Subgroups — #22624957

Order 9344.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989448	C₂	1	1	yes	maximal, characteristic
2	#17989448	C₂	1	1	yes	maximal, characteristic
3	#17988362	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#10596833	—	2	1	no	—
5	C₄⋊#10596833	—	2	1	no	—
6	C₂×#11924003	C₄	1	1	yes	characteristic
7	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
9	C₂×#10596833	—	4	1	no	—
10	C₂×#10596833	—	4	1	no	—
11	C₂×#10596831	Q₈	1	1	yes	characteristic
12	C₄×Dic₇₃	D₄	1	1	yes	characteristic
13	#11924003	C₈	1	2	yes	complemented
14	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₇₃	—	2	1	no	—
16	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
18	C₂×Dic₇₃	SD₁₆	1	1	yes	characteristic
19	#10596833	—	8	1	no	—
20	#10596833	—	8	1	no	—
21	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
22	C₈×C₇₃	M₁₆	1	1	yes	characteristic
23	#10596831	—	2	1	no	—
24	C₂²×C₇₃	#106	1	1	yes	characteristic
25	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₇₃	#108	1	1	yes	characteristic
27	Dic₇₃	—	2	1	no	—
28	Dic₇₃	—	2	1	no	—
29	C₂×C₇₃	#334	1	1	yes	characteristic
30	C₂×C₇₃	#365	1	1	yes	characteristic
31	C₂×C₇₃	#365	1	1	yes	characteristic
32	#1368	—	73	1	no	maximal, Sylow
33	C₇₃	#1368	1	1	yes	characteristic, complemented, Sylow
34	#346	—	73	1	no	—
35	#334	—	73	1	no	—
36	#334	—	73	1	no	—
37	C₂×C₁₆	—	73	1	no	—
38	C₂×C₁₆	#64408	1	1	yes	characteristic
39	C₄⋊C₈	—	146	1	no	—
40	C₄⋊C₈	—	146	1	no	—
41	C₄×C₈	—	73	1	no	—
42	C₂×C₈	—	292	1	no	—
43	C₂×C₈	—	292	1	no	—
44	C₂×C₈	—	73	1	no	—
45	C₂×C₈	C₂×#64408	1	1	yes	characteristic
46	C₄²	—	73	1	no	—
47	C₁₆	—	2	1	no	—
48	C₁₆	—	73	2	no	—
49	C₂×C₄	—	73	1	no	—
50	C₂×C₄	—	73	1	no	—
51	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
52	C₈	—	584	1	no	—
53	C₈	—	584	1	no	—
54	C₈	—	146	1	no	—
55	C₈	#11924036	1	1	yes	characteristic
56	C₈	#11924037	1	1	yes	characteristic
57	C₂²	#14556659	1	1	yes	characteristic
58	C₄	—	146	1	no	—
59	C₄	—	146	1	no	—
60	C₄	#14556658	1	1	yes	characteristic
61	C₄	#14556662	1	1	yes	characteristic
62	C₂	#17989449	1	1	yes	characteristic
63	C₂	#17989511	1	1	yes	characteristic
64	C₂	#17989512	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14556659
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#106
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1368
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #11924003	C₈	semidirect
33. C₇₃	#1368	semidirect