Subgroups — #22608116

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989019	C₂	1	1	yes	maximal, characteristic
2	#17988417	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556613	—	2	1	no	—
5	Dic₅₈₄	C₄	1	1	yes	characteristic
6	#14556536	—	2	1	no	—
7	D₁₁₆₈	C₄	1	1	yes	characteristic
8	#14556527	—	2	1	no	—
9	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₇₃	—	2	1	no	—
11	#11924028	—	4	1	no	—
12	Dic₂₉₂	—	2	1	no	—
13	#11924017	—	4	1	no	—
14	D₅₈₄	—	2	1	no	—
15	#11924012	—	4	1	no	—
16	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
17	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
20	C₂²⋊D₇₃	—	8	1	no	—
21	D₂₉₂	—	4	1	no	—
22	C₄×D₇₃	—	8	1	no	—
23	Dic₁₄₆	—	4	1	no	—
24	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
26	#10596831	—	8	1	no	—
27	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
28	C₂×D₇₃	—	8	1	no	—
29	C₄×C₇₃	#102	1	1	yes	characteristic
30	C₄×C₇₃	D₁₆	1	1	yes	characteristic
31	Dic₇₃	—	8	1	no	—
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	#357	1	1	yes	characteristic
34	D₇₃	—	16	1	no	—
35	#1417	—	73	1	no	maximal, Sylow
36	C₇₃	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	—	73	1	no	—
38	C₂×C₃₂	D₇₃	1	1	yes	characteristic, complemented
39	#368	—	73	1	no	—
40	#135	—	146	1	no	—
41	Q₃₂	—	73	1	no	—
42	SD₃₂	—	146	1	no	—
43	D₁₆	—	73	1	no	—
44	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
45	#108	—	146	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	292	1	no	—
48	Q₁₆	—	146	1	no	—
49	SD₁₆	—	292	1	no	—
50	D₈	—	146	1	no	—
51	M₁₆	—	292	1	no	—
52	C₂×C₈	D₂₉₂	1	1	yes	characteristic
53	C₁₆	C₄×D₇₃	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
55	Q₈	—	292	1	no	—
56	D₄	—	292	1	no	—
57	D₄	—	584	1	no	—
58	C₂×C₄	—	584	1	no	—
59	C₂×C₄	D₅₈₄	1	1	yes	characteristic
60	C₈	—	584	1	no	—
61	C₈	#11924005	1	1	yes	characteristic
62	C₈	#11924017	1	1	yes	characteristic
63	C₂²	—	584	1	no	—
64	C₂²	#14556536	1	1	yes	characteristic
65	C₄	—	584	1	no	—
66	C₄	#14556513	1	1	yes	characteristic
67	C₄	D₁₁₆₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	1168	1	no	—
70	C₂	#17988389	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₁₆₈
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	C₂×C₃₂×C₇₃	C₂
socle	C₂×C₇₃	#357
hypercenter	C₂×C₃₂	D₇₃
hypocenter	C₇₃	#1417
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #17988417	C₂	semidirect
3. C₂×C₃₂×C₇₃	C₂	semidirect
36. C₇₃	#1417	semidirect
38. C₂×C₃₂	D₇₃	semidirect