Group #24984579 — subgroups

Subgroups — #24984579

Order 11008.

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⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
2	#19132421	C₂	1	4	yes	maximal
3	C₄×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
5	C₂×C₄×C₄₃⋊C₈	—	2	2	no	—
6	#14582654	C₂²	1	4	yes	—
7	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₄₃	C₄	1	2	yes	—
9	C₄₃×#391	C₂²	1	2	yes	—
10	C₄₃×#389	—	2	2	no	—
11	C₄₃×#384	C₄	1	1	yes	characteristic
12	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
13	C₄³×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄₃⋊C₈	—	2	4	no	—
15	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
16	C₄×C₄₃⋊C₈	—	4	4	no	—
17	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄⋊Q₈×C₄₃	—	2	2	no	—
19	C₄⋊Q₈×C₄₃	C₈	1	4	yes	complemented
20	C₄×Q₈×C₄₃	—	4	4	no	—
21	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
22	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
24	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₄₃	—	2	2	no	—
26	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₄₃	D₄	1	2	yes	—
29	C₂×C₄²×C₄₃	D₄	1	2	yes	—
30	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
31	#95×C₄₃	—	2	4	no	—
32	C₂×Q₈×C₄₃	—	2	2	no	—
33	C₂×Q₈×C₄₃	—	4	2	no	—
34	C₂×Q₈×C₄₃	—	4	2	no	—
35	C₂×Q₈×C₄₃	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₄₃	—	2	2	no	—
37	C₂²×C₄×C₄₃	—	2	2	no	—
38	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
43	C₄⋊C₄×C₄₃	—	2	8	no	—
44	C₄⋊C₄×C₄₃	—	4	2	no	—
45	C₄⋊C₄×C₄₃	—	4	4	no	—
46	C₄⋊C₄×C₄₃	—	4	4	no	—
47	C₄²×C₄₃	—	2	2	no	—
48	C₄²×C₄₃	—	2	4	no	—
49	C₄²×C₄₃	—	4	1	no	—
50	C₄²×C₄₃	—	4	4	no	—
51	C₄²×C₄₃	C₂×C₈	1	2	yes	—
52	C₄²×C₄₃	M₁₆	1	2	yes	—
53	C₄²×C₄₃	SD₁₆	1	4	yes	—
54	C₄²×C₄₃	Q₁₆	1	4	yes	—
55	C₂×C₄₃⋊C₈	—	2	8	no	—
56	C₂×C₄₃⋊C₈	—	4	4	no	—
57	C₂×C₄₃⋊C₈	—	4	4	no	—
58	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	Q₈×C₄₃	—	4	4	no	—
60	Q₈×C₄₃	—	4	4	no	—
61	C₂×C₄×C₄₃	—	2	2	no	—
62	C₂×C₄×C₄₃	—	2	1	no	—
63	C₂×C₄×C₄₃	—	2	1	no	—
64	C₂×C₄×C₄₃	—	2	2	no	—
65	C₂×C₄×C₄₃	—	2	4	no	—
66	C₂×C₄×C₄₃	—	2	1	no	—
67	C₂×C₄×C₄₃	—	2	2	no	—
68	C₂×C₄×C₄₃	—	4	2	no	—
69	C₂×C₄×C₄₃	—	4	2	no	—
70	C₂×C₄×C₄₃	—	4	2	no	—
71	C₂×C₄×C₄₃	—	4	4	no	—
72	C₂×C₄×C₄₃	C₂²⋊C₈	1	4	yes	—
73	C₂×C₄×C₄₃	#100	1	2	yes	—
74	C₂×C₄×C₄₃	#103	1	4	yes	—
75	C₂×C₄×C₄₃	#103	1	4	yes	—
76	C₂×C₄×C₄₃	#104	1	4	yes	—
77	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
79	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
80	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
81	C₄₃⋊C₈	—	4	8	no	—
82	#7571	—	43	1	no	maximal, Sylow
83	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
84	C₂²×C₄₃	#410	1	1	yes	characteristic
85	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
86	C₂²×C₄₃	C₂×#103	1	2	yes	—
87	C₂²×C₄₃	C₂×#104	1	2	yes	—
88	C₄×C₄₃	—	2	1	no	—
89	C₄×C₄₃	—	2	1	no	—
90	C₄×C₄₃	—	2	2	no	—
91	C₄×C₄₃	—	2	2	no	—
92	C₄×C₄₃	—	4	4	no	—
93	C₄×C₄₃	—	4	1	no	—
94	C₄×C₄₃	—	8	2	no	—
95	C₄×C₄₃	Q₈⋊C₈	1	8	yes	—
96	C₄×C₄₃	#333	1	4	yes	—
97	C₄×C₄⋊Q₈	D₄₃	1	1	yes	characteristic
98	C₄×C₄⋊C₈	—	43	2	no	—
99	#1272	—	43	4	no	—
100	C₂×C₄₃	#1460	1	1	yes	characteristic
101	C₂×C₄₃	C₂×Q₈⋊C₈	1	2	yes	—
102	C₂×C₄₃	#1503	1	2	yes	—
103	C₂×C₄₃	#1525	1	1	yes	characteristic
104	C₂×C₄₃	C₂×#333	1	1	yes	characteristic
105	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
106	C₂×C₄×Q₈	Dic₄₃	1	2	yes	—
107	C₂×C₄⋊C₈	—	86	2	no	—
108	C₂×C₄×C₈	—	86	2	no	—
109	#391	C₂×D₄₃	1	2	yes	—
110	#389	—	2	2	no	—
111	#384	Dic₄₃	1	1	yes	characteristic
112	C₄×C₄⋊C₄	—	2	2	no	—
113	C₄³	C₂×D₄₃	1	1	yes	characteristic
114	#336	—	43	4	no	—
115	C₄₃	#7571	1	1	yes	characteristic, complemented, Sylow
116	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
117	C₂²×C₈	—	86	4	no	—
118	C₄⋊Q₈	—	2	2	no	—
119	C₄⋊Q₈	C₄₃⋊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×Dic₄₃	1	2	yes	—
125	C₂×C₄²	—	2	2	no	—
126	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
127	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
129	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
130	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
131	C₄⋊C₈	—	86	8	no	—
132	C₄×C₈	—	172	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×C₄₃⋊C₈	1	4	yes	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊Dic₄₃	1	2	yes	—
142	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
143	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
145	C₂×C₈	—	86	8	no	—
146	C₂×C₈	—	172	4	no	—
147	C₂×C₈	—	172	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×C₄₃⋊C₈	1	2	yes	—
157	C₄²	#10621877	1	2	yes	—
158	C₄²	#10621884	1	4	yes	—
159	C₄²	#10621885	1	4	yes	—
160	C₂³	C₂×C₂²⋊Dic₄₃	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⋊(C₄₃⋊C₈)	1	4	yes	—
175	C₂×C₄	#13063242	1	2	yes	—
176	C₂×C₄	#13063249	1	4	yes	—
177	C₂×C₄	#13063249	1	4	yes	—
178	C₂×C₄	#13063252	1	4	yes	—
179	C₂×C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
180	C₂×C₄	C₂×#10621877	1	1	yes	characteristic
181	C₂×C₄	C₂×#10621884	1	2	yes	—
182	C₂×C₄	C₂×#10621885	1	2	yes	—
183	C₈	—	172	8	no	—
184	C₂²	C₂×C₂²⋊(C₄₃⋊C₈)	1	1	yes	characteristic
185	C₂²	#14582873	1	1	yes	characteristic
186	C₂²	C₂×#13063242	1	1	yes	characteristic
187	C₂²	C₂×#13063249	1	2	yes	—
188	C₂²	C₂×#13063252	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	2	2	no	—
191	C₄	—	2	1	no	—
192	C₄	—	2	1	no	—
193	C₄	—	4	1	no	—
194	C₄	—	4	4	no	—
195	C₄	—	8	2	no	—
196	C₄	Q₈⋊(C₄₃⋊C₈)	1	8	yes	—
197	C₄	#14582648	1	4	yes	—
198	C₂	#19132916	1	1	yes	characteristic
199	C₂	C₂×Q₈⋊(C₄₃⋊C₈)	1	2	yes	—
200	C₂	#19133094	1	2	yes	—
201	C₂	#19133187	1	1	yes	characteristic
202	C₂	C₂×#14582648	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal

#19132421

C₂

yes

maximal

C₄×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

—

C₂×C₄×C₄₃⋊C₈

—

#14582654

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₃

C₄

yes

characteristic

C₂×C₄×Q₈×C₄₃

C₄

yes

—

C₄₃×#391

C₂²

yes

—

C₄₃×#389

—

C₄₃×#384

C₄

yes

characteristic

C₄×C₄⋊C₄×C₄₃

—

C₄³×C₄₃

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

—

C₄⋊(C₄₃⋊C₈)

—

C₄×C₄₃⋊C₈

—

C₂²×Q₈×C₄₃

C₂×C₄

yes

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₈

yes

complemented

C₄×Q₈×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

D₄

yes

—

C₂×C₄²×C₄₃

C₂³

yes

characteristic

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₈

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₄₃

C₂×D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

M₁₆

yes

—

C₄²×C₄₃

SD₁₆

yes

—

C₄²×C₄₃

Q₁₆

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₈

yes

—

C₂×C₄×C₄₃

#100

yes

—

C₂×C₄×C₄₃

#103

yes

—

C₂×C₄×C₄₃

#103

yes

—

C₂×C₄×C₄₃

#104

yes

—

C₂×C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×SD₁₆

yes

—

C₂×C₄×C₄₃

C₂×Q₁₆

yes

—

C₄₃⋊C₈

—

#7571

—

maximal, Sylow

C₂²×C₄₃

C₂×C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₂²×C₄₃

C₂×#104

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

Q₈⋊C₈

yes

—

C₄×C₄₃

#333

yes

—

C₄×C₄⋊Q₈

D₄₃

yes

characteristic

C₄×C₄⋊C₈

—

#1272

—

100

C₂×C₄₃

#1460

yes

characteristic

101

C₂×C₄₃

C₂×Q₈⋊C₈

yes

—

102

C₂×C₄₃

#1503

yes

—

103

C₂×C₄₃

#1525

yes

characteristic

104

C₂×C₄₃

C₂×#333

yes

characteristic

105

C₂×C₄⋊Q₈

Dic₄₃

yes

characteristic

106

C₂×C₄×Q₈

Dic₄₃

yes

—

107

C₂×C₄⋊C₈

—

108

C₂×C₄×C₈

—

109

#391

C₂×D₄₃

yes

—

110

#389

—

111

#384

Dic₄₃

yes

characteristic

112

C₄×C₄⋊C₄

—

113

C₄³

C₂×D₄₃

yes

characteristic

114

#336

—

115

C₄₃

#7571

yes

characteristic, complemented, Sylow

116

C₂²×Q₈

C₂×Dic₄₃

yes

—

117

C₂²×C₈

—

118

C₄⋊Q₈

—

119

C₄⋊Q₈

C₄₃⋊C₈

yes

complemented

120

C₄×Q₈

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

C₂×Dic₄₃

yes

—

125

C₂×C₄²

—

126

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

127

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

128

C₂×C₄²

C₂²⋊D₄₃

yes

—

129

C₂×C₄²

C₂²⋊D₄₃

yes

—

130

C₂×C₄²

C₂²×D₄₃

yes

characteristic

131

C₄⋊C₈

—

132

C₄×C₈

—

172

—

133

#95

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂×Q₈

—

137

C₂×Q₈

C₂×C₄₃⋊C₈

yes

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

141

C₂²×C₄

C₂²⋊Dic₄₃

yes

—

142

C₂²×C₄

C₂²⋊Dic₄₃

yes

characteristic

143

C₂²×C₄

C₂²×Dic₄₃

yes

characteristic

144

C₂²×C₄

C₂×C₂²⋊D₄₃

yes

—

145

C₂×C₈

—

146

C₂×C₈

—

172

—

147

C₂×C₈

—

172

—

148

C₄⋊C₄

—

149

C₄⋊C₄

—

150

C₄⋊C₄

—

151

C₄⋊C₄

—

152

C₄²

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

156

C₄²

C₂×C₄₃⋊C₈

yes

—

157

C₄²

#10621877

yes

—

158

C₄²

#10621884

yes

—

159

C₄²

#10621885

yes

—

160

C₂³

C₂×C₂²⋊Dic₄₃

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⋊(C₄₃⋊C₈)

yes

—

175

C₂×C₄

#13063242

yes

—

176

C₂×C₄

#13063249

yes

—

177

C₂×C₄

#13063249

yes

—

178

C₂×C₄

#13063252

yes

—

179

C₂×C₄

C₂²×C₄₃⋊C₈

yes

characteristic

180

C₂×C₄

C₂×#10621877

yes

characteristic

181

C₂×C₄

C₂×#10621884

yes

—

182

C₂×C₄

C₂×#10621885

yes

—

183

C₈

—

172

—

184

C₂²

C₂×C₂²⋊(C₄₃⋊C₈)

yes

characteristic

185

C₂²

#14582873

yes

characteristic

186

C₂²

C₂×#13063242

yes

characteristic

187

C₂²

C₂×#13063249

yes

—

188

C₂²

C₂×#13063252

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

—

196

C₄

Q₈⋊(C₄₃⋊C₈)

yes

—

197

C₄

#14582648

yes

—

198

C₂

#19132916

yes

characteristic

199

C₂

C₂×Q₈⋊(C₄₃⋊C₈)

yes

—

200

C₂

#19133094

yes

—

201

C₂

#19133187

yes

characteristic

202

C₂

C₂×#14582648

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄×C₄⋊Q₈×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#7571
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂²×C₄

C₂²⋊Dic₄₃

commutator

C₂×C₄×C₄₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₄₃

Fitting

C₄×C₄⋊Q₈×C₄₃

C₂

socle, prime radical

C₂³×C₄₃

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₄₃

C₂³

hypercenter

C₄×C₄⋊Q₈

D₄₃

hypocenter

C₄₃

#7571

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
19. C₄⋊Q₈×C₄₃	C₈	semidirect
115. C₄₃	#7571	semidirect
119. C₄⋊Q₈	C₄₃⋊C₈	semidirect

H ≅ G/N

type

19. C₄⋊Q₈×C₄₃

C₈

semidirect

115. C₄₃

#7571

semidirect

119. C₄⋊Q₈

C₄₃⋊C₈

semidirect

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

subgroup	index
C₄×C₄⋊(C₄₃⋊C₈)	2
#19132421	2
C₄×C₄⋊Q₈×C₄₃	2
#7571	43

subgroup

index

C₄×C₄⋊(C₄₃⋊C₈)

#19132421

C₄×C₄⋊Q₈×C₄₃

#7571

Subgroups — #24984579

Conjugacy classes of subgroups

Complements

Maximal subgroups