Subgroups — #22608121

Order 9344.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988421	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988417	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556527	—	2	1	no	—
5	#14556497	—	2	1	no	—
6	C₂×D₈×C₇₃	—	2	1	no	—
7	D₁₆×C₇₃	—	2	1	no	—
8	D₁₆×C₇₃	C₄	1	2	yes	—
9	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	#11924012	—	4	1	no	—
11	C₂×D₄×C₇₃	—	4	1	no	—
12	D₈×C₇₃	—	2	2	no	—
13	D₈×C₇₃	—	4	1	no	—
14	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₃	D₄	1	1	yes	characteristic
17	C₂³×C₇₃	—	8	1	no	—
18	D₄×C₇₃	—	4	2	no	—
19	D₄×C₇₃	—	8	1	no	—
20	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
21	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
23	#10596831	—	8	1	no	—
24	C₂²×C₇₃	—	8	2	no	—
25	C₂²×C₇₃	—	16	2	no	—
26	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
27	C₄×C₇₃	#102	1	1	yes	characteristic
28	C₄×C₇₃	D₁₆	1	1	yes	characteristic
29	C₂×C₇₃	—	2	1	no	—
30	C₂×C₇₃	—	16	2	no	—
31	C₂×C₇₃	#357	1	1	yes	characteristic
32	#1419	—	73	1	no	maximal, Sylow
33	C₇₃	#1419	1	1	yes	characteristic, complemented, Sylow
34	C₂×D₁₆	D₇₃	1	1	yes	characteristic
35	M₆₄	—	73	1	no	—
36	#368	—	73	1	no	—
37	C₂×D₈	—	2	1	no	—
38	D₁₆	—	2	1	no	—
39	D₁₆	Dic₇₃	1	2	yes	—
40	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
41	#108	—	146	1	no	—
42	C₃₂	—	146	1	no	—
43	C₂×D₄	—	4	1	no	—
44	D₈	—	2	2	no	—
45	D₈	—	4	1	no	—
46	M₁₆	—	292	1	no	—
47	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
48	C₁₆	C₂×Dic₇₃	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
50	C₂³	—	8	1	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	1	no	—
53	C₂×C₄	#11924013	1	1	yes	characteristic
54	C₈	—	584	1	no	—
55	C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
56	C₈	#11924016	1	1	yes	characteristic
57	C₂²	—	8	2	no	—
58	C₂²	—	16	2	no	—
59	C₂²	#14556535	1	1	yes	characteristic
60	C₄	#14556512	1	1	yes	characteristic
61	C₄	#14556532	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	16	2	no	—
64	C₂	#17988388	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988388
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	C₂×D₁₆×C₇₃	C₂
socle	C₂×C₇₃	#357
hypercenter	C₂×D₁₆	D₇₃
hypocenter	C₇₃	#1419
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. #17988421	C₂	semidirect
2. #17988417	C₂	semidirect
33. C₇₃	#1419	semidirect