Subgroups — #22625083

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989518	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989515	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989020	C₂	1	1	yes	maximal, characteristic
4	#14556662	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	#14556614	—	2	1	no	—
7	#14556534	—	2	1	no	—
8	D₁₁₆₈	C₄	1	1	yes	characteristic
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₇₃	C₄	1	1	yes	characteristic
11	#11924038	—	4	1	no	—
12	#11924029	—	4	1	no	—
13	#11924015	—	4	1	no	—
14	D₅₈₄	—	2	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	D₂₉₂	—	4	1	no	—
21	D₂₉₂	—	8	1	no	—
22	C₄×D₇₃	—	8	1	no	—
23	C₄×D₇₃	D₈	1	1	yes	characteristic
24	#10596833	—	8	1	no	—
25	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	#10596831	SD₁₆	1	1	yes	characteristic
27	C₂×D₇₃	—	8	1	no	—
28	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₇₃	—	8	1	no	—
30	C₄×C₇₃	#102	1	1	yes	characteristic
31	Dic₇₃	D₁₆	1	1	yes	characteristic
32	C₂×C₇₃	#357	1	1	yes	characteristic
33	D₇₃	—	2	1	no	—
34	D₇₃	—	16	1	no	—
35	#1417	—	73	1	no	maximal, Sylow
36	C₇₃	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	—	73	1	no	—
38	C₂×C₃₂	—	73	1	no	—
39	#368	—	73	1	no	—
40	#135	—	146	1	no	—
41	Q₃₂	#64408	1	1	yes	characteristic
42	SD₃₂	—	146	1	no	—
43	D₁₆	—	73	1	no	—
44	C₂×C₁₆	—	73	1	no	—
45	#108	—	146	1	no	—
46	C₃₂	—	146	1	no	—
47	#41	—	292	1	no	—
48	Q₁₆	—	2	1	no	—
49	SD₁₆	—	292	1	no	—
50	D₈	—	146	1	no	—
51	M₁₆	—	292	1	no	—
52	C₂×C₈	—	73	1	no	—
53	C₁₆	—	73	1	no	—
54	C₁₆	C₂×#64408	1	1	yes	characteristic
55	Q₈	—	4	1	no	—
56	D₄	—	292	1	no	—
57	D₄	—	584	1	no	—
58	C₂×C₄	—	584	1	no	—
59	C₂×C₄	—	73	1	no	—
60	C₈	—	584	1	no	—
61	C₈	—	73	1	no	—
62	C₈	C₂²⋊#64408	1	1	yes	characteristic
63	C₂²	—	584	1	no	—
64	C₂²	—	73	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	73	1	no	—
67	C₄	#14556653	1	1	yes	characteristic
68	C₂	—	1168	1	no	—
69	C₂	—	146	1	no	—
70	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	#1417
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
1. #17989518	C₂	semidirect
2. #17989515	C₂	semidirect
36. C₇₃	#1417	semidirect