Group #20265406 — subgroups

Subgroups — #20265406

Order 6464.

124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108063	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692234	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692229	C₂	1	1	yes	maximal, characteristic
4	#15692187	C₂	1	1	yes	maximal, characteristic, complemented
5	#15692180	C₂	1	1	yes	maximal, characteristic, complemented
6	#15692177	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₀₂	C₂²	1	1	yes	characteristic
9	C₂×D₄₀₄	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₁₀₁	—	2	1	no	—
11	#13108063	—	2	2	no	—
12	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
14	#13108053	—	2	1	no	—
15	C₂²⋊Dic₁₀₁	—	2	1	no	—
16	#13108051	—	2	1	no	—
17	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₀₁	—	2	2	no	—
19	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
21	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
22	C₂²×D₁₀₁	—	2	1	no	—
23	C₂×C₄×C₁₀₁	—	2	1	no	—
24	C₂×C₄×C₁₀₁	—	2	1	no	—
25	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
27	C₂²⋊D₁₀₁	—	4	2	no	—
28	C₂×Dic₁₀₁	—	2	1	no	—
29	C₂×Dic₁₀₁	—	2	1	no	—
30	C₂×Dic₁₀₁	—	2	1	no	—
31	D₄₀₄	—	2	1	no	—
32	D₄₀₄	—	2	1	no	—
33	Dic₂₀₂	—	2	1	no	—
34	Dic₂₀₂	—	2	1	no	—
35	C₈×C₁₀₁	—	2	1	no	—
36	C₈×C₁₀₁	D₄	1	2	yes	complemented
37	C₂²×C₁₀₁	—	2	1	no	—
38	C₂²×C₁₀₁	—	2	1	no	—
39	C₂²×C₁₀₁	SD₁₆	1	2	yes	complemented
40	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
41	C₂×D₁₀₁	—	4	1	no	—
42	C₂×D₁₀₁	—	4	1	no	—
43	C₂×D₁₀₁	—	4	1	no	—
44	C₄×C₁₀₁	—	2	1	no	—
45	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
46	C₄×C₁₀₁	#41	1	1	yes	characteristic
47	Dic₁₀₁	—	4	1	no	—
48	Dic₁₀₁	—	4	1	no	—
49	Dic₁₀₁	—	4	1	no	—
50	C₂×C₁₀₁	—	2	2	no	—
51	C₂×C₁₀₁	#121	1	1	yes	characteristic
52	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
53	C₂×C₁₀₁	#135	1	1	yes	characteristic
54	D₁₀₁	—	8	1	no	—
55	C₁₀₁	#465	1	1	yes	characteristic, complemented, Sylow
56	#465	—	101	1	no	maximal, Sylow
57	C₂×SD₁₆	—	101	1	no	—
58	C₂²×C₈	D₁₀₁	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈	—	101	1	no	—
60	#121	—	101	1	no	—
61	#106	—	101	1	no	—
62	#103	—	101	1	no	—
63	#102	—	101	1	no	—
64	C₂×Q₈	—	101	1	no	—
65	C₂×D₄	—	101	1	no	—
66	C₂×D₄	—	202	1	no	—
67	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
68	SD₁₆	—	202	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
71	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
72	C₄⋊C₄	—	101	1	no	—
73	C₄⋊C₄	—	101	1	no	—
74	C₄⋊C₄	—	202	1	no	—
75	C₂²⋊C₄	—	202	1	no	—
76	C₂²⋊C₄	—	202	1	no	—
77	C₂³	—	202	1	no	—
78	C₂³	D₄₀₄	1	1	yes	characteristic
79	Q₈	—	202	1	no	—
80	Q₈	—	202	1	no	—
81	D₄	—	404	2	no	—
82	D₄	—	202	1	no	—
83	D₄	—	202	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	202	1	no	—
87	C₂×C₄	—	202	1	no	—
88	C₂×C₄	—	202	1	no	—
89	C₂×C₄	D₄₀₄	1	1	yes	characteristic
90	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
91	C₈	—	2	1	no	—
92	C₈	C₂²⋊D₁₀₁	1	2	yes	complemented
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	404	1	no	—
96	C₂²	—	404	1	no	—
97	C₂²	—	404	1	no	—
98	C₂²	#13108063	1	2	yes	complemented
99	C₂²	C₂×D₄₀₄	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	404	1	no	—
102	C₄	—	404	1	no	—
103	C₄	—	404	1	no	—
104	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
105	C₄	#13108074	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	—	808	1	no	—
108	C₂	#15692229	1	1	yes	characteristic
109	C₂	C₂×#13108063	1	1	yes	characteristic
110	C₂	#15692277	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13108063

C₂

yes

maximal, characteristic, complemented

#15692234

C₂

yes

maximal, characteristic, complemented

#15692229

C₂

yes

maximal, characteristic

#15692187

C₂

yes

maximal, characteristic, complemented

#15692180

C₂

yes

maximal, characteristic, complemented

#15692177

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×C₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₀₂

C₂²

yes

characteristic

C₂×D₄₀₄

C₂²

yes

characteristic

C₂×C₂²⋊D₁₀₁

—

#13108063

—

C₄⋊Dic₁₀₁

C₂²

yes

characteristic

C₄⋊Dic₁₀₁

C₂²

yes

characteristic

#13108053

—

C₂²⋊Dic₁₀₁

—

#13108051

—

C₂²×C₄×C₁₀₁

C₂²

yes

characteristic

C₂×C₈×C₁₀₁

—

C₂×C₈×C₁₀₁

C₂²

yes

characteristic

C₂×C₈×C₁₀₁

C₂²

yes

characteristic

C₂³×C₁₀₁

D₄

yes

characteristic

C₂²×D₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

D₄

yes

characteristic

C₂×C₄×C₁₀₁

C₂³

yes

characteristic

C₂²⋊D₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

D₄₀₄

—

D₄₀₄

—

Dic₂₀₂

—

Dic₂₀₂

—

C₈×C₁₀₁

—

C₈×C₁₀₁

D₄

yes

complemented

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

SD₁₆

yes

complemented

C₂²×C₁₀₁

C₂×D₄

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₄×C₁₀₁

—

C₄×C₁₀₁

C₂×D₄

yes

characteristic

C₄×C₁₀₁

#41

yes

characteristic

Dic₁₀₁

—

Dic₁₀₁

—

Dic₁₀₁

—

C₂×C₁₀₁

—

C₂×C₁₀₁

#121

yes

characteristic

C₂×C₁₀₁

C₂×SD₁₆

yes

characteristic

C₂×C₁₀₁

#135

yes

characteristic

D₁₀₁

—

C₁₀₁

#465

yes

characteristic, complemented, Sylow

#465

—

101

maximal, Sylow

C₂×SD₁₆

—

101

—

C₂²×C₈

D₁₀₁

yes

characteristic, complemented

C₂²⋊Q₈

—

101

—

#121

—

101

—

#106

—

101

—

#103

—

101

—

#102

—

101

—

C₂×Q₈

—

101

—

C₂×D₄

—

101

—

C₂×D₄

—

202

—

C₂²×C₄

C₂×D₁₀₁

yes

characteristic

SD₁₆

—

202

—

C₂×C₈

—

C₂×C₈

C₂×D₁₀₁

yes

characteristic

C₂×C₈

C₂×D₁₀₁

yes

characteristic

C₄⋊C₄

—

101

—

C₄⋊C₄

—

101

—

C₄⋊C₄

—

202

—

C₂²⋊C₄

—

202

—

C₂²⋊C₄

—

202

—

C₂³

—

202

—

C₂³

D₄₀₄

yes

characteristic

Q₈

—

202

—

Q₈

—

202

—

D₄

—

404

—

D₄

—

202

—

D₄

—

202

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

D₄₀₄

yes

characteristic

C₂×C₄

C₂²×D₁₀₁

yes

characteristic

C₈

—

C₈

C₂²⋊D₁₀₁

yes

complemented

C₂²

—

C₂²

—

C₂²

—

404

—

C₂²

—

404

—

C₂²

—

404

—

C₂²

#13108063

yes

complemented

C₂²

C₂×D₄₀₄

yes

characteristic

100

C₄

—

101

C₄

—

404

—

102

C₄

—

404

—

103

C₄

—

404

—

104

C₄

C₂×C₂²⋊D₁₀₁

yes

characteristic

105

C₄

#13108074

yes

characteristic

106

C₂

—

107

C₂

—

808

—

108

C₂

#15692229

yes

characteristic

109

C₂

C₂×#13108063

yes

characteristic

110

C₂

#15692277

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₀₄
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	#465
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²

C₂×D₄₀₄

commutator

C₂×C₄×C₁₀₁

C₂³

Frattini

C₂×C₄

C₂²×D₁₀₁

Fitting

C₂²×C₈×C₁₀₁

C₂

socle

C₂²×C₁₀₁

C₂×D₄

hypercenter

C₂²×C₈

D₁₀₁

hypocenter

C₁₀₁

#465

LCS

G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
1. C₂×#13108063	C₂	semidirect
2. #15692234	C₂	semidirect
4. #15692187	C₂	semidirect
5. #15692180	C₂	semidirect
6. #15692177	C₂	semidirect
7. C₂²×C₈×C₁₀₁	C₂	semidirect
36. C₈×C₁₀₁	D₄	semidirect
39. C₂²×C₁₀₁	SD₁₆	semidirect
55. C₁₀₁	#465	semidirect
58. C₂²×C₈	D₁₀₁	semidirect
92. C₈	C₂²⋊D₁₀₁	semidirect
98. C₂²	#13108063	semidirect

H ≅ G/N

type

1. C₂×#13108063

C₂

semidirect

2. #15692234

C₂

semidirect

4. #15692187

C₂

semidirect

5. #15692180

C₂

semidirect

6. #15692177

C₂

semidirect

7. C₂²×C₈×C₁₀₁

C₂

semidirect

36. C₈×C₁₀₁

D₄

semidirect

39. C₂²×C₁₀₁

SD₁₆

semidirect

55. C₁₀₁

#465

semidirect

58. C₂²×C₈

D₁₀₁

semidirect

92. C₈

C₂²⋊D₁₀₁

semidirect

98. C₂²

#13108063

semidirect

Subgroups — #20265406

Conjugacy classes of subgroups

Complements