Subgroups — #22608128

Order 9344.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988421	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924003	C₄	1	1	yes	characteristic
5	C₈×Dic₇₃	C₄	1	1	yes	characteristic
6	#14556497	—	2	1	no	—
7	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₇₃	—	2	1	no	—
9	C₂×#10596831	C₈	1	1	yes	characteristic
10	C₄×Dic₇₃	C₈	1	1	yes	characteristic
11	#11924003	—	2	1	no	—
12	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₇₃	D₄	1	1	yes	characteristic
14	C₁₆×C₇₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₇₃	—	2	1	no	—
17	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₇₃	M₁₆	1	1	yes	characteristic
19	#10596831	C₁₆	1	2	yes	—
20	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
21	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
23	Dic₇₃	—	2	2	no	—
24	C₂×C₇₃	—	2	1	no	—
25	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
26	#1422	—	73	1	no	maximal, Sylow
27	C₇₃	#1422	1	1	yes	characteristic, complemented, Sylow
28	M₆₄	—	73	1	no	—
29	M₆₄	D₇₃	1	1	yes	characteristic
30	C₄×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
33	C₄×C₈	—	73	1	no	—
34	C₃₂	—	2	1	no	—
35	C₃₂	—	146	1	no	—
36	C₂×C₈	—	73	1	no	—
37	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
38	C₄²	—	73	1	no	—
39	C₁₆	—	146	1	no	—
40	C₁₆	Dic₁₄₆	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
42	C₂×C₄	—	146	1	no	—
43	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
44	C₈	—	73	2	no	—
45	C₈	#11924007	1	1	yes	characteristic
46	C₈	#11924011	1	1	yes	characteristic
47	C₂²	#14556530	1	1	yes	characteristic
48	C₄	—	146	2	no	—
49	C₄	#14556520	1	1	yes	characteristic
50	C₄	C₁₆×D₇₃	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	#17988405	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	M₆₄×C₇₃	C₂
socle	C₂×C₇₃	C₄⋊C₁₆
hypercenter	M₆₄	D₇₃
hypocenter	C₇₃	#1422
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
27. C₇₃	#1422	semidirect