Finite Group Databasebeta

← #97083

Subgroups — #97083

Order 512.

1242 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1242 conjugacy classes of subgroups — too many to draw. Only its 130 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×#398C211yesmaximal, characteristic
2#8698C212yesmaximal
3#8299C212yesmaximal
4#8299C212yesmaximal
5C23×C4⋊C4C411yescharacteristic
6C23×C4⋊C4C411yescharacteristic
7C23×C4⋊C4C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#398—24no—
10C2×#398—24no—
11C2×#398—24no—
12C22×#95C411yescharacteristic
13C22×#95C411yescharacteristic
14C22×#95C2211yescharacteristic
15#1779C2214yes—
16C2×#324—24no—
17C2×#324—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—22no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4—22no—
35C22×C4⋊C4—22no—
36C22×C4⋊C4—44no—
37C22×C4⋊C4—44no—
38C22×C4⋊C4—44no—
39C22×C4⋊C4—44no—
40C22×C4⋊C4D414yes—
41C22×C4⋊C4D414yes—
42C2×C22⋊C8—24no—
43C2×C22⋊C8—24no—
44C2×C22⋊C8—24no—
45#398—232no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—22no—
49C2×#95—22no—
50C2×#95—22no—
51C2×#95—22no—
52C2×#95—22no—
53C2×#95—22no—
54C2×#95D414yes—
55#324—48no—
56#324—48no—
57C25C22×C411yescharacteristic
58C23×C4—21no—
59C23×C4—21no—
60C23×C4—21no—
61C23×C4—21no—
62C23×C4—21no—
63C23×C4—21no—
64C23×C4—21no—
65C23×C4—21no—
66C23×C4—24no—
67C23×C4—24no—
68C23×C4—24no—
69C23×C4—24no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—24no—
75C23×C4—24no—
76C23×C4—24no—
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×C4—42no—
89C23×C4—42no—
90C23×C4—42no—
91C23×C4C22⋊C412yes—
92C23×C4C22⋊C412yes—
93C23×C4C22⋊C412yes—
94C23×C4C22⋊C412yes—
95C23×C4C22⋊C412yes—
96C23×C4C22⋊C412yes—
97C23×C4C2×D412yes—
98C23×C4C2×D412yes—
99C23×C4C2×D412yes—
100C22×C8—44no—
101C2×C4⋊C4—28no—
102C2×C4⋊C4—28no—
103C2×C4⋊C4—28no—
104C2×C4⋊C4—28no—
105C2×C4⋊C4—28no—
106C2×C4⋊C4—28no—
107C2×C4⋊C4—44no—
108C2×C4⋊C4—44no—
109C2×C4⋊C4—48no—
110C2×C4⋊C4—48no—
111C2×C4⋊C4—48no—
112C2×C4⋊C4—48no—
113C2×C4⋊C4—48no—
114C2×C4⋊C4—48no—
115C2×C4⋊C4—48no—
116C2×C4⋊C4—48no—
117C2×C4⋊C4—44no—
118C2×C4⋊C4—44no—
119C2×C4⋊C4—44no—
120C2×C4⋊C4—44no—
121C22⋊C8—48no—
122C22⋊C8—48no—
123C22⋊C8—48no—
124#95—28no—
125#95—28no—
126#95—28no—
127C24—22no—
128C24—22no—
129C24—22no—
130C24—22no—
131C24—22no—
132C24—22no—
133C24C2×C22⋊C411yescharacteristic
134C24C2×C22⋊C411yescharacteristic
135C24C2×C22⋊C411yescharacteristic
136C24#13114yes—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—24no—
143C22×C4—24no—
144C22×C4—24no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4—24no—
151C22×C4—24no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—416no—
171C22×C4—416no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—416no—
177C22×C4—416no—
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—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—88no—
211C22×C4—88no—
212C22×C4—88no—
213C22×C4#9914yes—
214C22×C4#9914yes—
215C22×C4#10114yes—
216C22×C4#10114yes—
217C22×C4#12014yes—
218C2×C8—84no—
219C2×C8—84no—
220C2×C8—84no—
221C4⋊C4—416no—
222C4⋊C4—416no—
223C4⋊C4—416no—
224C4⋊C4—416no—
225C23—28no—
226C23—28no—
227C23—28no—
228C23—28no—
229C23—28no—
230C23—28no—
231C23—28no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23#37911yescharacteristic
245C23#40812yes—
246C23#40812yes—
247C23#40812yes—
248C23C2×#9912yes—
249C23C2×#9912yes—
250C23#41012yes—
251C23C2×#10112yes—
252C23C2×#10112yes—
253C23#41312yes—
254C2×C4—28no—
255C2×C4—28no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—48no—
264C2×C4—44no—
265C2×C4—48no—
266C2×C4—48no—
267C2×C4—44no—
268C2×C4—48no—
269C2×C4—48no—
270C2×C4—48no—
271C2×C4—48no—
272C2×C4—48no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—84no—
292C2×C4—84no—
293C2×C4—84no—
294C2×C4—84no—
295C2×C4—84no—
296C2×C4—84no—
297C2×C4—84no—
298C2×C4—84no—
299C2×C4—84no—
300C8—164no—
301C22—232no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22#146814yes—
321C22#147014yes—
322C22#147214yes—
323C22#178011yescharacteristic
324C22#178111yescharacteristic
325C22#178111yescharacteristic
326C22#178211yescharacteristic
327C22#178411yescharacteristic
328C22#178411yescharacteristic
329C22#178511yescharacteristic
330C4—44no—
331C4—44no—
332C4—44no—
333C4—44no—
334C4—44no—
335C4—82no—
336C4—82no—
337C2—24no—
338C2—24no—
339C2—24no—
340C2#830411yescharacteristic
341C2#830611yescharacteristic
342C2#830811yescharacteristic
343C2#854211yescharacteristic
344C2#855011yescharacteristic
345C2#855111yescharacteristic
346C2#855411yescharacteristic
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×#3982
#86982
#82992