Finite Group Databasebeta

← #95129

Subgroups — #95129

Order 512.

914 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20715C212yesmaximal
2C4×#381C211yesmaximal, characteristic
3#7032C214yesmaximal
4C23×C42C2211yescharacteristic
5C2×#432—22no—
6C2×#381C412yes—
7C2×C4×C22⋊C4C412yes—
8#1817—22no—
9#1797—22no—
10#1797C414yescomplemented
11#1779C2214yes—
12#1749—22no—
13#1749C414yescomplemented
14#1434—22no—
15C22⋊#95C2212yes—
16C4×#95—22no—
17C24×C4C2×C411yescharacteristic
18C24×C4C2×C411yescharacteristic
19C24×C4C2311yescharacteristic
20C22×C22⋊C4C2×C414yes—
21C22×C42—22no—
22C22×C42—44no—
23C22×C42C2×C412yes—
24C22×C42C2×C412yes—
25C22×C42D412yes—
26C22×C42D412yes—
27C22×C42D412yes—
28C22×C42Q812yes—
29#432—48no—
30C2×C4⋊C8—24no—
31C2×C22⋊C8—24no—
32C2×C22⋊C8—24no—
33C2×C22⋊C8C2×C418yes—
34C2×#97—24no—
35#381—28no—
36C4×C22⋊C4—44no—
37C2×#95—24no—
38C2×#95—22no—
39C2×#95—24no—
40#336—24no—
41#336—24no—
42C25C22×C411yescharacteristic
43C23×C4—24no—
44C23×C4—24no—
45C23×C4—24no—
46C23×C4—44no—
47C23×C4—44no—
48C23×C4—42no—
49C23×C4—42no—
50C23×C4—42no—
51C23×C4C4212yes—
52C23×C4C4211yescharacteristic
53C23×C4C4211yescharacteristic
54C23×C4C22⋊C412yes—
55C23×C4C22⋊C411yescharacteristic
56C23×C4C22⋊C411yescharacteristic
57C23×C4C4⋊C412yes—
58C23×C4C4⋊C412yes—
59C23×C4C22×C412yes—
60C23×C4C2×D411yescharacteristic
61C23×C4C2×D412yes—
62C23×C4C2×Q811yescharacteristic
63C22×C8—28no—
64C2×C22⋊C4—24no—
65C2×C22⋊C4—44no—
66C2×C22⋊C4—44no—
67C2×C22⋊C4M1618yes—
68C2×C42—28no—
69C2×C42—44no—
70C2×C42—44no—
71C2×C42—44no—
72C2×C42—44no—
73C2×C42—44no—
74C2×C42—44no—
75C2×C42—48no—
76C2×C42C22⋊C412yes—
77C2×C42C22⋊C412yes—
78C2×C42C22⋊C412yes—
79C2×C42C22⋊C412yes—
80C2×C42C4⋊C412yes—
81C2×C42C4⋊C412yes—
82C2×C42C4⋊C412yes—
83C2×C42C4⋊C412yes—
84C4⋊C8—48no—
85C22⋊C8—48no—
86C22⋊C8—48no—
87C22⋊C8—48no—
88#97—48no—
89#95—216no—
90#95—48no—
91#95—44no—
92C24—22no—
93C24—22no—
94C24—42no—
95C24—42no—
96C24C2×C4211yescharacteristic
97C24C2×C22⋊C411yescharacteristic
98C24C2×C4⋊C411yescharacteristic
99C24C2×M1614yes—
100C22×C4—22no—
101C22×C4—24no—
102C22×C4—22no—
103C22×C4—22no—
104C22×C4—24no—
105C22×C4—24no—
106C22×C4—24no—
107C22×C4—24no—
108C22×C4—24no—
109C22×C4—24no—
110C22×C4—24no—
111C22×C4—24no—
112C22×C4—24no—
113C22×C4—24no—
114C22×C4—24no—
115C22×C4—24no—
116C22×C4—28no—
117C22×C4—41no—
118C22×C4—41no—
119C22×C4—42no—
120C22×C4—42no—
121C22×C4—41no—
122C22×C4—41no—
123C22×C4—42no—
124C22×C4—41no—
125C22×C4—41no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—42no—
132C22×C4—416no—
133C22×C4—48no—
134C22×C4—48no—
135C22×C4—416no—
136C22×C4—48no—
137C22×C4—48no—
138C22×C4—44no—
139C22×C4—44no—
140C22×C4#9512yes—
141C22×C4#9512yes—
142C22×C4#9512yes—
143C22×C4#9512yes—
144C22×C4#9914yes—
145C22×C4C2×C22⋊C412yes—
146C22×C4C2×C4⋊C412yes—
147C2×C8—48no—
148C2×C8—48no—
149C2×C8—48no—
150C22⋊C4—48no—
151C22⋊C4—48no—
152C42—24no—
153C42—24no—
154C42—24no—
155C42—24no—
156C42—42no—
157C42—42no—
158C42—42no—
159C42—42no—
160C42—88no—
161C23—22no—
162C23—22no—
163C23—24no—
164C23—24no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—22no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23—48no—
174C23—44no—
175C23—44no—
176C23—48no—
177C23C2×#9511yescharacteristic
178C23C4×M1612yes—
179C23#40712yes—
180C23C2×#9912yes—
181C23#41312yes—
182C23#42312yes—
183C2×C4—28no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—44no—
200C2×C4—44no—
201C2×C4—48no—
202C2×C4—48no—
203C2×C4—48no—
204C2×C4—48no—
205C2×C4—44no—
206C2×C4—44no—
207C2×C4—48no—
208C2×C4—44no—
209C2×C4—48no—
210C2×C4—416no—
211C2×C4—48no—
212C2×C4—84no—
213C2×C4—84no—
214C2×C4—88no—
215C2×C4#34214yes—
216C2×C4#34414yes—
217C2×C4#41014yes—
218C8—88no—
219C22—22no—
220C22—24no—
221C22—22no—
222C22—24no—
223C22—22no—
224C22—22no—
225C22—24no—
226C22—24no—
227C22—48no—
228C22—48no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22#146514yes—
236C22#172811yescharacteristic
237C22C2×#34211yescharacteristic
238C22#174012yes—
239C22#174211yescharacteristic
240C22C2×#34412yes—
241C4—24no—
242C4—24no—
243C4—24no—
244C4—42no—
245C4—42no—
246C4—42no—
247C4—88no—
248C2—24no—
249C2—42no—
250C2—42no—
251C2#791111yescharacteristic
252C2#793012yes—
253C2#810211yescharacteristic
254C2#810612yes—
255C2#811411yescharacteristic
subgroupG/H
center, socleC23C2×#95
commutatorC24C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. #1797C4semidirect
13. #1749C4semidirect

Maximal subgroups

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

subgroupindex
#207152
C4×#3812
#70322