Subgroups — #22608134

Order 9344.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556497	C₂	1	1	yes	maximal, characteristic
2	#17988417	C₂	1	1	yes	maximal, characteristic
3	#368×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556527	—	2	1	no	—
5	#14556497	C₄	1	2	yes	—
6	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
7	#108×C₇₃	—	2	1	no	—
8	#11924012	—	4	1	no	—
9	M₁₆×C₇₃	—	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	C₈×C₇₃	—	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	Q₃₂	1	1	yes	characteristic
19	C₄×C₇₃	#107	1	1	yes	characteristic
20	C₄×C₇₃	D₁₆	1	1	yes	characteristic
21	C₂×C₇₃	—	2	1	no	—
22	C₂×C₇₃	#366	1	1	yes	characteristic
23	#1425	—	73	1	no	maximal, Sylow
24	C₇₃	#1425	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃₂	—	73	1	no	—
26	#368	—	73	1	no	—
27	#368	D₇₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	146	1	no	—
31	C₃₂	—	73	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	292	1	no	—
34	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
35	C₁₆	Dic₁₄₆	1	1	yes	characteristic
36	C₁₆	C₄×D₇₃	1	1	yes	characteristic
37	C₂×C₄	#11924013	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	584	1	no	—
40	C₈	#11924007	1	1	yes	characteristic
41	C₈	#11924018	1	1	yes	characteristic
42	C₂²	#14556537	1	1	yes	characteristic
43	C₄	#14556524	1	1	yes	characteristic
44	C₄	#14556532	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#17988412	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556532
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	#368×C₇₃	C₂
socle	C₂×C₇₃	#366
hypercenter	#368	D₇₃
hypocenter	C₇₃	#1425
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
24. C₇₃	#1425	semidirect