Subgroups — #24905649

Order 10624.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128133	C₂	1	1	yes	maximal, characteristic
2	#19127535	C₂	1	1	yes	maximal, characteristic, complemented
3	#367×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14581814	—	2	1	no	—
5	Dic₆₆₄	C₄	1	1	yes	characteristic, complemented
6	#14581737	—	2	1	no	—
7	D₁₃₂₈	C₄	1	1	yes	characteristic, complemented
8	C₈₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	#107×C₈₃	—	2	1	no	—
11	#13050590	—	4	1	no	—
12	Dic₃₃₂	—	2	1	no	—
13	#13050579	—	4	1	no	—
14	D₆₆₄	—	2	1	no	—
15	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₈₃	—	4	1	no	—
17	C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₈₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₃	—	8	1	no	—
20	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
21	C₂²⋊D₈₃	—	8	1	no	—
22	D₃₃₂	—	4	1	no	—
23	C₄×D₈₃	—	8	1	no	—
24	Dic₁₆₆	—	4	1	no	—
25	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
27	C₂²×C₈₃	D₁₆	1	1	yes	characteristic
28	C₂×D₈₃	—	8	1	no	—
29	C₄×C₈₃	—	16	1	no	—
30	C₄×C₈₃	#102	1	1	yes	characteristic
31	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
32	Dic₈₃	—	8	1	no	—
33	C₂×C₈₃	—	2	1	no	—
34	C₂×C₈₃	#357	1	1	yes	characteristic
35	D₈₃	—	16	1	no	—
36	#1418	—	83	1	no	maximal, Sylow
37	C₈₃	#1418	1	1	yes	characteristic, complemented, Sylow
38	#508	—	83	1	no	—
39	M₆₄	—	83	1	no	—
40	#367	D₈₃	1	1	yes	characteristic, complemented
41	#135	—	166	1	no	—
42	Q₃₂	—	83	1	no	—
43	SD₃₂	—	166	1	no	—
44	D₁₆	—	83	1	no	—
45	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
46	#107	—	2	1	no	—
47	C₃₂	—	166	1	no	—
48	#41	—	332	1	no	—
49	Q₁₆	—	166	1	no	—
50	SD₁₆	—	332	1	no	—
51	D₈	—	166	1	no	—
52	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₁₆	C₄×D₈₃	1	1	yes	characteristic
55	C₁₆	D₃₃₂	1	1	yes	characteristic
56	Q₈	—	332	1	no	—
57	D₄	—	332	1	no	—
58	D₄	—	664	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	664	1	no	—
61	C₂×C₄	#13050575	1	1	yes	characteristic
62	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
63	C₈	#13050577	1	1	yes	characteristic
64	C₂²	—	664	1	no	—
65	C₂²	#14581733	1	1	yes	characteristic
66	C₄	—	16	1	no	—
67	C₄	—	664	1	no	—
68	C₄	#14581712	1	1	yes	characteristic
69	C₄	#14581735	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1328	1	no	—
72	C₂	#19127501	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127501
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	#367×C₈₃	C₂
socle	C₂×C₈₃	#357
prime radical	#19128133	C₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	#367	D₈₃
hypocenter	C₈₃	#1418
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #367

Complements

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

N	H ≅ G/N	type
2. #19127535	C₂	semidirect
3. #367×C₈₃	C₂	semidirect
5. Dic₆₆₄	C₄	semidirect
7. D₁₃₂₈	C₄	semidirect
37. C₈₃	#1418	semidirect
40. #367	D₈₃	semidirect