Group #20245096 — subgroups

Subgroups — #20245096

Order 6016.

228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094046	C₂	1	1	yes	maximal, characteristic
2	#15689161	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688928	C₂	1	2	yes	maximal, complemented
4	#15688925	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625350	—	2	1	no	—
7	#13094046	—	2	2	no	—
8	#13094046	C₄	1	4	yes	complemented
9	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#10625325	—	2	1	no	—
11	C₂×D₃₇₆	C₂²	1	1	yes	characteristic
12	#13093983	—	2	1	no	—
13	#13093958	C₂²	1	2	yes	—
14	#13093956	—	2	1	no	—
15	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₄₇	—	2	2	no	—
17	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₂²⋊D₄₇	—	4	1	no	—
20	#10625350	—	2	4	no	—
21	#10625350	—	4	2	no	—
22	C₂×D₁₈₈	—	2	1	no	—
23	C₂×C₄×D₄₇	—	4	1	no	—
24	C₂×Dic₉₄	—	2	1	no	—
25	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
27	C₂×C₈×C₄₇	D₄	1	2	yes	—
28	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
29	C₂²⋊Dic₄₇	—	4	1	no	—
30	C₄⋊Dic₄₇	—	2	2	no	—
31	C₄×Dic₄₇	—	4	1	no	—
32	Dic₁₈₈	—	2	1	no	—
33	Dic₁₈₈	C₂×C₄	1	2	yes	—
34	D₃₇₆	—	2	1	no	—
35	D₃₇₆	C₂×C₄	1	2	yes	—
36	#10625325	—	2	4	no	—
37	C₁₆×C₄₇	—	2	2	no	—
38	C₂³×C₄₇	D₈	1	1	yes	characteristic
39	C₂²×D₄₇	—	4	1	no	—
40	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
42	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
43	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₂²⋊D₄₇	—	4	4	no	—
45	C₂×Dic₄₇	—	4	1	no	—
46	C₂×Dic₄₇	—	4	2	no	—
47	D₁₈₈	—	2	2	no	—
48	D₁₈₈	—	4	1	no	—
49	C₄×D₄₇	—	4	4	no	—
50	Dic₉₄	—	2	2	no	—
51	Dic₉₄	—	4	1	no	—
52	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
53	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄₇	—	2	2	no	—
56	C₂²×C₄₇	#102	1	2	yes	—
57	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
58	C₂×D₄₇	—	4	2	no	—
59	C₂×D₄₇	—	8	2	no	—
60	C₄×C₄₇	#102	1	2	yes	—
61	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
62	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
63	Dic₄₇	—	4	2	no	—
64	Dic₄₇	—	8	2	no	—
65	#2138	—	47	1	no	maximal, Sylow
66	C₂×C₄₇	—	2	2	no	—
67	C₂×C₄₇	C₂×#102	1	1	yes	characteristic
68	C₂×C₄₇	#508	1	2	yes	—
69	D₄₇	—	8	2	no	—
70	C₂×#135	—	47	1	no	—
71	C₂²×C₁₆	D₄₇	1	1	yes	characteristic, complemented
72	#427	—	47	1	no	—
73	#358	—	47	2	no	—
74	#357	—	47	2	no	—
75	C₄₇	#2138	1	1	yes	characteristic, complemented, Sylow
76	C₂×#41	—	94	1	no	—
77	#135	—	47	4	no	—
78	#135	—	94	2	no	—
79	C₂×Q₁₆	—	47	1	no	—
80	C₂×SD₁₆	—	94	1	no	—
81	C₂×D₈	—	47	1	no	—
82	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
83	#117	—	94	1	no	—
84	C₂×C₁₆	—	2	2	no	—
85	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
86	#107	—	47	2	no	—
87	#106	—	94	1	no	—
88	#41	—	94	4	no	—
89	#41	—	188	2	no	—
90	C₂×Q₈	—	94	1	no	—
91	C₂×D₄	—	94	1	no	—
92	C₂×D₄	—	188	1	no	—
93	C₂²×C₄	—	188	1	no	—
94	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
95	Q₁₆	—	47	2	no	—
96	Q₁₆	—	94	1	no	—
97	SD₁₆	—	94	4	no	—
98	D₈	—	47	2	no	—
99	D₈	—	94	1	no	—
100	C₂×C₈	C₄×D₄₇	1	2	yes	—
101	C₂×C₈	D₁₈₈	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
103	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
104	C₄⋊C₄	—	94	2	no	—
105	C₂²⋊C₄	—	188	1	no	—
106	C₄²	—	188	1	no	—
107	C₁₆	—	2	2	no	—
108	C₂³	—	188	1	no	—
109	C₂³	D₃₇₆	1	1	yes	characteristic
110	Q₈	—	94	2	no	—
111	Q₈	—	188	1	no	—
112	D₄	—	94	2	no	—
113	D₄	—	188	4	no	—
114	D₄	—	188	1	no	—
115	C₂×C₄	—	188	2	no	—
116	C₂×C₄	—	188	1	no	—
117	C₂×C₄	—	188	4	no	—
118	C₂×C₄	#10625325	1	2	yes	—
119	C₂×C₄	D₃₇₆	1	1	yes	characteristic
120	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
121	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
122	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
123	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
124	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
125	C₂²	—	2	2	no	—
126	C₂²	—	376	2	no	—
127	C₂²	—	188	2	no	—
128	C₂²	#13093946	1	2	yes	—
129	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
130	C₄	—	376	2	no	—
131	C₄	—	188	2	no	—
132	C₄	#13093946	1	2	yes	—
133	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
134	C₄	C₂×#10625325	1	1	yes	characteristic
135	C₂	—	2	2	no	—
136	C₂	—	376	2	no	—
137	C₂	C₂×#13093946	1	1	yes	characteristic
138	C₂	#15689555	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094046

C₂

yes

maximal, characteristic

#15689161

C₂

yes

maximal, characteristic, complemented

#15688928

C₂

yes

maximal, complemented

#15688925

C₂

yes

maximal, complemented

C₂²×C₁₆×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂×#10625350

—

#13094046

—

#13094046

C₄

yes

complemented

C₂×Dic₁₈₈

C₂²

yes

characteristic

C₂×#10625325

—

C₂×D₃₇₆

C₂²

yes

characteristic

#13093983

—

#13093958

C₂²

yes

—

#13093956

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

#10625350

—

#10625350

—

C₂×D₁₈₈

—

C₂×C₄×D₄₇

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

C₂×C₄

yes

—

D₃₇₆

—

D₃₇₆

C₂×C₄

yes

—

#10625325

—

C₁₆×C₄₇

—

C₂³×C₄₇

D₈

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

#102

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

#102

yes

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2138

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#102

yes

characteristic

C₂×C₄₇

#508

yes

—

D₄₇

—

C₂×#135

—

C₂²×C₁₆

D₄₇

yes

characteristic, complemented

#427

—

#358

—

#357

—

C₄₇

#2138

yes

characteristic, complemented, Sylow

C₂×#41

—

#135

—

#135

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

—

—

188

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

—

188

—

C₂²×C₄

D₁₈₈

yes

characteristic

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

100

C₂×C₈

C₄×D₄₇

yes

—

101

C₂×C₈

D₁₈₈

yes

characteristic

102

C₂×C₈

C₂²⋊D₄₇

yes

—

103

C₂×C₈

C₂²×D₄₇

yes

characteristic

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

188

—

106

C₄²

—

188

—

107

C₁₆

—

108

C₂³

—

188

—

109

C₂³

D₃₇₆

yes

characteristic

110

Q₈

—

111

Q₈

—

188

—

112

D₄

—

113

D₄

—

188

—

114

D₄

—

188

—

115

C₂×C₄

—

188

—

116

C₂×C₄

—

188

—

117

C₂×C₄

—

188

—

118

C₂×C₄

#10625325

yes

—

119

C₂×C₄

D₃₇₆

yes

characteristic

120

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

121

C₂×C₄

C₂×D₁₈₈

yes

characteristic

122

C₈

(C₂×D₄₇)⋊C₄

yes

—

123

C₈

C₂×C₄×D₄₇

yes

characteristic

124

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

125

C₂²

—

126

C₂²

—

376

—

127

C₂²

—

188

—

128

C₂²

#13093946

yes

—

129

C₂²

C₂×D₃₇₆

yes

characteristic

130

C₄

—

376

—

131

C₄

—

188

—

132

C₄

#13093946

yes

—

133

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

134

C₄

C₂×#10625325

yes

characteristic

135

C₂

—

136

C₂

—

376

—

137

C₂

C₂×#13093946

yes

characteristic

138

C₂

#15689555

yes

—

	subgroup	G/H
center	C₂×C₄	D₃₇₆
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	#2138
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂×C₄

D₃₇₆

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂²×C₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂²×C₁₆

D₄₇

hypocenter

C₄₇

#2138

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
2. #15689161	C₂	semidirect
3. #15688928	C₂	semidirect
4. #15688925	C₂	semidirect
5. C₂²×C₁₆×C₄₇	C₂	semidirect
8. #13094046	C₄	semidirect
71. C₂²×C₁₆	D₄₇	semidirect
75. C₄₇	#2138	semidirect

H ≅ G/N

type

2. #15689161

C₂

semidirect

3. #15688928

C₂

semidirect

4. #15688925

C₂

semidirect

5. C₂²×C₁₆×C₄₇

C₂

semidirect

8. #13094046

C₄

semidirect

71. C₂²×C₁₆

D₄₇

semidirect

75. C₄₇

#2138

semidirect

Subgroups — #20245096

Conjugacy classes of subgroups

Complements