Subgroups — #22607982

Order 9344.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988989	C₂	1	1	yes	maximal, characteristic
2	#17988338	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556583	—	2	1	no	—
5	#14556525	C₄	1	1	yes	characteristic
6	#14556525	C₄	1	1	yes	characteristic
7	#14556523	—	2	1	no	—
8	C₄⋊#10596831	—	2	1	no	—
9	C₂×C₁₆×C₇₃	—	2	1	no	—
10	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×#10596831	—	4	1	no	—
12	C₄⋊Dic₇₃	—	2	1	no	—
13	C₄⋊Dic₇₃	—	2	1	no	—
14	#11924007	—	4	1	no	—
15	#11924007	—	4	1	no	—
16	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
18	C₄²×C₇₃	D₄	1	1	yes	characteristic
19	C₁₆×C₇₃	—	4	1	no	—
20	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
23	C₂×Dic₇₃	—	4	1	no	—
24	C₂×Dic₇₃	—	4	1	no	—
25	C₈×C₇₃	—	2	1	no	—
26	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
27	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
28	#10596831	—	8	1	no	—
29	C₂²×C₇₃	#102	1	1	yes	characteristic
30	C₄×C₇₃	—	2	1	no	—
31	C₄×C₇₃	—	2	1	no	—
32	C₄×C₇₃	#101	1	1	yes	characteristic
33	C₄×C₇₃	#103	1	1	yes	characteristic
34	Dic₇₃	—	8	1	no	—
35	Dic₇₃	—	8	1	no	—
36	C₂×C₇₃	#332	1	1	yes	characteristic
37	C₂×C₇₃	#359	1	1	yes	characteristic
38	C₂×C₇₃	#360	1	1	yes	characteristic
39	#1363	—	73	1	no	maximal, Sylow
40	C₇₃	#1363	1	1	yes	characteristic, complemented, Sylow
41	#499	—	73	1	no	—
42	C₄⋊C₁₆	D₇₃	1	1	yes	characteristic
43	#334	—	73	1	no	—
44	#125	—	146	1	no	—
45	C₂×C₁₆	—	2	1	no	—
46	#107	—	73	1	no	—
47	#107	—	73	1	no	—
48	#106	—	146	1	no	—
49	C₄⋊C₈	—	146	1	no	—
50	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
51	C₂×C₈	—	292	1	no	—
52	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
54	C₄⋊C₄	—	292	1	no	—
55	C₄⋊C₄	—	292	1	no	—
56	C₄⋊C₄	—	146	1	no	—
57	C₄⋊C₄	—	146	1	no	—
58	C₄²	D₂₉₂	1	1	yes	characteristic
59	C₁₆	—	4	1	no	—
60	C₂×C₄	—	292	1	no	—
61	C₂×C₄	—	292	1	no	—
62	C₂×C₄	#11924005	1	1	yes	characteristic
63	C₂×C₄	D₅₈₄	1	1	yes	characteristic
64	C₂×C₄	#11924017	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	584	1	no	—
67	C₈	#11924016	1	1	yes	characteristic
68	C₈	#11924018	1	1	yes	characteristic
69	C₂²	#14556513	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	584	1	no	—
73	C₄	—	584	1	no	—
74	C₄	#14556509	1	1	yes	characteristic
75	C₄	#14556514	1	1	yes	characteristic
76	C₂	#17988332	1	1	yes	characteristic
77	C₂	#17988395	1	1	yes	characteristic
78	C₂	#17988398	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556513
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₃
Fitting	C₄⋊C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	#102
hypercenter	C₄⋊C₁₆	D₇₃
hypocenter	C₇₃	#1363
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
40. C₇₃	#1363	semidirect