Subgroups — #14580708

Order 2624.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620283	C₂	1	4	yes	maximal, complemented
2	#13050164	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#66491	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×C₄₁	—	2	2	no	—
6	C₂×D₄×C₄₁	C₂²	1	2	yes	—
7	C₂×Dic₈₂	C₂²	1	2	yes	—
8	C₄²×C₄₁	C₂²	1	1	yes	characteristic
9	#10620283	—	2	8	no	—
10	C₄⋊Dic₄₁	—	2	2	no	—
11	C₂×#66491	C₂²	1	2	yes	—
12	C₂³×C₄₁	—	2	2	no	—
13	D₄×C₄₁	—	2	4	no	—
14	D₄×C₄₁	—	4	4	no	—
15	C₂×C₄×C₄₁	D₄	1	2	yes	—
16	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₁	—	2	2	no	—
18	Dic₈₂	—	2	4	no	—
19	#66491	D₄	1	4	yes	complemented
20	C₂²×C₄₁	—	4	2	no	—
21	C₂²×C₄₁	—	4	4	no	—
22	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
23	C₄×C₄₁	SD₁₆	1	4	yes	complemented
24	C₄×C₄₁	C₂×D₄	1	2	yes	—
25	Dic₄₁	—	4	2	no	—
26	C₂×C₄₁	—	8	2	no	—
27	C₂×C₄₁	#127	1	1	yes	characteristic
28	C₂×C₄₁	C₂×SD₁₆	1	2	yes	—
29	#492	—	41	1	no	maximal, Sylow
30	C₄₁	#492	1	1	yes	characteristic, complemented, Sylow
31	C₂×SD₁₆	—	41	4	no	—
32	C₄⋊Q₈	—	41	1	no	—
33	#127	D₄₁	1	1	yes	characteristic
34	C₄×C₈	—	41	1	no	—
35	C₂×Q₈	—	41	2	no	—
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	C₂×D₄₁	1	2	yes	—
38	SD₁₆	—	82	8	no	—
39	C₂×C₈	—	41	2	no	—
40	C₄⋊C₄	—	82	2	no	—
41	C₄²	C₂×D₄₁	1	1	yes	characteristic
42	C₂³	—	2	2	no	—
43	Q₈	—	82	4	no	—
44	D₄	—	2	4	no	—
45	D₄	—	4	4	no	—
46	C₂×C₄	—	82	2	no	—
47	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
48	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
49	C₈	—	41	4	no	—
50	C₂²	—	4	2	no	—
51	C₂²	—	4	4	no	—
52	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
53	C₄	—	164	2	no	—
54	C₄	#10620283	1	4	yes	complemented
55	C₄	D₄×D₄₁	1	2	yes	—
56	C₂	—	8	2	no	—
57	C₂	#13050160	1	1	yes	characteristic
58	C₂	C₂×#10620283	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting, prime radical	#127×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
hypercenter	#127	D₄₁
hypocenter	C₄₁	#492
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#10620283	C₂	semidirect
2. #13050164	C₂	semidirect
3. C₄×#66491	C₂	semidirect
19. #66491	D₄	semidirect
23. C₄×C₄₁	SD₁₆	semidirect
30. C₄₁	#492	semidirect
54. C₄	#10620283	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620283	2
#13050164	2
C₄×#66491	2
#127×C₄₁	2
#492	41