Subgroups — #20298396

Order 7232.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813620	C₂	1	1	yes	maximal, characteristic
2	#16813541	C₂	1	1	yes	maximal, characteristic
3	#101×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₂₆	C₄	1	1	yes	characteristic
5	#14268631	—	2	1	no	—
6	#14268626	—	2	1	no	—
7	#14268626	—	2	1	no	—
8	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
10	M₁₆×C₁₁₃	—	2	1	no	—
11	Q₈×C₁₁₃	—	4	1	no	—
12	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
15	C₂×Dic₁₁₃	—	2	1	no	—
16	C₂×Dic₁₁₃	—	2	1	no	—
17	Dic₂₂₆	—	4	1	no	—
18	C₈×C₁₁₃	—	4	1	no	—
19	#11744751	—	4	1	no	—
20	C₂²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₁₃	—	2	1	no	—
22	C₄×C₁₁₃	—	2	1	no	—
23	C₄×C₁₁₃	—	2	1	no	—
24	Dic₁₁₃	—	2	2	no	—
25	Dic₁₁₃	—	4	1	no	—
26	C₂×C₁₁₃	—	2	1	no	—
27	C₂×C₁₁₃	#99	1	1	yes	characteristic
28	C₁₁₃	#356	1	1	yes	characteristic, complemented, Sylow
29	#356	—	113	1	no	maximal, Sylow
30	C₄⋊Q₈	—	113	1	no	—
31	#101	—	113	1	no	—
32	#101	D₁₁₃	1	1	yes	characteristic
33	C₂×Q₈	—	113	1	no	—
34	C₂×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	226	1	no	—
37	C₄⋊C₄	—	226	1	no	—
38	C₄⋊C₄	—	226	1	no	—
39	C₄²	—	113	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	452	1	no	—
42	C₂×C₄	—	226	1	no	—
43	C₂×C₄	—	226	1	no	—
44	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
45	C₂×C₄	D₄₅₂	1	1	yes	characteristic
46	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
47	C₈	—	4	1	no	—
48	C₈	—	452	1	no	—
49	C₂²	#14268624	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	452	1	no	—
54	C₄	—	226	2	no	—
55	C₂	—	2	1	no	—
56	C₂	#16813536	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16813536
commutator	C₂×C₄×C₁₁₃	C₂×C₄
Frattini	C₂×Q₈	C₂×D₁₁₃
Fitting	#101×C₁₁₃	C₂
socle	C₂×C₁₁₃	#99
hypercenter	#101	D₁₁₃
hypocenter	C₁₁₃	#356
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
28. C₁₁₃	#356	semidirect