Subgroups — #22609536

Order 9344.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988967	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988933	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
5	C₂×Dic₂₉₂	—	2	2	no	—
6	#14556591	C₂²	1	2	yes	—
7	#14556512	—	2	8	no	—
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×Dic₁₄₆	—	2	2	no	—
13	Dic₂₉₂	—	4	4	no	—
14	C₂×#10596831	D₄	1	4	yes	—
15	C₄⋊Dic₇₃	—	2	4	no	—
16	C₂×D₄×C₇₃	—	2	2	no	—
17	C₂×D₄×C₇₃	—	2	4	no	—
18	D₈×C₇₃	—	4	4	no	—
19	C₂×C₈×C₇₃	D₄	1	2	yes	—
20	C₄²×C₇₃	C₂³	1	1	yes	characteristic
21	C₂³×C₇₃	—	4	2	no	—
22	D₄×C₇₃	—	4	4	no	—
23	D₄×C₇₃	—	4	8	no	—
24	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₇₃	—	4	2	no	—
27	Dic₁₄₆	—	4	4	no	—
28	C₈×C₇₃	D₈	1	4	yes	—
29	#10596831	—	2	4	no	—
30	C₂²×C₇₃	—	8	2	no	—
31	C₂²×C₇₃	—	8	4	no	—
32	C₂²×C₇₃	#127	1	1	yes	characteristic
33	C₄×C₇₃	C₂×D₈	1	2	yes	—
34	C₄×C₇₃	#135	1	4	yes	—
35	Dic₇₃	—	8	2	no	—
36	C₂×C₇₃	—	16	2	no	—
37	C₂×C₇₃	#493	1	1	yes	characteristic
38	C₂×C₇₃	#495	1	2	yes	—
39	#1709	—	73	1	no	maximal, Sylow
40	C₇₃	#1709	1	1	yes	characteristic, complemented, Sylow
41	#494	—	73	1	no	—
42	#493	D₇₃	1	1	yes	characteristic
43	#486	—	73	4	no	—
44	C₈²	—	73	1	no	—
45	C₂×Q₁₆	—	146	2	no	—
46	C₂×D₈	—	2	2	no	—
47	C₄⋊Q₈	—	73	2	no	—
48	#127	C₂×D₇₃	1	2	yes	—
49	#102	—	146	8	no	—
50	C₄×C₈	—	73	2	no	—
51	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
52	C₂×Q₈	—	146	2	no	—
53	C₂×D₄	—	2	4	no	—
54	C₂×D₄	—	2	2	no	—
55	Q₁₆	—	292	4	no	—
56	D₈	—	4	4	no	—
57	C₂×C₈	—	73	4	no	—
58	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
59	C₄⋊C₄	—	146	4	no	—
60	C₄²	C₂²×D₇₃	1	1	yes	characteristic
61	C₂³	—	4	2	no	—
62	Q₈	—	292	4	no	—
63	D₄	—	4	4	no	—
64	D₄	—	4	8	no	—
65	C₂×C₄	—	292	2	no	—
66	C₂×C₄	D₄×D₇₃	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
68	C₈	—	146	4	no	—
69	C₈	#11924013	1	4	yes	—
70	C₂²	—	8	2	no	—
71	C₂²	—	8	4	no	—
72	C₂²	#14556587	1	1	yes	characteristic
73	C₄	—	584	2	no	—
74	C₄	C₂×#11924013	1	2	yes	—
75	C₄	#14556610	1	4	yes	—
76	C₂	—	16	2	no	—
77	C₂	#17988963	1	1	yes	characteristic
78	C₂	#17988970	1	2	yes	—

	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	#1709
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. #17988967	C₂	semidirect
2. #17988933	C₂	semidirect
3. C₈×#10596831	C₂	semidirect
40. C₇₃	#1709	semidirect