Subgroups — #24907073

Order 10624.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128106	C₂	1	2	yes	maximal
2	#19128052	C₂	1	4	yes	maximal
3	C₈²×C₈₃	C₂	1	1	yes	maximal, characteristic
4	#14581792	C₂²	1	4	yes	—
5	#14581726	—	2	4	no	—
6	#14581717	—	2	8	no	—
7	C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₈₃	C₂²	1	2	yes	—
9	C₂×Dic₁₆₆	—	2	4	no	—
10	C₄⋊Dic₈₃	—	2	4	no	—
11	C₄⋊Dic₈₃	—	2	4	no	—
12	C₂×C₈×C₈₃	D₄	1	4	yes	—
13	C₂×C₈×C₈₃	D₄	1	2	yes	—
14	C₄²×C₈₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
17	C₂×Dic₈₃	—	4	4	no	—
18	Dic₁₆₆	—	4	8	no	—
19	C₈×C₈₃	—	2	4	no	—
20	C₈×C₈₃	Q₁₆	1	4	yes	—
21	C₂²×C₈₃	#127	1	1	yes	characteristic
22	C₄×C₈₃	C₂×Q₁₆	1	2	yes	—
23	C₄×C₈₃	#135	1	4	yes	—
24	Dic₈₃	—	8	4	no	—
25	C₂×C₈₃	#494	1	1	yes	characteristic
26	C₂×C₈₃	#495	1	2	yes	—
27	#1710	—	83	1	no	maximal, Sylow
28	C₈₃	#1710	1	1	yes	characteristic, complemented, Sylow
29	#500	—	83	2	no	—
30	#487	—	83	4	no	—
31	C₈²	D₈₃	1	1	yes	characteristic
32	C₄⋊Q₈	—	83	4	no	—
33	#107	—	166	4	no	—
34	#103	—	166	8	no	—
35	C₄×C₈	C₂×D₈₃	1	2	yes	—
36	C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
37	C₂×Q₈	—	166	4	no	—
38	C₂×C₈	D₃₃₂	1	4	yes	—
39	C₂×C₈	D₃₃₂	1	2	yes	—
40	C₄⋊C₄	—	166	4	no	—
41	C₄⋊C₄	—	166	4	no	—
42	C₄²	C₂²×D₈₃	1	1	yes	characteristic
43	Q₈	—	332	8	no	—
44	C₂×C₄	—	332	4	no	—
45	C₂×C₄	C₂×D₃₃₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₃₃₂	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	Dic₃₃₂	1	4	yes	—
49	C₂²	#14581789	1	1	yes	characteristic
50	C₄	—	664	4	no	—
51	C₄	C₂×Dic₃₃₂	1	2	yes	—
52	C₄	#14581814	1	4	yes	—
53	C₂	#19128081	1	1	yes	characteristic
54	C₂	#19128085	1	2	yes	—

	subgroup	G/H
center	C₂²	#14581789
commutator, cosocle	C₄²×C₈₃	C₂³
Frattini	C₄²	C₂²×D₈₃
Fitting	C₈²×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#127
hypercenter	C₈²	D₈₃
hypocenter	C₈₃	#1710
LCS	G ▷ C₄²×C₈₃ ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
28. C₈₃	#1710	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19128106	2
#19128052	2
C₈²×C₈₃	2
#1710	83