Subgroups — #20299513

Order 7232.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813695	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813693	C₂	1	1	yes	maximal, characteristic, complemented
3	#16813645	C₂	1	1	yes	maximal, characteristic
4	#14268657	—	2	1	no	—
5	#14268650	—	2	1	no	—
6	#14268648	—	2	1	no	—
7	#14268634	—	2	1	no	—
8	D₉₀₄	C₄	1	1	yes	characteristic
9	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic
11	Q₈×C₁₁₃	—	2	1	no	—
12	D₄₅₂	—	2	1	no	—
13	D₄₅₂	—	4	1	no	—
14	C₄×D₁₁₃	—	4	1	no	—
15	C₄×D₁₁₃	D₄	1	1	yes	characteristic
16	#11744753	—	4	1	no	—
17	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	#11744751	D₄	1	1	yes	characteristic
19	C₂×D₁₁₃	—	4	1	no	—
20	C₂×D₁₁₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₁₃	—	4	1	no	—
22	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₁₃	D₈	1	1	yes	characteristic
24	C₂×C₁₁₃	#102	1	1	yes	characteristic
25	D₁₁₃	—	2	1	no	—
26	D₁₁₃	—	8	1	no	—
27	C₁₁₃	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	113	1	no	maximal, Sylow
29	#135	—	113	1	no	—
30	C₂×C₁₆	—	113	1	no	—
31	#108	—	113	1	no	—
32	#41	—	226	1	no	—
33	Q₁₆	#90673	1	1	yes	characteristic
34	SD₁₆	—	226	1	no	—
35	D₈	—	113	1	no	—
36	M₁₆	—	226	1	no	—
37	C₂×C₈	—	113	1	no	—
38	C₁₆	—	226	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	452	1	no	—
41	D₄	—	226	1	no	—
42	C₂×C₄	—	113	1	no	—
43	C₂×C₄	—	452	1	no	—
44	C₈	—	113	1	no	—
45	C₈	—	452	1	no	—
46	C₈	C₂×#90673	1	1	yes	characteristic
47	C₂²	—	113	1	no	—
48	C₂²	—	452	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	113	1	no	—
51	C₄	C₂²⋊#90673	1	1	yes	characteristic
52	C₂	—	904	1	no	—
53	C₂	—	226	1	no	—
54	C₂	#16813684	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16813684
commutator	C₈×C₁₁₃	C₂×C₄
Frattini	C₈	C₂×#90673
Fitting	Q₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	#102
hypercenter	Q₁₆	#90673
hypocenter	C₁₁₃	#359
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #16813695	C₂	semidirect
2. #16813693	C₂	semidirect
27. C₁₁₃	#359	semidirect