Group #20246596 — subgroups

Subgroups — #395×D₄₇ #20246596

Order 6016.

908 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 223 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	C₂²×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×D₄₇	C₂	1	3	yes	maximal
3	#15689044	C₂	1	3	yes	maximal, complemented
4	#15689043	C₂	1	3	yes	maximal, complemented
5	#15689042	C₂	1	1	yes	maximal, characteristic, complemented
6	#95×D₄₇	C₂	1	3	yes	maximal
7	C₄₇×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₉₄	C₂²	1	3	yes	—
9	C₂×Q₈×D₄₇	—	2	12	no	—
10	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
12	C₂²×C₄×D₄₇	C₂²	1	3	yes	—
13	C₂×C₄⋊Dic₄₇	C₂²	1	3	yes	—
14	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
15	C₂×Dic₄₇⋊C₄	C₂²	1	3	yes	—
16	C₄⋊C₄×D₄₇	—	2	12	no	—
17	C₄₇⋊#95	C₂²	1	3	yes	—
18	C₄₇⋊#95	C₂²	1	6	yes	—
19	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
21	#95×C₄₇	C₂²	1	3	yes	—
22	C₂³×D₄₇	C₂³	1	1	yes	characteristic
23	C₂×Q₈×C₄₇	—	2	6	no	—
24	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
26	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
27	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
28	C₂²×Dic₄₇	C₂³	1	3	yes	—
29	C₂²×Dic₄₇	C₂³	1	3	yes	—
30	Q₈×D₄₇	—	2	32	no	—
31	C₂×C₄×D₄₇	—	2	6	no	—
32	C₂×C₄×D₄₇	—	2	12	no	—
33	C₂×C₄×D₄₇	—	2	6	no	—
34	C₂×C₄×D₄₇	—	2	6	no	—
35	C₂×C₄×D₄₇	D₄	1	12	yes	—
36	C₂×C₄×D₄₇	Q₈	1	12	yes	complemented
37	C₂×Dic₉₄	—	2	6	no	—
38	C₂×Dic₉₄	—	2	12	no	—
39	C₄⋊C₄×C₄₇	—	2	6	no	—
40	C₄⋊Dic₄₇	—	2	6	no	—
41	Dic₄₇⋊C₄	—	2	6	no	—
42	Dic₄₇⋊C₄	—	2	6	no	—
43	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
44	C₂²×D₄₇	C₂×D₄	1	6	yes	—
45	C₂²×D₄₇	C₂×Q₈	1	6	yes	—
46	C₂²×D₄₇	#41	1	2	yes	—
47	Q₈×C₄₇	—	2	8	no	—
48	C₂×C₄×C₄₇	—	2	3	no	—
49	C₂×C₄×C₄₇	—	2	6	no	—
50	C₂×C₄×C₄₇	—	2	3	no	—
51	C₂×C₄×C₄₇	—	2	3	no	—
52	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
53	C₂×C₄×C₄₇	C₂×Q₈	1	6	yes	complemented
54	C₂×Dic₄₇	—	2	3	no	—
55	C₂×Dic₄₇	—	2	6	no	—
56	C₂×Dic₄₇	—	2	3	no	—
57	C₂×Dic₄₇	—	2	3	no	—
58	C₂×Dic₄₇	C₂×D₄	1	6	yes	—
59	C₂×Dic₄₇	C₂×Q₈	1	6	yes	complemented
60	C₄×D₄₇	—	2	24	no	—
61	C₄×D₄₇	—	2	24	no	—
62	C₄×D₄₇	—	4	4	no	—
63	Dic₉₄	—	2	24	no	—
64	C₂²×C₄₇	C₂²×D₄	1	3	yes	—
65	C₂²×C₄₇	C₂²×Q₈	1	3	yes	—
66	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
67	C₂×D₄₇	#120	1	4	yes	—
68	C₂×D₄₇	C₂²⋊Q₈	1	12	yes	—
69	C₂×D₄₇	C₄⋊Q₈	1	12	yes	—
70	C₄×C₄₇	—	2	6	no	—
71	C₄×C₄₇	—	2	6	no	—
72	C₄×C₄₇	—	4	1	no	—
73	Dic₄₇	—	2	6	no	—
74	Dic₄₇	—	2	6	no	—
75	Dic₄₇	—	4	1	no	—
76	C₂×#395	—	47	1	no	maximal, Sylow
77	C₂×C₄₇	C₂×#120	1	1	yes	characteristic
78	C₂×C₄₇	C₂×C₂²⋊Q₈	1	3	yes	—
79	C₂×C₄₇	C₂×C₄⋊Q₈	1	3	yes	—
80	D₄₇	#395	1	8	yes	direct product factor
81	C₂³×Q₈	—	47	1	no	—
82	C₂²×C₄⋊C₄	—	47	3	no	—
83	#395	—	47	1	no	—
84	#395	—	47	3	no	—
85	#395	—	47	3	no	—
86	#395	D₄₇	1	1	yes	characteristic, direct product factor
87	C₂×#95	—	47	3	no	—
88	C₄₇	C₂×#395	1	1	yes	characteristic, complemented, Sylow
89	C₂²×Q₈	—	47	3	no	—
90	C₂²×Q₈	—	94	12	no	—
91	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
92	C₂³×C₄	—	47	3	no	—
93	C₂³×C₄	—	47	3	no	—
94	C₂³×C₄	—	47	1	no	—
95	C₂×C₄⋊C₄	—	47	3	no	—
96	C₂×C₄⋊C₄	—	47	3	no	—
97	C₂×C₄⋊C₄	—	47	3	no	—
98	C₂×C₄⋊C₄	—	94	12	no	—
99	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
100	#95	—	47	3	no	—
101	#95	—	47	6	no	—
102	#95	C₂×D₄₇	1	3	yes	—
103	C₂⁴	—	47	1	no	—
104	C₂×Q₈	—	2	6	no	—
105	C₂×Q₈	—	94	12	no	—
106	C₂×Q₈	—	94	32	no	—
107	C₂×Q₈	—	94	6	no	—
108	C₂²×C₄	—	47	3	no	—
109	C₂²×C₄	—	47	3	no	—
110	C₂²×C₄	—	47	12	no	—
111	C₂²×C₄	—	47	12	no	—
112	C₂²×C₄	—	47	1	no	—
113	C₂²×C₄	—	94	6	no	—
114	C₂²×C₄	—	94	6	no	—
115	C₂²×C₄	—	94	12	no	—
116	C₂²×C₄	—	94	6	no	—
117	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
118	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
119	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
120	C₄⋊C₄	—	2	6	no	—
121	C₄⋊C₄	—	94	6	no	—
122	C₄⋊C₄	—	94	6	no	—
123	C₄⋊C₄	—	94	6	no	—
124	C₂³	—	47	6	no	—
125	C₂³	—	47	6	no	—
126	C₂³	—	47	2	no	—
127	C₂³	C₂³×D₄₇	1	1	yes	characteristic
128	Q₈	—	2	8	no	—
129	Q₈	—	94	24	no	—
130	C₂×C₄	—	2	3	no	—
131	C₂×C₄	—	2	6	no	—
132	C₂×C₄	—	2	3	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	47	6	no	—
135	C₂×C₄	—	47	6	no	—
136	C₂×C₄	—	94	24	no	—
137	C₂×C₄	—	94	24	no	—
138	C₂×C₄	—	94	3	no	—
139	C₂×C₄	—	94	6	no	—
140	C₂×C₄	—	94	3	no	—
141	C₂×C₄	—	94	3	no	—
142	C₂×C₄	—	188	4	no	—
143	C₂×C₄	D₄×D₄₇	1	6	yes	—
144	C₂×C₄	Q₈×D₄₇	1	6	yes	complemented
145	C₂²	—	47	4	no	—
146	C₂²	—	47	12	no	—
147	C₂²	—	47	12	no	—
148	C₂²	C₂×D₄×D₄₇	1	3	yes	—
149	C₂²	C₂×Q₈×D₄₇	1	3	yes	—
150	C₂²	#41×D₄₇	1	1	yes	characteristic
151	C₄	—	2	6	no	—
152	C₄	—	2	6	no	—
153	C₄	—	4	1	no	—
154	C₄	—	94	6	no	—
155	C₄	—	94	6	no	—
156	C₄	—	188	1	no	—
157	C₂	—	47	8	no	—
158	C₂	#120×D₄₇	1	1	yes	characteristic
159	C₂	C₂²⋊Q₈×D₄₇	1	3	yes	—
160	C₂	C₄⋊Q₈×D₄₇	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₈×D₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×D₄₇

C₂

yes

maximal

#15689044

C₂

yes

maximal, complemented

#15689043

C₂

yes

maximal, complemented

#15689042

C₂

yes

maximal, characteristic, complemented

#95×D₄₇

C₂

yes

maximal

C₄₇×#395

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₉₄

C₂²

yes

—

C₂×Q₈×D₄₇

—

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

—

C₂²×C₄×D₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄⋊C₄×D₄₇

—

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

—

C₂³×D₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

Q₈×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

D₄

yes

—

C₂×C₄×D₄₇

Q₈

yes

complemented

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

C₂×D₄

yes

—

C₂²×D₄₇

C₂×Q₈

yes

—

C₂²×D₄₇

#41

yes

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

complemented

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×Q₈

yes

complemented

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

C₂²×Q₈

yes

—

C₂²×C₄₇

C₂×#41

yes

characteristic

C₂×D₄₇

#120

yes

—

C₂×D₄₇

C₂²⋊Q₈

yes

—

C₂×D₄₇

C₄⋊Q₈

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

—

D₄₇

#395

yes

direct product factor

C₂³×Q₈

—

C₂²×C₄⋊C₄

—

—

—

—

D₄₇

yes

characteristic, direct product factor

C₂×#95

—

C₄₇

C₂×#395

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

100

#95

—

101

#95

—

102

#95

C₂×D₄₇

yes

—

103

C₂⁴

—

104

C₂×Q₈

—

105

C₂×Q₈

—

106

C₂×Q₈

—

107

C₂×Q₈

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

C₂²×D₄₇

yes

characteristic

118

C₂²×C₄

C₂²×D₄₇

yes

—

119

C₂²×C₄

C₂²×D₄₇

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

122

C₄⋊C₄

—

123

C₄⋊C₄

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

C₂³×D₄₇

yes

characteristic

128

Q₈

—

129

Q₈

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

188

—

143

C₂×C₄

D₄×D₄₇

yes

—

144

C₂×C₄

Q₈×D₄₇

yes

complemented

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

C₂×D₄×D₄₇

yes

—

149

C₂²

C₂×Q₈×D₄₇

yes

—

150

C₂²

#41×D₄₇

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

—

156

C₄

—

188

—

157

C₂

—

158

C₂

#120×D₄₇

yes

characteristic

159

C₂

C₂²⋊Q₈×D₄₇

yes

—

160

C₂

C₄⋊Q₈×D₄₇

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄₇×#395	C₂
hypercenter	#395	D₄₇
hypocenter	C₄₇	C₂×#395
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄₇×#395

C₂

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
3. #15689044	C₂	semidirect
4. #15689043	C₂	semidirect
5. #15689042	C₂	semidirect
7. C₄₇×#395	C₂	semidirect
36. C₂×C₄×D₄₇	Q₈	semidirect
53. C₂×C₄×C₄₇	C₂×Q₈	semidirect
59. C₂×Dic₄₇	C₂×Q₈	semidirect
80. D₄₇	#395	direct (N × H)
86. #395	D₄₇	direct (N × H)
88. C₄₇	C₂×#395	semidirect
144. C₂×C₄	Q₈×D₄₇	semidirect

H ≅ G/N

type

3. #15689044

C₂

semidirect

4. #15689043

C₂

semidirect

5. #15689042

C₂

semidirect

7. C₄₇×#395

C₂

semidirect

36. C₂×C₄×D₄₇

Q₈

semidirect

53. C₂×C₄×C₄₇

C₂×Q₈

semidirect

59. C₂×Dic₄₇

C₂×Q₈

semidirect

80. D₄₇

#395

direct (N × H)

86. #395

D₄₇

direct (N × H)

88. C₄₇

C₂×#395

semidirect

144. C₂×C₄

Q₈×D₄₇

semidirect

Subgroups — #395×D₄₇ #20246596

Conjugacy classes of subgroups

Complements

Subgroups — #395×D47 #20246596

Conjugacy classes of subgroups

Complements

Subgroups — #395×D₄₇ #20246596