Subgroups — #22608137

Order 9344.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988417	C₂	1	1	yes	maximal, characteristic
2	#17988415	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556527	—	2	1	no	—
5	#14556525	—	2	1	no	—
6	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
7	C₃₂×C₇₃	C₄	1	2	yes	complemented
8	#11924012	—	4	1	no	—
9	C₄⋊Dic₇₃	—	4	1	no	—
10	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
11	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
14	C₂×Dic₇₃	—	8	1	no	—
15	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
17	#10596831	—	8	1	no	—
18	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
19	C₄×C₇₃	#107	1	1	yes	characteristic
20	C₄×C₇₃	SD₃₂	1	1	yes	characteristic
21	Dic₇₃	—	16	1	no	—
22	C₂×C₇₃	—	2	1	no	—
23	C₂×C₇₃	#367	1	1	yes	characteristic
24	#1426	—	73	1	no	maximal, Sylow
25	C₇₃	#1426	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	D₇₃	1	1	yes	characteristic
27	#368	—	73	1	no	—
28	#367	—	73	1	no	—
29	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
30	#108	—	146	1	no	—
31	#107	—	146	1	no	—
32	C₃₂	Dic₇₃	1	2	yes	complemented
33	M₁₆	—	292	1	no	—
34	C₂×C₈	D₂₉₂	1	1	yes	characteristic
35	C₄⋊C₄	—	292	1	no	—
36	C₁₆	Dic₁₄₆	1	1	yes	characteristic
37	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
38	C₂×C₄	—	584	1	no	—
39	C₂×C₄	D₅₈₄	1	1	yes	characteristic
40	C₈	—	584	1	no	—
41	C₈	C₄⋊Dic₇₃	1	1	yes	characteristic
42	C₈	Dic₂₉₂	1	1	yes	characteristic
43	C₂²	#14556536	1	1	yes	characteristic
44	C₄	—	1168	1	no	—
45	C₄	#14556525	1	1	yes	characteristic
46	C₄	#14556536	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#17988415	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988415
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	M₆₄×C₇₃	C₂
socle	C₂×C₇₃	#367
hypercenter	M₆₄	D₇₃
hypocenter	C₇₃	#1426
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
7. C₃₂×C₇₃	C₄	semidirect
25. C₇₃	#1426	semidirect
32. C₃₂	Dic₇₃	semidirect