Subgroups — C₂×#13050164 #14580880

Order 2624.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₂	C₂	1	2	yes	maximal
2	#13050164	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊Dic₄₁	C₂	1	4	yes	maximal
4	C₂×C₄²×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₄₁	C₂²	1	2	yes	—
7	C₂²×Dic₄₁	C₂²	1	4	yes	—
8	C₂×Dic₈₂	—	2	8	no	—
9	C₂×Dic₈₂	C₂²	1	8	yes	—
10	C₄²×C₄₁	C₂²	1	4	yes	—
11	C₄⋊Dic₄₁	C₂²	1	16	yes	—
12	C₂³×C₄₁	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₄₁	D₄	1	4	yes	—
14	C₂×C₄×C₄₁	Q₈	1	8	yes	complemented
15	C₂×C₄×C₄₁	C₂³	1	2	yes	—
16	C₂×C₄×C₄₁	C₂³	1	4	yes	—
17	C₂×Dic₄₁	—	2	8	no	—
18	C₂×Dic₄₁	C₂³	1	8	yes	—
19	Dic₈₂	—	2	16	no	—
20	C₂²×C₄₁	C₂×D₄	1	2	yes	—
21	C₂²×C₄₁	C₂×Q₈	1	4	yes	—
22	C₂²×C₄₁	C₂⁴	1	1	yes	characteristic
23	C₄×C₄₁	C₂×D₄	1	4	yes	—
24	C₄×C₄₁	C₂×Q₈	1	8	yes	complemented
25	Dic₄₁	—	2	8	no	—
26	C₂×C₄₁	C₄⋊Q₈	1	4	yes	complemented
27	C₂×C₄₁	C₂²×D₄	1	1	yes	characteristic
28	C₂×C₄₁	C₂²×Q₈	1	2	yes	—
29	C₂×C₄⋊Q₈	—	41	1	no	maximal, Sylow
30	C₄₁	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²×Q₈	—	41	2	no	—
32	C₄⋊Q₈	—	41	8	no	—
33	C₂×C₄⋊C₄	—	41	4	no	—
34	C₂×C₄²	D₄₁	1	1	yes	characteristic
35	C₂×Q₈	—	41	8	no	—
36	C₂×Q₈	—	82	8	no	—
37	C₂²×C₄	—	41	4	no	—
38	C₂²×C₄	C₂×D₄₁	1	2	yes	—
39	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
40	C₄⋊C₄	—	41	16	no	—
41	C₄²	C₂×D₄₁	1	4	yes	—
42	C₂³	C₂²×D₄₁	1	1	yes	characteristic
43	Q₈	—	82	16	no	—
44	C₂×C₄	—	41	8	no	—
45	C₂×C₄	—	82	8	no	—
46	C₂×C₄	Dic₈₂	1	8	yes	complemented
47	C₂×C₄	D₁₆₄	1	4	yes	—
48	C₂×C₄	C₂²×D₄₁	1	4	yes	—
49	C₂×C₄	C₂²×D₄₁	1	2	yes	—
50	C₂²	C₂×Dic₈₂	1	4	yes	—
51	C₂²	C₂×D₁₆₄	1	2	yes	—
52	C₂²	C₂³×D₄₁	1	1	yes	characteristic
53	C₄	—	82	8	no	—
54	C₄	C₂×Dic₈₂	1	8	yes	complemented
55	C₄	C₂×D₁₆₄	1	4	yes	—
56	C₂	#13050164	1	4	yes	direct product factor
57	C₂	C₂²×D₁₆₄	1	1	yes	characteristic
58	C₂	C₂²×Dic₈₂	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₄₁
commutator, cosocle	C₂²×C₄₁	C₂⁴
Frattini	C₂²	C₂³×D₄₁
Fitting	C₂×C₄²×C₄₁	C₂
socle, prime radical	C₂³×C₄₁	C₂³
hypercenter	C₂×C₄²	D₄₁
hypocenter	C₄₁	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #13050164	C₂	direct (N × H)
14. C₂×C₄×C₄₁	Q₈	semidirect
24. C₄×C₄₁	C₂×Q₈	semidirect
26. C₂×C₄₁	C₄⋊Q₈	semidirect
30. C₄₁	C₂×C₄⋊Q₈	semidirect
46. C₂×C₄	Dic₈₂	semidirect
54. C₄	C₂×Dic₈₂	semidirect
56. C₂	#13050164	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₂	2
#13050164	2
C₂×C₄⋊Dic₄₁	2
C₂×C₄²×C₄₁	2
C₂×C₄⋊Q₈	41

Subgroups — C2×#13050164 #14580880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050164 #14580880