Subgroups — #22609545

Order 9344.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988964	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988963	C₂	1	4	yes	maximal, complemented
3	C₈×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅₈₄	—	2	2	no	—
6	C₂×#11924013	—	2	8	no	—
7	#14556588	C₂²	1	2	yes	—
8	C₄×#10596831	C₂²	1	2	yes	—
9	C₂×D₈×C₇₃	—	2	2	no	—
10	#127×C₇₃	C₂²	1	2	yes	—
11	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×D₂₉₂	—	2	4	no	—
13	C₂×D₂₉₂	—	2	2	no	—
14	D₅₈₄	—	4	4	no	—
15	#11924013	—	4	16	no	—
16	C₂×#10596831	D₄	1	4	yes	—
17	C₂×D₄×C₇₃	—	2	2	no	—
18	C₂×D₄×C₇₃	—	2	4	no	—
19	D₈×C₇₃	—	4	4	no	—
20	C₂×C₈×C₇₃	D₄	1	2	yes	—
21	C₄²×C₇₃	C₂³	1	1	yes	characteristic
22	C₂³×C₇₃	—	4	2	no	—
23	C₂²×D₇₃	—	4	2	no	—
24	D₄×C₇₃	—	4	4	no	—
25	D₄×C₇₃	—	4	8	no	—
26	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
28	D₂₉₂	—	4	8	no	—
29	D₂₉₂	—	4	4	no	—
30	C₈×C₇₃	D₈	1	4	yes	complemented
31	#10596831	D₈	1	8	yes	complemented
32	C₂²×C₇₃	—	8	4	no	—
33	C₂²×C₇₃	—	8	2	no	—
34	C₂²×C₇₃	#127	1	1	yes	characteristic
35	C₂×D₇₃	—	8	4	no	—
36	C₂×D₇₃	—	8	2	no	—
37	C₄×C₇₃	C₂×D₈	1	4	yes	—
38	C₄×C₇₃	C₂×D₈	1	2	yes	—
39	C₂×C₇₃	—	16	2	no	—
40	C₂×C₇₃	#493	1	2	yes	—
41	C₂×C₇₃	#493	1	1	yes	characteristic
42	D₇₃	—	16	2	no	—
43	#1712	—	73	1	no	maximal, Sylow
44	C₇₃	#1712	1	1	yes	characteristic, complemented, Sylow
45	#493	—	73	4	no	—
46	#493	—	73	1	no	—
47	#493	D₇₃	1	1	yes	characteristic, complemented
48	C₈²	—	73	1	no	—
49	C₂×D₈	—	2	2	no	—
50	C₂×D₈	—	146	8	no	—
51	C₂×D₈	—	146	2	no	—
52	#127	—	73	2	no	—
53	#127	C₂×D₇₃	1	2	yes	—
54	C₄×C₈	—	73	2	no	—
55	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	146	4	no	—
59	C₂×D₄	—	146	2	no	—
60	D₈	—	4	4	no	—
61	D₈	—	292	16	no	—
62	D₈	—	292	4	no	—
63	C₂×C₈	—	73	4	no	—
64	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
65	C₄²	C₂²×D₇₃	1	1	yes	characteristic
66	C₂³	—	4	2	no	—
67	C₂³	—	292	2	no	—
68	D₄	—	4	8	no	—
69	D₄	—	4	4	no	—
70	D₄	—	292	8	no	—
71	D₄	—	292	4	no	—
72	C₂×C₄	D₄×D₇₃	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
74	C₈	—	73	8	no	—
75	C₈	#11924013	1	4	yes	complemented
76	C₂²	—	8	4	no	—
77	C₂²	—	8	2	no	—
78	C₂²	—	584	4	no	—
79	C₂²	—	584	2	no	—
80	C₂²	#14556587	1	1	yes	characteristic
81	C₄	D₈×D₇₃	1	4	yes	—
82	C₄	C₂×#11924013	1	2	yes	—
83	C₂	—	16	2	no	—
84	C₂	—	1168	2	no	—
85	C₂	#17988962	1	2	yes	—
86	C₂	#17988963	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556587
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#493×C₇₃	C₂
socle	C₂²×C₇₃	#127
hypercenter	#493	D₇₃
hypocenter	C₇₃	#1712
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #17988964	C₂	semidirect
2. #17988963	C₂	semidirect
3. C₈×#10596831	C₂	semidirect
4. #493×C₇₃	C₂	semidirect
30. C₈×C₇₃	D₈	semidirect
31. #10596831	D₈	semidirect
44. C₇₃	#1712	semidirect
47. #493	D₇₃	semidirect
75. C₈	#11924013	semidirect