₃	C₂×C₄	1	2	yes	—
18	Dic₂₂₆	C₈	1	1	yes	characteristic
19	C₈×C₁₁₃	C₂×C₄	1	2	yes	—
20	#11744751	C₂×C₄	1	1	yes	characteristic
21	#11744751	C₂³	1	1	yes	characteristic
22	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₁₃	C₂×C₈	1	2	yes	—
24	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₁₃	C₂×C₈	1	2	yes	—
27	C₂×C₁₁₃	—	2	1	no	—
28	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
29	D₁₁₃	—	2	2	no	—
30	C₁₁₃	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	113	1	no	maximal, Sylow
32	#131	—	113	1	no	—
33	M₃₂	—	113	1	no	—
34	M₃₂	—	113	2	no	—
35	C₂×C₁₆	—	113	1	no	—
36	C₂×C₁₆	—	113	2	no	—
37	#41	—	113	1	no	—
38	M₁₆	—	113	2	no	—
39	M₁₆	#90673	1	1	yes	characteristic
40	C₂×C₈	—	113	1	no	—
41	C₂×C₈	—	113	2	no	—
42	C₁₆	—	113	1	no	—
43	C₁₆	—	113	1	no	—
44	C₁₆	—	113	2	no	—
45	Q₈	—	113	1	no	—
46	D₄	—	113	2	no	—
47	D₄	—	113	1	no	—
48	C₂×C₄	—	113	2	no	—
49	C₂×C₄	C₂×#90673	1	1	yes	characteristic
50	C₈	—	113	1	no	—
51	C₈	—	113	1	no	—
52	C₈	C₂×#90673	1	2	yes	—
53	C₂²	—	113	2	no	—
54	C₂²	#14268655	1	1	yes	characteristic
55	C₄	—	113	2	no	—
56	C₄	#14268655	1	1	yes	characteristic
57	C₄	C₂²×#90673	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	226	2	no	—
60	C₂	C₂×#14268655	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#90673
commutator, socle	C₂×C₁₁₃	C₂²×C₈
Fitting	M₁₆×C₁₁₃	C₄
hypercenter	M₁₆	#90673
hypocenter	C₁₁₃	#504
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #16813697	C₂	semidirect
2. #16813696	C₂	semidirect
3. #16813695	C₂	semidirect
4. C₂×#14268650	C₂	semidirect
30. C₁₁₃	#504	semidirect