Subgroups — #24905517

Order 10624.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128106	C₂	1	1	yes	maximal, characteristic
2	#19127454	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#14581792	—	2	1	no	—
5	#14581726	—	2	1	no	—
6	#14581726	C₄	1	2	yes	—
7	C₄⋊(C₈₃⋊C₈)	—	2	1	no	—
8	C₂×C₁₆×C₈₃	—	2	1	no	—
9	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₆₆	—	4	1	no	—
11	C₂×C₈₃⋊C₈	—	4	1	no	—
12	C₄⋊Dic₈₃	—	2	2	no	—
13	C₄⋊Dic₈₃	—	4	1	no	—
14	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
16	C₄²×C₈₃	D₄	1	1	yes	characteristic
17	C₁₆×C₈₃	—	4	1	no	—
18	C₂×C₄×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
20	C₂×C₄×C₈₃	SD₁₆	1	1	yes	characteristic
21	C₂×Dic₈₃	—	4	2	no	—
22	Dic₁₆₆	—	8	1	no	—
23	Dic₁₆₆	—	8	1	no	—
24	C₈×C₈₃	—	2	1	no	—
25	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
26	C₈×C₈₃	Q₁₆	1	1	yes	characteristic
27	C₈₃⋊C₈	—	8	1	no	—
28	C₂²×C₈₃	#102	1	1	yes	characteristic
29	C₄×C₈₃	—	2	1	no	—
30	C₄×C₈₃	#101	1	1	yes	characteristic
31	C₄×C₈₃	#103	1	1	yes	characteristic
32	C₄×C₈₃	D₁₆	1	1	yes	characteristic
33	C₄×C₈₃	SD₃₂	1	1	yes	characteristic
34	Dic₈₃	—	8	2	no	—
35	C₂×C₈₃	#332	1	1	yes	characteristic
36	C₂×C₈₃	#357	1	1	yes	characteristic
37	C₂×C₈₃	#362	1	1	yes	characteristic
38	#1364	—	83	1	no	maximal, Sylow
39	C₈₃	#1364	1	1	yes	characteristic, complemented, Sylow
40	#500	—	83	1	no	—
41	C₄⋊C₁₆	D₈₃	1	1	yes	characteristic
42	#335	—	83	1	no	—
43	C₄⋊Q₈	—	166	1	no	—
44	C₂×C₁₆	—	2	1	no	—
45	#107	—	83	2	no	—
46	#107	—	166	1	no	—
47	C₄⋊C₈	—	166	1	no	—
48	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
49	C₂×Q₈	—	332	1	no	—
50	C₂×C₈	—	332	1	no	—
51	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
53	C₄⋊C₄	—	332	1	no	—
54	C₄⋊C₄	—	166	2	no	—
55	C₄²	D₃₃₂	1	1	yes	characteristic
56	C₁₆	—	4	1	no	—
57	Q₈	—	664	1	no	—
58	Q₈	—	664	1	no	—
59	C₂×C₄	—	332	2	no	—
60	C₂×C₄	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
61	C₂×C₄	D₆₆₄	1	1	yes	characteristic
62	C₂×C₄	#13050579	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	664	1	no	—
65	C₈	#13050578	1	1	yes	characteristic
66	C₈	#13050580	1	1	yes	characteristic
67	C₂²	#14581714	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	664	2	no	—
70	C₄	#14581710	1	1	yes	characteristic
71	C₄	#14581715	1	1	yes	characteristic
72	C₄	D₁₃₂₈	1	1	yes	characteristic
73	C₄	#14581737	1	1	yes	characteristic
74	C₂	#19127446	1	1	yes	characteristic
75	C₂	#19127503	1	1	yes	characteristic
76	C₂	#19127518	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14581714
commutator	C₂×C₈×C₈₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₈₃
Fitting	C₄⋊C₁₆×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#102
cosocle	C₄×C₈×C₈₃	C₂²
hypercenter	C₄⋊C₁₆	D₈₃
hypocenter	C₈₃	#1364
LCS	G ▷ C₂×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
39. C₈₃	#1364	semidirect