Subgroups — #22608125

Order 9344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic
2	#17988417	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₂	—	2	1	no	—
5	Dic₅₈₄	—	2	1	no	—
6	Dic₅₈₄	C₄	1	2	yes	—
7	#14556527	—	2	1	no	—
8	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	C₃₂×C₇₃	—	2	1	no	—
10	C₂×Dic₁₄₆	—	4	1	no	—
11	Dic₂₉₂	—	2	2	no	—
12	Dic₂₉₂	—	4	1	no	—
13	#11924012	—	4	1	no	—
14	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
18	C₂×Dic₇₃	—	8	1	no	—
19	Dic₁₄₆	—	4	2	no	—
20	Dic₁₄₆	—	8	1	no	—
21	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
23	#10596831	—	8	1	no	—
24	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
25	C₄×C₇₃	#102	1	1	yes	characteristic
26	C₄×C₇₃	D₁₆	1	1	yes	characteristic
27	Dic₇₃	—	8	2	no	—
28	C₂×C₇₃	—	2	1	no	—
29	C₂×C₇₃	#357	1	1	yes	characteristic
30	#1420	—	73	1	no	maximal, Sylow
31	C₇₃	#1420	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₃₂	—	73	1	no	—
33	M₆₄	D₇₃	1	1	yes	characteristic
34	#368	—	73	1	no	—
35	C₂×Q₁₆	—	146	1	no	—
36	Q₃₂	—	73	2	no	—
37	Q₃₂	—	146	1	no	—
38	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
39	#108	—	146	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	292	1	no	—
42	Q₁₆	—	292	1	no	—
43	Q₁₆	—	146	2	no	—
44	M₁₆	—	292	1	no	—
45	C₂×C₈	D₂₉₂	1	1	yes	characteristic
46	C₁₆	C₄×D₇₃	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
48	Q₈	—	292	2	no	—
49	Q₈	—	584	1	no	—
50	C₂×C₄	—	584	1	no	—
51	C₂×C₄	D₅₈₄	1	1	yes	characteristic
52	C₈	—	584	1	no	—
53	C₈	#11924005	1	1	yes	characteristic
54	C₈	#11924017	1	1	yes	characteristic
55	C₂²	#14556536	1	1	yes	characteristic
56	C₄	—	584	2	no	—
57	C₄	#14556513	1	1	yes	characteristic
58	C₄	D₁₁₆₈	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#17988389	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988389
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	M₆₄×C₇₃	C₂
socle	C₂×C₇₃	#357
hypercenter	M₆₄	D₇₃
hypocenter	C₇₃	#1420
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
31. C₇₃	#1420	semidirect