Subgroups — #22612237

Order 9344.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989016	C₂	1	2	yes	maximal, complemented
2	Dic₁₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988425	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556610	—	2	2	no	—
7	Dic₅₈₄	C₂²	1	2	yes	—
8	#14556535	—	2	2	no	—
9	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
10	#14556497	C₂²	1	1	yes	characteristic
11	D₁₆×C₇₃	C₂²	1	2	yes	—
12	C₃₂×C₇₃	C₂²	1	1	yes	characteristic
13	#11924027	—	4	2	no	—
14	Dic₂₉₂	—	2	2	no	—
15	#11924016	—	4	2	no	—
16	C₈×D₇₃	D₄	1	1	yes	characteristic
17	#11924003	D₄	1	1	yes	characteristic
18	D₈×C₇₃	—	2	2	no	—
19	C₁₆×C₇₃	C₂³	1	1	yes	characteristic
20	D₄×C₇₃	—	4	2	no	—
21	C₂²⋊D₇₃	—	8	2	no	—
22	C₂×Dic₇₃	—	8	2	no	—
23	C₄×D₇₃	D₈	1	1	yes	characteristic
24	Dic₁₄₆	—	4	2	no	—
25	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
26	#10596831	D₈	1	1	yes	characteristic
27	C₂²×C₇₃	—	8	2	no	—
28	C₂×D₇₃	D₁₆	1	1	yes	characteristic
29	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
30	Dic₇₃	—	8	2	no	—
31	Dic₇₃	D₁₆	1	1	yes	characteristic
32	C₂×C₇₃	—	16	2	no	—
33	C₂×C₇₃	C₂×D₁₆	1	1	yes	characteristic
34	D₇₃	—	2	1	no	—
35	#2262	—	73	1	no	maximal, Sylow
36	C₇₃	#2262	1	1	yes	characteristic, complemented, Sylow
37	#508	—	73	2	no	—
38	Q₆₄	—	73	1	no	—
39	SD₆₄	—	73	2	no	—
40	D₃₂	D₇₃	1	1	yes	characteristic, complemented
41	C₂×C₃₂	—	73	1	no	—
42	#135	—	146	2	no	—
43	Q₃₂	—	73	2	no	—
44	SD₃₂	—	146	2	no	—
45	D₁₆	C₂×D₇₃	1	2	yes	—
46	C₂×C₁₆	—	73	1	no	—
47	C₃₂	—	73	1	no	—
48	C₃₂	C₂×D₇₃	1	1	yes	characteristic
49	#41	—	292	2	no	—
50	Q₁₆	—	146	2	no	—
51	SD₁₆	—	292	2	no	—
52	D₈	—	2	2	no	—
53	C₂×C₈	—	73	1	no	—
54	C₁₆	—	73	1	no	—
55	C₁₆	C₂²×D₇₃	1	1	yes	characteristic
56	Q₈	—	292	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	584	2	no	—
59	C₂×C₄	—	584	2	no	—
60	C₂×C₄	—	73	1	no	—
61	C₈	—	73	1	no	—
62	C₈	D₄×D₇₃	1	1	yes	characteristic
63	C₂²	—	8	2	no	—
64	C₂²	—	73	1	no	—
65	C₄	—	584	2	no	—
66	C₄	—	73	1	no	—
67	C₄	D₈×D₇₃	1	1	yes	characteristic
68	C₂	—	16	2	no	—
69	C₂	—	146	1	no	—
70	C₂	D₁₆×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₇₃
commutator	C₁₆×C₇₃	C₂³
Frattini	C₁₆	C₂²×D₇₃
Fitting	D₃₂×C₇₃	C₂
socle	C₂×C₇₃	C₂×D₁₆
hypercenter	D₃₂	D₇₃
hypocenter	C₇₃	#2262
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #17989016	C₂	semidirect
2. Dic₁₁₆₈	C₂	semidirect
3. #17988425	C₂	semidirect
4. C₃₂×D₇₃	C₂	semidirect
5. D₃₂×C₇₃	C₂	semidirect
36. C₇₃	#2262	semidirect
40. D₃₂	D₇₃	semidirect