Subgroups — #20299517

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813697	C₂	1	1	yes	maximal, characteristic
2	#16813692	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268657	—	2	1	no	—
5	#14268650	—	2	1	no	—
6	Q₈×D₁₁₃	—	2	1	no	—
7	Dic₄₅₂	C₄	1	1	yes	characteristic
8	#14268637	—	2	1	no	—
9	C₈×D₁₁₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic
11	Q₈×C₁₁₃	—	2	1	no	—
12	C₄×D₁₁₃	—	4	1	no	—
13	C₄×D₁₁₃	D₄	1	1	yes	characteristic
14	Dic₂₂₆	—	2	1	no	—
15	Dic₂₂₆	—	4	1	no	—
16	#11744753	—	4	1	no	—
17	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	#11744751	D₄	1	1	yes	characteristic
19	C₂×D₁₁₃	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₁₃	—	4	1	no	—
21	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₁₃	—	4	1	no	—
23	Dic₁₁₃	D₈	1	1	yes	characteristic
24	C₂×C₁₁₃	#102	1	1	yes	characteristic
25	D₁₁₃	—	2	1	no	—
26	C₁₁₃	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	113	1	no	maximal, Sylow
28	C₂×Q₁₆	—	113	1	no	—
29	M₃₂	—	113	1	no	—
30	#108	—	113	1	no	—
31	C₂×Q₈	—	226	1	no	—
32	Q₁₆	—	113	1	no	—
33	Q₁₆	—	226	1	no	—
34	Q₁₆	#90673	1	1	yes	characteristic
35	M₁₆	—	226	1	no	—
36	C₂×C₈	—	113	1	no	—
37	C₁₆	—	226	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	452	1	no	—
40	Q₈	—	226	1	no	—
41	C₂×C₄	—	113	1	no	—
42	C₂×C₄	—	452	1	no	—
43	C₈	—	113	1	no	—
44	C₈	—	452	1	no	—
45	C₈	C₂×#90673	1	1	yes	characteristic
46	C₂²	—	113	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	113	1	no	—
49	C₄	—	452	1	no	—
50	C₄	C₂²⋊#90673	1	1	yes	characteristic
51	C₂	—	226	1	no	—
52	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	#362
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
26. C₁₁₃	#362	semidirect