Finite Group Databasebeta

← #207759

Subgroups — #207759

Order 512.

796 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2655C211yesmaximal, characteristic
2#21912C211yesmaximal, characteristic
3#20536C211yesmaximal, characteristic
4#9881C212yesmaximal
5#9654C212yesmaximal
6#9082C212yesmaximal
7#9082C212yesmaximal
8#8154C212yesmaximal
9#8154C212yesmaximal
10C2×#431C2212yes—
11#2655—24no—
12#2655—24no—
13C2×#401C411yescharacteristic
14C2×#400C411yescharacteristic
15C2×#400C411yescharacteristic
16C2×#400C411yescharacteristic
17C2×#400C411yescharacteristic
18C2×#398C411yescharacteristic
19C2×#398C411yescharacteristic
20C2×#398C411yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#387C2211yescharacteristic
23C2×#387C2211yescharacteristic
24C2×#387C2211yescharacteristic
25C2×#387C2211yescharacteristic
26C2×#387C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28#1916—24no—
29#1817C2212yes—
30#1797C2212yes—
31#1770—24no—
32#1749C2212yes—
33#1749C2212yes—
34C4×C22⋊C8C2212yes—
35C2×#324C2214yes—
36C2×#324C2214yes—
37#1280C2214yes—
38#1280C2214yes—
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C4⋊C4C2×C411yescharacteristic
43C22×C4⋊C4C2×C411yescharacteristic
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54#431—28no—
55C2×C4⋊C8—22no—
56C2×C4⋊C8—22no—
57C2×C22⋊C8C2314yes—
58C2×C22⋊C8C2314yes—
59C2×#97—22no—
60C2×#97—22no—
61C2×C4×C8—22no—
62C2×C4×C8—22no—
63#401—24no—
64#400—24no—
65#400—24no—
66#400—24no—
67#400—24no—
68#398—24no—
69#398—24no—
70#398—24no—
71#389—22no—
72#389—22no—
73#387—22no—
74#387—22no—
75#387—22no—
76#387—22no—
77#387—22no—
78#387—22no—
79#387—22no—
80#387—22no—
81#387—22no—
82#387—22no—
83C4×C4⋊C4D414yes—
84C4×C4⋊C4D414yes—
85C2×#95C2×C411yescharacteristic
86C2×#95C2×C411yescharacteristic
87C2×#95C2×C411yescharacteristic
88C2×#95C2×C411yescharacteristic
89C2×#95C2×C411yescharacteristic
90C2×#95C2×C411yescharacteristic
91C2×#95C2×C411yescharacteristic
92C2×#95C2×C411yescharacteristic
93C2×#95C2×C411yescharacteristic
94C2×#95C2×C411yescharacteristic
95C2×#95C2×C411yescharacteristic
96C2×#95C2×C411yescharacteristic
97C2×#95C2×C411yescharacteristic
98C2×#95C2×C411yescharacteristic
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103C2×#95C2311yescharacteristic
104C2×#95C2311yescharacteristic
105#336—22no—
106#336—24no—
107#336—22no—
108#336—22no—
109#336—22no—
110#324—28no—
111#324—28no—
112C23×C4C22×C411yescharacteristic
113C23×C4C22×C411yescharacteristic
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C411yescharacteristic
116C23×C4C22×C411yescharacteristic
117C23×C4C22×C411yescharacteristic
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—24no—
128C22×C8—24no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—81no—
150C2×C4⋊C4—81no—
151C2×C4⋊C4—81no—
152C2×C4⋊C4—81no—
153C2×C4⋊C4C22⋊C414yes—
154C2×C4⋊C4C22⋊C414yes—
155C2×C42—24no—
156C2×C42—81no—
157C2×C42—81no—
158C2×C42C2×D412yes—
159C2×C42C2×D412yes—
160C2×C42C2×D412yes—
161C2×C42C2×D412yes—
162C2×C42C2×D412yes—
163C2×C42C2×D412yes—
164C4⋊C8—28no—
165C4⋊C8—82no—
166C22⋊C8—24no—
167C22⋊C8—24no—
168C22⋊C8—24no—
169C22⋊C8#4118yes—
170#97—82no—
171#97—82no—
172C4×C8—28no—
173C4×C8—82no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—22no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95C22⋊C414yes—
195#95C22⋊C414yes—
196C24C23×C411yescharacteristic
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C2×C22⋊C412yes—
249C22×C4C2×C22⋊C412yes—
250C22×C4C2×C22⋊C412yes—
251C22×C4C2×C22⋊C412yes—
252C22×C4C2×C22⋊C412yes—
253C22×C4C2×C22⋊C412yes—
254C22×C4#13114yes—
255C22×C4C22×D411yescharacteristic
256C22×C4C22×D411yescharacteristic
257C22×C4C2×#4114yes—
258C2×C8—28no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—44no—
264C4⋊C4—28no—
265C4⋊C4—44no—
266C4⋊C4—44no—
267C4⋊C4—44no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—44no—
273C4⋊C4—44no—
274C4⋊C4—82no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C4⋊C4—82no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C22×C22⋊C411yescharacteristic
290C23C4×#4112yes—
291C23C2×#13112yes—
292C23#56812yes—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—28no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4#40814yes—
354C2×C4#52512yes—
355C2×C4#53212yes—
356C8—48no—
357C8—84no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22#229711yescharacteristic
365C22C2×#40811yescharacteristic
366C22#287911yescharacteristic
367C22#288311yescharacteristic
368C22#288411yescharacteristic
369C22#288911yescharacteristic
370C22#288911yescharacteristic
371C22#296814yes—
372C4—24no—
373C4—22no—
374C4—22no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—81no—
388C2—24no—
389C2#1738811yescharacteristic
390C2#1739111yescharacteristic
391C2#1740611yescharacteristic
392C2#1741011yescharacteristic
393C2#2137711yescharacteristic
394C2#2142311yescharacteristic
395C2#2142911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#26552
#219122
#205362
#98812
#96542
#90822
#81542