Finite Group Databasebeta

← #238087

Subgroups — #238087

Order 512.

920 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 920 conjugacy classes of subgroups — too many to draw. Only its 178 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#37481C211yesmaximal, characteristic
2#20688C212yesmaximal
3#20688C211yesmaximal, characteristic
4#10393C218yesmaximal
5#8102C212yesmaximal
6#8100C211yesmaximal, characteristic
7C22×#117C2211yescharacteristic
8#2842C2214yes—
9#2667—24no—
10#2629—22no—
11#2608—22no—
12#2441—24no—
13#2280C2212yes—
14#2280C2211yescharacteristic
15#2280C2211yescharacteristic
16#2280C2212yes—
17#1820—22no—
18#1820—24no—
19#1819C2214yes—
20#1819C2218yes—
21#1740—22no—
22#1740—24no—
23#1304C2214yes—
24#1304C2218yes—
25C24×C4C2311yescharacteristic
26C2×#125—22no—
27C2×#117—21no—
28C2×#117—22no—
29C2×#117—22no—
30C2×#117—21no—
31C2×#117—21no—
32C2×#117—22no—
33C2×#117—22no—
34C2×#117—21no—
35C2×#117—22no—
36C2×#117—21no—
37C2×#117D412yes—
38C2×#117D414yes—
39C22×C4⋊C4Q812yes—
40C22×C22⋊C4C2312yes—
41C22×C42Q812yes—
42#399—28no—
43#398—28no—
44#396—28no—
45#396—28no—
46#389—28no—
47#389—24no—
48#387—28no—
49#384—22no—
50#381—21no—
51#381—22no—
52#381D412yes—
53#381D414yes—
54#380—22no—
55#380—22no—
56#380—22no—
57#380—22no—
58#380—22no—
59#380—22no—
60#379C2314yes—
61#379C2312yes—
62#379C2314yes—
63#379C2312yes—
64C4×C22⋊C4—22no—
65C4×C22⋊C4—22no—
66C4×C22⋊C4—22no—
67C4×C22⋊C4—22no—
68C4×C22⋊C4—22no—
69C4×C22⋊C4—22no—
70#342—28no—
71#342—216no—
72C25C2411yescharacteristic
73C23×C4—44no—
74C23×C4C2×D412yes—
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×D412yes—
78C23×C4C2×Q814yes—
79C23×C4C2×Q811yescharacteristic
80C23×C4C2×Q811yescharacteristic
81C23×C4#4111yescharacteristic
82C23×C4#4112yes—
83C23×C4#4112yes—
84C23×C4#4111yescharacteristic
85#125—84no—
86#117—42no—
87#117—41no—
88#117—41no—
89#117—42no—
90#117—41no—
91#117—41no—
92#117—42no—
93#117—42no—
94#117—42no—
95#117—42no—
96#117—44no—
97#117—48no—
98#117—48no—
99#117—44no—
100C2×C4⋊C4—24no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—28no—
108C2×C4⋊C4—28no—
109C2×C4⋊C4—28no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—42no—
113C2×C22⋊C4—22no—
114C2×C22⋊C4—24no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—24no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—24no—
119C2×C22⋊C4—24no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—22no—
123C2×C22⋊C4—24no—
124C2×C22⋊C4—24no—
125C2×C22⋊C4—24no—
126C2×C22⋊C4C2×D414yes—
127C2×C22⋊C4C2×D418yes—
128C2×C42—22no—
129C2×C42—24no—
130C2×C42—22no—
131C2×C42—22no—
132C2×C42—24no—
133C2×C42—24no—
134C2×C42—42no—
135C2×C42—41no—
136#95—28no—
137#95—24no—
138#95—24no—
139#95—24no—
140#95—42no—
141#95—42no—
142#95—42no—
143C24—42no—
144C24—82no—
145C24C22×D411yescharacteristic
146C24C22×D412yes—
147C24C22×Q811yescharacteristic
148C24C2×#4111yescharacteristic
149C24C2×#4112yes—
150C22×C4—28no—
151C22×C4—24no—
152C22×C4—24no—
153C22×C4—28no—
154C22×C4—24no—
155C22×C4—24no—
156C22×C4—24no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—44no—
161C22×C4—44no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—44no—
165C22×C4—44no—
166C22×C4—42no—
167C22×C4—84no—
168C22×C4#12012yes—
169C22×C4#12011yescharacteristic
170C22×C4#12011yescharacteristic
171C22×C4C22⋊Q812yes—
172C22×C4C22⋊Q811yescharacteristic
173C22×C4C22⋊Q812yes—
174C22×C4C22⋊Q811yescharacteristic
175C22×C4C22⋊Q811yescharacteristic
176C22×C4C22⋊Q812yes—
177C22×C4C22⋊Q811yescharacteristic
178C22×C4C22⋊Q812yes—
179C22×C4#12412yes—
180C22×C4#12411yescharacteristic
181C22×C4#12411yescharacteristic
182C22×C4#12412yes—
183C22×C4#12412yes—
184C22×C4#12412yes—
185C22×C4#12412yes—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—48no—
191C4⋊C4—82no—
192C4⋊C4—84no—
193C4⋊C4—82no—
194C4⋊C4—88no—
195C4⋊C4—88no—
196C4⋊C4—88no—
197C22⋊C4—42no—
198C22⋊C4—44no—
199C22⋊C4—42no—
200C22⋊C4—44no—
201C22⋊C4—48no—
202C22⋊C4—44no—
203C22⋊C4—48no—
204C22⋊C4—84no—
205C22⋊C4—82no—
206C22⋊C4—84no—
207C22⋊C4—82no—
208C22⋊C4—84no—
209C22⋊C4—84no—
210C22⋊C4—84no—
211C42—44no—
212C42—42no—
213C42—42no—
214C42—44no—
215C42—84no—
216C42—84no—
217C42—82no—
218C23—22no—
219C23—24no—
220C23—41no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—41no—
229C23—42no—
230C23—88no—
231C23C2×#12011yescharacteristic
232C23C2×C22⋊Q812yes—
233C23C2×C22⋊Q811yescharacteristic
234C23C2×#12412yes—
235C23C2×#12411yescharacteristic
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—48no—
256C2×C4—48no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—48no—
260C2×C4—84no—
261C2×C4—84no—
262C2×C4—84no—
263C2×C4—84no—
264C2×C4—82no—
265C2×C4—84no—
266C2×C4—84no—
267C2×C4—84no—
268C2×C4#39312yes—
269C2×C4#39311yescharacteristic
270C2×C4#39312yes—
271C2×C4#39311yescharacteristic
272C2×C4#39311yescharacteristic
273C2×C4#39311yescharacteristic
274C2×C4#45814yes—
275C22—22no—
276C22—22no—
277C22—21no—
278C22—22no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—22no—
285C22—22no—
286C22—44no—
287C22—82no—
288C22—84no—
289C22—82no—
290C22—84no—
291C22C2×#39311yescharacteristic
292C22C2×#45812yes—
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—84no—
298C4—88no—
299C4—84no—
300C4—164no—
301C4—162no—
302C4#203012yes—
303C4#203012yes—
304C2—22no—
305C2—42no—
306C2—41no—
307C2—42no—
308C2—41no—
309C2C2×#203011yescharacteristic
310C2#2347412yes—
subgroupG/H
center, socleC22C2×#393
commutator, Frattini, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C25 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#374812
#206882
#103932
#81022
#81002