Subgroups — #20298870

Order 7232.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813653	C₂	1	2	yes	maximal
2	#16813628	C₂	1	1	yes	maximal, characteristic
3	#16813558	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813541	C₂	1	2	yes	maximal, complemented
5	C₂×Q₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14268647	C₂²	1	1	yes	characteristic
7	#14268637	—	2	2	no	—
8	#14268634	—	2	2	no	—
9	#14268631	C₂²	1	1	yes	characteristic
10	#14268631	C₂²	1	2	yes	—
11	#14268630	—	2	1	no	—
12	C₈×D₁₁₃	—	2	1	no	—
13	C₂×Q₈×C₁₁₃	C₂²	1	2	yes	—
14	Q₁₆×C₁₁₃	—	2	1	no	—
15	Q₁₆×C₁₁₃	—	2	1	no	—
16	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	Q₈×C₁₁₃	—	2	2	no	—
18	Q₈×C₁₁₃	—	2	2	no	—
19	C₂×C₄×C₁₁₃	—	2	2	no	—
20	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
21	C₂²⋊D₁₁₃	—	2	1	no	—
22	D₄₅₂	D₄	1	1	yes	characteristic
23	C₄×D₁₁₃	—	2	1	no	—
24	Dic₂₂₆	D₄	1	1	yes	characteristic
25	C₈×C₁₁₃	D₄	1	1	yes	characteristic
26	C₈×C₁₁₃	D₄	1	1	yes	characteristic
27	#11744751	—	2	1	no	—
28	#11744751	—	2	2	no	—
29	C₂²×C₁₁₃	#41	1	1	yes	characteristic
30	C₂×D₁₁₃	—	2	1	no	—
31	C₄×C₁₁₃	—	4	2	no	—
32	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
34	Dic₁₁₃	—	2	1	no	—
35	C₂×C₁₁₃	—	2	1	no	—
36	C₂×C₁₁₃	#121	1	1	yes	characteristic
37	D₁₁₃	—	4	1	no	—
38	C₁₁₃	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	113	1	no	maximal, Sylow
40	#137	—	113	2	no	—
41	C₂×Q₁₆	D₁₁₃	1	1	yes	characteristic, complemented
42	#131	—	113	1	no	—
43	#108	—	113	1	no	—
44	#101	—	113	2	no	—
45	#41	—	113	1	no	—
46	C₂×Q₈	C₂×D₁₁₃	1	2	yes	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	2	1	no	—
49	Q₁₆	—	226	2	no	—
50	SD₁₆	—	226	2	no	—
51	M₁₆	—	113	1	no	—
52	M₁₆	—	113	2	no	—
53	M₁₆	—	226	1	no	—
54	C₂×C₈	—	226	1	no	—
55	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	—	113	1	no	—
59	D₄	—	113	1	no	—
60	D₄	—	226	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	226	1	no	—
63	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
64	C₈	—	226	2	no	—
65	C₈	—	226	1	no	—
66	C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
67	C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
68	C₂²	—	226	1	no	—
69	C₂²	#14268646	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	226	1	no	—
72	C₄	D₄×D₁₁₃	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	452	1	no	—
76	C₂	#16813593	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16813593
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₂×Q₁₆×C₁₁₃	C₂
socle	C₂×C₁₁₃	#121
hypercenter	C₂×Q₁₆	D₁₁₃
hypocenter	C₁₁₃	#473
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #16813558	C₂	semidirect
4. #16813541	C₂	semidirect
5. C₂×Q₁₆×C₁₁₃	C₂	semidirect
38. C₁₁₃	#473	semidirect
41. C₂×Q₁₆	D₁₁₃	semidirect