Subgroups — #38786983

Order 25664.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₀₁⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#20264349	C₂	1	1	yes	maximal, characteristic
3	#20264376	—	2	2	no	—
4	#20264375	—	2	2	no	—
5	#20264374	C₄	1	4	yes	—
6	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
7	#20264349	—	2	2	no	—
8	C₂×#15691999	C₄	1	1	yes	characteristic
9	C₂×C₈×C₄₀₁	C₄	1	1	yes	characteristic
10	#15692006	—	2	4	no	—
11	C₂²×D₄₀₁	Q₈	1	1	yes	characteristic
12	C₂×Dic₄₀₁	D₄	1	1	yes	characteristic
13	C₄×D₄₀₁	C₂×C₄	1	2	yes	—
14	C₄×D₄₀₁	D₄	1	2	yes	—
15	#15691999	—	2	1	no	—
16	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₄₀₁	—	2	1	no	—
18	C₂²×C₄₀₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₄₀₁	—	4	1	no	—
20	C₂×D₄₀₁	C₄⋊C₄	1	2	yes	—
21	C₄×C₄₀₁	C₄²	1	1	yes	characteristic
22	C₄×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₄₀₁	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄₀₁	—	2	1	no	—
25	C₂×C₄₀₁	#95	1	1	yes	characteristic
26	D₄₀₁	—	2	2	no	—
27	C₄₀₁	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	401	1	no	maximal, Sylow
29	C₂×M₁₆	—	401	2	no	—
30	C₂×M₁₆	—	401	1	no	—
31	C₂²×C₄	—	401	1	no	—
32	M₁₆	—	802	2	no	—
33	M₁₆	—	802	2	no	—
34	M₁₆	—	802	2	no	—
35	C₂×C₈	—	401	4	no	—
36	C₂×C₈	—	401	1	no	—
37	C₂×C₈	#13107944	1	1	yes	characteristic
38	C₂³	—	401	1	no	—
39	C₂×C₄	—	401	1	no	—
40	C₂×C₄	—	401	2	no	—
41	C₂×C₄	—	401	2	no	—
42	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	802	4	no	—
45	C₈	—	802	1	no	—
46	C₂²	—	1604	1	no	—
47	C₂²	—	401	2	no	—
48	C₂²	C₄⋊#13107944	1	1	yes	characteristic
49	C₄	—	401	2	no	—
50	C₄	C₄×#13107944	1	1	yes	characteristic
51	C₄	C₂²⋊#13107944	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	802	2	no	—
54	C₂	(C₂×#13107944)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#13107944
commutator	C₄×C₄₀₁	C₄²
Frattini	C₂×C₄	C₂×#13107944
Fitting	C₂×C₈×C₄₀₁	C₄
socle	C₂×C₄₀₁	#95
prime radical	C₂²×D₄₀₁	Q₈
cosocle	C₂×C₄×D₄₀₁	C₂²
hypercenter	C₂×C₈	#13107944
hypocenter	C₄₀₁	#338
LCS	G ▷ C₄×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
27. C₄₀₁	#338	semidirect

Maximal subgroups

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

subgroup	index
D₄₀₁⋊M₁₆	2
C₂×#20264349	2
#338	401