Subgroups — D₄₀₁⋊M₁₆ #27165822

Order 12832.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264376	C₂	1	2	yes	maximal, complemented
2	#20264375	C₂	1	2	yes	maximal, complemented
3	#20264374	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₄₀₁	C₂	1	1	yes	maximal, characteristic
5	#15692006	C₂²	1	4	yes	complemented
6	C₂²×D₄₀₁	C₄	1	1	yes	characteristic
7	C₂×Dic₄₀₁	C₂²	1	1	yes	characteristic
8	C₄×D₄₀₁	C₄	1	1	yes	characteristic
9	C₄×D₄₀₁	C₄	1	1	yes	characteristic
10	C₄×D₄₀₁	C₂²	1	1	yes	characteristic
11	C₄×D₄₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₄₀₁	C₄	1	1	yes	characteristic
13	C₂²×C₄₀₁	C₂×C₄	1	1	yes	characteristic
14	C₂×D₄₀₁	—	2	2	no	—
15	C₂×D₄₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₄₀₁	C₂×C₄	1	1	yes	characteristic
17	C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
19	Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
20	Dic₄₀₁	C₂³	1	1	yes	characteristic
21	C₂×C₄₀₁	—	2	1	no	—
22	C₂×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
23	D₄₀₁	—	2	1	no	—
24	D₄₀₁	M₁₆	1	2	yes	complemented
25	C₄₀₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	401	1	no	maximal, Sylow
27	C₂²×C₄	—	401	1	no	—
28	M₁₆	—	401	2	no	—
29	M₁₆	—	401	2	no	—
30	C₂×C₈	—	401	2	no	—
31	C₂³	—	401	1	no	—
32	C₂×C₄	—	401	1	no	—
33	C₂×C₄	—	401	1	no	—
34	C₂×C₄	—	401	1	no	—
35	C₂×C₄	—	401	1	no	—
36	C₂×C₄	—	401	1	no	—
37	C₂×C₄	#13107944	1	1	yes	characteristic
38	C₈	—	401	4	no	—
39	C₂²	—	802	2	no	—
40	C₂²	—	401	1	no	—
41	C₂²	—	401	1	no	—
42	C₂²	C₂×#13107944	1	1	yes	characteristic
43	C₄	—	401	1	no	—
44	C₄	—	401	1	no	—
45	C₄	C₂×#13107944	1	1	yes	characteristic
46	C₄	C₂×#13107944	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	802	1	no	—
49	C₂	—	401	2	no	—
50	C₂	C₂²×#13107944	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13107944
commutator, socle	C₂×C₄₀₁	C₂²×C₄
Frattini	C₂	C₂²×#13107944
Fitting	C₂×C₄×C₄₀₁	C₄
prime radical	C₂²×D₄₀₁	C₄
cosocle	Dic₄₀₁	C₂³
hypercenter	C₂×C₄	#13107944
hypocenter	C₄₀₁	C₂×M₁₆
LCS	G ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20264376	C₂	semidirect
2. #20264375	C₂	semidirect
3. #20264374	C₂	semidirect
5. #15692006	C₂²	semidirect
24. D₄₀₁	M₁₆	semidirect
25. C₄₀₁	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#20264376	2
#20264375	2
#20264374	2
C₂×C₄×D₄₀₁	2
C₂×M₁₆	401

Subgroups — D401⋊M16 #27165822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₀₁⋊M₁₆ #27165822