Group #26104260 — subgroups

Subgroups — #26104260

Order 12032.

516 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 207 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	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
2	#20241214	C₂	1	4	yes	maximal
3	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
5	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
6	#15688878	C₂²	1	4	yes	—
7	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
9	C₄₇×#391	C₂²	1	2	yes	—
10	C₄₇×#389	—	2	2	no	—
11	C₄₇×#384	C₄	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
13	C₄³×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄₇⋊C₈	—	2	4	no	—
15	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
16	C₄×C₄₇⋊C₈	—	4	4	no	—
17	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
18	C₄⋊Q₈×C₄₇	—	2	2	no	—
19	C₄⋊Q₈×C₄₇	C₈	1	4	yes	complemented
20	C₄×Q₈×C₄₇	—	4	4	no	—
21	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
23	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
24	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₄₇	—	2	2	no	—
26	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₄₇	D₄	1	2	yes	—
29	C₂×C₄²×C₄₇	D₄	1	2	yes	—
30	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
31	#95×C₄₇	—	2	4	no	—
32	C₂×Q₈×C₄₇	—	2	2	no	—
33	C₂×Q₈×C₄₇	—	4	2	no	—
34	C₂×Q₈×C₄₇	—	4	2	no	—
35	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₄₇	—	2	2	no	—
37	C₂²×C₄×C₄₇	—	2	2	no	—
38	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
43	C₄⋊C₄×C₄₇	—	2	8	no	—
44	C₄⋊C₄×C₄₇	—	4	4	no	—
45	C₄⋊C₄×C₄₇	—	4	2	no	—
46	C₄⋊C₄×C₄₇	—	4	4	no	—
47	C₄²×C₄₇	—	2	2	no	—
48	C₄²×C₄₇	—	2	4	no	—
49	C₄²×C₄₇	—	4	1	no	—
50	C₄²×C₄₇	—	4	4	no	—
51	C₄²×C₄₇	C₂×C₈	1	2	yes	—
52	C₄²×C₄₇	M₁₆	1	2	yes	—
53	C₄²×C₄₇	SD₁₆	1	4	yes	—
54	C₄²×C₄₇	Q₁₆	1	4	yes	—
55	C₂×C₄₇⋊C₈	—	2	8	no	—
56	C₂×C₄₇⋊C₈	—	4	4	no	—
57	C₂×C₄₇⋊C₈	—	4	4	no	—
58	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	Q₈×C₄₇	—	4	4	no	—
60	Q₈×C₄₇	—	4	4	no	—
61	C₂×C₄×C₄₇	—	2	2	no	—
62	C₂×C₄×C₄₇	—	2	1	no	—
63	C₂×C₄×C₄₇	—	2	1	no	—
64	C₂×C₄×C₄₇	—	2	2	no	—
65	C₂×C₄×C₄₇	—	2	4	no	—
66	C₂×C₄×C₄₇	—	2	1	no	—
67	C₂×C₄×C₄₇	—	2	2	no	—
68	C₂×C₄×C₄₇	—	4	2	no	—
69	C₂×C₄×C₄₇	—	4	2	no	—
70	C₂×C₄×C₄₇	—	4	2	no	—
71	C₂×C₄×C₄₇	—	4	4	no	—
72	C₂×C₄×C₄₇	C₂²⋊C₈	1	4	yes	—
73	C₂×C₄×C₄₇	#100	1	2	yes	—
74	C₂×C₄×C₄₇	#103	1	4	yes	—
75	C₂×C₄×C₄₇	#103	1	4	yes	—
76	C₂×C₄×C₄₇	#104	1	4	yes	—
77	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
78	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
79	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
80	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
81	C₄₇⋊C₈	—	4	8	no	—
82	#7571	—	47	1	no	maximal, Sylow
83	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
84	C₂²×C₄₇	#410	1	1	yes	characteristic
85	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
86	C₂²×C₄₇	C₂×#103	1	2	yes	—
87	C₂²×C₄₇	C₂×#104	1	2	yes	—
88	C₄×C₄₇	—	2	1	no	—
89	C₄×C₄₇	—	2	1	no	—
90	C₄×C₄₇	—	2	2	no	—
91	C₄×C₄₇	—	2	2	no	—
92	C₄×C₄₇	—	4	4	no	—
93	C₄×C₄₇	—	4	1	no	—
94	C₄×C₄₇	—	8	2	no	—
95	C₄×C₄₇	Q₈⋊C₈	1	8	yes	—
96	C₄×C₄₇	#333	1	4	yes	—
97	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
98	C₄×C₄⋊C₈	—	47	2	no	—
99	#1272	—	47	4	no	—
100	C₂×C₄₇	#1460	1	1	yes	characteristic
101	C₂×C₄₇	C₂×Q₈⋊C₈	1	2	yes	—
102	C₂×C₄₇	#1503	1	2	yes	—
103	C₂×C₄₇	#1525	1	1	yes	characteristic
104	C₂×C₄₇	C₂×#333	1	1	yes	characteristic
105	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
106	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
107	C₂×C₄⋊C₈	—	94	2	no	—
108	C₂×C₄×C₈	—	94	2	no	—
109	#391	C₂×D₄₇	1	2	yes	—
110	#389	—	2	2	no	—
111	#384	Dic₄₇	1	1	yes	characteristic
112	C₄×C₄⋊C₄	—	2	2	no	—
113	C₄³	C₂×D₄₇	1	1	yes	characteristic
114	#336	—	47	4	no	—
115	C₄₇	#7571	1	1	yes	characteristic, complemented, Sylow
116	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
117	C₂²×C₈	—	94	4	no	—
118	C₄⋊Q₈	—	2	2	no	—
119	C₄⋊Q₈	C₄₇⋊C₈	1	4	yes	complemented
120	C₄×Q₈	—	4	4	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
125	C₂×C₄²	—	2	2	no	—
126	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
127	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
129	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
130	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
131	C₄⋊C₈	—	94	8	no	—
132	C₄×C₈	—	188	4	no	—
133	#95	—	2	4	no	—
134	C₂×Q₈	—	2	2	no	—
135	C₂×Q₈	—	4	2	no	—
136	C₂×Q₈	—	4	2	no	—
137	C₂×Q₈	C₂×C₄₇⋊C₈	1	4	yes	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
142	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
143	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
145	C₂×C₈	—	94	8	no	—
146	C₂×C₈	—	188	4	no	—
147	C₂×C₈	—	188	4	no	—
148	C₄⋊C₄	—	2	8	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	4	4	no	—
151	C₄⋊C₄	—	4	4	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	2	4	no	—
154	C₄²	—	4	1	no	—
155	C₄²	—	4	4	no	—
156	C₄²	C₂×C₄₇⋊C₈	1	2	yes	—
157	C₄²	#10625329	1	2	yes	—
158	C₄²	#10625336	1	4	yes	—
159	C₄²	#10625337	1	4	yes	—
160	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
161	Q₈	—	4	4	no	—
162	Q₈	—	4	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	4	2	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	4	yes	—
175	C₂×C₄	#13093941	1	2	yes	—
176	C₂×C₄	#13093948	1	4	yes	—
177	C₂×C₄	#13093948	1	4	yes	—
178	C₂×C₄	#13093951	1	4	yes	—
179	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
180	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
181	C₂×C₄	C₂×#10625336	1	2	yes	—
182	C₂×C₄	C₂×#10625337	1	2	yes	—
183	C₈	—	188	8	no	—
184	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
185	C₂²	#15689097	1	1	yes	characteristic
186	C₂²	C₂×#13093941	1	1	yes	characteristic
187	C₂²	C₂×#13093948	1	2	yes	—
188	C₂²	C₂×#13093951	1	2	yes	—
189	C₄	—	2	1	no	—
190	C₄	—	2	1	no	—
191	C₄	—	2	2	no	—
192	C₄	—	2	2	no	—
193	C₄	—	4	4	no	—
194	C₄	—	4	1	no	—
195	C₄	—	8	2	no	—
196	C₄	Q₈⋊(C₄₇⋊C₈)	1	8	yes	—
197	C₄	#15688872	1	4	yes	—
198	C₂	#20241709	1	1	yes	characteristic
199	C₂	C₂×Q₈⋊(C₄₇⋊C₈)	1	2	yes	—
200	C₂	#20241887	1	2	yes	—
201	C₂	#20241980	1	1	yes	characteristic
202	C₂	C₂×#15688872	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₄⋊(C₄₇⋊C₈)

C₂

yes

maximal

#20241214

C₂

yes

maximal

C₄×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₇⋊C₈)

—

C₂×C₄×C₄₇⋊C₈

—

#15688878

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₇

C₄

yes

characteristic

C₂×C₄×Q₈×C₄₇

C₄

yes

—

C₄₇×#391

C₂²

yes

—

C₄₇×#389

—

C₄₇×#384

C₄

yes

characteristic

C₄×C₄⋊C₄×C₄₇

—

C₄³×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂²×Q₈×C₄₇

C₂×C₄

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₈

yes

complemented

C₄×Q₈×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₂×C₄²×C₄₇

—

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

D₄

yes

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#95×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₈

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₈

yes

—

C₄²×C₄₇

M₁₆

yes

—

C₄²×C₄₇

SD₁₆

yes

—

C₄²×C₄₇

Q₁₆

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₈

yes

—

C₂×C₄×C₄₇

#100

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

#103

yes

—

C₂×C₄×C₄₇

#104

yes

—

C₂×C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂×SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×Q₁₆

yes

—

C₄₇⋊C₈

—

#7571

—

maximal, Sylow

C₂²×C₄₇

C₂×C₂²⋊C₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

C₂×#104

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

Q₈⋊C₈

yes

—

C₄×C₄₇

#333

yes

—

C₄×C₄⋊Q₈

D₄₇

yes

characteristic

C₄×C₄⋊C₈

—

#1272

—

100

C₂×C₄₇

#1460

yes

characteristic

101

C₂×C₄₇

C₂×Q₈⋊C₈

yes

—

102

C₂×C₄₇

#1503

yes

—

103

C₂×C₄₇

#1525

yes

characteristic

104

C₂×C₄₇

C₂×#333

yes

characteristic

105

C₂×C₄⋊Q₈

Dic₄₇

yes

characteristic

106

C₂×C₄×Q₈

Dic₄₇

yes

—

107

C₂×C₄⋊C₈

—

108

C₂×C₄×C₈

—

109

#391

C₂×D₄₇

yes

—

110

#389

—

111

#384

Dic₄₇

yes

characteristic

112

C₄×C₄⋊C₄

—

113

C₄³

C₂×D₄₇

yes

characteristic

114

#336

—

115

C₄₇

#7571

yes

characteristic, complemented, Sylow

116

C₂²×Q₈

C₂×Dic₄₇

yes

—

117

C₂²×C₈

—

118

C₄⋊Q₈

—

119

C₄⋊Q₈

C₄₇⋊C₈

yes

complemented

120

C₄×Q₈

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

C₂×Dic₄₇

yes

—

125

C₂×C₄²

—

126

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

127

C₂×C₄²

C₂×Dic₄₇

yes

characteristic

128

C₂×C₄²

C₂²⋊D₄₇

yes

—

129

C₂×C₄²

C₂²⋊D₄₇

yes

—

130

C₂×C₄²

C₂²×D₄₇

yes

characteristic

131

C₄⋊C₈

—

132

C₄×C₈

—

188

—

133

#95

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

C₂×C₄₇⋊C₈

yes

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

141

C₂²×C₄

C₂²⋊Dic₄₇

yes

—

142

C₂²×C₄

C₂²⋊Dic₄₇

yes

characteristic

143

C₂²×C₄

C₂²×Dic₄₇

yes

characteristic

144

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

—

145

C₂×C₈

—

146

C₂×C₈

—

188

—

147

C₂×C₈

—

188

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

C₂×C₄₇⋊C₈

yes

—

157

C₄²

#10625329

yes

—

158

C₄²

#10625336

yes

—

159

C₄²

#10625337

yes

—

160

C₂³

C₂×C₂²⋊Dic₄₇

yes

characteristic

161

Q₈

—

162

Q₈

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₂²⋊(C₄₇⋊C₈)

yes

—

175

C₂×C₄

#13093941

yes

—

176

C₂×C₄

#13093948

yes

—

177

C₂×C₄

#13093948

yes

—

178

C₂×C₄

#13093951

yes

—

179

C₂×C₄

C₂²×C₄₇⋊C₈

yes

characteristic

180

C₂×C₄

C₂×#10625329

yes

characteristic

181

C₂×C₄

C₂×#10625336

yes

—

182

C₂×C₄

C₂×#10625337

yes

—

183

C₈

—

188

—

184

C₂²

C₂×C₂²⋊(C₄₇⋊C₈)

yes

characteristic

185

C₂²

#15689097

yes

characteristic

186

C₂²

C₂×#13093941

yes

characteristic

187

C₂²

C₂×#13093948

yes

—

188

C₂²

C₂×#13093951

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

Q₈⋊(C₄₇⋊C₈)

yes

—

197

C₄

#15688872

yes

—

198

C₂

#20241709

yes

characteristic

199

C₂

C₂×Q₈⋊(C₄₇⋊C₈)

yes

—

200

C₂

#20241887

yes

—

201

C₂

#20241980

yes

characteristic

202

C₂

C₂×#15688872

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#7571
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄×C₄⋊Q₈×C₄₇

C₂

socle, prime radical

C₂³×C₄₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₇

C₂³

hypercenter

C₄×C₄⋊Q₈

D₄₇

hypocenter

C₄₇

#7571

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
19. C₄⋊Q₈×C₄₇	C₈	semidirect
115. C₄₇	#7571	semidirect
119. C₄⋊Q₈	C₄₇⋊C₈	semidirect

H ≅ G/N

type

19. C₄⋊Q₈×C₄₇

C₈

semidirect

115. C₄₇

#7571

semidirect

119. C₄⋊Q₈

C₄₇⋊C₈

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₄⋊(C₄₇⋊C₈)	2
#20241214	2
C₄×C₄⋊Q₈×C₄₇	2
#7571	47

subgroup

index

C₄×C₄⋊(C₄₇⋊C₈)

#20241214

C₄×C₄⋊Q₈×C₄₇

#7571

Subgroups — #26104260

Conjugacy classes of subgroups

Complements

Maximal subgroups