Group #20253919 — subgroups

Subgroups — #20253919

Order 6016.

340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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	#15689751	C₂	1	2	yes	maximal
2	#15689532	C₂	1	4	yes	maximal, complemented
3	#15689525	C₂	1	2	yes	maximal, complemented
4	#15689521	C₂	1	2	yes	maximal, complemented
5	#15689165	C₂	1	2	yes	maximal
6	#15689161	C₂	1	1	yes	maximal, characteristic
7	C₂×#13093956	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#405	C₂	1	1	yes	maximal, characteristic
9	#13094024	C₂²	1	4	yes	—
10	#13094023	—	2	2	no	—
11	#13094016	C₂²	1	4	yes	—
12	#13094015	—	2	2	no	—
13	#13094001	—	2	4	no	—
14	#13093983	C₂²	1	2	yes	—
15	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
16	#13093958	C₂²	1	4	yes	—
17	#13093958	C₂²	1	2	yes	—
18	#13093956	C₂²	1	1	yes	characteristic
19	#13093956	C₂²	1	2	yes	—
20	#13093956	C₂²	1	4	yes	—
21	#13093956	C₂²	1	1	yes	characteristic
22	#13093956	C₂²	1	2	yes	—
23	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	#117×C₄₇	C₂²	1	1	yes	characteristic
26	#97×C₄₇	C₂²	1	2	yes	—
27	C₄×C₈×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂²×Dic₄₇	—	2	2	no	—
30	C₂×Dic₉₄	—	2	4	no	—
31	M₁₆×C₄₇	Q₈	1	4	yes	complemented
32	C₂×C₈×C₄₇	Q₈	1	4	yes	complemented
33	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₄₇	C₂³	1	2	yes	—
36	C₄⋊C₄×C₄₇	D₄	1	2	yes	—
37	C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
38	C₄²×C₄₇	C₂³	1	2	yes	—
39	C₂²⋊Dic₄₇	—	2	2	no	—
40	C₄⋊Dic₄₇	—	2	2	no	—
41	C₄⋊Dic₄₇	—	2	4	no	—
42	C₄⋊Dic₄₇	C₂³	1	4	yes	—
43	C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	Dic₄₇⋊C₄	—	2	4	no	—
46	Dic₄₇⋊C₄	—	2	4	no	—
47	C₄×Dic₄₇	—	2	2	no	—
48	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
50	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
52	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
53	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
54	C₂×Dic₄₇	—	2	2	no	—
55	C₂×Dic₄₇	—	2	2	no	—
56	C₂×Dic₄₇	—	2	4	no	—
57	C₂×Dic₄₇	—	8	2	no	—
58	Dic₉₄	—	8	4	no	—
59	C₈×C₄₇	C₂×Q₈	1	2	yes	—
60	C₈×C₄₇	C₂×Q₈	1	2	yes	—
61	C₈×C₄₇	C₂×Q₈	1	4	yes	—
62	C₂²×C₄₇	—	2	2	no	—
63	C₂²×C₄₇	C₄⋊Q₈	1	2	yes	—
64	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
65	C₄×C₄₇	—	2	4	no	—
66	C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
67	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
68	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
69	Dic₄₇	—	4	2	no	—
70	Dic₄₇	—	4	4	no	—
71	Dic₄₇	—	4	2	no	—
72	#3163	—	47	1	no	maximal, Sylow
73	C₂×C₄₇	—	2	2	no	—
74	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄₇	#577	1	2	yes	—
76	#544	—	47	2	no	—
77	#501	—	47	4	no	—
78	#499	—	47	2	no	—
79	#498	—	47	2	no	—
80	#428	—	47	2	no	—
81	#427	—	47	1	no	—
82	C₂×#106	—	47	1	no	—
83	#405	D₄₇	1	1	yes	characteristic
84	C₄₇	#3163	1	1	yes	characteristic, complemented, Sylow
85	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
86	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
87	C₄⋊Q₈	—	47	4	no	—
88	C₄⋊Q₈	—	94	2	no	—
89	#125	—	47	4	no	—
90	#125	—	94	2	no	—
91	C₂²⋊Q₈	—	94	4	no	—
92	#117	—	47	2	no	—
93	#117	C₂×D₄₇	1	1	yes	characteristic
94	C₂×C₄⋊C₄	—	47	2	no	—
95	#107	—	47	2	no	—
96	#107	—	47	4	no	—
97	#106	—	47	2	no	—
98	#106	—	47	2	no	—
99	#106	—	47	1	no	—
100	#106	—	47	1	no	—
101	#106	—	47	4	no	—
102	#97	C₂×D₄₇	1	2	yes	—
103	C₄×C₈	C₂×D₄₇	1	2	yes	—
104	C₂×Q₈	—	94	4	no	—
105	C₂²×C₄	—	94	2	no	—
106	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
107	M₁₆	Dic₉₄	1	4	yes	complemented
108	C₂×C₈	Dic₉₄	1	4	yes	complemented
109	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
110	C₂×C₈	C₂²×D₄₇	1	2	yes	—
111	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
112	C₄⋊C₄	—	47	4	no	—
113	C₄⋊C₄	—	47	2	no	—
114	C₄⋊C₄	—	47	2	no	—
115	C₄⋊C₄	—	94	4	no	—
116	C₄⋊C₄	—	94	4	no	—
117	C₄⋊C₄	—	94	2	no	—
118	C₄⋊C₄	—	94	4	no	—
119	C₄⋊C₄	D₁₈₈	1	2	yes	—
120	C₂²⋊C₄	—	94	2	no	—
121	C₂²⋊C₄	D₁₈₈	1	2	yes	—
122	C₄²	—	94	2	no	—
123	C₄²	C₂²×D₄₇	1	2	yes	—
124	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
125	Q₈	—	376	4	no	—
126	C₂×C₄	—	94	2	no	—
127	C₂×C₄	—	94	2	no	—
128	C₂×C₄	—	94	4	no	—
129	C₂×C₄	—	376	2	no	—
130	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
131	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
132	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
133	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
134	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
135	C₈	C₂×Dic₉₄	1	2	yes	—
136	C₈	C₂×Dic₉₄	1	2	yes	—
137	C₈	C₂×Dic₉₄	1	4	yes	—
138	C₂²	—	2	2	no	—
139	C₂²	#13094024	1	2	yes	—
140	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
141	C₄	—	2	4	no	—
142	C₄	—	188	4	no	—
143	C₄	—	188	2	no	—
144	C₄	—	188	2	no	—
145	C₄	#13094024	1	2	yes	—
146	C₄	C₂²×Dic₉₄	1	1	yes	characteristic
147	C₄	C₂²×Dic₉₄	1	1	yes	characteristic
148	C₂	—	2	2	no	—
149	C₂	C₂×#13094024	1	1	yes	characteristic
150	C₂	#15689935	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689751

C₂

yes

maximal

#15689532

C₂

yes

maximal, complemented

#15689525

C₂

yes

maximal, complemented

#15689521

C₂

yes

maximal, complemented

#15689165

C₂

yes

maximal

#15689161

C₂

yes

maximal, characteristic

C₂×#13093956

C₂

yes

maximal, characteristic

C₄₇×#405

C₂

yes

maximal, characteristic

#13094024

C₂²

yes

—

#13094023

—

#13094016

C₂²

yes

—

#13094015

—

#13094001

—

#13093983

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093958

C₂²

yes

—

#13093958

C₂²

yes

—

#13093956

C₂²

yes

characteristic

#13093956

C₂²

yes

—

#13093956

C₂²

yes

—

#13093956

C₂²

yes

characteristic

#13093956

C₂²

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#117×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

M₁₆×C₄₇

Q₈

yes

complemented

C₂×C₈×C₄₇

Q₈

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

D₄

yes

—

C₂²⋊C₄×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

—

C₈×C₄₇

C₂×Q₈

yes

—

C₈×C₄₇

C₂×Q₈

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

C₄⋊Q₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

C₂²×Q₈

yes

characteristic

C₄×C₄₇

C₂²×Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#3163

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

#577

yes

—

—

—

—

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#3163

yes

characteristic, complemented, Sylow

C₂×M₁₆

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₂²⋊Q₈

—

#117

—

#117

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

—

—

—

—

—

100

#106

—

101

#106

—

102

#97

C₂×D₄₇

yes

—

103

C₄×C₈

C₂×D₄₇

yes

—

104

C₂×Q₈

—

105

C₂²×C₄

—

106

C₂²×C₄

C₂²×D₄₇

yes

characteristic

107

M₁₆

Dic₉₄

yes

complemented

108

C₂×C₈

Dic₉₄

yes

complemented

109

C₂×C₈

C₂²×D₄₇

yes

characteristic

110

C₂×C₈

C₂²×D₄₇

yes

—

111

C₂×C₈

C₂²×D₄₇

yes

characteristic

112

C₄⋊C₄

—

113

C₄⋊C₄

—

114

C₄⋊C₄

—

115

C₄⋊C₄

—

116

C₄⋊C₄

—

117

C₄⋊C₄

—

118

C₄⋊C₄

—

119

C₄⋊C₄

D₁₈₈

yes

—

120

C₂²⋊C₄

—

121

C₂²⋊C₄

D₁₈₈

yes

—

122

C₄²

—

123

C₄²

C₂²×D₄₇

yes

—

124

C₂³

C₂×D₁₈₈

yes

characteristic

125

Q₈

—

376

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

376

—

130

C₂×C₄

C₂×Dic₉₄

yes

—

131

C₂×C₄

C₂×Dic₉₄

yes

—

132

C₂×C₄

C₂×D₁₈₈

yes

—

133

C₂×C₄

C₂×D₁₈₈

yes

characteristic

134

C₂×C₄

C₂³×D₄₇

yes

characteristic

135

C₈

C₂×Dic₉₄

yes

—

136

C₈

C₂×Dic₉₄

yes

—

137

C₈

C₂×Dic₉₄

yes

—

138

C₂²

—

139

C₂²

#13094024

yes

—

140

C₂²

C₂²×D₁₈₈

yes

characteristic

141

C₄

—

142

C₄

—

188

—

143

C₄

—

188

—

144

C₄

—

188

—

145

C₄

#13094024

yes

—

146

C₄

C₂²×Dic₉₄

yes

characteristic

147

C₄

C₂²×Dic₉₄

yes

characteristic

148

C₂

—

149

C₂

C₂×#13094024

yes

characteristic

150

C₂

#15689935

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#405	D₄₇
hypocenter	C₄₇	#3163
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

subgroup

G/H

center

C₂²

C₂²×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₄₇×#405

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ #117 ◁ #405

N	H ≅ G/N	type
2. #15689532	C₂	semidirect
3. #15689525	C₂	semidirect
4. #15689521	C₂	semidirect
31. M₁₆×C₄₇	Q₈	semidirect
32. C₂×C₈×C₄₇	Q₈	semidirect
84. C₄₇	#3163	semidirect
107. M₁₆	Dic₉₄	semidirect
108. C₂×C₈	Dic₉₄	semidirect

H ≅ G/N

type

2. #15689532

C₂

semidirect

3. #15689525

C₂

semidirect

4. #15689521

C₂

semidirect

31. M₁₆×C₄₇

Q₈

semidirect

32. C₂×C₈×C₄₇

Q₈

semidirect

84. C₄₇

#3163

semidirect

107. M₁₆

Dic₉₄

semidirect

108. C₂×C₈

Dic₉₄

semidirect

Subgroups — #20253919

Conjugacy classes of subgroups

Complements