Subgroups — #22625086

Order 9344.

78 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	#17989516	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556662	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	D₈×D₇₃	—	2	1	no	—
7	D₁₁₆₈	C₄	1	1	yes	characteristic
8	#14556532	—	2	1	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	D₁₆×C₇₃	C₄	1	1	yes	characteristic
11	#11924038	—	4	1	no	—
12	D₄×D₇₃	—	4	1	no	—
13	D₅₈₄	—	2	1	no	—
14	#11924013	—	4	1	no	—
15	C₈×D₇₃	D₄	1	1	yes	characteristic
16	#11924003	D₄	1	1	yes	characteristic
17	D₈×C₇₃	—	2	1	no	—
18	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×D₇₃	—	8	1	no	—
20	D₄×C₇₃	—	4	1	no	—
21	C₂²⋊D₇₃	—	8	1	no	—
22	D₂₉₂	—	4	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	C₂²×C₇₃	—	8	1	no	—
28	C₂×D₇₃	—	8	1	no	—
29	C₂×D₇₃	—	16	2	no	—
30	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
31	C₄×C₇₃	#102	1	1	yes	characteristic
32	Dic₇₃	D₁₆	1	1	yes	characteristic
33	C₂×C₇₃	—	16	1	no	—
34	C₂×C₇₃	#357	1	1	yes	characteristic
35	D₇₃	—	2	1	no	—
36	D₇₃	—	16	1	no	—
37	#1419	—	73	1	no	maximal, Sylow
38	C₇₃	#1419	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₆	—	73	1	no	—
40	M₆₄	—	73	1	no	—
41	#368	—	73	1	no	—
42	C₂×D₈	—	146	1	no	—
43	D₁₆	—	73	1	no	—
44	D₁₆	—	146	1	no	—
45	D₁₆	#64408	1	1	yes	characteristic
46	C₂×C₁₆	—	73	1	no	—
47	#108	—	146	1	no	—
48	C₃₂	—	146	1	no	—
49	C₂×D₄	—	292	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	292	1	no	—
52	D₈	—	146	1	no	—
53	M₁₆	—	292	1	no	—
54	C₂×C₈	—	73	1	no	—
55	C₁₆	—	73	1	no	—
56	C₁₆	C₂×#64408	1	1	yes	characteristic
57	C₂³	—	584	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	292	1	no	—
60	D₄	—	584	1	no	—
61	C₂×C₄	—	73	1	no	—
62	C₈	—	584	1	no	—
63	C₈	—	73	1	no	—
64	C₈	C₂²⋊#64408	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	584	1	no	—
67	C₂²	—	73	1	no	—
68	C₂²	—	1168	2	no	—
69	C₄	—	73	1	no	—
70	C₄	#14556653	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	1168	1	no	—
73	C₂	—	146	1	no	—
74	C₂	#17989499	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989499
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₁₆	C₂×#64408
Fitting	D₁₆×C₇₃	C₄
socle	C₂×C₇₃	#357
hypercenter	D₁₆	#64408
hypocenter	C₇₃	#1419
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #17989520	C₂	semidirect
2. #17989516	C₂	semidirect
38. C₇₃	#1419	semidirect