Finite Group Databasebeta

← #504749

Subgroups — #504749

Order 512.

411 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27993C211yesmaximal, characteristic
2#23160C211yesmaximal, characteristic
3#13516C211yesmaximal, characteristic
4#13507C211yesmaximal, characteristic
5#13453C211yesmaximal, characteristic
6#13453C211yesmaximal, characteristic
7#13178C211yesmaximal, characteristic
8#13168C211yesmaximal, characteristic
9#13111C211yesmaximal, characteristic
10#13111C211yesmaximal, characteristic
11#13111C211yesmaximal, characteristic
12#13110C211yesmaximal, characteristic
13#13110C211yesmaximal, characteristic
14#13105C211yesmaximal, characteristic
15#12674C211yesmaximal, characteristic
16C2×#499C2211yescharacteristic
17#2509—21no—
18#2370—21no—
19C2×#367C2211yescharacteristic
20C2×#367C2211yescharacteristic
21C2×#367C2211yescharacteristic
22C2×#367C2211yescharacteristic
23C2×#366C2211yescharacteristic
24C2×#366C2211yescharacteristic
25C2×C4⋊C16C2211yescharacteristic
26C2×#346C2211yescharacteristic
27#2101—21no—
28#2088—21no—
29#1989—21no—
30#1942C2211yescharacteristic
31#1942C2211yescharacteristic
32#1942C2211yescharacteristic
33#1942C2211yescharacteristic
34#1942C2211yescharacteristic
35#1942C2211yescharacteristic
36#1920—21no—
37#1919—21no—
38#1919—21no—
39#1846C2211yescharacteristic
40C4×#107C2211yescharacteristic
41C4×#107C2211yescharacteristic
42C4×#107C2211yescharacteristic
43C4×#107C2211yescharacteristic
44C8×C4⋊C4C2211yescharacteristic
45#1380C2211yescharacteristic
46#1380C2211yescharacteristic
47#1380C2211yescharacteristic
48#1380C2211yescharacteristic
49#1380C2211yescharacteristic
50#1380C2211yescharacteristic
51#1380C2211yescharacteristic
52#1380C2211yescharacteristic
53#1380C2211yescharacteristic
54#1380C2211yescharacteristic
55#1374C2211yescharacteristic
56#1374C2211yescharacteristic
57#1374C2211yescharacteristic
58#1374C2211yescharacteristic
59C2×#125—21no—
60C22×C16C2311yescharacteristic
61C22×C16C2311yescharacteristic
62C22×C16C2311yescharacteristic
63C22×C16C2311yescharacteristic
64#499—22no—
65#499—22no—
66C2×#107C2311yescharacteristic
67C2×#107C2311yescharacteristic
68C2×#107C2311yescharacteristic
69C2×#107C2311yescharacteristic
70C2×#107C2311yescharacteristic
71C2×#107C2311yescharacteristic
72C2×#107C2311yescharacteristic
73C2×#107C2311yescharacteristic
74C2×#106—21no—
75C2×#106—21no—
76C2×C4⋊C8D411yescharacteristic
77C2×C4×C8C2311yescharacteristic
78C2×C4×C8C2311yescharacteristic
79C2×C4×C8C2311yescharacteristic
80#400—41no—
81#400—41no—
82#389—21no—
83#389—21no—
84#389—21no—
85#389—21no—
86#389—21no—
87#389—21no—
88#389—41no—
89#389—41no—
90#387—41no—
91#387—41no—
92#387—41no—
93#382—21no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—41no—
99C4×C4⋊C4D411yescharacteristic
100#367—22no—
101#367—22no—
102#367—22no—
103#367Q814yes—
104#366—22no—
105#366—22no—
106C4⋊C16—22no—
107#346—22no—
108#340—21no—
109#340—21no—
110#340—21no—
111#340—21no—
112#340—21no—
113#340—21no—
114#340—21no—
115#340—21no—
116#340—21no—
117#340—21no—
118#336D411yescharacteristic
119#336D411yescharacteristic
120C22×C8C2×D411yescharacteristic
121C22×C8C2×D411yescharacteristic
122C22×C8C2×D411yescharacteristic
123C22×C8C2411yescharacteristic
124#125—24no—
125#125—42no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—41no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4D811yescharacteristic
143C2×C4⋊C4D811yescharacteristic
144C2×C42—41no—
145C2×C42—41no—
146C2×C42—41no—
147C2×C42—41no—
148C2×C42C2×D411yescharacteristic
149C2×C42C2×D411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C16—21no—
152C2×C16—21no—
153C2×C16—21no—
154C2×C16—21no—
155C2×C16—21no—
156C2×C16—21no—
157C2×C16—21no—
158C2×C16—21no—
159C2×C16—21no—
160C2×C16—21no—
161C2×C16C2×Q812yes—
162C2×C16#4112yes—
163#107—21no—
164#107—21no—
165#107—21no—
166#107—21no—
167#107—21no—
168#107—21no—
169#107—21no—
170#107—21no—
171#107—21no—
172#107—21no—
173#107—21no—
174#107—21no—
175#107C2×Q812yes—
176#107C2×Q812yes—
177#107#4112yes—
178#107#4112yes—
179#106—24no—
180#106—42no—
181C4⋊C8—41no—
182C4×C8—21no—
183C4×C8—21no—
184C4×C8—21no—
185C4×C8—21no—
186C4×C8—21no—
187C4×C8—21no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193#95—41no—
194#95—41no—
195#95—41no—
196#95—41no—
197#95—41no—
198#95—41no—
199#95—41no—
200#95D811yescharacteristic
201#95D811yescharacteristic
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4C2×D811yescharacteristic
211C22×C4C2×D811yescharacteristic
212C22×C4C2×D811yescharacteristic
213C22×C4C2×D811yescharacteristic
214C22×C4C2×D811yescharacteristic
215C22×C4C2×D811yescharacteristic
216C22×C4C22×D411yescharacteristic
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8C22×Q811yescharacteristic
227C2×C8C2×#4111yescharacteristic
228C2×C8C2×#4111yescharacteristic
229C2×C8C2×#4111yescharacteristic
230C2×C82−1+411yescharacteristic
231C2×C82−1+411yescharacteristic
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—44no—
239C4⋊C4—44no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—82no—
253C4⋊C4—82no—
254C4⋊C4—82no—
255C4⋊C4—161no—
256C4⋊C4—161no—
257C4⋊C4—161no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—82no—
265C42—161no—
266C42—161no—
267C42—161no—
268C16—22no—
269C16—22no—
270C16—41no—
271C16—41no—
272C23C22×D811yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#52511yescharacteristic
316C2×C4#54711yescharacteristic
317C2×C4D4×Q811yescharacteristic
318C2×C4#57511yescharacteristic
319C2×C4#57811yescharacteristic
320C2×C4#57811yescharacteristic
321C8—41no—
322C8—41no—
323C8—41no—
324C8#53311yescharacteristic
325C8#54111yescharacteristic
326C8#55211yescharacteristic
327C8#55711yescharacteristic
328C22#310011yescharacteristic
329C22#333411yescharacteristic
330C22Q8×D811yescharacteristic
331C22#341411yescharacteristic
332C22#341411yescharacteristic
333C22#341611yescharacteristic
334C22#341611yescharacteristic
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—82no—
344C4—82no—
345C4—161no—
346C4—161no—
347C4—161no—
348C4—161no—
349C4#246211yescharacteristic
350C4#312711yescharacteristic
351C4#334911yescharacteristic
352C4#339011yescharacteristic
353C2#2685611yescharacteristic
354C2#3367111yescharacteristic
355C2#3368511yescharacteristic
356C2#3391711yescharacteristic
357C2#3391811yescharacteristic
358C2#3395511yescharacteristic
359C2#3395511yescharacteristic
subgroupG/H
center, socle, prime radicalC23C22×D8
commutator, Frattini, cosocleC22×C8C24
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#279932
#231602
#135162
#135072
#134532
#131782
#131682
#131112
#131102
#131052
#126742