Subgroups — #22626948

Order 9344.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11924040	C₂	1	2	yes	maximal
2	C₈×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924040	C₄	1	4	yes	—
4	C₄×#10596833	C₄	1	1	yes	characteristic
5	C₄×#10596833	C₂²	1	1	yes	characteristic
6	C₈×Dic₇₃	C₄	1	1	yes	characteristic
7	#11924040	—	2	4	no	—
8	C₂×#10596833	C₈	1	2	yes	—
9	C₂×#10596833	C₂×C₄	1	2	yes	—
10	C₂×#10596831	C₈	1	1	yes	characteristic
11	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
13	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
15	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
16	#10596833	—	2	2	no	—
17	#10596833	M₁₆	1	4	yes	—
18	C₈×C₇₃	C₁₆	1	2	yes	complemented
19	#10596831	C₁₆	1	2	yes	complemented
20	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
21	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
23	Dic₇₃	#97	1	2	yes	—
24	Dic₇₃	M₃₂	1	2	yes	—
25	C₂×C₇₃	#322	1	1	yes	characteristic
26	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
27	C₂×C₇₃	#346	1	1	yes	characteristic
28	#1312	—	73	1	no	maximal, Sylow
29	C₇₃	#1312	1	1	yes	characteristic, complemented, Sylow
30	C₄×C₁₆	—	73	2	no	—
31	C₈²	—	73	1	no	—
32	C₂×C₁₆	—	73	4	no	—
33	C₄×C₈	—	73	1	no	—
34	C₄×C₈	—	73	1	no	—
35	C₄×C₈	—	73	1	no	—
36	C₂×C₈	—	73	2	no	—
37	C₂×C₈	—	73	1	no	—
38	C₂×C₈	—	73	2	no	—
39	C₂×C₈	#10596842	1	1	yes	characteristic
40	C₄²	—	73	1	no	—
41	C₁₆	—	146	4	no	—
42	C₂×C₄	—	73	1	no	—
43	C₂×C₄	—	73	1	no	—
44	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
45	C₈	—	73	4	no	—
46	C₈	—	73	2	no	—
47	C₈	—	146	2	no	—
48	C₈	#11924040	1	2	yes	complemented
49	C₂²	C₄×#10596842	1	1	yes	characteristic
50	C₄	—	73	2	no	—
51	C₄	—	73	2	no	—
52	C₄	C₂×#11924040	1	1	yes	characteristic
53	C₄	#14556686	1	1	yes	characteristic
54	C₂	#17989671	1	1	yes	characteristic
55	C₂	C₄×#11924040	1	1	yes	characteristic
56	C₂	#17989682	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₄×C₁₆
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1312
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
18. C₈×C₇₃	C₁₆	semidirect
19. #10596831	C₁₆	semidirect
29. C₇₃	#1312	semidirect
48. C₈	#11924040	semidirect