Subgroups — #24905516

Order 10624.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128103	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#334×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#14581784	—	2	1	no	—
5	C₂×C₈₃⋊C₁₆	—	2	1	no	—
6	#14581726	C₄	1	1	yes	characteristic
7	#14581726	C₄	1	1	yes	characteristic
8	#14581724	—	2	1	no	—
9	C₄⋊C₈×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₈₃	—	2	1	no	—
12	C₄⋊Dic₈₃	—	2	1	no	—
13	Dic₈₃⋊C₄	—	4	1	no	—
14	Dic₈₃⋊C₄	—	4	1	no	—
15	C₈₃⋊C₁₆	—	4	1	no	—
16	C₂×C₈×C₈₃	—	4	1	no	—
17	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
19	C₄²×C₈₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
23	C₂×Dic₈₃	—	4	1	no	—
24	C₂×Dic₈₃	—	4	1	no	—
25	C₈×C₈₃	—	2	1	no	—
26	C₈×C₈₃	—	8	1	no	—
27	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
28	C₈×C₈₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₈₃	#102	1	1	yes	characteristic
30	C₄×C₈₃	—	2	1	no	—
31	C₄×C₈₃	—	2	1	no	—
32	C₄×C₈₃	#101	1	1	yes	characteristic
33	C₄×C₈₃	#103	1	1	yes	characteristic
34	Dic₈₃	—	8	1	no	—
35	Dic₈₃	—	8	1	no	—
36	C₂×C₈₃	#332	1	1	yes	characteristic
37	C₂×C₈₃	#359	1	1	yes	characteristic
38	C₂×C₈₃	#360	1	1	yes	characteristic
39	#1363	—	83	1	no	maximal, Sylow
40	C₈₃	#1363	1	1	yes	characteristic, complemented, Sylow
41	#499	—	83	1	no	—
42	C₄⋊C₁₆	—	83	1	no	—
43	#334	D₈₃	1	1	yes	characteristic
44	#125	—	166	1	no	—
45	C₂×C₁₆	—	166	1	no	—
46	#107	—	83	1	no	—
47	#107	—	83	1	no	—
48	#106	—	166	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
51	C₂×C₈	—	4	1	no	—
52	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
53	C₂×C₈	D₃₃₂	1	1	yes	characteristic
54	C₄⋊C₄	—	332	1	no	—
55	C₄⋊C₄	—	332	1	no	—
56	C₄⋊C₄	—	166	1	no	—
57	C₄⋊C₄	—	166	1	no	—
58	C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
59	C₁₆	—	332	1	no	—
60	C₂×C₄	—	332	1	no	—
61	C₂×C₄	—	332	1	no	—
62	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
63	C₂×C₄	#13050575	1	1	yes	characteristic
64	C₂×C₄	#13050577	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	8	1	no	—
67	C₈	#13050579	1	1	yes	characteristic
68	C₈	Dic₃₃₂	1	1	yes	characteristic
69	C₂²	#14581712	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	664	1	no	—
73	C₄	—	664	1	no	—
74	C₄	#14581710	1	1	yes	characteristic
75	C₄	#14581717	1	1	yes	characteristic
76	C₂	#19127448	1	1	yes	characteristic
77	C₂	#19127507	1	1	yes	characteristic
78	C₂	#19127510	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581712
commutator	C₂×C₈×C₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₃
Fitting	#334×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#102
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	#334	D₈₃
hypocenter	C₈₃	#1363
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
40. C₈₃	#1363	semidirect