Subgroups — #22625080

Order 9344.

82 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	#17989513	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556660	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	D₈×D₇₃	—	2	1	no	—
7	D₁₁₆₈	C₄	1	1	yes	characteristic, complemented
8	#14556532	—	2	1	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	D₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#64408	—	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	C₂×#64408	—	8	1	no	—
21	D₄×C₇₃	—	4	1	no	—
22	C₂²⋊D₇₃	—	8	1	no	—
23	D₂₉₂	—	4	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	C₂²×C₇₃	—	8	1	no	—
28	C₂×D₇₃	—	8	1	no	—
29	C₂×D₇₃	—	16	1	no	—
30	C₂×D₇₃	—	16	1	no	—
31	C₂×D₇₃	D₁₆	1	1	yes	characteristic
32	#64408	—	16	1	no	—
33	C₄×C₇₃	#102	1	1	yes	characteristic
34	Dic₇₃	SD₃₂	1	1	yes	characteristic
35	C₂×C₇₃	—	16	1	no	—
36	C₂×C₇₃	#357	1	1	yes	characteristic
37	D₇₃	—	16	1	no	—
38	D₇₃	D₃₂	1	1	yes	characteristic
39	D₇₃	SD₆₄	1	1	yes	characteristic
40	#1415	—	73	1	no	maximal, Sylow
41	C₇₃	#1415	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₁₆	—	73	1	no	—
43	C₂×C₃₂	—	73	1	no	—
44	#366	—	73	1	no	—
45	C₂×D₈	—	146	1	no	—
46	D₁₆	—	73	1	no	—
47	D₁₆	—	146	1	no	—
48	D₁₆	#64408	1	1	yes	characteristic, complemented
49	C₂×C₁₆	—	73	1	no	—
50	#107	—	146	1	no	—
51	C₃₂	—	146	1	no	—
52	C₂×D₄	—	292	1	no	—
53	D₈	—	2	1	no	—
54	D₈	—	292	1	no	—
55	D₈	—	146	1	no	—
56	C₂×C₈	—	73	1	no	—
57	C₄⋊C₄	—	292	1	no	—
58	C₁₆	—	73	1	no	—
59	C₁₆	C₂×#64408	1	1	yes	characteristic
60	C₂³	—	584	1	no	—
61	D₄	—	4	1	no	—
62	D₄	—	292	1	no	—
63	D₄	—	584	1	no	—
64	C₂×C₄	—	584	1	no	—
65	C₂×C₄	—	73	1	no	—
66	C₈	—	73	1	no	—
67	C₈	C₂²⋊#64408	1	1	yes	characteristic
68	C₂²	—	8	1	no	—
69	C₂²	—	584	1	no	—
70	C₂²	—	73	1	no	—
71	C₂²	—	1168	1	no	—
72	C₂²	—	1168	1	no	—
73	C₄	—	73	1	no	—
74	C₄	—	1168	1	no	—
75	C₄	#14556653	1	1	yes	characteristic
76	C₂	—	16	1	no	—
77	C₂	—	73	1	no	—
78	C₂	—	73	1	no	—
79	C₂	—	1168	1	no	—
80	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	#1415
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. #17989518	C₂	semidirect
2. #17989513	C₂	semidirect
7. D₁₁₆₈	C₄	semidirect
10. D₁₆×C₇₃	C₄	semidirect
41. C₇₃	#1415	semidirect
48. D₁₆	#64408	semidirect