Subgroups — #22608070

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
2	#17988421	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
5	#14556530	—	2	1	no	—
6	#14556530	—	2	1	no	—
7	C₂×#11924003	C₄	1	1	yes	characteristic
8	#14556497	—	2	1	no	—
9	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₇₃	—	2	1	no	—
11	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
12	C₂×#10596831	C₈	1	1	yes	characteristic
13	C₈×D₇₃	—	2	1	no	—
14	C₈×D₇₃	—	2	1	no	—
15	#11924003	—	2	1	no	—
16	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₇₃	D₄	1	1	yes	characteristic
18	C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	C₂²×D₇₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
22	C₄×D₇₃	—	2	1	no	—
23	C₄×D₇₃	—	2	1	no	—
24	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₃	M₁₆	1	1	yes	characteristic
26	#10596831	—	2	1	no	—
27	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₇₃	—	2	1	no	—
29	C₂×D₇₃	—	4	1	no	—
30	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₇₃	M₃₂	1	1	yes	characteristic
32	Dic₇₃	—	2	1	no	—
33	C₂×C₇₃	—	2	1	no	—
34	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₇₃	—	4	1	no	—
36	#1400	—	73	1	no	maximal, Sylow
37	C₇₃	#1400	1	1	yes	characteristic, complemented, Sylow
38	C₂×M₃₂	—	73	1	no	—
39	M₆₄	—	73	1	no	—
40	M₆₄	D₇₃	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	73	1	no	—
42	M₃₂	—	146	1	no	—
43	M₃₂	—	146	1	no	—
44	C₂×C₁₆	—	73	1	no	—
45	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	146	1	no	—
48	C₂²×C₄	—	73	1	no	—
49	C₂×C₈	—	73	1	no	—
50	C₂×C₈	—	146	1	no	—
51	C₂×C₈	—	146	1	no	—
52	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
53	C₁₆	—	146	1	no	—
54	C₁₆	D₂₉₂	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
56	C₂³	—	73	1	no	—
57	C₂×C₄	—	73	1	no	—
58	C₂×C₄	—	146	1	no	—
59	C₂×C₄	—	146	1	no	—
60	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
61	C₈	—	146	1	no	—
62	C₈	#11924005	1	1	yes	characteristic
63	C₈	#11924011	1	1	yes	characteristic
64	C₂²	—	292	1	no	—
65	C₂²	—	146	1	no	—
66	C₂²	C₁₆×D₇₃	1	1	yes	characteristic
67	C₄	—	146	1	no	—
68	C₄	#14556503	1	1	yes	characteristic
69	C₄	#14556530	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	292	1	no	—
72	C₂	#17988366	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#11924005
commutator	C₂²×C₇₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	M₆₄×C₇₃	C₂
socle	C₂×C₇₃	C₂²⋊C₁₆
hypercenter	M₆₄	D₇₃
hypocenter	C₇₃	#1400
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #17988421	C₂	semidirect
3. M₆₄×C₇₃	C₂	semidirect
37. C₇₃	#1400	semidirect
40. M₆₄	D₇₃	semidirect