Group #20246001 — subgroups

Subgroups — #20246001

Order 6016.

816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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	#15688997	C₂	1	4	yes	maximal, complemented
4	#15688994	C₂	1	4	yes	maximal, complemented
5	#15688983	C₂	1	1	yes	maximal, characteristic, complemented
6	#15688981	C₂	1	2	yes	maximal, complemented
7	C₄₇×#380	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×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
12	C₂×Dic₄₇⋊C₄	C₂²	1	4	yes	complemented
13	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂×(C₂×D₄₇)⋊C₄	C₄	1	8	yes	complemented
15	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
16	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
17	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
18	C₂²⋊C₄×D₄₇	—	2	8	no	—
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×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
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	4	yes	—
29	C₂³×D₄₇	D₄	1	4	yes	—
30	C₂³×D₄₇	Q₈	1	4	yes	—
31	C₂³×D₄₇	C₂³	1	2	yes	—
32	C₂²×C₄×C₄₇	—	4	2	no	—
33	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	complemented
34	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
35	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×Dic₄₇	—	4	2	no	—
38	C₂²×Dic₄₇	C₂×C₄	1	4	yes	complemented
39	C₂²×Dic₄₇	C₂³	1	4	yes	—
40	C₂²×Dic₄₇	C₂³	1	2	yes	—
41	C₂×C₄×D₄₇	—	2	8	no	—
42	C₂×C₄×D₄₇	—	4	4	no	—
43	C₂×C₄×D₄₇	—	4	4	no	—
44	C₄⋊C₄×C₄₇	—	4	2	no	—
45	C₂²⋊C₄×C₄₇	—	2	4	no	—
46	C₂²⋊Dic₄₇	—	2	4	no	—
47	(C₂×D₄₇)⋊C₄	—	2	8	no	—
48	(C₂×D₄₇)⋊C₄	C₂×C₄	1	8	yes	complemented
49	(C₂×D₄₇)⋊C₄	C₂×C₄	1	8	yes	complemented
50	C₄⋊Dic₄₇	—	4	2	no	—
51	Dic₄₇⋊C₄	—	4	4	no	—
52	C₂³×C₄₇	—	2	2	no	—
53	C₂³×C₄₇	—	2	2	no	—
54	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
55	C₂³×C₄₇	C₂×D₄	1	2	yes	—
56	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
57	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
58	C₂²×D₄₇	—	2	4	no	—
59	C₂²×D₄₇	—	2	4	no	—
60	C₂²×D₄₇	—	4	4	no	—
61	C₂²×D₄₇	—	4	4	no	—
62	C₂²×D₄₇	—	4	8	no	—
63	C₂²×D₄₇	—	4	8	no	—
64	C₂²×D₄₇	C₄⋊C₄	1	16	yes	complemented
65	C₂²×D₄₇	C₂²×C₄	1	4	yes	—
66	C₂²×D₄₇	C₂×D₄	1	4	yes	—
67	C₂²×D₄₇	C₂×Q₈	1	4	yes	—
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	—	2	2	no	—
70	C₂×C₄×C₄₇	—	2	4	no	—
71	C₂×C₄×C₄₇	—	2	4	no	—
72	C₂×C₄×C₄₇	—	2	4	no	—
73	C₂×C₄×C₄₇	—	4	4	no	—
74	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
75	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
76	C₂×Dic₄₇	—	2	4	no	—
77	C₂×Dic₄₇	—	2	4	no	—
78	C₂×Dic₄₇	—	2	4	no	—
79	C₂×Dic₄₇	—	2	4	no	—
80	C₂×Dic₄₇	—	4	4	no	—
81	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
82	C₄×D₄₇	—	4	16	no	—
83	C₂²×C₄₇	—	2	2	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	—	2	4	no	—
86	C₂²×C₄₇	—	2	4	no	—
87	C₂²×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
88	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
89	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
90	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
91	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
92	C₂²×C₄₇	H(5,𝔽₂)	1	2	yes	—
93	C₂×D₄₇	—	2	4	no	—
94	C₂×D₄₇	—	2	4	no	—
95	C₂×D₄₇	—	2	8	no	—
96	C₂×D₄₇	—	2	8	no	—
97	C₂×D₄₇	—	4	16	no	—
98	C₂×D₄₇	C₂×C₄⋊C₄	1	8	yes	—
99	C₄×C₄₇	—	2	2	no	—
100	C₄×C₄₇	—	2	2	no	—
101	C₄×C₄₇	—	4	4	no	—
102	Dic₄₇	—	2	4	no	—
103	Dic₄₇	—	4	4	no	—
104	#2315	—	47	1	no	maximal, Sylow
105	C₂×C₄₇	—	2	4	no	—
106	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄₇	#518	1	1	yes	characteristic
108	C₂×C₄₇	#518	1	1	yes	characteristic
109	C₂×C₄₇	#534	1	2	yes	—
110	C₂×C₄₇	#543	1	2	yes	—
111	D₄₇	—	2	8	no	—
112	C₂²×C₂²⋊C₄	—	47	1	no	—
113	C₂²×C₂²⋊C₄	—	47	2	no	—
114	#385	—	47	4	no	—
115	#385	—	47	4	no	—
116	#380	—	47	1	no	—
117	#380	—	47	2	no	—
118	#380	D₄₇	1	1	yes	characteristic, complemented
119	C₄₇	#2315	1	1	yes	characteristic, complemented, Sylow
120	C₂⁵	—	47	1	no	—
121	C₂³×C₄	—	47	1	no	—
122	C₂³×C₄	—	47	4	no	—
123	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
124	C₂×C₄⋊C₄	—	47	4	no	—
125	C₂×C₄⋊C₄	—	47	2	no	—
126	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
127	C₂×C₂²⋊C₄	—	47	8	no	—
128	C₂×C₂²⋊C₄	—	47	2	no	—
129	C₂×C₂²⋊C₄	—	47	2	no	—
130	C₂×C₂²⋊C₄	—	47	2	no	—
131	C₂×C₂²⋊C₄	—	47	4	no	—
132	C₂×C₂²⋊C₄	—	94	8	no	—
133	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
134	#95	—	47	4	no	—
135	#95	—	47	2	no	—
136	#95	C₂×D₄₇	1	2	yes	complemented
137	C₂⁴	—	47	2	no	—
138	C₂⁴	—	47	4	no	—
139	C₂⁴	—	47	4	no	—
140	C₂⁴	—	47	4	no	—
141	C₂⁴	—	188	2	no	—
142	C₂⁴	—	188	2	no	—
143	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
144	C₂²×C₄	—	4	2	no	—
145	C₂²×C₄	—	47	2	no	—
146	C₂²×C₄	—	47	4	no	—
147	C₂²×C₄	—	47	4	no	—
148	C₂²×C₄	—	94	8	no	—
149	C₂²×C₄	—	188	4	no	—
150	C₂²×C₄	—	188	4	no	—
151	C₂²×C₄	—	188	2	no	—
152	C₂²×C₄	C₄×D₄₇	1	4	yes	complemented
153	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
154	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
155	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	188	4	no	—
158	C₄⋊C₄	—	188	2	no	—
159	C₂²⋊C₄	—	2	4	no	—
160	C₂²⋊C₄	—	47	8	no	—
161	C₂²⋊C₄	—	47	8	no	—
162	C₂²⋊C₄	—	94	8	no	—
163	C₂²⋊C₄	—	94	4	no	—
164	C₂³	—	2	2	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	47	4	no	—
167	C₂³	—	47	4	no	—
168	C₂³	—	47	4	no	—
169	C₂³	—	47	16	no	—
170	C₂³	—	94	4	no	—
171	C₂³	—	94	4	no	—
172	C₂³	—	188	8	no	—
173	C₂³	—	188	4	no	—
174	C₂³	—	188	4	no	—
175	C₂³	—	188	8	no	—
176	C₂³	C₂×C₄×D₄₇	1	2	yes	—
177	C₂³	D₄×D₄₇	1	2	yes	—
178	C₂³	Q₈×D₄₇	1	2	yes	—
179	C₂³	C₂³×D₄₇	1	1	yes	characteristic
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	47	4	no	—
187	C₂×C₄	—	94	4	no	—
188	C₂×C₄	—	94	4	no	—
189	C₂×C₄	—	94	4	no	—
190	C₂×C₄	—	94	4	no	—
191	C₂×C₄	—	188	16	no	—
192	C₂×C₄	—	188	4	no	—
193	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
194	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
195	C₂²	—	2	4	no	—
196	C₂²	—	2	2	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	2	4	no	—
199	C₂²	—	47	8	no	—
200	C₂²	—	94	8	no	—
201	C₂²	—	94	4	no	—
202	C₂²	—	94	4	no	—
203	C₂²	—	94	8	no	—
204	C₂²	—	188	16	no	—
205	C₂²	C₄⋊C₄×D₄₇	1	4	yes	—
206	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
207	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
208	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
209	C₂²	#13094069	1	2	yes	—
210	C₂²	#13094070	1	2	yes	—
211	C₄	—	2	2	no	—
212	C₄	—	2	2	no	—
213	C₄	—	4	4	no	—
214	C₄	—	94	4	no	—
215	C₄	—	188	4	no	—
216	C₂	—	2	4	no	—
217	C₂	—	94	8	no	—
218	C₂	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
219	C₂	#15689596	1	1	yes	characteristic
220	C₂	#15689597	1	1	yes	characteristic
221	C₂	#15689681	1	2	yes	—
222	C₂	#15689748	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×(C₂×D₄₇)⋊C₄

C₂

yes

maximal, characteristic

C₂×C₂²⋊C₄×D₄₇

C₂

yes

maximal

#15688997

C₂

yes

maximal, complemented

#15688994

C₂

yes

maximal, complemented

#15688983

C₂

yes

maximal, characteristic, complemented

#15688981

C₂

yes

maximal, complemented

C₄₇×#380

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₇

C₂²

yes

characteristic

C₂³×Dic₄₇

C₂²

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

complemented

C₂×Dic₄₇⋊C₄

C₂²

yes

complemented

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

—

C₄₇⋊#95

C₂²

yes

complemented

C₄₇⋊#95

C₂²

yes

complemented

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

complemented

C₂×C₂²⋊C₄×C₄₇

C₂²

yes

—

#95×C₄₇

C₂²

yes

complemented

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂³×D₄₇

—

C₂³×D₄₇

—

C₂³×D₄₇

C₂×C₄

yes

—

C₂³×D₄₇

D₄

yes

—

C₂³×D₄₇

Q₈

yes

—

C₂³×D₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

complemented

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

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

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

complemented

(C₂×D₄₇)⋊C₄

C₂×C₄

yes

complemented

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₄⋊C₄

yes

complemented

C₂²×D₄₇

C₂²×C₄

yes

—

C₂²×D₄₇

C₂×D₄

yes

—

C₂²×D₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

—

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×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₄×D₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

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×C₄⋊C₄

yes

—

C₄×C₄₇

—

100

C₄×C₄₇

—

101

C₄×C₄₇

—

102

Dic₄₇

—

103

Dic₄₇

—

104

#2315

—

maximal, Sylow

105

C₂×C₄₇

—

106

C₂×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

107

C₂×C₄₇

#518

yes

characteristic

108

C₂×C₄₇

#518

yes

characteristic

109

C₂×C₄₇

#534

yes

—

110

C₂×C₄₇

#543

yes

—

111

D₄₇

—

112

C₂²×C₂²⋊C₄

—

113

C₂²×C₂²⋊C₄

—

114

#385

—

115

#385

—

116

#380

—

117

#380

—

118

#380

D₄₇

yes

characteristic, complemented

119

C₄₇

#2315

yes

characteristic, complemented, Sylow

120

C₂⁵

—

121

C₂³×C₄

—

122

C₂³×C₄

—

123

C₂³×C₄

C₂×D₄₇

yes

characteristic

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

C₂×D₄₇

yes

complemented

127

C₂×C₂²⋊C₄

—

128

C₂×C₂²⋊C₄

—

129

C₂×C₂²⋊C₄

—

130

C₂×C₂²⋊C₄

—

131

C₂×C₂²⋊C₄

—

132

C₂×C₂²⋊C₄

—

133

C₂×C₂²⋊C₄

C₂×D₄₇

yes

—

134

#95

—

135

#95

—

136

#95

C₂×D₄₇

yes

complemented

137

C₂⁴

—

138

C₂⁴

—

139

C₂⁴

—

140

C₂⁴

—

141

C₂⁴

—

188

—

142

C₂⁴

—

188

—

143

C₂⁴

C₂²×D₄₇

yes

characteristic

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

—

188

—

150

C₂²×C₄

—

188

—

151

C₂²×C₄

—

188

—

152

C₂²×C₄

C₄×D₄₇

yes

complemented

153

C₂²×C₄

C₂²×D₄₇

yes

—

154

C₂²×C₄

C₂²×D₄₇

yes

characteristic

155

C₂²×C₄

C₂²×D₄₇

yes

characteristic

156

C₄⋊C₄

—

157

C₄⋊C₄

—

188

—

158

C₄⋊C₄

—

188

—

159

C₂²⋊C₄

—

160

C₂²⋊C₄

—

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₂²⋊C₄

—

164

C₂³

—

165

C₂³

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

188

—

173

C₂³

—

188

—

174

C₂³

—

188

—

175

C₂³

—

188

—

176

C₂³

C₂×C₄×D₄₇

yes

—

177

C₂³

D₄×D₄₇

yes

—

178

C₂³

Q₈×D₄₇

yes

—

179

C₂³

C₂³×D₄₇

yes

characteristic

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

188

—

192

C₂×C₄

—

188

—

193

C₂×C₄

C₂×C₄×D₄₇

yes

—

194

C₂×C₄

C₂×C₄×D₄₇

yes

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

188

—

205

C₂²

C₄⋊C₄×D₄₇

yes

—

206

C₂²

C₂²×C₄×D₄₇

yes

characteristic

207

C₂²

C₂×D₄×D₄₇

yes

characteristic

208

C₂²

C₂×Q₈×D₄₇

yes

characteristic

209

C₂²

#13094069

yes

—

210

C₂²

#13094070

yes

—

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

188

—

216

C₂

—

217

C₂

—

218

C₂

C₂×C₄⋊C₄×D₄₇

yes

characteristic

219

C₂

#15689596

yes

characteristic

220

C₂

#15689597

yes

characteristic

221

C₂

#15689681

yes

—

222

C₂

#15689748

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#380	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	#380	D₄₇
hypocenter	C₄₇	#2315
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #380

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₄₇×#380

C₂

socle

C₂³×C₄₇

C₂⁴

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ #380

N	H ≅ G/N	type
3. #15688997	C₂	semidirect
4. #15688994	C₂	semidirect
5. #15688983	C₂	semidirect
6. #15688981	C₂	semidirect
7. C₄₇×#380	C₂	semidirect
11. C₂×C₄⋊Dic₄₇	C₂²	semidirect
12. C₂×Dic₄₇⋊C₄	C₂²	semidirect
14. C₂×(C₂×D₄₇)⋊C₄	C₄	semidirect
19. C₄₇⋊#95	C₂²	semidirect
20. C₄₇⋊#95	C₂²	semidirect
22. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
24. #95×C₄₇	C₂²	semidirect
33. C₂²×C₄×C₄₇	C₂×C₄	semidirect
38. C₂²×Dic₄₇	C₂×C₄	semidirect
48. (C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
49. (C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
64. C₂²×D₄₇	C₄⋊C₄	semidirect
118. #380	D₄₇	semidirect
119. C₄₇	#2315	semidirect
126. C₂×C₄⋊C₄	C₂×D₄₇	semidirect
136. #95	C₂×D₄₇	semidirect
152. C₂²×C₄	C₄×D₄₇	semidirect

H ≅ G/N

type

3. #15688997

C₂

semidirect

4. #15688994

C₂

semidirect

5. #15688983

C₂

semidirect

6. #15688981

C₂

semidirect

7. C₄₇×#380

C₂

semidirect

11. C₂×C₄⋊Dic₄₇

C₂²

semidirect

12. C₂×Dic₄₇⋊C₄

C₂²

semidirect

14. C₂×(C₂×D₄₇)⋊C₄

C₄

semidirect

19. C₄₇⋊#95

C₂²

semidirect

20. C₄₇⋊#95

C₂²

semidirect

22. C₂×C₄⋊C₄×C₄₇

C₂²

semidirect

24. #95×C₄₇

C₂²

semidirect

33. C₂²×C₄×C₄₇

C₂×C₄

semidirect

38. C₂²×Dic₄₇

C₂×C₄

semidirect

48. (C₂×D₄₇)⋊C₄

C₂×C₄

semidirect

49. (C₂×D₄₇)⋊C₄

C₂×C₄

semidirect

64. C₂²×D₄₇

C₄⋊C₄

semidirect

118. #380

D₄₇

semidirect

119. C₄₇

#2315

semidirect

126. C₂×C₄⋊C₄

C₂×D₄₇

semidirect

136. #95

C₂×D₄₇

semidirect

152. C₂²×C₄

C₄×D₄₇

semidirect

Subgroups — #20246001

Conjugacy classes of subgroups

Complements