Subgroups — #22608113

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic
2	#17988413	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₂	—	2	1	no	—
5	Dic₅₈₄	—	2	1	no	—
6	Dic₅₈₄	C₄	1	2	yes	complemented
7	#14556525	—	2	1	no	—
8	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	C₃₂×C₇₃	—	2	1	no	—
10	C₂×Dic₁₄₆	—	4	1	no	—
11	Dic₂₉₂	—	2	2	no	—
12	Dic₂₉₂	—	4	1	no	—
13	C₄⋊Dic₇₃	—	4	1	no	—
14	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₇₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
18	C₂×Dic₇₃	—	8	1	no	—
19	C₂×Dic₇₃	—	8	1	no	—
20	Dic₁₄₆	—	4	2	no	—
21	Dic₁₄₆	—	8	1	no	—
22	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
24	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
25	C₄×C₇₃	#102	1	1	yes	characteristic
26	C₄×C₇₃	SD₃₂	1	1	yes	characteristic
27	Dic₇₃	—	8	2	no	—
28	Dic₇₃	—	16	1	no	—
29	C₂×C₇₃	#357	1	1	yes	characteristic
30	C₂×C₇₃	SD₆₄	1	1	yes	characteristic
31	C₂×C₇₃	Q₆₄	1	1	yes	characteristic
32	#1416	—	73	1	no	maximal, Sylow
33	C₇₃	#1416	1	1	yes	characteristic, complemented, Sylow
34	C₂×Q₃₂	—	73	1	no	—
35	C₂×C₃₂	D₇₃	1	1	yes	characteristic
36	#366	—	73	1	no	—
37	C₂×Q₁₆	—	146	1	no	—
38	Q₃₂	—	73	2	no	—
39	Q₃₂	—	146	1	no	—
40	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
41	#107	—	146	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×Q₈	—	292	1	no	—
44	Q₁₆	—	292	1	no	—
45	Q₁₆	—	146	2	no	—
46	C₂×C₈	D₂₉₂	1	1	yes	characteristic
47	C₄⋊C₄	—	292	1	no	—
48	C₁₆	C₄×D₇₃	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
50	Q₈	—	292	2	no	—
51	Q₈	—	584	1	no	—
52	C₂×C₄	—	584	1	no	—
53	C₂×C₄	—	584	1	no	—
54	C₂×C₄	D₅₈₄	1	1	yes	characteristic
55	C₈	#11924005	1	1	yes	characteristic
56	C₈	#11924017	1	1	yes	characteristic
57	C₂²	D₁₁₆₈	1	1	yes	characteristic
58	C₄	—	584	2	no	—
59	C₄	—	1168	1	no	—
60	C₄	#14556513	1	1	yes	characteristic
61	C₄	#14556536	1	1	yes	characteristic
62	C₂	#17988389	1	1	yes	characteristic
63	C₂	#17988426	1	1	yes	characteristic
64	C₂	Dic₁₁₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₁₆₈
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	C₂×C₃₂×C₇₃	C₂
socle	C₂²×C₇₃	D₁₆
hypercenter	C₂×C₃₂	D₇₃
hypocenter	C₇₃	#1416
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. Dic₅₈₄	C₄	semidirect
33. C₇₃	#1416	semidirect