Subgroups — C₂×#27165833 #38787232

Order 25664.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165833	C₂	1	4	yes	maximal, direct product factor
2	C₂×#20264378	C₂	1	2	yes	maximal, complemented
3	C₂²×#15692006	C₂	1	1	yes	maximal, characteristic
4	#20264378	C₂²	1	4	yes	complemented
5	C₂×#15692006	C₄	1	2	yes	—
6	C₂×#15692006	C₄	1	1	yes	characteristic
7	C₂×#15692006	C₂²	1	1	yes	characteristic
8	C₂×#15692006	C₂²	1	2	yes	—
9	C₂²×Dic₄₀₁	C₄	1	1	yes	characteristic
10	#15692006	C₂×C₄	1	1	yes	characteristic
11	#15692006	C₂×C₄	1	2	yes	—
12	#15692006	C₂³	1	1	yes	characteristic
13	C₂×Dic₄₀₁	C₈	1	2	yes	—
14	C₂×Dic₄₀₁	C₈	1	1	yes	characteristic
15	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄₀₁	C₈	1	1	yes	characteristic
18	C₂²×C₄₀₁	—	2	2	no	—
19	C₂²×C₄₀₁	C₂×C₈	1	2	yes	—
20	C₂²×C₄₀₁	C₂×C₈	1	1	yes	characteristic
21	Dic₄₀₁	C₂×C₈	1	2	yes	—
22	Dic₄₀₁	C₂×C₈	1	1	yes	characteristic
23	Dic₄₀₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄₀₁	—	2	2	no	—
25	C₂×C₄₀₁	M₃₂	1	2	yes	complemented
26	C₂×C₄₀₁	C₂²×C₈	1	1	yes	characteristic
27	C₄₀₁	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₃₂	—	401	1	no	maximal, Sylow
29	C₂²×C₈	—	401	1	no	—
30	M₃₂	—	401	4	no	—
31	C₂×C₁₆	—	401	2	no	—
32	C₂²×C₄	—	401	1	no	—
33	C₂×C₈	—	401	1	no	—
34	C₂×C₈	—	401	2	no	—
35	C₂×C₈	—	401	2	no	—
36	C₂×C₈	—	401	1	no	—
37	C₁₆	—	401	4	no	—
38	C₂³	#15692008	1	1	yes	characteristic
39	C₂×C₄	—	401	2	no	—
40	C₂×C₄	—	401	2	no	—
41	C₂×C₄	—	401	1	no	—
42	C₂×C₄	—	401	1	no	—
43	C₈	—	401	1	no	—
44	C₈	—	401	1	no	—
45	C₈	—	401	2	no	—
46	C₂²	—	2	2	no	—
47	C₂²	C₂×#15692008	1	2	yes	—
48	C₂²	C₂×#15692008	1	1	yes	characteristic
49	C₄	—	401	1	no	—
50	C₄	—	401	2	no	—
51	C₄	—	401	1	no	—
52	C₂	—	2	2	no	—
53	C₂	#27165833	1	2	yes	direct product factor
54	C₂	C₂²×#15692008	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15692008
commutator	C₂×C₄₀₁	C₂²×C₈
Frattini	C₂	C₂²×#15692008
Fitting, prime radical	C₂³×C₄₀₁	C₈
socle	C₂²×C₄₀₁	C₂×C₈
cosocle	#15692006	C₂³
hypercenter	C₂³	#15692008
hypocenter	C₄₀₁	C₂×M₃₂
LCS	G ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. #27165833	C₂	direct (N × H)
2. C₂×#20264378	C₂	semidirect
4. #20264378	C₂²	semidirect
25. C₂×C₄₀₁	M₃₂	semidirect
27. C₄₀₁	C₂×M₃₂	semidirect
53. C₂	#27165833	direct (N × H)

Maximal subgroups

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

subgroup	index
#27165833	2
C₂×#20264378	2
C₂²×#15692006	2
C₂×M₃₂	401

Subgroups — C2×#27165833 #38787232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27165833 #38787232