Subgroups — #22608118

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988421	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988415	C₂	1	1	yes	maximal, characteristic, complemented
3	#508×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556525	—	2	1	no	—
5	#14556497	—	2	1	no	—
6	#135×C₇₃	—	2	1	no	—
7	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
8	SD₃₂×C₇₃	—	2	1	no	—
9	D₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₇₃	—	4	1	no	—
12	#41×C₇₃	—	4	1	no	—
13	Q₁₆×C₇₃	—	2	1	no	—
14	SD₁₆×C₇₃	—	4	1	no	—
15	D₈×C₇₃	—	2	1	no	—
16	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
17	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	Q₈×C₇₃	—	4	1	no	—
20	D₄×C₇₃	—	4	1	no	—
21	D₄×C₇₃	—	8	1	no	—
22	C₂×C₄×C₇₃	—	8	1	no	—
23	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
24	C₂×Dic₇₃	—	8	1	no	—
25	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
27	C₂²×C₇₃	—	8	1	no	—
28	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
29	C₄×C₇₃	—	8	1	no	—
30	C₄×C₇₃	#102	1	1	yes	characteristic
31	C₄×C₇₃	SD₃₂	1	1	yes	characteristic
32	Dic₇₃	—	16	1	no	—
33	C₂×C₇₃	—	2	1	no	—
34	C₂×C₇₃	—	16	1	no	—
35	C₂×C₇₃	#357	1	1	yes	characteristic
36	#1418	—	73	1	no	maximal, Sylow
37	C₇₃	#1418	1	1	yes	characteristic, complemented, Sylow
38	#508	D₇₃	1	1	yes	characteristic
39	M₆₄	—	73	1	no	—
40	#367	—	73	1	no	—
41	#135	—	2	1	no	—
42	Q₃₂	Dic₇₃	1	1	yes	characteristic, complemented
43	SD₃₂	—	2	1	no	—
44	D₁₆	Dic₇₃	1	1	yes	characteristic, complemented
45	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
46	#107	—	146	1	no	—
47	C₃₂	—	146	1	no	—
48	#41	—	4	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	4	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
53	C₄⋊C₄	—	292	1	no	—
54	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	8	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	584	1	no	—
61	C₂×C₄	#11924013	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
63	C₈	#11924016	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	#14556532	1	1	yes	characteristic
66	C₄	—	8	1	no	—
67	C₄	—	1168	1	no	—
68	C₄	#14556512	1	1	yes	characteristic
69	C₄	#14556535	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	16	1	no	—
72	C₂	#17988388	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988388
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	#508×C₇₃	C₂
socle	C₂×C₇₃	#357
hypercenter	#508	D₇₃
hypocenter	C₇₃	#1418
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. #17988421	C₂	semidirect
2. #17988415	C₂	semidirect
7. Q₃₂×C₇₃	C₄	semidirect
9. D₁₆×C₇₃	C₄	semidirect
37. C₇₃	#1418	semidirect
42. Q₃₂	Dic₇₃	semidirect
44. D₁₆	Dic₇₃	semidirect