Subgroups — #22624956

Order 9344.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989448	C₂	1	2	yes	maximal
2	#17988362	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596833	—	2	2	no	—
4	C₂×#11924003	C₄	1	1	yes	characteristic
5	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
7	C₂×#10596833	—	4	2	no	—
8	C₂×#10596831	Q₈	1	1	yes	characteristic
9	C₄×Dic₇₃	D₄	1	1	yes	characteristic
10	#11924003	—	2	1	no	—
11	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₇₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₇₃	SD₁₆	1	2	yes	—
15	#10596833	—	8	2	no	—
16	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
17	C₈×C₇₃	M₁₆	1	1	yes	characteristic
18	#10596831	—	2	1	no	—
19	C₂²×C₇₃	#106	1	1	yes	characteristic
20	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₇₃	#108	1	1	yes	characteristic
22	Dic₇₃	—	2	2	no	—
23	C₂×C₇₃	#334	1	1	yes	characteristic
24	C₂×C₇₃	#365	1	2	yes	—
25	#1368	—	73	1	no	maximal, Sylow
26	C₇₃	#1368	1	1	yes	characteristic, complemented, Sylow
27	#346	—	73	1	no	—
28	#334	—	73	2	no	—
29	C₂×C₁₆	—	73	1	no	—
30	C₂×C₁₆	#64408	1	1	yes	characteristic
31	C₄⋊C₈	—	146	2	no	—
32	C₄×C₈	—	73	1	no	—
33	C₂×C₈	—	292	2	no	—
34	C₂×C₈	—	73	1	no	—
35	C₂×C₈	C₂×#64408	1	1	yes	characteristic
36	C₄²	—	73	1	no	—
37	C₁₆	—	146	1	no	—
38	C₁₆	#10596833	1	2	yes	complemented
39	C₂×C₄	—	73	2	no	—
40	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
41	C₈	—	584	2	no	—
42	C₈	—	146	1	no	—
43	C₈	C₂×#10596833	1	1	yes	characteristic
44	C₈	#11924038	1	1	yes	characteristic
45	C₂²	#14556659	1	1	yes	characteristic
46	C₄	—	146	2	no	—
47	C₄	C₄⋊#10596833	1	1	yes	characteristic
48	C₄	#14556661	1	1	yes	characteristic
49	C₂	#17989448	1	1	yes	characteristic
50	C₂	#17989512	1	2	yes	—

	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
12. C₁₆×C₇₃	C₈	semidirect
26. C₇₃	#1368	semidirect
38. C₁₆	#10596833	semidirect