Subgroups — #14580690

Order 2624.

96 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	#13050088	C₂	1	2	yes	maximal, complemented
3	#13050085	C₂	1	2	yes	maximal
4	C₄×#66491	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²⋊C₄×C₄₁	—	2	2	no	—
9	C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₁	C₂²	1	2	yes	—
11	#10620279	—	2	2	no	—
12	C₂×#66491	C₂²	1	2	yes	—
13	C₂³×C₄₁	—	2	1	no	—
14	Q₈×C₄₁	—	2	2	no	—
15	D₄×C₄₁	—	2	2	no	—
16	C₂×C₄×C₄₁	—	2	1	no	—
17	C₂×C₄×C₄₁	D₄	1	2	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	—	2	2	no	—
20	#66491	—	2	2	no	—
21	C₂²×C₄₁	—	4	1	no	—
22	C₂²×C₄₁	—	4	2	no	—
23	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₁	—	2	2	no	—
25	C₄×C₄₁	—	4	1	no	—
26	C₄×C₄₁	#41	1	2	yes	—
27	Dic₄₁	—	4	2	no	—
28	C₂×C₄₁	—	8	1	no	—
29	C₂×C₄₁	#124	1	1	yes	characteristic
30	C₂×C₄₁	#135	1	2	yes	—
31	#488	—	41	1	no	maximal, Sylow
32	C₄₁	#488	1	1	yes	characteristic, complemented, Sylow
33	#125	—	41	1	no	—
34	#124	D₄₁	1	1	yes	characteristic
35	#103	—	41	2	no	—
36	#102	—	41	2	no	—
37	C₄×C₈	—	41	1	no	—
38	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
39	C₂×D₄	C₂×D₄₁	1	1	yes	characteristic
40	C₂×C₈	—	41	2	no	—
41	C₄⋊C₄	—	41	2	no	—
42	C₄⋊C₄	—	82	2	no	—
43	C₂²⋊C₄	—	2	2	no	—
44	C₄²	C₂×D₄₁	1	1	yes	characteristic
45	C₂³	—	2	1	no	—
46	Q₈	—	2	2	no	—
47	D₄	—	2	2	no	—
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	—	82	2	no	—
50	C₂×C₄	C₂²⋊D₄₁	1	2	yes	—
51	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
52	C₈	—	82	2	no	—
53	C₂²	—	4	1	no	—
54	C₂²	—	4	2	no	—
55	C₂²	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	4	1	no	—
58	C₄	—	164	2	no	—
59	C₄	#10620308	1	2	yes	—
60	C₂	—	8	1	no	—
61	C₂	#13050151	1	1	yes	characteristic
62	C₂	#13050184	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#124×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	C₂×D₄×C₄₁	C₂²
hypercenter	#124	D₄₁
hypocenter	C₄₁	#488
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. #13050156	C₂	semidirect
2. #13050088	C₂	semidirect
4. C₄×#66491	C₂	semidirect
32. C₄₁	#488	semidirect

Maximal subgroups

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

subgroup	index
#13050156	2
#13050088	2
#13050085	2
C₄×#66491	2
#124×C₄₁	2
#488	41