Subgroups — #22607993

Order 9344.

74 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	#17988408	C₂	1	1	yes	maximal, characteristic
3	#364×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556583	C₄	1	2	yes	—
5	#14556531	—	2	1	no	—
6	#14556525	—	2	1	no	—
7	#14556523	—	2	1	no	—
8	M₃₂×C₇₃	—	2	1	no	—
9	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₇₃	—	2	2	no	—
11	#11924007	—	4	2	no	—
12	#11924003	—	4	1	no	—
13	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
14	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
15	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₃	—	4	1	no	—
17	C₂×C₄×C₇₃	—	2	1	no	—
18	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₇₃	—	4	2	no	—
20	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
21	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
22	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
23	C₈×C₇₃	Q₁₆	1	1	yes	characteristic
24	C₂²×C₇₃	#100	1	1	yes	characteristic
25	C₄×C₇₃	—	4	1	no	—
26	C₄×C₇₃	#103	1	1	yes	characteristic
27	C₄×C₇₃	#103	1	1	yes	characteristic
28	Dic₇₃	—	8	2	no	—
29	C₂×C₇₃	—	2	1	no	—
30	C₂×C₇₃	#333	1	1	yes	characteristic
31	#1366	—	73	1	no	maximal, Sylow
32	C₇₃	#1366	1	1	yes	characteristic, complemented, Sylow
33	#499	—	73	1	no	—
34	#364	—	73	1	no	—
35	#364	D₇₃	1	1	yes	characteristic
36	#125	—	73	2	no	—
37	M₃₂	—	2	1	no	—
38	M₃₂	—	146	1	no	—
39	#107	—	146	1	no	—
40	#106	—	146	1	no	—
41	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
42	C₂×C₈	D₂₉₂	1	1	yes	characteristic
43	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
44	C₄⋊C₄	—	292	2	no	—
45	C₄⋊C₄	—	146	2	no	—
46	C₄²	C₄×D₇₃	1	1	yes	characteristic
47	C₁₆	—	4	1	no	—
48	C₁₆	—	292	1	no	—
49	C₂×C₄	—	2	1	no	—
50	C₂×C₄	—	292	2	no	—
51	C₂×C₄	#11924005	1	1	yes	characteristic
52	C₈	#11924016	1	1	yes	characteristic
53	C₈	#11924017	1	1	yes	characteristic
54	C₈	#11924018	1	1	yes	characteristic
55	C₈	Dic₂₉₂	1	1	yes	characteristic
56	C₂²	#14556507	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	584	2	no	—
59	C₄	#14556514	1	1	yes	characteristic
60	C₄	#14556516	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	#17988335	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988335
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₃
Fitting	#364×C₇₃	C₂
socle	C₂×C₇₃	#333
hypercenter	#364	D₇₃
hypocenter	C₇₃	#1366
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
32. C₇₃	#1366	semidirect