Subgroups — #22624953

Order 9344.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924031	C₂	1	2	yes	maximal
2	C₈×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924031	—	2	2	no	—
4	C₄×#10596831	C₄	1	1	yes	characteristic
5	C₄×#10596831	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
7	#11924031	—	4	2	no	—
8	C₂×#10596831	—	2	1	no	—
9	C₂×#10596831	D₄	1	1	yes	characteristic
10	C₂×#10596831	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
13	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
17	C₈×C₇₃	—	2	1	no	—
18	C₈×C₇₃	C₁₆	1	2	yes	complemented
19	#10596831	—	2	2	no	—
20	#10596831	—	2	1	no	—
21	#10596831	SD₁₆	1	2	yes	—
22	C₂²×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₇₃	—	2	1	no	—
24	C₄×C₇₃	#106	1	1	yes	characteristic
25	C₄×C₇₃	#108	1	1	yes	characteristic
26	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₇₃	M₃₂	1	1	yes	characteristic
28	C₂×C₇₃	#334	1	1	yes	characteristic
29	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
30	C₂×C₇₃	#364	1	1	yes	characteristic
31	#1367	—	73	1	no	maximal, Sylow
32	C₇₃	#1367	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊C₁₆	—	73	2	no	—
34	C₈²	—	73	1	no	—
35	C₂×C₁₆	—	146	2	no	—
36	C₄×C₈	—	73	1	no	—
37	C₄×C₈	—	73	1	no	—
38	C₄×C₈	#64408	1	1	yes	characteristic
39	C₂×C₈	—	73	1	no	—
40	C₂×C₈	—	73	1	no	—
41	C₂×C₈	—	146	1	no	—
42	C₂×C₈	#10596833	1	1	yes	characteristic
43	C₂×C₈	#10596833	1	1	yes	characteristic
44	C₄²	C₂×#64408	1	1	yes	characteristic
45	C₁₆	—	292	2	no	—
46	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
47	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
48	C₂×C₄	#11924038	1	1	yes	characteristic
49	C₈	—	2	1	no	—
50	C₈	—	73	2	no	—
51	C₈	—	146	2	no	—
52	C₈	—	146	1	no	—
53	C₈	#11924031	1	2	yes	complemented
54	C₂²	C₄⋊#10596833	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	#14556659	1	1	yes	characteristic
57	C₄	#14556661	1	1	yes	characteristic
58	C₄	C₂×#11924031	1	1	yes	characteristic
59	C₄	#14556665	1	1	yes	characteristic
60	C₂	#17989448	1	1	yes	characteristic
61	C₂	C₄⋊#11924031	1	1	yes	characteristic
62	C₂	#17989509	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#64408
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₄²	C₂×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₄⋊C₈
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1367
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
18. C₈×C₇₃	C₁₆	semidirect
32. C₇₃	#1367	semidirect
53. C₈	#11924031	semidirect