Subgroups — #14580360

Order 2624.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620277	C₂	1	2	yes	maximal
2	C₄⋊#66491	C₂	1	4	yes	maximal, complemented
3	C₂×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₁	C₄	1	2	yes	—
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₄²×C₄₁	C₄	1	1	yes	characteristic
7	C₄²×C₄₁	C₄	1	1	yes	characteristic
8	C₄²×C₄₁	C₂²	1	2	yes	—
9	#10620277	—	2	4	no	—
10	C₂×#66491	C₂²	1	4	yes	—
11	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₁	—	2	4	no	—
13	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₄₁	D₄	1	2	yes	—
17	C₂×C₄×C₄₁	Q₈	1	2	yes	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	#66491	—	2	4	no	—
20	C₂²×C₄₁	—	2	2	no	—
21	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
22	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₄₁	—	2	2	no	—
24	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
25	C₄×C₄₁	M₁₆	1	4	yes	complemented
26	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
27	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄₁	—	2	2	no	—
29	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄₁	C₂×M₁₆	1	2	yes	—
31	#423	—	41	1	no	maximal, Sylow
32	C₄₁	#423	1	1	yes	characteristic, complemented, Sylow
33	C₂×M₁₆	—	41	2	no	—
34	C₂×C₄²	D₄₁	1	1	yes	characteristic
35	C₄⋊C₈	—	41	4	no	—
36	C₂²×C₄	Dic₄₁	1	2	yes	—
37	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
38	M₁₆	—	82	4	no	—
39	C₂×C₈	—	41	4	no	—
40	C₄²	Dic₄₁	1	1	yes	characteristic
41	C₄²	Dic₄₁	1	1	yes	characteristic
42	C₄²	C₂×D₄₁	1	2	yes	—
43	C₂³	C₂×Dic₄₁	1	1	yes	characteristic
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	Dic₈₂	1	2	yes	—
46	C₂×C₄	D₁₆₄	1	2	yes	—
47	C₂×C₄	C₂×Dic₄₁	1	2	yes	—
48	C₂×C₄	C₂×Dic₄₁	1	2	yes	—
49	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
51	C₈	—	82	4	no	—
52	C₂²	—	2	2	no	—
53	C₂²	C₄⋊Dic₄₁	1	2	yes	—
54	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
55	C₄	—	2	2	no	—
56	C₄	#10620277	1	4	yes	complemented
57	C₄	C₄⋊Dic₄₁	1	2	yes	—
58	C₄	C₂×Dic₈₂	1	1	yes	characteristic
59	C₄	C₂×D₁₆₄	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×C₄⋊Dic₄₁	1	1	yes	characteristic
62	C₂	C₂×#10620277	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₂×C₄²×C₄₁	C₂
prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂×C₄²	D₄₁
hypocenter	C₄₁	#423
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#66491	C₂	semidirect
25. C₄×C₄₁	M₁₆	semidirect
32. C₄₁	#423	semidirect
56. C₄	#10620277	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620277	2
C₄⋊#66491	2
C₂×C₄²×C₄₁	2
#423	41