Subgroups — #38786982

Order 25664.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165816	C₂	1	2	yes	maximal
2	C₂×#20264349	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13107944	—	2	2	no	—
4	C₂²⋊#13107944	—	2	2	no	—
5	C₄×#13107944	C₄	1	4	yes	complemented
6	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
7	#20264349	—	2	2	no	—
8	C₂×#15691999	C₄	1	1	yes	characteristic, complemented
9	C₂×C₈×C₄₀₁	C₄	1	1	yes	characteristic, complemented
10	C₂×#13107944	—	2	4	no	—
11	C₂²×D₄₀₁	D₄	1	1	yes	characteristic
12	C₂×Dic₄₀₁	Q₈	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	C₂²⋊C₄	1	2	yes	—
21	#13107944	—	4	4	no	—
22	C₄×C₄₀₁	C₄²	1	1	yes	characteristic
23	C₄×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₄₀₁	C₄⋊C₄	1	2	yes	—
25	C₂×C₄₀₁	—	2	1	no	—
26	C₂×C₄₀₁	#95	1	1	yes	characteristic
27	D₄₀₁	—	2	2	no	—
28	C₄₀₁	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
29	H(3,ℤ/4)	—	401	1	no	maximal, Sylow
30	C₂×M₁₆	—	401	1	no	—
31	#117	—	401	2	no	—
32	C₂²×C₄	—	401	1	no	—
33	M₁₆	—	802	2	no	—
34	C₂×C₈	—	401	1	no	—
35	C₂×C₈	#13107944	1	1	yes	characteristic, complemented
36	C₄⋊C₄	—	802	2	no	—
37	C₂²⋊C₄	—	802	2	no	—
38	C₄²	—	401	4	no	—
39	C₂³	—	401	1	no	—
40	C₂×C₄	—	802	4	no	—
41	C₂×C₄	—	401	1	no	—
42	C₂×C₄	—	401	2	no	—
43	C₂×C₄	—	401	2	no	—
44	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	802	1	no	—
47	C₂²	—	1604	1	no	—
48	C₂²	—	401	2	no	—
49	C₂²	C₄⋊#13107944	1	1	yes	characteristic
50	C₄	—	1604	4	no	—
51	C₄	—	401	2	no	—
52	C₄	C₄×#13107944	1	1	yes	characteristic
53	C₄	C₂²⋊#13107944	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	802	2	no	—
56	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	D₄
cosocle	C₂×C₄×D₄₀₁	C₂²
hypercenter	C₂×C₈	#13107944
hypocenter	C₄₀₁	H(3,ℤ/4)
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
5. C₄×#13107944	C₄	semidirect
8. C₂×#15691999	C₄	semidirect
9. C₂×C₈×C₄₀₁	C₄	semidirect
28. C₄₀₁	H(3,ℤ/4)	semidirect
35. C₂×C₈	#13107944	semidirect

Maximal subgroups

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

subgroup	index
#27165816	2
C₂×#20264349	2
H(3,ℤ/4)	401