Group #20243680 — subgroups

Subgroups — #20243680

Order 6016.

432 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 133 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×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂×D₄₇)⋊C₈	C₂	1	2	yes	maximal, complemented
4	#15688877	C₂	1	2	yes	maximal, complemented
5	C₂³×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₄×C₂²⋊D₄₇	—	2	2	no	—
10	C₄×C₂²⋊D₄₇	—	2	2	no	—
11	C₂×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
12	C₂×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
16	(C₂×D₄₇)⋊C₈	—	2	4	no	—
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₄₇	—	2	2	no	—
19	C₂²×C₈×C₄₇	—	2	4	no	—
20	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
21	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
22	C₂³×D₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₄₇	—	2	2	no	—
24	C₂²×C₄×C₄₇	—	2	2	no	—
25	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₄₇	D₄	1	2	yes	—
27	C₂²×C₄×C₄₇	D₄	1	2	yes	—
28	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊D₄₇	—	2	2	no	—
30	C₂×C₂²⋊D₄₇	—	2	2	no	—
31	C₂×C₂²⋊D₄₇	C₈	1	4	yes	complemented
32	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×Dic₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×D₄₇	—	2	2	no	—
36	C₂×C₄×D₄₇	—	2	1	no	—
37	C₂×C₄×D₄₇	—	2	1	no	—
38	C₂×C₄×D₄₇	—	2	2	no	—
39	C₂×C₈×C₄₇	—	2	8	no	—
40	C₂×C₈×C₄₇	—	2	2	no	—
41	C₂×C₈×C₄₇	—	2	2	no	—
42	C₂×C₈×C₄₇	D₄	1	4	yes	complemented
43	C₂²⋊Dic₄₇	—	2	2	no	—
44	(C₂×D₄₇)⋊C₄	—	2	2	no	—
45	Dic₄₇⋊C₄	—	2	2	no	—
46	C₄×Dic₄₇	—	2	1	no	—
47	C₄×Dic₄₇	—	2	1	no	—
48	C₂×C₄₇⋊C₈	—	2	2	no	—
49	C₂×C₄₇⋊C₈	—	2	2	no	—
50	C₂×C₄₇⋊C₈	—	2	2	no	—
51	C₂³×C₄₇	—	2	2	no	—
52	C₂³×C₄₇	—	2	2	no	—
53	C₂³×C₄₇	C₂²⋊C₄	1	2	yes	—
54	C₂³×C₄₇	C₂×C₈	1	2	yes	—
55	C₂³×C₄₇	M₁₆	1	2	yes	—
56	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	C₂²×D₄₇	—	2	1	no	—
58	C₂²×D₄₇	—	2	2	no	—
59	C₂²×D₄₇	—	2	1	no	—
60	C₂²×D₄₇	—	2	2	no	—
61	C₂²×D₄₇	C₂×C₈	1	2	yes	complemented
62	C₂×C₄×C₄₇	—	2	2	no	—
63	C₂×C₄×C₄₇	—	2	2	no	—
64	C₂×C₄×C₄₇	—	2	4	no	—
65	C₂×C₄×C₄₇	—	2	2	no	—
66	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
69	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₄₇	#41	1	2	yes	—
71	C₂²⋊D₄₇	—	2	8	no	—
72	C₂×Dic₄₇	—	2	1	no	—
73	C₂×Dic₄₇	—	2	1	no	—
74	C₂×Dic₄₇	—	2	1	no	—
75	C₂×Dic₄₇	—	2	1	no	—
76	C₂×Dic₄₇	—	2	2	no	—
77	C₂×Dic₄₇	—	2	2	no	—
78	C₂×Dic₄₇	C₂×C₈	1	2	yes	complemented
79	C₄×D₄₇	—	4	1	no	—
80	C₄×D₄₇	—	4	2	no	—
81	C₄×D₄₇	—	4	1	no	—
82	C₈×C₄₇	—	2	4	no	—
83	C₄₇⋊C₈	—	4	2	no	—
84	C₂²×C₄₇	—	2	2	no	—
85	C₂²×C₄₇	—	2	2	no	—
86	C₂²×C₄₇	—	2	4	no	—
87	C₂²×C₄₇	—	2	4	no	—
88	C₂²×C₄₇	C₂²⋊C₈	1	4	yes	complemented
89	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄₇	C₄×D₄	1	2	yes	—
91	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
92	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
93	C₂²×C₄₇	#131	1	2	yes	—
94	C₂×D₄₇	—	2	2	no	—
95	C₂×D₄₇	—	2	4	no	—
96	C₂×D₄₇	—	4	1	no	—
97	C₂×D₄₇	—	4	1	no	—
98	C₂×D₄₇	—	4	2	no	—
99	C₄×C₄₇	—	2	2	no	—
100	C₄×C₄₇	#120	1	1	yes	characteristic
101	C₄×C₄₇	#121	1	2	yes	—
102	C₄×C₄₇	#123	1	1	yes	characteristic
103	Dic₄₇	—	2	2	no	—
104	Dic₄₇	—	4	1	no	—
105	Dic₄₇	—	4	1	no	—
106	#1869	—	47	1	no	maximal, Sylow
107	C₂×C₄₇	—	2	4	no	—
108	C₂×C₄₇	#386	1	1	yes	characteristic
109	C₂×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
110	C₂×C₄₇	#408	1	1	yes	characteristic
111	C₂×C₄₇	C₈×D₄	1	2	yes	—
112	C₂×C₄₇	#435	1	2	yes	—
113	D₄₇	—	4	2	no	—
114	C₂³×C₈	D₄₇	1	1	yes	characteristic, complemented
115	C₂×C₄×D₄	—	47	1	no	—
116	C₂×C₂²⋊C₈	—	47	1	no	—
117	C₂×C₂²⋊C₈	—	47	2	no	—
118	#336	—	47	2	no	—
119	C₄₇	#1869	1	1	yes	characteristic, complemented, Sylow
120	C₂²×D₄	—	47	1	no	—
121	C₂³×C₄	—	47	1	no	—
122	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
123	C₂²×C₈	—	2	2	no	—
124	C₂²×C₈	—	2	4	no	—
125	C₂²×C₈	—	47	2	no	—
126	C₂²×C₈	C₂×D₄₇	1	2	yes	—
127	C₄×D₄	—	94	2	no	—
128	C₄×D₄	—	94	2	no	—
129	C₂×C₄⋊C₄	—	47	1	no	—
130	C₂×C₂²⋊C₄	—	47	1	no	—
131	C₂×C₂²⋊C₄	—	47	1	no	—
132	C₂×C₄²	—	47	1	no	—
133	C₂²⋊C₈	—	94	2	no	—
134	C₂²⋊C₈	—	94	4	no	—
135	C₂⁴	—	47	1	no	—
136	C₂⁴	C₄×D₄₇	1	1	yes	characteristic
137	C₂×D₄	—	47	4	no	—
138	C₂×D₄	—	94	2	no	—
139	C₂×D₄	—	94	2	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	47	1	no	—
143	C₂²×C₄	—	47	1	no	—
144	C₂²×C₄	—	47	1	no	—
145	C₂²×C₄	—	94	1	no	—
146	C₂²×C₄	—	94	2	no	—
147	C₂²×C₄	—	94	2	no	—
148	C₂²×C₄	—	94	1	no	—
149	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
150	C₂²×C₄	D₁₈₈	1	2	yes	—
151	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
152	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
153	C₂×C₈	—	2	8	no	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	—	2	2	no	—
156	C₂×C₈	—	94	2	no	—
157	C₂×C₈	—	94	2	no	—
158	C₂×C₈	—	94	2	no	—
159	C₂×C₈	C₂²⋊D₄₇	1	4	yes	complemented
160	C₄⋊C₄	—	94	2	no	—
161	C₂²⋊C₄	—	94	2	no	—
162	C₂²⋊C₄	—	94	2	no	—
163	C₄²	—	94	1	no	—
164	C₄²	—	94	1	no	—
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	—	47	2	no	—
168	C₂³	—	94	1	no	—
169	C₂³	—	94	2	no	—
170	C₂³	—	94	1	no	—
171	C₂³	—	94	2	no	—
172	C₂³	C₈×D₄₇	1	2	yes	—
173	C₂³	#10625324	1	2	yes	—
174	C₂³	(C₂×D₄₇)⋊C₄	1	2	yes	—
175	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
176	D₄	—	94	8	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	47	2	no	—
182	C₂×C₄	—	94	1	no	—
183	C₂×C₄	—	94	1	no	—
184	C₂×C₄	—	94	1	no	—
185	C₂×C₄	—	94	1	no	—
186	C₂×C₄	—	94	2	no	—
187	C₂×C₄	—	94	2	no	—
188	C₂×C₄	—	188	1	no	—
189	C₂×C₄	—	188	2	no	—
190	C₂×C₄	—	188	1	no	—
191	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
192	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
193	C₂×C₄	#10625350	1	2	yes	—
194	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
195	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
196	C₈	—	2	4	no	—
197	C₈	—	188	2	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	2	no	—
200	C₂²	—	2	4	no	—
201	C₂²	—	2	4	no	—
202	C₂²	—	94	2	no	—
203	C₂²	—	94	4	no	—
204	C₂²	—	188	1	no	—
205	C₂²	—	188	1	no	—
206	C₂²	—	188	2	no	—
207	C₂²	(C₂×D₄₇)⋊C₈	1	4	yes	complemented
208	C₂²	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
209	C₂²	C₄×C₂²⋊D₄₇	1	2	yes	—
210	C₂²	C₂×C₈×D₄₇	1	1	yes	characteristic
211	C₂²	C₂×#10625324	1	1	yes	characteristic
212	C₂²	#13094030	1	2	yes	—
213	C₄	—	2	2	no	—
214	C₄	—	94	2	no	—
215	C₄	—	188	1	no	—
216	C₄	—	188	1	no	—
217	C₄	#13093993	1	1	yes	characteristic
218	C₄	#13093998	1	2	yes	—
219	C₄	#13094007	1	1	yes	characteristic
220	C₂	—	2	4	no	—
221	C₂	—	188	2	no	—
222	C₂	#15689002	1	1	yes	characteristic
223	C₂	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
224	C₂	#15689089	1	1	yes	characteristic
225	C₂	C₈×C₂²⋊D₄₇	1	2	yes	—
226	C₂	#15689194	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₂²⋊D₄₇

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic, complemented

C₂×(C₂×D₄₇)⋊C₈

C₂

yes

maximal, complemented

#15688877

C₂

yes

maximal, complemented

C₂³×C₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₄₇

C₄

yes

characteristic

C₂²×C₄×D₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₄×C₂²⋊D₄₇

—

C₄×C₂²⋊D₄₇

—

C₂×Dic₄₇⋊C₄

C₄

yes

characteristic

C₂×C₂²⋊Dic₄₇

C₄

yes

characteristic

C₂×(C₂×D₄₇)⋊C₄

C₄

yes

characteristic

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

C₂²⋊(C₄₇⋊C₈)

—

(C₂×D₄₇)⋊C₈

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂×C₄

yes

characteristic

C₂³×D₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

—

C₂×C₂²⋊D₄₇

C₈

yes

complemented

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

complemented

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²⋊C₄

yes

—

C₂³×C₄₇

C₂×C₈

yes

—

C₂³×C₄₇

M₁₆

yes

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

C₂×C₈

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×C₈

yes

complemented

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

complemented

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₂²×C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₂²×C₄₇

#131

yes

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

100

C₄×C₄₇

#120

yes

characteristic

101

C₄×C₄₇

#121

yes

—

102

C₄×C₄₇

#123

yes

characteristic

103

Dic₄₇

—

104

Dic₄₇

—

105

Dic₄₇

—

106

#1869

—

maximal, Sylow

107

C₂×C₄₇

—

108

C₂×C₄₇

#386

yes

characteristic

109

C₂×C₄₇

C₂×C₂²⋊C₈

yes

characteristic

110

C₂×C₄₇

#408

yes

characteristic

111

C₂×C₄₇

C₈×D₄

yes

—

112

C₂×C₄₇

#435

yes

—

113

D₄₇

—

114

C₂³×C₈

D₄₇

yes

characteristic, complemented

115

C₂×C₄×D₄

—

116

C₂×C₂²⋊C₈

—

117

C₂×C₂²⋊C₈

—

118

#336

—

119

C₄₇

#1869

yes

characteristic, complemented, Sylow

120

C₂²×D₄

—

121

C₂³×C₄

—

122

C₂³×C₄

C₂×D₄₇

yes

characteristic

123

C₂²×C₈

—

124

C₂²×C₈

—

125

C₂²×C₈

—

126

C₂²×C₈

C₂×D₄₇

yes

—

127

C₄×D₄

—

128

C₄×D₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₂²⋊C₄

—

131

C₂×C₂²⋊C₄

—

132

C₂×C₄²

—

133

C₂²⋊C₈

—

134

C₂²⋊C₈

—

135

C₂⁴

—

136

C₂⁴

C₄×D₄₇

yes

characteristic

137

C₂×D₄

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

C₄×D₄₇

yes

characteristic

150

C₂²×C₄

D₁₈₈

yes

—

151

C₂²×C₄

C₂²⋊D₄₇

yes

—

152

C₂²×C₄

C₂²×D₄₇

yes

characteristic

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

C₂²⋊D₄₇

yes

complemented

160

C₄⋊C₄

—

161

C₂²⋊C₄

—

162

C₂²⋊C₄

—

163

C₄²

—

164

C₄²

—

165

C₂³

—

166

C₂³

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₈×D₄₇

yes

—

173

C₂³

#10625324

yes

—

174

C₂³

(C₂×D₄₇)⋊C₄

yes

—

175

C₂³

C₂×C₄×D₄₇

yes

characteristic

176

D₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

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

—

188

—

189

C₂×C₄

—

188

—

190

C₂×C₄

—

188

—

191

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

192

C₂×C₄

C₂×D₁₈₈

yes

characteristic

193

C₂×C₄

#10625350

yes

—

194

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

195

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

196

C₈

—

197

C₈

—

188

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

—

188

—

205

C₂²

—

188

—

206

C₂²

—

188

—

207

C₂²

(C₂×D₄₇)⋊C₈

yes

complemented

208

C₂²

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

209

C₂²

C₄×C₂²⋊D₄₇

yes

—

210

C₂²

C₂×C₈×D₄₇

yes

characteristic

211

C₂²

C₂×#10625324

yes

characteristic

212

C₂²

#13094030

yes

—

213

C₄

—

214

C₄

—

215

C₄

—

188

—

216

C₄

—

188

—

217

C₄

#13093993

yes

characteristic

218

C₄

#13093998

yes

—

219

C₄

#13094007

yes

characteristic

220

C₂

—

221

C₂

—

188

—

222

C₂

#15689002

yes

characteristic

223

C₂

C₂×(C₂×D₄₇)⋊C₈

yes

characteristic

224

C₂

#15689089

yes

characteristic

225

C₂

C₈×C₂²⋊D₄₇

yes

—

226

C₂

#15689194

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₈
Fitting	C₂³×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂³×C₈	D₄₇
hypocenter	C₄₇	#1869
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂²×C₈

Fitting

C₂³×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂²×C₄

hypercenter

C₂³×C₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂³×C₈

N	H ≅ G/N	type
2. C₂×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
3. C₂×(C₂×D₄₇)⋊C₈	C₂	semidirect
4. #15688877	C₂	semidirect
5. C₂³×C₈×C₄₇	C₂	semidirect
31. C₂×C₂²⋊D₄₇	C₈	semidirect
42. C₂×C₈×C₄₇	D₄	semidirect
61. C₂²×D₄₇	C₂×C₈	semidirect
78. C₂×Dic₄₇	C₂×C₈	semidirect
88. C₂²×C₄₇	C₂²⋊C₈	semidirect
114. C₂³×C₈	D₄₇	semidirect
119. C₄₇	#1869	semidirect
159. C₂×C₈	C₂²⋊D₄₇	semidirect
207. C₂²	(C₂×D₄₇)⋊C₈	semidirect

H ≅ G/N

type

2. C₂×C₂²⋊(C₄₇⋊C₈)

C₂

semidirect

3. C₂×(C₂×D₄₇)⋊C₈

C₂

semidirect

4. #15688877

C₂

semidirect

5. C₂³×C₈×C₄₇

C₂

semidirect

31. C₂×C₂²⋊D₄₇

C₈

semidirect

42. C₂×C₈×C₄₇

D₄

semidirect

61. C₂²×D₄₇

C₂×C₈

semidirect

78. C₂×Dic₄₇

C₂×C₈

semidirect

88. C₂²×C₄₇

C₂²⋊C₈

semidirect

114. C₂³×C₈

D₄₇

semidirect

119. C₄₇

#1869

semidirect

159. C₂×C₈

C₂²⋊D₄₇

semidirect

207. C₂²

(C₂×D₄₇)⋊C₈

semidirect

Subgroups — #20243680

Conjugacy classes of subgroups

Complements