Subgroups — #24905765

Order 10624.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13050573	C₂	1	3	yes	maximal
2	#19127422	C₂	1	3	yes	maximal, complemented
3	C₈²×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13050573	C₄	1	6	yes	—
5	C₄²×D₈₃	C₂²	1	1	yes	characteristic
6	#14581702	C₄	1	6	yes	—
7	C₄×C₈₃⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₈₃	C₂²	1	3	yes	—
9	C₂×C₄×D₈₃	C₂×C₄	1	3	yes	—
10	#13050573	—	2	12	no	—
11	C₂×C₈₃⋊C₈	C₂×C₄	1	6	yes	—
12	C₄×Dic₈₃	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₈₃	C₂×C₄	1	6	yes	—
14	C₄²×C₈₃	C₂³	1	1	yes	characteristic
15	C₂²×D₈₃	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₈₃	C₂²×C₄	1	3	yes	—
17	C₂×Dic₈₃	C₄²	1	3	yes	—
18	C₄×D₈₃	—	2	6	no	—
19	C₈×C₈₃	M₁₆	1	12	yes	complemented
20	C₈₃⋊C₈	—	2	6	no	—
21	C₂²×C₈₃	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₈₃	—	2	3	no	—
23	C₄×C₈₃	C₂×M₁₆	1	6	yes	—
24	Dic₈₃	—	2	3	no	—
25	C₂×C₈₃	C₄×M₁₆	1	3	yes	—
26	D₈₃	—	4	1	no	—
27	#1455	—	83	1	no	maximal, Sylow
28	C₈₃	#1455	1	1	yes	characteristic, complemented, Sylow
29	C₄×M₁₆	—	83	3	no	—
30	#322	—	83	3	no	—
31	C₈²	D₈₃	1	1	yes	characteristic, complemented
32	C₂×M₁₆	—	83	6	no	—
33	C₂×C₄²	—	83	1	no	—
34	#97	—	83	6	no	—
35	C₄×C₈	—	83	3	no	—
36	C₄×C₈	C₂×D₈₃	1	3	yes	—
37	C₂²×C₄	—	83	3	no	—
38	M₁₆	—	166	12	no	—
39	C₂×C₈	—	83	6	no	—
40	C₂×C₈	C₄×D₈₃	1	6	yes	—
41	C₄²	—	83	3	no	—
42	C₄²	C₂²×D₈₃	1	1	yes	characteristic
43	C₂³	—	83	1	no	—
44	C₂×C₄	—	83	3	no	—
45	C₂×C₄	—	166	6	no	—
46	C₂×C₄	C₂×C₄×D₈₃	1	3	yes	—
47	C₈	—	166	6	no	—
48	C₈	#13050573	1	12	yes	complemented
49	C₂²	—	166	3	no	—
50	C₂²	C₄²×D₈₃	1	1	yes	characteristic
51	C₄	—	166	3	no	—
52	C₄	C₂×#13050573	1	6	yes	—
53	C₂	—	332	1	no	—
54	C₂	C₄×#13050573	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₈₃
commutator, socle	C₂²×C₈₃	C₂×C₄²
Fitting	C₈²×C₈₃	C₂
prime radical	C₂²×D₈₃	C₄²
cosocle	C₄²×C₈₃	C₂³
hypercenter	C₈²	D₈₃
hypocenter	C₈₃	#1455
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #19127422	C₂	semidirect
3. C₈²×C₈₃	C₂	semidirect
19. C₈×C₈₃	M₁₆	semidirect
28. C₈₃	#1455	semidirect
31. C₈²	D₈₃	semidirect
48. C₈	#13050573	semidirect