Subgroups — #24905430

Order 10624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127477	C₂	1	1	yes	maximal, characteristic, complemented
2	#19127452	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
6	C₂×D₈×C₈₃	C₄	1	1	yes	characteristic
7	C₄×D₄×C₈₃	—	2	1	no	—
8	#107×C₈₃	C₄	1	1	yes	characteristic
9	#102×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₂×C₈₃⋊C₈	—	4	1	no	—
12	C₈₃⋊C₁₆	—	2	2	no	—
13	C₂×D₄×C₈₃	—	2	1	no	—
14	C₂²×C₄×C₈₃	—	4	1	no	—
15	D₈×C₈₃	—	2	1	no	—
16	D₈×C₈₃	C₈	1	2	yes	complemented
17	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
19	C₄⋊C₄×C₈₃	—	2	1	no	—
20	C₂²⋊C₄×C₈₃	—	4	1	no	—
21	C₄²×C₈₃	D₄	1	1	yes	characteristic
22	C₂³×C₈₃	—	4	1	no	—
23	D₄×C₈₃	—	2	2	no	—
24	D₄×C₈₃	—	4	1	no	—
25	C₂×C₄×C₈₃	—	4	1	no	—
26	C₂×C₄×C₈₃	—	8	2	no	—
27	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₈₃	—	2	1	no	—
31	C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₈₃	M₁₆	1	1	yes	characteristic
33	C₈₃⋊C₈	—	8	1	no	—
34	C₂²×C₈₃	—	4	2	no	—
35	C₂²×C₈₃	—	8	1	no	—
36	C₂²×C₈₃	—	8	1	no	—
37	C₂²×C₈₃	#102	1	1	yes	characteristic
38	C₄×C₈₃	—	2	1	no	—
39	C₄×C₈₃	—	2	1	no	—
40	C₄×C₈₃	—	8	1	no	—
41	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₈₃	#104	1	1	yes	characteristic
43	C₂×C₈₃	—	8	2	no	—
44	C₂×C₈₃	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₈₃	#360	1	1	yes	characteristic
46	C₂×C₈₃	#361	1	1	yes	characteristic
47	#1333	—	83	1	no	maximal, Sylow
48	C₈₃	#1333	1	1	yes	characteristic, complemented, Sylow
49	C₄×D₈	D₈₃	1	1	yes	characteristic
50	#346	—	83	1	no	—
51	#334	—	83	1	no	—
52	C₂×D₈	Dic₈₃	1	1	yes	characteristic
53	C₄×D₄	—	2	1	no	—
54	C₂×C₁₆	—	166	1	no	—
55	#107	Dic₈₃	1	1	yes	characteristic
56	C₄⋊C₈	—	166	1	no	—
57	#102	—	2	1	no	—
58	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
59	C₂×D₄	—	2	1	no	—
60	C₂²×C₄	—	4	1	no	—
61	D₈	—	2	1	no	—
62	D₈	C₈₃⋊C₈	1	2	yes	complemented
63	C₂×C₈	—	332	1	no	—
64	C₂×C₈	C₂×Dic₈₃	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	4	1	no	—
68	C₄²	C₂²⋊D₈₃	1	1	yes	characteristic
69	C₁₆	—	166	2	no	—
70	C₂³	—	4	1	no	—
71	D₄	—	2	2	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
76	C₂×C₄	#13050575	1	1	yes	characteristic
77	C₂×C₄	#13050578	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	664	1	no	—
80	C₈	C₂×C₈₃⋊C₈	1	1	yes	characteristic
81	C₈	#13050574	1	1	yes	characteristic
82	C₂²	—	4	2	no	—
83	C₂²	—	8	1	no	—
84	C₂²	—	8	1	no	—
85	C₂²	#14581713	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	C₂²⋊(C₈₃⋊C₈)	1	1	yes	characteristic
90	C₄	#14581719	1	1	yes	characteristic
91	C₂	—	8	2	no	—
92	C₂	D₄⋊(C₈₃⋊C₈)	1	1	yes	characteristic
93	C₂	#19127511	1	1	yes	characteristic
94	C₂	#19127514	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581713
commutator	C₈×C₈₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	C₄×D₈×C₈₃	C₂
socle	C₂²×C₈₃	#102
prime radical	C₂×D₈×C₈₃	C₄
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	C₄×D₈	D₈₃
hypocenter	C₈₃	#1333
LCS	G ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #19127477	C₂	semidirect
2. #19127452	C₂	semidirect
16. D₈×C₈₃	C₈	semidirect
48. C₈₃	#1333	semidirect
62. D₈	C₈₃⋊C₈	semidirect