Subgroups — #22608126

Order 9344.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556497	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×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	C₁₆	1	1	yes	characteristic
17	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
18	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
19	C₈×C₇₃	M₁₆	1	1	yes	characteristic
20	#10596831	—	2	1	no	—
21	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₇₃	M₃₂	1	1	yes	characteristic
24	Dic₇₃	—	2	1	no	—
25	Dic₇₃	C₃₂	1	2	yes	complemented
26	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₇₃	M₆₄	1	1	yes	characteristic
29	C₄⋊C₃₂	—	73	1	no	maximal, Sylow
30	C₇₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃₂	—	73	1	no	—
32	C₂×C₃₂	D₇₃	1	1	yes	characteristic
33	C₄×C₁₆	—	73	1	no	—
34	C₂×C₁₆	—	73	1	no	—
35	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
36	C₄×C₈	—	73	1	no	—
37	C₃₂	—	2	1	no	—
38	C₃₂	—	146	1	no	—
39	C₂×C₈	—	73	1	no	—
40	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
41	C₄²	—	73	1	no	—
42	C₁₆	—	146	1	no	—
43	C₁₆	Dic₁₄₆	1	1	yes	characteristic
44	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
45	C₂×C₄	—	73	1	no	—
46	C₂×C₄	—	73	1	no	—
47	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
48	C₈	—	146	1	no	—
49	C₈	#11924007	1	1	yes	characteristic
50	C₈	#11924011	1	1	yes	characteristic
51	C₂²	C₁₆×D₇₃	1	1	yes	characteristic
52	C₄	—	73	2	no	—
53	C₄	—	146	1	no	—
54	C₄	#14556520	1	1	yes	characteristic
55	C₄	#14556530	1	1	yes	characteristic
56	C₂	#17988405	1	1	yes	characteristic
57	C₂	C₃₂×D₇₃	1	1	yes	characteristic
58	C₂	#17988420	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×D₇₃
commutator	C₂×C₇₃	C₂×C₃₂
Fitting	C₂×C₃₂×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₁₆
hypercenter	C₂×C₃₂	D₇₃
hypocenter	C₇₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
25. Dic₇₃	C₃₂	semidirect
30. C₇₃	C₄⋊C₃₂	semidirect