Group #20265091 — subgroups

Subgroups — #20265091

Order 6464.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13108053	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Dic₁₀₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₁₀₁	C₂	1	2	yes	maximal, complemented
4	#15692162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₀₁	C₂²	1	2	yes	—
7	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₀₁	C₂²	1	1	yes	characteristic
9	#13108053	—	2	2	no	—
10	C₂²⋊Dic₁₀₁	—	2	4	no	—
11	C₂²⋊Dic₁₀₁	—	2	4	no	—
12	C₂⁴×C₁₀₁	C₂²	1	2	yes	—
13	C₂×D₄×C₁₀₁	—	2	4	no	—
14	C₂×D₄×C₁₀₁	—	2	2	no	—
15	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
16	C₂³×C₁₀₁	—	2	2	no	—
17	C₂³×C₁₀₁	—	2	2	no	—
18	C₂³×C₁₀₁	—	2	2	no	—
19	C₂³×C₁₀₁	—	2	2	no	—
20	C₂³×C₁₀₁	—	2	2	no	—
21	C₂³×C₁₀₁	—	2	2	no	—
22	C₂³×C₁₀₁	D₄	1	4	yes	—
23	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
24	D₄×C₁₀₁	—	2	8	no	—
25	C₂×C₄×C₁₀₁	—	2	2	no	—
26	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
27	C₂×Dic₁₀₁	—	2	1	no	—
28	C₂×Dic₁₀₁	—	2	1	no	—
29	C₂×Dic₁₀₁	—	2	2	no	—
30	C₂×Dic₁₀₁	—	2	2	no	—
31	C₂×Dic₁₀₁	—	2	2	no	—
32	C₂×Dic₁₀₁	—	2	1	no	—
33	C₂×Dic₁₀₁	—	2	2	no	—
34	C₂×Dic₁₀₁	D₄	1	2	yes	complemented
35	C₂²×C₁₀₁	—	2	4	no	—
36	C₂²×C₁₀₁	—	2	4	no	—
37	C₂²×C₁₀₁	—	2	4	no	—
38	C₂²×C₁₀₁	—	4	2	no	—
39	C₂²×C₁₀₁	—	4	2	no	—
40	C₂²×C₁₀₁	—	4	2	no	—
41	C₂²×C₁₀₁	—	4	2	no	—
42	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₁₀₁	C₂×D₄	1	2	yes	—
44	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₁₀₁	#41	1	1	yes	characteristic
46	C₂²×C₁₀₁	#41	1	2	yes	—
47	C₄×C₁₀₁	—	2	2	no	—
48	Dic₁₀₁	—	2	2	no	—
49	Dic₁₀₁	—	4	1	no	—
50	Dic₁₀₁	—	4	2	no	—
51	C₂×C₁₀₁	—	4	4	no	—
52	C₂×C₁₀₁	#120	1	1	yes	characteristic
53	C₂×C₁₀₁	#121	1	1	yes	characteristic
54	C₂×C₁₀₁	#121	1	2	yes	—
55	C₂×C₁₀₁	#123	1	2	yes	—
56	C₂×C₁₀₁	#124	1	1	yes	characteristic
57	C₁₀₁	#394	1	1	yes	characteristic, complemented, Sylow
58	#394	—	101	1	no	maximal, Sylow
59	C₂²×D₄	D₁₀₁	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	101	1	no	—
61	C₂×C₂²⋊C₄	—	101	2	no	—
62	C₂×C₂²⋊C₄	—	101	2	no	—
63	#95	—	101	1	no	—
64	C₂⁴	C₂×D₁₀₁	1	2	yes	—
65	C₂×D₄	—	2	4	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂²×C₄	—	101	1	no	—
68	C₂²×C₄	—	101	2	no	—
69	C₂²×C₄	—	101	1	no	—
70	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
71	C₄⋊C₄	—	202	2	no	—
72	C₂²⋊C₄	—	202	4	no	—
73	C₂²⋊C₄	—	202	4	no	—
74	C₂³	—	2	2	no	—
75	C₂³	—	2	2	no	—
76	C₂³	—	2	2	no	—
77	C₂³	—	2	2	no	—
78	C₂³	—	2	2	no	—
79	C₂³	—	2	2	no	—
80	C₂³	C₂²⋊D₁₀₁	1	4	yes	—
81	C₂³	C₂²×D₁₀₁	1	1	yes	characteristic
82	D₄	—	2	8	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	101	2	no	—
85	C₂×C₄	—	202	2	no	—
86	C₂×C₄	—	202	2	no	—
87	C₂×C₄	—	202	2	no	—
88	C₂×C₄	—	202	1	no	—
89	C₂×C₄	—	202	2	no	—
90	C₂×C₄	—	202	1	no	—
91	C₂×C₄	—	202	1	no	—
92	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
93	C₂²	—	2	4	no	—
94	C₂²	—	2	4	no	—
95	C₂²	—	2	4	no	—
96	C₂²	—	4	2	no	—
97	C₂²	—	4	2	no	—
98	C₂²	—	4	2	no	—
99	C₂²	—	4	2	no	—
100	C₂²	D₄×D₁₀₁	1	1	yes	characteristic
101	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
102	C₂²	C₂×C₂²⋊D₁₀₁	1	2	yes	—
103	C₂²	#13108073	1	1	yes	characteristic
104	C₂²	#13108073	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	404	1	no	—
107	C₄	—	404	2	no	—
108	C₄	—	202	2	no	—
109	C₂	—	4	4	no	—
110	C₂	#15692224	1	1	yes	characteristic
111	C₂	#15692226	1	1	yes	characteristic
112	C₂	#15692227	1	2	yes	—
113	C₂	#15692236	1	2	yes	—
114	C₂	#15692242	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13108053

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊Dic₁₀₁

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₁₀₁

C₂

yes

maximal, complemented

#15692162

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₁₀₁

C₂

yes

maximal, characteristic

C₂²×Dic₁₀₁

C₂²

yes

—

C₂²×Dic₁₀₁

C₂²

yes

characteristic

C₂²×Dic₁₀₁

C₂²

yes

characteristic

#13108053

—

C₂²⋊Dic₁₀₁

—

C₂²⋊Dic₁₀₁

—

C₂⁴×C₁₀₁

C₂²

yes

—

C₂×D₄×C₁₀₁

—

C₂×D₄×C₁₀₁

—

C₂²×C₄×C₁₀₁

C₂²

yes

characteristic

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

D₄

yes

—

C₂³×C₁₀₁

C₂³

yes

characteristic

D₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

D₄

yes

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

D₄

yes

complemented

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

C₂×D₄

yes

characteristic

C₂²×C₁₀₁

C₂×D₄

yes

—

C₂²×C₁₀₁

C₂×D₄

yes

C₂²×C₁₀₁

yes

C₂²×C₁₀₁

yes

—

C₄×C₁₀₁

—

Dic₁₀₁

—

Dic₁₀₁

—

Dic₁₀₁

—

C₂×C₁₀₁

—

C₂×C₁₀₁

yes

C₂×C₁₀₁

yes

C₂×C₁₀₁

yes

—

C₂×C₁₀₁

#123

yes

—

C₂×C₁₀₁

#124

yes

characteristic

C₁₀₁

#394

yes

characteristic, complemented, Sylow

#394

—

101

maximal, Sylow

C₂²×D₄

D₁₀₁

yes

characteristic

C₂×C₄⋊C₄

—

101

—

C₂×C₂²⋊C₄

—

101

—

C₂×C₂²⋊C₄

—

101

—

#95

—

101

—

C₂⁴

C₂×D₁₀₁

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

C₂×D₁₀₁

yes

characteristic

C₄⋊C₄

—

202

—

C₂²⋊C₄

—

202

—

C₂²⋊C₄

—

202

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊D₁₀₁

yes

—

C₂³

C₂²×D₁₀₁

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

101

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

C₂²⋊D₁₀₁

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

D₄×D₁₀₁

yes

characteristic

101

C₂²

C₂×C₂²⋊D₁₀₁

yes

characteristic

102

C₂²

C₂×C₂²⋊D₁₀₁

yes

—

103

C₂²

#13108073

yes

characteristic

104

C₂²

#13108073

yes

—

105

C₄

—

106

C₄

—

404

—

107

C₄

—

404

—

108

C₄

—

202

—

109

C₂

—

110

C₂

#15692224

yes

characteristic

111

C₂

#15692226

yes

characteristic

112

C₂

#15692227

yes

—

113

C₂

#15692236

yes

—

114

C₂

#15692242

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₁
commutator, socle	C₂³×C₁₀₁	C₂³
Fitting	C₂²×D₄×C₁₀₁	C₂
hypercenter	C₂²×D₄	D₁₀₁
hypocenter	C₁₀₁	#394
LCS	G ▷ C₂³×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₀₁

commutator, socle

C₂³×C₁₀₁

C₂³

Fitting

C₂²×D₄×C₁₀₁

C₂

hypercenter

C₂²×D₄

D₁₀₁

C₁₀₁

G ▷ C₂³×C₁₀₁ ▷ C₁₀₁

C₁ ◁ C₂³ ◁ C₂²×D₄

N	H ≅ G/N	type
1. C₂×#13108053	C₂	semidirect
2. C₂×C₂²⋊Dic₁₀₁	C₂	semidirect
3. C₂×C₂²⋊Dic₁₀₁	C₂	semidirect
4. #15692162	C₂	semidirect
34. C₂×Dic₁₀₁	D₄	semidirect
57. C₁₀₁	#394	semidirect

H ≅ G/N

type

1. C₂×#13108053

C₂

semidirect

2. C₂×C₂²⋊Dic₁₀₁

C₂

semidirect

3. C₂×C₂²⋊Dic₁₀₁

C₂

semidirect

4. #15692162

C₂

semidirect

34. C₂×Dic₁₀₁

D₄

semidirect

57. C₁₀₁

#394

semidirect

Subgroups — #20265091

Conjugacy classes of subgroups

Complements