Subgroups — #38787095

Order 25664.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27165816	C₂	1	2	yes	maximal, complemented
2	#27165796	C₂	1	4	yes	maximal, complemented
3	C₂×#20264367	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#13107944	—	2	2	no	—
5	C₂²⋊#13107944	C₂²	1	4	yes	—
6	C₄×#13107944	—	2	2	no	—
7	#20264367	—	2	2	no	—
8	#20264367	—	2	2	no	—
9	C₂×D₁₆₀₄	C₄	1	1	yes	characteristic, complemented
10	C₂×D₁₆₀₄	C₂²	1	2	yes	—
11	C₂×C₄×D₄₀₁	C₄	1	2	yes	complemented
12	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₀₁	C₄	1	1	yes	characteristic, complemented
14	C₂×#13107944	—	2	4	no	—
15	C₂²×D₄₀₁	C₂×C₄	1	2	yes	—
16	C₂²×D₄₀₁	C₂³	1	1	yes	characteristic
17	D₁₆₀₄	—	2	4	no	—
18	D₁₆₀₄	—	2	2	no	—
19	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
20	C₄×D₄₀₁	—	2	2	no	—
21	C₄×D₄₀₁	—	2	2	no	—
22	C₄×D₄₀₁	D₄	1	2	yes	—
23	C₄×D₄₀₁	D₄	1	2	yes	—
24	Q₈×C₄₀₁	—	2	2	no	—
25	C₂×C₄×C₄₀₁	C₂×C₄	1	2	yes	—
26	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₀₁	—	2	2	no	—
29	C₂×D₄₀₁	—	4	1	no	—
30	C₂×D₄₀₁	—	4	2	no	—
31	C₂×D₄₀₁	C₂×D₄	1	2	yes	—
32	#13107944	—	4	4	no	—
33	C₄×C₄₀₁	—	2	2	no	—
34	C₄×C₄₀₁	C₂²⋊C₄	1	2	yes	—
35	Dic₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄₀₁	—	2	1	no	—
38	C₂×C₄₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	D₄₀₁	—	2	2	no	—
40	D₄₀₁	—	4	2	no	—
41	C₄₀₁	#410	1	1	yes	characteristic, complemented, Sylow
42	#410	—	401	1	no	maximal, Sylow
43	C₂×#41	—	401	1	no	—
44	#117	—	401	2	no	—
45	#99	—	401	4	no	—
46	#41	—	802	2	no	—
47	#41	—	802	2	no	—
48	C₂×Q₈	#13107944	1	1	yes	characteristic, complemented
49	C₂×D₄	—	401	2	no	—
50	C₂×D₄	—	401	1	no	—
51	C₂²×C₄	—	401	2	no	—
52	C₂²×C₄	—	401	1	no	—
53	C₄⋊C₄	—	802	2	no	—
54	C₂²⋊C₄	—	401	4	no	—
55	C₄²	—	802	2	no	—
56	C₂³	—	401	2	no	—
57	C₂³	—	401	1	no	—
58	Q₈	—	2	2	no	—
59	D₄	—	802	4	no	—
60	D₄	—	802	2	no	—
61	C₂×C₄	—	802	2	no	—
62	C₂×C₄	—	802	2	no	—
63	C₂×C₄	—	802	4	no	—
64	C₂×C₄	—	401	1	no	—
65	C₂×C₄	—	401	2	no	—
66	C₂×C₄	—	401	2	no	—
67	C₂×C₄	C₂×#13107944	1	2	yes	—
68	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
69	C₂²	—	802	2	no	—
70	C₂²	—	1604	1	no	—
71	C₂²	—	1604	2	no	—
72	C₂²	—	401	2	no	—
73	C₂²	C₂²×#13107944	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	1604	4	no	—
76	C₄	—	401	1	no	—
77	C₄	—	401	1	no	—
78	C₄	C₂²⋊#13107944	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	802	2	no	—
81	C₂	—	1604	2	no	—
82	C₂	C₂×C₂²⋊#13107944	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#13107944
commutator	C₂²×C₄₀₁	C₂²×C₄
Frattini	C₂²	C₂²×#13107944
Fitting	C₂×Q₈×C₄₀₁	C₄
socle	C₂×C₄₀₁	C₂×C₂²⋊C₄
prime radical	C₂×#20264367	C₂
cosocle	C₂²×D₄₀₁	C₂³
hypercenter	C₂×Q₈	#13107944
hypocenter	C₄₀₁	#410
LCS	G ▷ C₂²×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #27165816	C₂	semidirect
2. #27165796	C₂	semidirect
9. C₂×D₁₆₀₄	C₄	semidirect
11. C₂×C₄×D₄₀₁	C₄	semidirect
13. C₂×Q₈×C₄₀₁	C₄	semidirect
41. C₄₀₁	#410	semidirect
48. C₂×Q₈	#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
#27165796	2
C₂×#20264367	2
#410	401