Subgroups — #22626995

Order 9344.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924040	C₂	1	2	yes	maximal
2	C₈×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924040	—	2	2	no	—
4	C₄×#10596833	C₄	1	1	yes	characteristic
5	C₄×#10596833	C₂²	1	1	yes	characteristic
6	C₈×Dic₇₃	C₄	1	1	yes	characteristic
7	#11924040	—	4	2	no	—
8	C₂×#10596833	—	2	1	no	—
9	C₂×#10596833	D₄	1	1	yes	characteristic
10	C₂×#10596833	Q₈	1	1	yes	characteristic
11	C₂×#10596831	C₈	1	1	yes	characteristic
12	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
15	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
16	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
17	#10596833	—	2	2	no	—
18	#10596833	—	2	1	no	—
19	#10596833	D₈	1	1	yes	characteristic
20	#10596833	Q₁₆	1	1	yes	characteristic
21	C₈×C₇₃	C₁₆	1	2	yes	complemented
22	#10596831	—	2	1	no	—
23	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
25	C₄×C₇₃	M₃₂	1	1	yes	characteristic
26	Dic₇₃	—	2	1	no	—
27	Dic₇₃	#107	1	1	yes	characteristic
28	Dic₇₃	#108	1	1	yes	characteristic
29	C₂×C₇₃	#335	1	1	yes	characteristic
30	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₇₃	#364	1	1	yes	characteristic
32	#1370	—	73	1	no	maximal, Sylow
33	C₇₃	#1370	1	1	yes	characteristic, complemented, Sylow
34	C₄⋊C₁₆	—	73	2	no	—
35	C₈²	—	73	1	no	—
36	C₂×C₁₆	—	146	2	no	—
37	C₄×C₈	—	73	1	no	—
38	C₄×C₈	—	73	1	no	—
39	C₄×C₈	—	73	1	no	—
40	C₂×C₈	—	73	1	no	—
41	C₂×C₈	—	73	1	no	—
42	C₂×C₈	—	73	1	no	—
43	C₂×C₈	—	146	1	no	—
44	C₂×C₈	#10596842	1	1	yes	characteristic
45	C₄²	—	73	1	no	—
46	C₁₆	—	292	2	no	—
47	C₂×C₄	—	73	1	no	—
48	C₂×C₄	—	73	1	no	—
49	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
50	C₈	—	73	1	no	—
51	C₈	—	73	1	no	—
52	C₈	—	146	1	no	—
53	C₈	—	146	2	no	—
54	C₈	—	146	1	no	—
55	C₈	#11924040	1	2	yes	complemented
56	C₂²	C₄⋊#10596842	1	1	yes	characteristic
57	C₄	—	73	1	no	—
58	C₄	—	73	1	no	—
59	C₄	—	146	1	no	—
60	C₄	C₂×#11924040	1	1	yes	characteristic
61	C₄	#14556688	1	1	yes	characteristic
62	C₂	#17989677	1	1	yes	characteristic
63	C₂	C₄⋊#11924040	1	1	yes	characteristic
64	C₂	#17989692	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10596842
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄⋊C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1370
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
21. C₈×C₇₃	C₁₆	semidirect
33. C₇₃	#1370	semidirect
55. C₈	#11924040	semidirect