Subgroups — #14580700

Order 2624.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050156	C₂	1	1	yes	maximal, characteristic, complemented
2	#13050085	C₂	1	4	yes	maximal, complemented
3	#13050075	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	C₄²×C₄₁	C₂²	1	1	yes	characteristic
8	C₄⋊Dic₄₁	C₂²	1	2	yes	—
9	#10620279	—	2	2	no	—
10	C₂×#66491	C₂²	1	2	yes	—
11	C₂³×C₄₁	—	2	2	no	—
12	D₄×C₄₁	—	2	4	no	—
13	D₄×C₄₁	—	4	4	no	—
14	C₂×C₄×C₄₁	D₄	1	2	yes	—
15	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₁	—	2	2	no	—
17	#66491	—	2	2	no	—
18	C₂²×C₄₁	—	4	2	no	—
19	C₂²×C₄₁	—	4	4	no	—
20	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
21	C₄×C₄₁	—	2	2	no	—
22	C₄×C₄₁	#41	1	2	yes	—
23	Dic₄₁	—	4	2	no	—
24	C₂×C₄₁	—	8	2	no	—
25	C₂×C₄₁	#124	1	1	yes	characteristic
26	C₂×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
27	#490	—	41	1	no	maximal, Sylow
28	C₄₁	#490	1	1	yes	characteristic, complemented, Sylow
29	#127	D₄₁	1	1	yes	characteristic
30	#125	—	41	1	no	—
31	#102	—	41	4	no	—
32	#97	—	41	1	no	—
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₄₁	1	2	yes	—
35	C₂×C₈	—	41	2	no	—
36	C₄⋊C₄	—	41	2	no	—
37	C₄⋊C₄	—	82	2	no	—
38	C₄²	C₂×D₄₁	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	82	2	no	—
43	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
44	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
45	C₈	—	82	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	164	2	no	—
51	C₄	#10620308	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#13050151	1	1	yes	characteristic
54	C₂	#13050190	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	#490
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. #13050156	C₂	semidirect
2. #13050085	C₂	semidirect
3. #13050075	C₂	semidirect
28. C₄₁	#490	semidirect

Maximal subgroups

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

subgroup	index
#13050156	2
#13050085	2
#13050075	2
#127×C₄₁	2
#490	41