Subgroups — #22625085

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989520	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989514	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989020	C₂	1	1	yes	maximal, characteristic
4	#14556660	—	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, complemented
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#64408	—	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	C₂×#64408	—	8	1	no	—
20	Q₈×C₇₃	—	4	1	no	—
21	D₂₉₂	—	4	1	no	—
22	D₂₉₂	—	8	1	no	—
23	C₄×D₇₃	—	8	1	no	—
24	C₄×D₇₃	D₈	1	1	yes	characteristic
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	D₁₆	1	1	yes	characteristic
29	#64408	—	16	1	no	—
30	C₄×C₇₃	—	8	1	no	—
31	C₄×C₇₃	#102	1	1	yes	characteristic
32	Dic₇₃	SD₃₂	1	1	yes	characteristic
33	C₂×C₇₃	#357	1	1	yes	characteristic
34	D₇₃	—	2	1	no	—
35	D₇₃	—	16	1	no	—
36	#1418	—	73	1	no	maximal, Sylow
37	C₇₃	#1418	1	1	yes	characteristic, complemented, Sylow
38	#508	—	73	1	no	—
39	M₆₄	—	73	1	no	—
40	#367	—	73	1	no	—
41	#135	—	146	1	no	—
42	Q₃₂	#64408	1	1	yes	characteristic, complemented
43	SD₃₂	—	146	1	no	—
44	D₁₆	—	73	1	no	—
45	C₂×C₁₆	—	73	1	no	—
46	#107	—	146	1	no	—
47	C₃₂	—	146	1	no	—
48	#41	—	292	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	292	1	no	—
51	D₈	—	146	1	no	—
52	C₂×C₈	—	73	1	no	—
53	C₄⋊C₄	—	292	1	no	—
54	C₁₆	—	73	1	no	—
55	C₁₆	C₂×#64408	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	292	1	no	—
58	D₄	—	584	1	no	—
59	C₂×C₄	—	584	1	no	—
60	C₂×C₄	—	584	1	no	—
61	C₂×C₄	—	73	1	no	—
62	C₈	—	73	1	no	—
63	C₈	C₂²⋊#64408	1	1	yes	characteristic
64	C₂²	—	584	1	no	—
65	C₂²	—	73	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	73	1	no	—
68	C₄	—	1168	1	no	—
69	C₄	#14556653	1	1	yes	characteristic
70	C₂	—	1168	1	no	—
71	C₂	—	146	1	no	—
72	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	#1418
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. #17989520	C₂	semidirect
2. #17989514	C₂	semidirect
8. D₁₁₆₈	C₄	semidirect
10. Q₃₂×C₇₃	C₄	semidirect
37. C₇₃	#1418	semidirect
42. Q₃₂	#64408	semidirect