Subgroups — #22627026

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989695	C₂	1	2	yes	maximal, complemented
2	C₂×#14556666	C₂	1	1	yes	maximal, characteristic
3	#14556681	—	2	2	no	—
4	#14556666	—	2	2	no	—
5	C₂×#11924031	C₄	1	1	yes	characteristic
6	C₂×#11924031	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	2	1	no	—
9	#11924031	D₄	1	2	yes	—
10	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
11	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
12	C₈×D₇₃	—	2	1	no	—
13	C₈×D₇₃	—	2	1	no	—
14	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
15	C₂²×D₇₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
18	C₄×D₇₃	—	2	1	no	—
19	C₄×D₇₃	—	2	1	no	—
20	C₈×C₇₃	—	2	1	no	—
21	#10596831	C₂²⋊C₄	1	1	yes	characteristic
22	#10596831	M₁₆	1	1	yes	characteristic
23	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₇₃	—	2	1	no	—
25	C₂×D₇₃	—	4	1	no	—
26	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₇₃	M₃₂	1	1	yes	characteristic
28	Dic₇₃	—	2	1	no	—
29	C₂×C₇₃	—	2	1	no	—
30	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
31	D₇₃	—	4	1	no	—
32	#1400	—	73	1	no	maximal, Sylow
33	C₇₃	#1400	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₃₂	—	73	1	no	—
35	M₆₄	—	73	2	no	—
36	C₂²×C₈	—	73	1	no	—
37	M₃₂	—	146	2	no	—
38	C₂×C₁₆	—	73	1	no	—
39	C₂×C₁₆	—	73	1	no	—
40	C₃₂	—	146	2	no	—
41	C₂²×C₄	—	73	1	no	—
42	C₂×C₈	—	73	1	no	—
43	C₂×C₈	—	146	1	no	—
44	C₂×C₈	—	146	1	no	—
45	C₂×C₈	#10596842	1	1	yes	characteristic
46	C₁₆	—	73	2	no	—
47	C₁₆	—	146	1	no	—
48	C₂³	—	73	1	no	—
49	C₂×C₄	—	73	1	no	—
50	C₂×C₄	—	146	1	no	—
51	C₂×C₄	—	146	1	no	—
52	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	73	1	no	—
55	C₈	—	73	1	no	—
56	C₂²	—	292	1	no	—
57	C₂²	—	146	1	no	—
58	C₂²	#14556686	1	1	yes	characteristic
59	C₄	—	146	1	no	—
60	C₄	C₂²⋊#10596842	1	1	yes	characteristic
61	C₄	#14556688	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	292	1	no	—
64	C₂	#17989684	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#10596842
commutator	C₂²×C₇₃	C₂×C₁₆
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂×C₇₃	C₂²⋊C₁₆
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1400
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #17989695	C₂	semidirect
33. C₇₃	#1400	semidirect