Group #20245740 — subgroups

Subgroups — #20245740

Order 6016.

912 conjugacy classes of subgroups; only the 325 normal subgroups are shown.

normal subgroups only

This group has 912 conjugacy classes of subgroups — too many to draw. Only its 325 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×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊C₄×D₄₇	C₂	1	2	yes	maximal
3	C₂²⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	C₄×(C₂×D₄₇)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688970	C₂	1	4	yes	maximal, complemented
7	C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄×D₄₇	C₂²	1	4	yes	—
11	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
12	C₂×(C₂×D₄₇)⋊C₄	C₄	1	8	yes	complemented
13	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
14	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
15	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
16	C₂²⋊C₄×D₄₇	C₄	1	16	yes	complemented
17	C₂×C₄×Dic₄₇	C₂²	1	2	yes	complemented
18	C₂×C₄×Dic₄₇	C₂²	1	4	yes	complemented
19	C₄₇⋊#95	C₂²	1	4	yes	complemented
20	C₄₇⋊#95	C₂²	1	2	yes	complemented
21	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂×C₄²×C₄₇	C₂²	1	2	yes	complemented
24	#95×C₄₇	C₂²	1	2	yes	complemented
25	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
26	C₂³×D₄₇	—	4	2	no	—
27	C₂³×D₄₇	—	4	2	no	—
28	C₂³×D₄₇	C₂×C₄	1	8	yes	—
29	C₂³×D₄₇	C₂×C₄	1	4	yes	—
30	C₂³×D₄₇	C₂³	1	2	yes	—
31	C₂²×C₄×C₄₇	—	4	2	no	—
32	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
33	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
35	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₇	—	4	2	no	—
37	C₂²×Dic₄₇	C₂×C₄	1	4	yes	complemented
38	C₂²×Dic₄₇	C₂³	1	2	yes	—
39	C₂²×Dic₄₇	C₂³	1	4	yes	—
40	C₂×C₄×D₄₇	—	4	4	no	—
41	C₂×C₄×D₄₇	—	4	4	no	—
42	C₂×C₄×D₄₇	C₂×C₄	1	16	yes	complemented
43	C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
44	C₄²×C₄₇	—	4	2	no	—
45	C₂²⋊Dic₄₇	C₂×C₄	1	8	yes	complemented
46	(C₂×D₄₇)⋊C₄	C₂×C₄	1	16	yes	complemented
47	(C₂×D₄₇)⋊C₄	C₂×C₄	1	8	yes	complemented
48	(C₂×D₄₇)⋊C₄	C₂×C₄	1	8	yes	complemented
49	C₄×Dic₄₇	—	4	2	no	—
50	C₄×Dic₄₇	—	4	4	no	—
51	C₂³×C₄₇	—	2	2	no	—
52	C₂³×C₄₇	—	2	2	no	—
53	C₂³×C₄₇	C₂²×C₄	1	4	yes	—
54	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
55	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
56	C₂²×D₄₇	—	2	4	no	—
57	C₂²×D₄₇	—	2	4	no	—
58	C₂²×D₄₇	—	4	16	no	—
59	C₂²×D₄₇	—	4	4	no	—
60	C₂²×D₄₇	—	4	4	no	—
61	C₂²×D₄₇	C₄²	1	16	yes	complemented
62	C₂²×D₄₇	C₂²×C₄	1	4	yes	—
63	C₂²×D₄₇	C₂²×C₄	1	4	yes	—
64	C₂²×D₄₇	C₂²×C₄	1	4	yes	—
65	C₂×C₄×C₄₇	—	2	4	no	—
66	C₂×C₄×C₄₇	—	2	2	no	—
67	C₂×C₄×C₄₇	—	2	4	no	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	4	4	no	—
70	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
73	C₂×Dic₄₇	—	2	4	no	—
74	C₂×Dic₄₇	—	2	4	no	—
75	C₂×Dic₄₇	—	2	4	no	—
76	C₂×Dic₄₇	—	4	4	no	—
77	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
78	C₂×Dic₄₇	C₂²×C₄	1	8	yes	—
79	C₄×D₄₇	—	4	16	no	—
80	C₂²×C₄₇	—	2	2	no	—
81	C₂²×C₄₇	—	2	2	no	—
82	C₂²×C₄₇	—	2	8	no	—
83	C₂²×C₄₇	C₂×C₄²	1	4	yes	—
84	C₂²×C₄₇	C₂³×C₄	1	2	yes	—
85	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
86	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
87	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
88	C₂×D₄₇	—	2	8	no	—
89	C₂×D₄₇	—	2	8	no	—
90	C₂×D₄₇	—	2	4	no	—
91	C₂×D₄₇	—	2	4	no	—
92	C₂×D₄₇	—	4	16	no	—
93	C₂×D₄₇	C₂×C₄²	1	8	yes	—
94	C₄×C₄₇	—	2	8	no	—
95	C₄×C₄₇	—	2	2	no	—
96	C₄×C₄₇	—	2	2	no	—
97	Dic₄₇	—	2	8	no	—
98	Dic₄₇	—	2	4	no	—
99	#2273	—	47	1	no	maximal, Sylow
100	C₂×C₄₇	—	2	4	no	—
101	C₂×C₄₇	C₂²×C₄²	1	1	yes	characteristic
102	C₂×C₄₇	#518	1	4	yes	—
103	C₂×C₄₇	#518	1	1	yes	characteristic
104	C₂×C₄₇	#518	1	1	yes	characteristic
105	D₄₇	—	2	8	no	—
106	C₂²×C₂²⋊C₄	—	47	1	no	—
107	C₂²×C₂²⋊C₄	—	47	2	no	—
108	C₄×C₂²⋊C₄	—	47	1	no	—
109	C₄×C₂²⋊C₄	—	47	2	no	—
110	C₄×C₂²⋊C₄	—	47	4	no	—
111	C₄×C₂²⋊C₄	—	47	4	no	—
112	C₄×C₂²⋊C₄	D₄₇	1	1	yes	characteristic, complemented
113	C₄₇	#2273	1	1	yes	characteristic, complemented, Sylow
114	C₂⁵	—	47	1	no	—
115	C₂³×C₄	—	47	1	no	—
116	C₂³×C₄	—	47	4	no	—
117	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
118	C₂×C₂²⋊C₄	—	47	2	no	—
119	C₂×C₂²⋊C₄	—	47	8	no	—
120	C₂×C₂²⋊C₄	—	47	2	no	—
121	C₂×C₂²⋊C₄	—	47	4	no	—
122	C₂×C₂²⋊C₄	—	47	2	no	—
123	C₂×C₂²⋊C₄	—	47	16	no	—
124	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
125	C₂×C₄²	—	47	4	no	—
126	C₂×C₄²	—	47	2	no	—
127	C₂×C₄²	C₂×D₄₇	1	2	yes	complemented
128	#95	—	47	2	no	—
129	#95	—	47	4	no	—
130	#95	C₂×D₄₇	1	2	yes	complemented
131	C₂⁴	—	47	2	no	—
132	C₂⁴	—	47	4	no	—
133	C₂⁴	—	47	8	no	—
134	C₂⁴	—	188	2	no	—
135	C₂⁴	—	188	2	no	—
136	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	—	47	4	no	—
139	C₂²×C₄	—	47	2	no	—
140	C₂²×C₄	—	47	4	no	—
141	C₂²×C₄	—	47	16	no	—
142	C₂²×C₄	—	188	4	no	—
143	C₂²×C₄	—	188	4	no	—
144	C₂²×C₄	—	188	2	no	—
145	C₂²×C₄	C₄×D₄₇	1	4	yes	complemented
146	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
147	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
148	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
149	C₂²⋊C₄	—	47	8	no	—
150	C₂²⋊C₄	—	47	8	no	—
151	C₂²⋊C₄	—	47	8	no	—
152	C₂²⋊C₄	—	47	16	no	—
153	C₂²⋊C₄	C₄×D₄₇	1	8	yes	complemented
154	C₄²	—	4	2	no	—
155	C₄²	—	188	2	no	—
156	C₄²	—	188	4	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	2	no	—
159	C₂³	—	47	4	no	—
160	C₂³	—	47	4	no	—
161	C₂³	—	47	4	no	—
162	C₂³	—	47	16	no	—
163	C₂³	—	94	4	no	—
164	C₂³	—	94	4	no	—
165	C₂³	—	188	16	no	—
166	C₂³	—	188	4	no	—
167	C₂³	—	188	4	no	—
168	C₂³	C₂×C₄×D₄₇	1	4	yes	—
169	C₂³	C₂×C₄×D₄₇	1	2	yes	—
170	C₂³	C₂³×D₄₇	1	1	yes	characteristic
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	47	8	no	—
177	C₂×C₄	—	47	4	no	—
178	C₂×C₄	—	94	4	no	—
179	C₂×C₄	—	94	4	no	—
180	C₂×C₄	—	94	4	no	—
181	C₂×C₄	—	188	16	no	—
182	C₂×C₄	—	188	4	no	—
183	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
184	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
185	C₂×C₄	C₂×C₄×D₄₇	1	8	yes	—
186	C₂²	—	2	8	no	—
187	C₂²	—	2	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	47	8	no	—
190	C₂²	—	94	8	no	—
191	C₂²	—	94	8	no	—
192	C₂²	—	94	4	no	—
193	C₂²	—	94	4	no	—
194	C₂²	—	188	16	no	—
195	C₂²	C₄²×D₄₇	1	4	yes	—
196	C₂²	C₂²×C₄×D₄₇	1	2	yes	—
197	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
198	C₂²	#13094069	1	2	yes	—
199	C₂²	#13094070	1	2	yes	—
200	C₄	—	2	8	no	—
201	C₄	—	2	2	no	—
202	C₄	—	2	2	no	—
203	C₄	—	94	8	no	—
204	C₄	—	94	4	no	—
205	C₂	—	2	4	no	—
206	C₂	—	94	8	no	—
207	C₂	C₂×C₄²×D₄₇	1	1	yes	characteristic
208	C₂	#15689595	1	4	yes	—
209	C₂	#15689596	1	1	yes	characteristic
210	C₂	#15689597	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×(C₂×D₄₇)⋊C₄

C₂

yes

maximal, characteristic

C₂×C₂²⋊C₄×D₄₇

C₂

yes

maximal

C₂²⋊C₄×Dic₄₇

C₂

yes

maximal, complemented

C₄×(C₂×D₄₇)⋊C₄

C₂

yes

maximal, complemented

C₄×C₂²⋊Dic₄₇

C₂

yes

maximal, characteristic, complemented

#15688970

C₂

yes

maximal, complemented

C₄×C₂²⋊C₄×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₄

yes

complemented

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₇)⋊C₄

C₂²

yes

—

C₂²⋊C₄×D₄₇

C₄

yes

complemented

C₂×C₄×Dic₄₇

C₂²

yes

complemented

C₂×C₄×Dic₄₇

C₂²

yes

complemented

C₄₇⋊#95

C₂²

yes

complemented

C₄₇⋊#95

C₂²

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

complemented

#95×C₄₇

C₂²

yes

complemented

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

C₂×C₄

yes

—

C₂³×D₄₇

C₂×C₄

yes

—

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

complemented

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

C₂×C₄

yes

complemented

C₂²⋊C₄×C₄₇

C₂×C₄

yes

complemented

C₄²×C₄₇

—

C₂²⋊Dic₄₇

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₄²

yes

complemented

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₄×D₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄²

yes

—

C₂²×C₄₇

C₂³×C₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂²×C₄₇

H(5,𝔽₂)

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

C₂×C₄²

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

—

#2273

—

maximal, Sylow

100

C₂×C₄₇

—

101

C₂×C₄₇

C₂²×C₄²

yes

characteristic

102

C₂×C₄₇

#518

yes

—

103

C₂×C₄₇

#518

yes

characteristic

104

C₂×C₄₇

#518

yes

characteristic

105

D₄₇

—

106

C₂²×C₂²⋊C₄

—

107

C₂²×C₂²⋊C₄

—

108

C₄×C₂²⋊C₄

—

109

C₄×C₂²⋊C₄

—

110

C₄×C₂²⋊C₄

—

111

C₄×C₂²⋊C₄

—

112

C₄×C₂²⋊C₄

D₄₇

yes

characteristic, complemented

113

C₄₇

#2273

yes

characteristic, complemented, Sylow

114

C₂⁵

—

115

C₂³×C₄

—

116

C₂³×C₄

—

117

C₂³×C₄

C₂×D₄₇

yes

characteristic

118

C₂×C₂²⋊C₄

—

119

C₂×C₂²⋊C₄

—

120

C₂×C₂²⋊C₄

—

121

C₂×C₂²⋊C₄

—

122

C₂×C₂²⋊C₄

—

123

C₂×C₂²⋊C₄

—

124

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

125

C₂×C₄²

—

126

C₂×C₄²

—

127

C₂×C₄²

C₂×D₄₇

yes

complemented

128

#95

—

129

#95

—

130

#95

C₂×D₄₇

yes

complemented

131

C₂⁴

—

132

C₂⁴

—

133

C₂⁴

—

134

C₂⁴

—

188

—

135

C₂⁴

—

188

—

136

C₂⁴

C₂²×D₄₇

yes

characteristic

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

188

—

143

C₂²×C₄

—

188

—

144

C₂²×C₄

—

188

—

145

C₂²×C₄

C₄×D₄₇

yes

complemented

146

C₂²×C₄

C₂²×D₄₇

yes

characteristic

147

C₂²×C₄

C₂²×D₄₇

yes

—

148

C₂²×C₄

C₂²×D₄₇

yes

characteristic

149

C₂²⋊C₄

—

150

C₂²⋊C₄

—

151

C₂²⋊C₄

—

152

C₂²⋊C₄

—

153

C₂²⋊C₄

C₄×D₄₇

yes

complemented

154

C₄²

—

155

C₄²

—

188

—

156

C₄²

—

188

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

—

165

C₂³

—

188

—

166

C₂³

—

188

—

167

C₂³

—

188

—

168

C₂³

C₂×C₄×D₄₇

yes

—

169

C₂³

C₂×C₄×D₄₇

yes

—

170

C₂³

C₂³×D₄₇

yes

characteristic

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

188

—

182

C₂×C₄

—

188

—

183

C₂×C₄

C₂×C₄×D₄₇

yes

—

184

C₂×C₄

C₂×C₄×D₄₇

yes

—

185

C₂×C₄

C₂×C₄×D₄₇

yes

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

188

—

195

C₂²

C₄²×D₄₇

yes

—

196

C₂²

C₂²×C₄×D₄₇

yes

—

197

C₂²

C₂²×C₄×D₄₇

yes

characteristic

198

C₂²

#13094069

yes

—

199

C₂²

#13094070

yes

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₂

—

206

C₂

—

207

C₂

C₂×C₄²×D₄₇

yes

characteristic

208

C₂

#15689595

yes

—

209

C₂

#15689596

yes

characteristic

210

C₂

#15689597

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂×C₄₇	C₂²×C₄²
Fitting	C₄×C₂²⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₄×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#2273
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂×C₄₇

C₂²×C₄²

Fitting

C₄×C₂²⋊C₄×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₄×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₄×C₂²⋊C₄

N	H ≅ G/N	type
3. C₂²⋊C₄×Dic₄₇	C₂	semidirect
4. C₄×(C₂×D₄₇)⋊C₄	C₂	semidirect
5. C₄×C₂²⋊Dic₄₇	C₂	semidirect
6. #15688970	C₂	semidirect
7. C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
12. C₂×(C₂×D₄₇)⋊C₄	C₄	semidirect
16. C₂²⋊C₄×D₄₇	C₄	semidirect
17. C₂×C₄×Dic₄₇	C₂²	semidirect
18. C₂×C₄×Dic₄₇	C₂²	semidirect
19. C₄₇⋊#95	C₂²	semidirect
20. C₄₇⋊#95	C₂²	semidirect
23. C₂×C₄²×C₄₇	C₂²	semidirect
24. #95×C₄₇	C₂²	semidirect
32. C₂²×C₄×C₄₇	C₂×C₄	semidirect
37. C₂²×Dic₄₇	C₂×C₄	semidirect
42. C₂×C₄×D₄₇	C₂×C₄	semidirect
43. C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
45. C₂²⋊Dic₄₇	C₂×C₄	semidirect
46. (C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
47. (C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
48. (C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
61. C₂²×D₄₇	C₄²	semidirect
112. C₄×C₂²⋊C₄	D₄₇	semidirect
113. C₄₇	#2273	semidirect
127. C₂×C₄²	C₂×D₄₇	semidirect
130. #95	C₂×D₄₇	semidirect
145. C₂²×C₄	C₄×D₄₇	semidirect
153. C₂²⋊C₄	C₄×D₄₇	semidirect

H ≅ G/N

type

3. C₂²⋊C₄×Dic₄₇

C₂

semidirect

4. C₄×(C₂×D₄₇)⋊C₄

C₂

semidirect

5. C₄×C₂²⋊Dic₄₇

C₂

semidirect

6. #15688970

C₂

semidirect

7. C₄×C₂²⋊C₄×C₄₇

C₂

semidirect

12. C₂×(C₂×D₄₇)⋊C₄

C₄

semidirect

16. C₂²⋊C₄×D₄₇

C₄

semidirect

17. C₂×C₄×Dic₄₇

C₂²

semidirect

18. C₂×C₄×Dic₄₇

C₂²

semidirect

19. C₄₇⋊#95

C₂²

semidirect

20. C₄₇⋊#95

C₂²

semidirect

23. C₂×C₄²×C₄₇

C₂²

semidirect

24. #95×C₄₇

C₂²

semidirect

32. C₂²×C₄×C₄₇

C₂×C₄

semidirect

37. C₂²×Dic₄₇

C₂×C₄

semidirect

42. C₂×C₄×D₄₇

C₂×C₄

semidirect

43. C₂²⋊C₄×C₄₇

C₂×C₄

semidirect

45. C₂²⋊Dic₄₇

C₂×C₄

semidirect

46. (C₂×D₄₇)⋊C₄

C₂×C₄

semidirect

47. (C₂×D₄₇)⋊C₄

C₂×C₄

semidirect

48. (C₂×D₄₇)⋊C₄

C₂×C₄

semidirect

61. C₂²×D₄₇

C₄²

semidirect

112. C₄×C₂²⋊C₄

D₄₇

semidirect

113. C₄₇

#2273

semidirect

127. C₂×C₄²

C₂×D₄₇

semidirect

130. #95

C₂×D₄₇

semidirect

145. C₂²×C₄

C₄×D₄₇

semidirect

153. C₂²⋊C₄

C₄×D₄₇

semidirect

Subgroups — #20245740

Conjugacy classes of subgroups

Complements