Subgroups — #24905445

Order 10624.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₈₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	#19127477	C₂	1	1	yes	maximal, characteristic
3	#446×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈₃⋊C₁₆	—	2	1	no	—
5	C₂×C₈₃⋊C₁₆	—	2	1	no	—
6	C₄×Q₈×C₈₃	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₈₃	—	2	1	no	—
8	C₄⋊C₈×C₈₃	C₄	1	1	yes	characteristic
9	#97×C₈₃	—	2	1	no	—
10	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
11	C₈₃⋊C₁₆	—	2	2	no	—
12	C₈₃⋊C₁₆	—	4	1	no	—
13	C₂×Q₈×C₈₃	C₈	1	1	yes	characteristic
14	C₂×C₈×C₈₃	—	2	1	no	—
15	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₈₃	—	2	1	no	—
18	C₄⋊C₄×C₈₃	C₈	1	1	yes	characteristic
19	C₄²×C₈₃	—	2	1	no	—
20	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
21	Q₈×C₈₃	—	4	1	no	—
22	C₂×C₄×C₈₃	—	2	1	no	—
23	C₂×C₄×C₈₃	—	2	1	no	—
24	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₈₃	M₁₆	1	1	yes	characteristic
27	C₈×C₈₃	—	2	1	no	—
28	C₈×C₈₃	—	4	1	no	—
29	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₈₃	Q₁₆	1	1	yes	characteristic
31	C₂²×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₈₃	—	2	1	no	—
33	C₄×C₈₃	—	2	1	no	—
34	C₄×C₈₃	—	4	1	no	—
35	C₄×C₈₃	—	4	1	no	—
36	C₄×C₈₃	#103	1	1	yes	characteristic
37	C₄×C₈₃	#104	1	1	yes	characteristic
38	C₂×C₈₃	Q₈⋊C₈	1	1	yes	characteristic
39	C₂×C₈₃	#349	1	1	yes	characteristic
40	C₂×C₈₃	#350	1	1	yes	characteristic
41	#1338	—	83	1	no	maximal, Sylow
42	C₈₃	#1338	1	1	yes	characteristic, complemented, Sylow
43	#446	D₈₃	1	1	yes	characteristic
44	C₄⋊C₁₆	—	83	1	no	—
45	#346	—	83	1	no	—
46	C₄×Q₈	Dic₈₃	1	1	yes	characteristic
47	C₂×C₁₆	—	166	1	no	—
48	C₂×C₁₆	—	166	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄⋊C₈	Dic₈₃	1	1	yes	characteristic
51	#97	—	2	1	no	—
52	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
53	C₂×Q₈	C₈₃⋊C₈	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₈₃⋊C₈	1	1	yes	characteristic
59	C₄²	—	2	1	no	—
60	C₄²	C₂×Dic₈₃	1	1	yes	characteristic
61	C₁₆	—	332	1	no	—
62	C₁₆	—	166	2	no	—
63	Q₈	—	4	1	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₂²⋊Dic₈₃	1	1	yes	characteristic
67	C₂×C₄	C₂×C₈₃⋊C₈	1	1	yes	characteristic
68	C₂×C₄	#13050574	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	4	1	no	—
71	C₈	#13050577	1	1	yes	characteristic
72	C₈	#13050580	1	1	yes	characteristic
73	C₂²	C₂²⋊(C₈₃⋊C₈)	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	#14581716	1	1	yes	characteristic
79	C₄	#14581719	1	1	yes	characteristic
80	C₂	Q₈⋊(C₈₃⋊C₈)	1	1	yes	characteristic
81	C₂	#19127483	1	1	yes	characteristic
82	C₂	#19127485	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₈₃
commutator	C₂×C₄×C₈₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₈₃
Fitting	#446×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	C₂²⋊C₈
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	#446	D₈₃
hypocenter	C₈₃	#1338
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #446

Complements

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

N	H ≅ G/N	type
42. C₈₃	#1338	semidirect