Subgroups — #22626997

Order 9344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989677	C₂	1	2	yes	maximal
2	C₁₆×#64408	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	D₈	1	1	yes	characteristic
15	C₂×#64408	Q₁₆	1	1	yes	characteristic
16	#10596842	—	8	2	no	—
17	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
18	#10596833	—	2	1	no	—
19	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
20	#10596831	M₁₆	1	1	yes	characteristic
21	C₂×D₇₃	#107	1	1	yes	characteristic
22	#64408	—	2	1	no	—
23	#64408	D₁₆	1	1	yes	characteristic
24	#64408	Q₃₂	1	1	yes	characteristic
25	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
26	Dic₇₃	#108	1	1	yes	characteristic
27	C₂×C₇₃	#335	1	1	yes	characteristic
28	D₇₃	#366	1	1	yes	characteristic
29	D₇₃	#368	1	1	yes	characteristic
30	#1371	—	73	1	no	maximal, Sylow
31	C₇₃	#1371	1	1	yes	characteristic, complemented, Sylow
32	C₄×C₁₆	—	73	1	no	—
33	#335	—	73	2	no	—
34	C₂×C₁₆	—	73	1	no	—
35	C₂×C₁₆	—	73	1	no	—
36	C₄⋊C₈	—	146	2	no	—
37	C₄×C₈	—	73	1	no	—
38	C₂×C₈	—	292	2	no	—
39	C₂×C₈	—	73	1	no	—
40	C₂×C₈	—	73	1	no	—
41	C₄²	—	73	1	no	—
42	C₁₆	—	73	1	no	—
43	C₁₆	—	146	1	no	—
44	C₁₆	#10596842	1	1	yes	characteristic, complemented
45	C₂×C₄	—	73	1	no	—
46	C₂×C₄	—	73	1	no	—
47	C₂×C₄	—	73	1	no	—
48	C₈	—	584	2	no	—
49	C₈	—	73	1	no	—
50	C₈	—	146	1	no	—
51	C₈	C₂×#10596842	1	1	yes	characteristic
52	C₂²	—	73	1	no	—
53	C₄	—	73	1	no	—
54	C₄	—	73	1	no	—
55	C₄	—	73	1	no	—
56	C₄	—	146	1	no	—
57	C₄	C₄⋊#10596842	1	1	yes	characteristic
58	C₂	—	73	1	no	—
59	C₂	—	73	1	no	—
60	C₂	#17989677	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989677
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₈	C₂×#10596842
Fitting	C₁₆×C₇₃	C₈
socle	C₂×C₇₃	#335
hypercenter	C₁₆	#10596842
hypocenter	C₇₃	#1371
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
31. C₇₃	#1371	semidirect
44. C₁₆	#10596842	semidirect