Finite Group Databasebeta

← #95120

Subgroups — #95120

Order 512.

1030 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 170 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
2#13756C211yesmaximal, characteristic
3#7032C214yesmaximal
4C22×#117C412yes—
5C23×C42C2211yescharacteristic
6C2×#432—22no—
7#1817—22no—
8#1797—22no—
9#1797C414yescomplemented
10#1779C2214yes—
11#1749—22no—
12#1749C414yescomplemented
13C4⋊#95—22no—
14C22⋊#95C412yes—
15C22⋊#95C2212yes—
16C4×#95—22no—
17C24×C4C2×C411yescharacteristic
18C24×C4C2×C411yescharacteristic
19C24×C4C2311yescharacteristic
20C2×#117—28no—
21C2×#117—44no—
22C2×#117—44no—
23C22×C4⋊C4—22no—
24C22×C22⋊C4C2×C414yes—
25C22×C42—22no—
26C22×C42—44no—
27C22×C42C2×C412yes—
28C22×C42C2×C412yes—
29C22×C42D412yes—
30C22×C42D411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D412yes—
33C22×C42Q811yescharacteristic
34C22×C42Q811yescharacteristic
35#432—48no—
36C2×C4⋊C8—24no—
37C2×C22⋊C8—24no—
38C2×C22⋊C8—24no—
39C2×C22⋊C8C2×C418yes—
40C2×#97—24no—
41C2×#95—24no—
42C2×#95—24no—
43#336—24no—
44#336—24no—
45C25C22×C411yescharacteristic
46C23×C4—24no—
47C23×C4—24no—
48C23×C4—22no—
49C23×C4—22no—
50C23×C4—24no—
51C23×C4—44no—
52C23×C4—44no—
53C23×C4—42no—
54C23×C4—42no—
55C23×C4C4211yescharacteristic
56C23×C4C4211yescharacteristic
57C23×C4C4212yes—
58C23×C4C22⋊C412yes—
59C23×C4C22⋊C411yescharacteristic
60C23×C4C22⋊C411yescharacteristic
61C23×C4C4⋊C411yescharacteristic
62C23×C4C4⋊C411yescharacteristic
63C23×C4C4⋊C411yescharacteristic
64C23×C4C4⋊C411yescharacteristic
65C23×C4C22×C412yes—
66C23×C4C2×D411yescharacteristic
67C23×C4C2×D412yes—
68C23×C4C2×Q811yescharacteristic
69C22×C8—28no—
70#117—432no—
71C2×C4⋊C4—28no—
72C2×C4⋊C4—44no—
73C2×C4⋊C4—44no—
74C2×C22⋊C4—24no—
75C2×C22⋊C4—44no—
76C2×C22⋊C4—44no—
77C2×C22⋊C4M1618yes—
78C2×C42—28no—
79C2×C42—28no—
80C2×C42—44no—
81C2×C42—44no—
82C2×C42—42no—
83C2×C42—42no—
84C2×C42—42no—
85C2×C42—42no—
86C2×C42—44no—
87C2×C42—44no—
88C2×C42—44no—
89C2×C42C22⋊C412yes—
90C2×C42C22⋊C412yes—
91C2×C42C22⋊C412yes—
92C2×C42C22⋊C412yes—
93C2×C42C4⋊C412yes—
94C2×C42C4⋊C412yes—
95C2×C42C4⋊C412yes—
96C2×C42C4⋊C412yes—
97C4⋊C8—48no—
98C22⋊C8—48no—
99C22⋊C8—48no—
100C22⋊C8—48no—
101#97—48no—
102#95—48no—
103#95—48no—
104C24—22no—
105C24—21no—
106C24—21no—
107C24—42no—
108C24—42no—
109C24C2×C4211yescharacteristic
110C24C2×C22⋊C411yescharacteristic
111C24C2×C4⋊C411yescharacteristic
112C24C2×M1614yes—
113C22×C4—216no—
114C22×C4—216no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—22no—
119C22×C4—22no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—24no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—28no—
141C22×C4—42no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—42no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—416no—
154C22×C4—416no—
155C22×C4—48no—
156C22×C4—48no—
157C22×C4—44no—
158C22×C4—44no—
159C22×C4#9512yes—
160C22×C4#9511yescharacteristic
161C22×C4#9511yescharacteristic
162C22×C4#9511yescharacteristic
163C22×C4#9511yescharacteristic
164C22×C4#9512yes—
165C22×C4#9914yes—
166C22×C4#10012yes—
167C22×C4#10112yes—
168C22×C4C2×C22⋊C412yes—
169C22×C4C2×C4⋊C412yes—
170C2×C8—48no—
171C2×C8—48no—
172C2×C8—48no—
173C4⋊C4—416no—
174C22⋊C4—48no—
175C22⋊C4—48no—
176C42—24no—
177C42—24no—
178C42—24no—
179C42—24no—
180C42—42no—
181C42—42no—
182C42—42no—
183C42—42no—
184C42—416no—
185C23—22no—
186C23—22no—
187C23—24no—
188C23—24no—
189C23—21no—
190C23—21no—
191C23—22no—
192C23—22no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23—22no—
197C23—48no—
198C23—44no—
199C23—44no—
200C23—44no—
201C23—44no—
202C23C2×#9511yescharacteristic
203C23C4×M1612yes—
204C23#40712yes—
205C23C2×#9912yes—
206C23C2×#10011yescharacteristic
207C23C2×#10111yescharacteristic
208C23#42312yes—
209C2×C4—28no—
210C2×C4—28no—
211C2×C4—28no—
212C2×C4—28no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—24no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4—48no—
238C2×C4—48no—
239C2×C4—48no—
240C2×C4—48no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—416no—
244C2×C4—48no—
245C2×C4—84no—
246C2×C4—88no—
247C2×C4—84no—
248C2×C4#34212yes—
249C2×C4#34212yes—
250C2×C4#34312yes—
251C2×C4#34312yes—
252C2×C4#34414yes—
253C2×C4#41014yes—
254C8—88no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—24no—
260C22—22no—
261C22—22no—
262C22—24no—
263C22—24no—
264C22—48no—
265C22—48no—
266C22—41no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22#146212yes—
273C22#146312yes—
274C22#172811yescharacteristic
275C22C2×#34211yescharacteristic
276C22#174012yes—
277C22C2×#34311yescharacteristic
278C22C2×#34412yes—
279C4—24no—
280C4—24no—
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—42no—
286C4—42no—
287C4—88no—
288C2—22no—
289C2—22no—
290C2—42no—
291C2—42no—
292C2#790911yescharacteristic
293C2#793012yes—
294C2#810011yescharacteristic
295C2#810912yes—
296C2#811211yescharacteristic
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
9. #1797C4semidirect
12. #1749C4semidirect

Maximal subgroups

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

subgroupindex
#207152
#137562
#70322