Subgroups — #38787132

Order 25664.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165804	C₂	1	2	yes	maximal, complemented
2	#27165794	C₂	1	2	yes	maximal
3	C₄×#15692006	C₂	1	2	yes	maximal, complemented
4	C₄²×D₄₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#15692006	C₂²	1	4	yes	—
6	C₂×C₄×D₄₀₁	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₀₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
9	C₄×Dic₄₀₁	C₄	1	1	yes	characteristic
10	C₄×Dic₄₀₁	C₂²	1	1	yes	characteristic
11	C₄×Dic₄₀₁	C₂²	1	1	yes	characteristic
12	C₄²×C₄₀₁	C₄	1	1	yes	characteristic
13	#15692006	—	2	4	no	—
14	C₂²×D₄₀₁	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₄₀₁	C₂³	1	1	yes	characteristic
18	C₄×D₄₀₁	—	2	2	no	—
19	C₄×D₄₀₁	—	2	2	no	—
20	C₄×D₄₀₁	C₈	1	4	yes	complemented
21	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×D₄₀₁	—	2	1	no	—
26	C₂×D₄₀₁	—	2	1	no	—
27	C₂×D₄₀₁	C₂×C₈	1	2	yes	—
28	C₄×C₄₀₁	—	2	1	no	—
29	C₄×C₄₀₁	—	2	1	no	—
30	C₄×C₄₀₁	C₂×C₈	1	2	yes	—
31	Dic₄₀₁	C₂×C₈	1	2	yes	—
32	Dic₄₀₁	M₁₆	1	2	yes	—
33	Dic₄₀₁	#41	1	2	yes	—
34	C₂×C₄₀₁	#117	1	1	yes	characteristic
35	C₂×C₄₀₁	C₂²×C₈	1	1	yes	characteristic
36	C₂×C₄₀₁	C₂×M₁₆	1	1	yes	characteristic
37	D₄₀₁	—	2	2	no	—
38	C₄₀₁	#431	1	1	yes	characteristic, complemented, Sylow
39	#431	—	401	1	no	maximal, Sylow
40	C₂×C₄²	—	401	1	no	—
41	C₄⋊C₈	—	401	2	no	—
42	C₂²⋊C₈	—	401	2	no	—
43	C₄×C₈	—	401	2	no	—
44	C₂²×C₄	—	401	1	no	—
45	C₂²×C₄	—	401	1	no	—
46	C₂²×C₄	—	401	1	no	—
47	C₂×C₈	—	401	4	no	—
48	C₄²	—	401	1	no	—
49	C₄²	—	401	1	no	—
50	C₄²	—	401	1	no	—
51	C₄²	#13107944	1	1	yes	characteristic
52	C₂³	—	401	1	no	—
53	C₂×C₄	—	802	2	no	—
54	C₂×C₄	—	802	2	no	—
55	C₂×C₄	—	401	1	no	—
56	C₂×C₄	—	401	1	no	—
57	C₂×C₄	—	401	1	no	—
58	C₂×C₄	—	401	4	no	—
59	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
60	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
61	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
62	C₈	—	802	4	no	—
63	C₂²	—	802	1	no	—
64	C₂²	—	802	1	no	—
65	C₂²	—	401	2	no	—
66	C₂²	C₂²×#13107944	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	401	2	no	—
70	C₄	—	401	2	no	—
71	C₄	—	401	2	no	—
72	C₄	#20264374	1	2	yes	—
73	C₂	—	802	2	no	—
74	C₂	#27165816	1	1	yes	characteristic
75	C₂	C₂×#20264374	1	1	yes	characteristic
76	C₂	D₄₀₁⋊M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13107944
commutator	C₂×C₄₀₁	C₂²×C₈
Frattini	C₂²	C₂²×#13107944
Fitting	C₄²×C₄₀₁	C₄
socle	C₂²×C₄₀₁	C₂²×C₄
prime radical	C₂²×D₄₀₁	C₂×C₄
cosocle	C₂×Dic₄₀₁	C₂³
hypercenter	C₄²	#13107944
hypocenter	C₄₀₁	#431
LCS	G ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. #27165804	C₂	semidirect
3. C₄×#15692006	C₂	semidirect
20. C₄×D₄₀₁	C₈	semidirect
38. C₄₀₁	#431	semidirect

Maximal subgroups

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

subgroup	index
#27165804	2
#27165794	2
C₄×#15692006	2
C₄²×D₄₀₁	2
#431	401