Subgroups — C₂×#13050110 #14580763

Order 2624.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₄	C₂	1	1	yes	maximal, characteristic
2	#13050110	C₂	1	4	yes	maximal, direct product factor
3	C₂×#10620268	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₄₁	—	2	1	no	—
6	C₂×Dic₈₂	—	2	1	no	—
7	Q₁₆×C₄₁	—	2	1	no	—
8	Q₁₆×C₄₁	C₂²	1	2	yes	—
9	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	Dic₁₆₄	—	2	1	no	—
11	Dic₁₆₄	C₂²	1	2	yes	—
12	#10620268	C₂²	1	2	yes	—
13	Q₈×C₄₁	—	2	2	no	—
14	Q₈×C₄₁	—	4	1	no	—
15	C₂×C₄×C₄₁	—	4	1	no	—
16	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
17	C₂×Dic₄₁	—	4	1	no	—
18	Dic₈₂	—	2	2	no	—
19	Dic₈₂	—	4	1	no	—
20	C₈×C₄₁	D₄	1	1	yes	characteristic
21	C₈×C₄₁	C₂³	1	1	yes	characteristic
22	C₂²×C₄₁	D₈	1	1	yes	characteristic
23	C₄×C₄₁	—	4	2	no	—
24	C₄×C₄₁	D₈	1	1	yes	characteristic
25	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
26	Dic₄₁	—	4	2	no	—
27	C₂×C₄₁	Q₃₂	1	2	yes	complemented
28	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
29	C₂×Q₃₂	—	41	1	no	maximal, Sylow
30	C₄₁	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×Q₁₆	—	41	1	no	—
32	C₂×Q₁₆	D₄₁	1	1	yes	characteristic
33	Q₃₂	—	41	4	no	—
34	C₂×C₁₆	—	41	1	no	—
35	C₂×Q₈	—	2	1	no	—
36	C₂×Q₈	—	82	1	no	—
37	Q₁₆	—	2	1	no	—
38	Q₁₆	—	41	2	no	—
39	Q₁₆	—	82	1	no	—
40	Q₁₆	C₂×D₄₁	1	2	yes	—
41	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
42	C₁₆	—	41	2	no	—
43	Q₈	—	2	2	no	—
44	Q₈	—	4	1	no	—
45	Q₈	—	82	2	no	—
46	Q₈	—	164	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	164	1	no	—
49	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
50	C₈	C₂²⋊D₄₁	1	1	yes	characteristic
51	C₈	C₂²×D₄₁	1	1	yes	characteristic
52	C₂²	#10620282	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	164	2	no	—
55	C₄	#10620282	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
57	C₂	#13050110	1	2	yes	direct product factor
58	C₂	C₂×#10620282	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10620282
commutator, cosocle	C₈×C₄₁	C₂³
Frattini	C₈	C₂²×D₄₁
Fitting	C₂×Q₁₆×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	D₈
hypercenter	C₂×Q₁₆	D₄₁
hypocenter	C₄₁	C₂×Q₃₂
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13050110	C₂	direct (N × H)
27. C₂×C₄₁	Q₃₂	semidirect
30. C₄₁	C₂×Q₃₂	semidirect
57. C₂	#13050110	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₆₄	2
#13050110	2
C₂×#10620268	2
C₂×Q₁₆×C₄₁	2
C₂×Q₃₂	41

Subgroups — C2×#13050110 #14580763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050110 #14580763