Finite Group Databasebeta

← #98511

Subgroups — #98511

Order 512.

778 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×#2565C211yesmaximal, characteristic
2#8718C212yesmaximal
3#8153C212yesmaximal
4#7629C212yesmaximal
5C22×#125C411yescharacteristic
6C22×C4×Q8C411yescharacteristic
7#2565—24no—
8#2565—24no—
9C2×#398—22no—
10C2×#391C411yescharacteristic
11C2×#391C2211yescharacteristic
12C2×#387—22no—
13C2×#384C411yescharacteristic
14C2×#382C2211yescharacteristic
15C2×C4×C4⋊C4C2211yescharacteristic
16#1749C2214yes—
17C2×#324—22no—
18#1295—24no—
19#1280—22no—
20#1272—24no—
21C23×Q8C2×C411yescharacteristic
22C2×#125—22no—
23C2×#125—22no—
24C2×#125—42no—
25C2×#125—42no—
26C2×C4×Q8—22no—
27C2×C4×Q8—22no—
28C2×C4×Q8—42no—
29C2×C4×Q8—42no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4C2×C411yescharacteristic
35C22×C4⋊C4C2×C411yescharacteristic
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4D412yes—
38C22×C42—21no—
39C22×C42C2×C411yescharacteristic
40C22×C42C2×C411yescharacteristic
41C22×C42C2311yescharacteristic
42C2×C22⋊C8—24no—
43C2×#97—24no—
44#398—216no—
45#391—22no—
46#391—22no—
47#391—22no—
48#391D414yes—
49#387—216no—
50#384—22no—
51#384—22no—
52#382—22no—
53#382D414yes—
54C4×C4⋊C4—22no—
55C4×C4⋊C4—22no—
56C2×#95—22no—
57C2×#95—22no—
58C2×#95—22no—
59C2×#95D412yes—
60#336—24no—
61#324—28no—
62C22×Q8—24no—
63C22×Q8—21no—
64C22×Q8—42no—
65C22×Q8—41no—
66C22×Q8—41no—
67C22×Q8C22⋊C412yes—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4C22⋊C411yescharacteristic
73C23×C4C22⋊C411yescharacteristic
74C23×C4C22⋊C412yes—
75C23×C4C22×C411yescharacteristic
76C23×C4C2×D412yes—
77C22×C8—44no—
78#125—48no—
79#125—48no—
80C4×Q8—48no—
81C4×Q8—48no—
82C2×C4⋊C4—24no—
83C2×C4⋊C4—24no—
84C2×C4⋊C4—24no—
85C2×C4⋊C4—28no—
86C2×C4⋊C4—24no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—24no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—41no—
97C2×C4⋊C4—41no—
98C2×C4⋊C4—44no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—42no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—44no—
106C2×C4⋊C4C22⋊C412yes—
107C2×C4⋊C4C22⋊C412yes—
108C2×C4⋊C4C22⋊C412yes—
109C2×C42—22no—
110C2×C42—22no—
111C2×C42—21no—
112C2×C42—21no—
113C2×C42—24no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—42no—
117C2×C42—42no—
118C2×C42—42no—
119C2×C42—42no—
120C2×C42C2×D412yes—
121C2×C42C2×D412yes—
122C22⋊C8—28no—
123C22⋊C8—44no—
124#97—48no—
125#95—28no—
126#95—28no—
127#95—28no—
128#95—24no—
129C24C2×C22⋊C411yescharacteristic
130C2×Q8—24no—
131C2×Q8—22no—
132C2×Q8—42no—
133C2×Q8—48no—
134C2×Q8—48no—
135C2×Q8—42no—
136C2×Q8—42no—
137C2×Q8—42no—
138C2×Q8#10114yes—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—44no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4#10012yes—
178C22×C4#10012yes—
179C22×C4#10414yes—
180C22×C4C2×C22⋊C411yescharacteristic
181C22×C4C2×C22⋊C411yescharacteristic
182C22×C4#12014yes—
183C2×C8—48no—
184C2×C8—84no—
185C2×C8—84no—
186C4⋊C4—48no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—416no—
191C4⋊C4—42no—
192C4⋊C4—48no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—48no—
196C4⋊C4—48no—
197C42—24no—
198C42—24no—
199C42—24no—
200C42—42no—
201C42—42no—
202C42—48no—
203C42—42no—
204C23—22no—
205C23—21no—
206C23—21no—
207C23#37911yescharacteristic
208C23C2×#10011yescharacteristic
209C23C2×#10011yescharacteristic
210C23C2×#10412yes—
211C23#42112yes—
212Q8—44no—
213Q8—48no—
214Q8—44no—
215C2×C4—24no—
216C2×C4—24no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—24no—
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—44no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4#41012yes—
260C2×C4C2×#10112yes—
261C8—88no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22#152511yescharacteristic
271C22#153012yes—
272C22#153611yescharacteristic
273C22#178211yescharacteristic
274C22#178311yescharacteristic
275C22#178411yescharacteristic
276C22#178912yes—
277C22#179612yes—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—44no—
282C4—42no—
283C4—44no—
284C4—44no—
285C4—82no—
286C4—82no—
287C4—82no—
288C2—21no—
289C2—21no—
290C2—22no—
291C2#833711yescharacteristic
292C2#836312yes—
293C2#837412yes—
294C2#852411yescharacteristic
295C2#855511yescharacteristic
subgroupG/H
center, socleC23#379
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25652
#87182
#81532
#76292