Finite Group Databasebeta

← #97088

Subgroups — #97088

Order 512.

1070 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 1070 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C22×#400C211yesmaximal, characteristic
2#8698C212yesmaximal
3#8698C212yesmaximal
4#8299C212yesmaximal
5C23×C4⋊C4C411yescharacteristic
6C23×C4⋊C4C2211yescharacteristic
7C2×#400—24no—
8C2×#400—24no—
9C2×#400—24no—
10C22×#95C411yescharacteristic
11C22×#95C411yescharacteristic
12C22×#95C411yescharacteristic
13C22×#95C2211yescharacteristic
14C22×#95C2211yescharacteristic
15#1779C2214yes—
16C2×#324—24no—
17#1280—24no—
18#1280—24no—
19C24×C4C2×C411yescharacteristic
20C24×C4C2×C411yescharacteristic
21C24×C4C2×C411yescharacteristic
22C24×C4C2×C411yescharacteristic
23C24×C4C2×C411yescharacteristic
24C24×C4C2×C411yescharacteristic
25C24×C4C2311yescharacteristic
26C22×C4⋊C4—22no—
27C22×C4⋊C4—22no—
28C22×C4⋊C4—22no—
29C22×C4⋊C4—22no—
30C22×C4⋊C4—22no—
31C22×C4⋊C4—44no—
32C22×C4⋊C4—44no—
33C22×C4⋊C4D414yes—
34C2×C22⋊C8—24no—
35C2×C22⋊C8—24no—
36C2×C22⋊C8—24no—
37#400—232no—
38C2×#95—22no—
39C2×#95—22no—
40C2×#95—22no—
41C2×#95—22no—
42C2×#95—22no—
43C2×#95—22no—
44C2×#95—22no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—22no—
49C2×#95—22no—
50C2×#95—22no—
51C2×#95D414yes—
52C2×#95D414yes—
53#324—48no—
54C25C22×C411yescharacteristic
55C23×C4—21no—
56C23×C4—21no—
57C23×C4—21no—
58C23×C4—21no—
59C23×C4—24no—
60C23×C4—24no—
61C23×C4—21no—
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—24no—
70C23×C4—24no—
71C23×C4—24no—
72C23×C4—42no—
73C23×C4—42no—
74C23×C4—42no—
75C23×C4—42no—
76C23×C4—42no—
77C23×C4—42no—
78C23×C4—42no—
79C23×C4—42no—
80C23×C4—42no—
81C23×C4—42no—
82C23×C4—42no—
83C23×C4—42no—
84C23×C4—42no—
85C23×C4—42no—
86C23×C4—42no—
87C23×C4—42no—
88C23×C4C22⋊C412yes—
89C23×C4C22⋊C412yes—
90C23×C4C22⋊C412yes—
91C23×C4C22⋊C412yes—
92C23×C4C22⋊C412yes—
93C23×C4C22⋊C412yes—
94C23×C4C2×D412yes—
95C23×C4C2×D412yes—
96C23×C4C2×D412yes—
97C22×C8—44no—
98C2×C4⋊C4—28no—
99C2×C4⋊C4—28no—
100C2×C4⋊C4—28no—
101C2×C4⋊C4—44no—
102C2×C4⋊C4—48no—
103C2×C4⋊C4—48no—
104C2×C4⋊C4—48no—
105C2×C4⋊C4—48no—
106C2×C4⋊C4—44no—
107C2×C4⋊C4—44no—
108C22⋊C8—48no—
109C22⋊C8—48no—
110C22⋊C8—48no—
111#95—28no—
112#95—28no—
113#95—28no—
114#95—28no—
115#95—28no—
116C24—22no—
117C24—22no—
118C24—22no—
119C24—22no—
120C24—22no—
121C24—22no—
122C24C2×C22⋊C411yescharacteristic
123C24C2×C22⋊C411yescharacteristic
124C24C2×C22⋊C411yescharacteristic
125C24#13114yes—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—24no—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—24no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—24no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—24no—
145C22×C4—24no—
146C22×C4—24no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—416no—
154C22×C4—42no—
155C22×C4—416no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—88no—
198C22×C4—88no—
199C22×C4—88no—
200C22×C4—88no—
201C22×C4—88no—
202C22×C4#9914yes—
203C22×C4#10114yes—
204C22×C4#12014yes—
205C2×C8—84no—
206C2×C8—84no—
207C2×C8—84no—
208C4⋊C4—416no—
209C4⋊C4—416no—
210C23—28no—
211C23—28no—
212C23—28no—
213C23—28no—
214C23—28no—
215C23—28no—
216C23—28no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23#37911yescharacteristic
230C23#40812yes—
231C23#40812yes—
232C23#40812yes—
233C23C2×#9912yes—
234C23#41012yes—
235C23#41012yes—
236C23C2×#10112yes—
237C23#41312yes—
238C23#41312yes—
239C2×C4—28no—
240C2×C4—24no—
241C2×C4—24no—
242C2×C4—24no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—48no—
246C2×C4—44no—
247C2×C4—48no—
248C2×C4—48no—
249C2×C4—48no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—84no—
269C2×C4—84no—
270C2×C4—84no—
271C2×C4—84no—
272C2×C4—84no—
273C2×C4—84no—
274C2×C4—84no—
275C2×C4—84no—
276C2×C4—84no—
277C2×C4—84no—
278C2×C4—84no—
279C2×C4—84no—
280C2×C4—84no—
281C2×C4—84no—
282C2×C4—84no—
283C8—164no—
284C22—232no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22#146814yes—
304C22#147014yes—
305C22#147314yes—
306C22#178011yescharacteristic
307C22#178111yescharacteristic
308C22#178211yescharacteristic
309C22#178211yescharacteristic
310C22#178411yescharacteristic
311C22#178511yescharacteristic
312C22#178511yescharacteristic
313C4—44no—
314C4—44no—
315C4—44no—
316C4—82no—
317C4—82no—
318C4—82no—
319C4—82no—
320C2—24no—
321C2—24no—
322C2—24no—
323C2#830411yescharacteristic
324C2#830611yescharacteristic
325C2#830911yescharacteristic
326C2#854411yescharacteristic
327C2#855011yescharacteristic
328C2#855411yescharacteristic
329C2#855611yescharacteristic
subgroupG/H
center, socleC23#379
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
C22×#4002
#86982
#82992