Subgroups — #22626946

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64408⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×#10596842	C₂	1	1	yes	maximal, characteristic
3	C₁₆×#64408	C₂	1	1	yes	maximal, characteristic
4	#14556686	C₄	1	2	yes	—
5	C₄×#10596842	C₄	1	2	yes	—
6	#14556664	C₄	1	1	yes	characteristic
7	C₈×#64408	C₂²	1	1	yes	characteristic
8	C₁₆×D₇₃	C₄	1	1	yes	characteristic
9	C₂×#10596842	C₈	1	4	yes	—
10	#11924040	C₈	1	4	yes	complemented
11	#11924036	C₂×C₄	1	1	yes	characteristic
12	C₄×#64408	C₂×C₄	1	1	yes	characteristic
13	#11924031	C₈	1	2	yes	complemented
14	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
15	#11924003	C₈	1	1	yes	characteristic, complemented
16	C₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
17	C₂×#64408	C₂×C₈	1	2	yes	—
18	#10596842	—	2	4	no	—
19	C₄×D₇₃	C₄²	1	1	yes	characteristic
20	#10596833	C₂×C₈	1	2	yes	—
21	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
22	#10596831	C₂×C₈	1	1	yes	characteristic
23	C₂×D₇₃	C₄×C₈	1	1	yes	characteristic
24	#64408	M₃₂	1	4	yes	—
25	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
26	Dic₇₃	C₄×C₈	1	1	yes	characteristic
27	C₂×C₇₃	C₈²	1	1	yes	characteristic
28	D₇₃	#346	1	2	yes	—
29	#1311	—	73	1	no	maximal, Sylow
30	C₇₃	#1311	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₆	—	73	1	no	—
32	C₄×C₁₆	—	73	1	no	—
33	C₈²	—	73	1	no	—
34	C₂×C₁₆	—	73	2	no	—
35	C₂×C₁₆	—	73	1	no	—
36	C₂×C₁₆	—	73	1	no	—
37	C₄×C₈	—	73	2	no	—
38	C₄×C₈	—	73	1	no	—
39	C₂×C₈	—	73	1	no	—
40	C₂×C₈	—	73	1	no	—
41	C₂×C₈	—	73	4	no	—
42	C₄²	—	73	1	no	—
43	C₁₆	—	73	2	no	—
44	C₁₆	—	73	4	no	—
45	C₁₆	—	73	1	no	—
46	C₁₆	#10596842	1	1	yes	characteristic, complemented
47	C₂×C₄	—	73	2	no	—
48	C₂×C₄	—	73	1	no	—
49	C₈	—	73	2	no	—
50	C₈	—	73	1	no	—
51	C₈	—	146	4	no	—
52	C₈	C₂×#10596842	1	1	yes	characteristic
53	C₂²	—	73	1	no	—
54	C₄	—	73	4	no	—
55	C₄	—	73	1	no	—
56	C₄	C₄×#10596842	1	1	yes	characteristic
57	C₂	—	73	2	no	—
58	C₂	C₈×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×#10596842
commutator, socle	C₂×C₇₃	C₈²
Fitting	C₁₆×C₇₃	C₈
hypercenter	C₁₆	#10596842
hypocenter	C₇₃	#1311
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
10. #11924040	C₈	semidirect
13. #11924031	C₈	semidirect
15. #11924003	C₈	semidirect
16. C₁₆×C₇₃	C₈	semidirect
30. C₇₃	#1311	semidirect
46. C₁₆	#10596842	semidirect