Subgroups — #38787057

Order 25664.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊#13107944	C₂	1	2	yes	maximal
2	(C₂×#13107944)⋊C₄	C₂	1	4	yes	maximal, complemented
3	C₂²×C₄×D₄₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13107944	C₂²	1	4	yes	—
5	C₂²⋊#13107944	—	2	4	no	—
6	C₂³×D₄₀₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₀₁	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₄₀₁	—	2	4	no	—
9	C₂×C₄×D₄₀₁	C₄	1	2	yes	complemented
10	C₂×C₄×D₄₀₁	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₀₁	C₄	1	1	yes	characteristic, complemented
12	C₂×#13107944	—	2	4	no	—
13	C₂×#13107944	—	2	8	no	—
14	C₂²×D₄₀₁	—	2	4	no	—
15	C₂²×D₄₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×D₄₀₁	D₄	1	4	yes	—
17	C₂²×D₄₀₁	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₀₁	—	2	2	no	—
19	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
20	C₄×D₄₀₁	—	2	4	no	—
21	C₄×D₄₀₁	—	2	4	no	—
22	C₂³×C₄₀₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₀₁	—	2	2	no	—
24	C₂×C₄×C₄₀₁	C₂×C₄	1	2	yes	—
25	C₂²×C₄₀₁	—	2	2	no	—
26	C₂²×C₄₀₁	C₂²⋊C₄	1	2	yes	—
27	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₀₁	—	2	2	no	—
29	C₂×D₄₀₁	—	2	8	no	—
30	C₂×D₄₀₁	C₂²⋊C₄	1	2	yes	—
31	C₂×D₄₀₁	C₂×D₄	1	2	yes	—
32	C₂×D₄₀₁	#41	1	4	yes	—
33	#13107944	—	4	4	no	—
34	C₄×C₄₀₁	—	2	2	no	—
35	Dic₄₀₁	—	2	2	no	—
36	C₂×C₄₀₁	—	2	2	no	—
37	C₂×C₄₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄₀₁	#117	1	2	yes	—
39	D₄₀₁	—	2	2	no	—
40	D₄₀₁	#123	1	4	yes	—
41	C₄₀₁	#381	1	1	yes	characteristic, complemented, Sylow
42	#381	—	401	1	no	maximal, Sylow
43	C₂³×C₄	—	401	1	no	—
44	C₂×C₂²⋊C₄	—	401	2	no	—
45	#95	—	401	4	no	—
46	C₂⁴	—	401	1	no	—
47	C₂²×C₄	—	802	4	no	—
48	C₂²×C₄	—	401	4	no	—
49	C₂²×C₄	—	401	1	no	—
50	C₂²×C₄	—	401	2	no	—
51	C₂²×C₄	—	401	2	no	—
52	C₂²×C₄	#13107944	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	802	4	no	—
54	C₂³	—	802	4	no	—
55	C₂³	—	401	4	no	—
56	C₂³	—	401	1	no	—
57	C₂³	—	401	1	no	—
58	C₂³	C₂×#13107944	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	802	4	no	—
61	C₂×C₄	—	802	4	no	—
62	C₂×C₄	—	802	2	no	—
63	C₂×C₄	—	802	4	no	—
64	C₂×C₄	—	802	8	no	—
65	C₂×C₄	—	401	2	no	—
66	C₂×C₄	C₂×#13107944	1	2	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	—	802	8	no	—
69	C₂²	—	802	2	no	—
70	C₂²	—	401	2	no	—
71	C₂²	—	401	2	no	—
72	C₂²	—	401	4	no	—
73	C₂²	C₂²⋊#13107944	1	2	yes	—
74	C₂²	C₂²×#13107944	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	802	2	no	—
77	C₄	—	1604	4	no	—
78	C₂	—	2	2	no	—
79	C₂	—	802	2	no	—
80	C₂	—	401	4	no	—
81	C₂	C₂×C₂²⋊#13107944	1	1	yes	characteristic
82	C₂	#27165816	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13107944
commutator, socle	C₂²×C₄₀₁	C₂²×C₄
Fitting	C₂²×C₄×C₄₀₁	C₄
prime radical	C₂³×D₄₀₁	C₂²
cosocle	C₂²×D₄₀₁	C₂³
hypercenter	C₂²×C₄	#13107944
hypocenter	C₄₀₁	#381
LCS	G ▷ C₂²×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. (C₂×#13107944)⋊C₄	C₂	semidirect
7. C₂²×Dic₄₀₁	C₄	semidirect
9. C₂×C₄×D₄₀₁	C₄	semidirect
11. C₂²×C₄×C₄₀₁	C₄	semidirect
41. C₄₀₁	#381	semidirect
52. C₂²×C₄	#13107944	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊#13107944	2
(C₂×#13107944)⋊C₄	2
C₂²×C₄×D₄₀₁	2
#381	401