Subgroups — #22625087

Order 9344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989520	C₂	1	1	yes	maximal, characteristic
2	#17989516	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556662	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	Q₁₆×D₇₃	—	2	1	no	—
7	Dic₅₈₄	C₄	1	1	yes	characteristic
8	#14556537	—	2	1	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₇₃	C₄	1	1	yes	characteristic
11	#11924038	—	4	1	no	—
12	Q₈×D₇₃	—	4	1	no	—
13	Dic₂₉₂	—	2	1	no	—
14	#11924018	—	4	1	no	—
15	C₈×D₇₃	D₄	1	1	yes	characteristic
16	#11924003	D₄	1	1	yes	characteristic
17	Q₁₆×C₇₃	—	2	1	no	—
18	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	Q₈×C₇₃	—	4	1	no	—
20	C₄×D₇₃	—	8	1	no	—
21	C₄×D₇₃	D₈	1	1	yes	characteristic
22	Dic₁₄₆	—	4	1	no	—
23	Dic₁₄₆	—	8	1	no	—
24	#10596833	—	8	1	no	—
25	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	#10596831	SD₁₆	1	1	yes	characteristic
27	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
28	C₄×C₇₃	—	8	1	no	—
29	C₄×C₇₃	#102	1	1	yes	characteristic
30	Dic₇₃	—	8	1	no	—
31	Dic₇₃	D₁₆	1	1	yes	characteristic
32	C₂×C₇₃	#357	1	1	yes	characteristic
33	D₇₃	—	2	1	no	—
34	#1420	—	73	1	no	maximal, Sylow
35	C₇₃	#1420	1	1	yes	characteristic, complemented, Sylow
36	C₂×Q₃₂	—	73	1	no	—
37	M₆₄	—	73	1	no	—
38	#368	—	73	1	no	—
39	C₂×Q₁₆	—	146	1	no	—
40	Q₃₂	—	73	1	no	—
41	Q₃₂	—	146	1	no	—
42	Q₃₂	#64408	1	1	yes	characteristic
43	C₂×C₁₆	—	73	1	no	—
44	#108	—	146	1	no	—
45	C₃₂	—	146	1	no	—
46	C₂×Q₈	—	292	1	no	—
47	Q₁₆	—	2	1	no	—
48	Q₁₆	—	292	1	no	—
49	Q₁₆	—	146	1	no	—
50	M₁₆	—	292	1	no	—
51	C₂×C₈	—	73	1	no	—
52	C₁₆	—	73	1	no	—
53	C₁₆	C₂×#64408	1	1	yes	characteristic
54	Q₈	—	4	1	no	—
55	Q₈	—	292	1	no	—
56	Q₈	—	584	1	no	—
57	C₂×C₄	—	584	1	no	—
58	C₂×C₄	—	73	1	no	—
59	C₈	—	584	1	no	—
60	C₈	—	73	1	no	—
61	C₈	C₂²⋊#64408	1	1	yes	characteristic
62	C₂²	—	73	1	no	—
63	C₄	—	8	1	no	—
64	C₄	—	584	1	no	—
65	C₄	—	73	1	no	—
66	C₄	#14556653	1	1	yes	characteristic
67	C₂	—	146	1	no	—
68	C₂	#17989499	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989499
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₁₆	C₂×#64408
Fitting	Q₃₂×C₇₃	C₄
socle	C₂×C₇₃	#357
hypercenter	Q₃₂	#64408
hypocenter	C₇₃	#1420
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

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