Subgroups — #22626992

Order 9344.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989676	C₂	1	2	yes	maximal
2	#17989474	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#10596842	—	2	2	no	—
4	#14556664	C₄	1	1	yes	characteristic
5	C₈×#64408	C₂²	1	1	yes	characteristic
6	C₁₆×D₇₃	C₄	1	1	yes	characteristic
7	C₂×#10596842	—	4	2	no	—
8	#11924036	Q₈	1	1	yes	characteristic
9	C₄×#64408	D₄	1	1	yes	characteristic
10	#11924031	—	2	1	no	—
11	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
12	#11924003	C₈	1	1	yes	characteristic, complemented
13	C₁₆×C₇₃	C₈	1	1	yes	characteristic, complemented
14	C₂×#64408	SD₁₆	1	2	yes	—
15	#10596842	—	8	2	no	—
16	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
17	#10596833	—	2	1	no	—
18	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
19	#10596831	M₁₆	1	1	yes	characteristic
20	C₂×D₇₃	#106	1	1	yes	characteristic
21	#64408	—	2	2	no	—
22	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	Dic₇₃	#108	1	1	yes	characteristic
24	C₂×C₇₃	#334	1	1	yes	characteristic
25	D₇₃	#365	1	2	yes	—
26	#1368	—	73	1	no	maximal, Sylow
27	C₇₃	#1368	1	1	yes	characteristic, complemented, Sylow
28	#346	—	73	1	no	—
29	#334	—	73	2	no	—
30	C₂×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₄⋊C₈	—	146	2	no	—
33	C₄×C₈	—	73	1	no	—
34	C₂×C₈	—	292	2	no	—
35	C₂×C₈	—	73	1	no	—
36	C₂×C₈	—	73	1	no	—
37	C₄²	—	73	1	no	—
38	C₁₆	—	73	1	no	—
39	C₁₆	—	146	1	no	—
40	C₁₆	#10596842	1	1	yes	characteristic, complemented
41	C₂×C₄	—	73	1	no	—
42	C₂×C₄	—	73	2	no	—
43	C₈	—	584	2	no	—
44	C₈	—	73	1	no	—
45	C₈	—	146	1	no	—
46	C₈	C₂×#10596842	1	1	yes	characteristic
47	C₂²	—	73	1	no	—
48	C₄	—	73	1	no	—
49	C₄	—	146	2	no	—
50	C₄	C₄⋊#10596842	1	1	yes	characteristic
51	C₂	—	73	2	no	—
52	C₂	#17989676	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989676
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₈	C₂×#10596842
Fitting	C₁₆×C₇₃	C₈
socle	C₂×C₇₃	#334
hypercenter	C₁₆	#10596842
hypocenter	C₇₃	#1368
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
12. #11924003	C₈	semidirect
13. C₁₆×C₇₃	C₈	semidirect
27. C₇₃	#1368	semidirect
40. C₁₆	#10596842	semidirect