Finite Group Databasebeta

← #330782

Subgroups — #330782

Order 512.

502 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33289C211yesmaximal, characteristic
2#29984C211yesmaximal, characteristic
3#29983C211yesmaximal, characteristic
4#21341C211yesmaximal, characteristic
5#10656C212yesmaximal
6#10655C212yesmaximal
7#10624C212yesmaximal
8#10623C212yesmaximal
9#9905C211yesmaximal, characteristic
10#9903C211yesmaximal, characteristic
11#8785C211yesmaximal, characteristic
12#2868C2211yescharacteristic
13#2868C2211yescharacteristic
14#2295C2211yescharacteristic
15#2100—21no—
16#2099—21no—
17#2096—21no—
18#2095—21no—
19#2058—21no—
20#2057—21no—
21#2024—21no—
22#2024—21no—
23#1990—21no—
24#1990—21no—
25#1990—21no—
26#1990—21no—
27#1984C2211yescharacteristic
28#1984C2211yescharacteristic
29#1948C2212yes—
30#1947C2212yes—
31#1939C2211yescharacteristic
32#1939C2211yescharacteristic
33#1916—21no—
34#1916—21no—
35#1834C2212yes—
36#1834C2212yes—
37#1831C2211yescharacteristic
38#1831C2211yescharacteristic
39#1803C2212yes—
40#1803C2212yes—
41#1768—21no—
42#1767C2211yescharacteristic
43#1746—21no—
44C42×C8C2211yescharacteristic
45#1296C2212yes—
46#1296C2212yes—
47#1296C2212yes—
48#1296C2212yes—
49#1277C2212yes—
50#1277C2212yes—
51C2×C4⋊Q8—21no—
52C2×C4⋊Q8—21no—
53C2×C4⋊Q8—21no—
54C2×C4⋊Q8—21no—
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4×Q8C2311yescharacteristic
58C2×#107—22no—
59C2×#106—22no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8C2312yes—
63C2×C4⋊C8C2312yes—
64C2×C4⋊C8C2311yescharacteristic
65C2×C4⋊C8C2311yescharacteristic
66C2×#103—22no—
67C2×#103—22no—
68C2×#97—21no—
69C2×C4×C8D411yescharacteristic
70C2×C4×C8D411yescharacteristic
71C2×C4×C8D411yescharacteristic
72C2×C4×C8D411yescharacteristic
73C2×C4×C8C2311yescharacteristic
74C2×C4×C8C2311yescharacteristic
75#391D411yescharacteristic
76#391D411yescharacteristic
77#389D411yescharacteristic
78#389D411yescharacteristic
79#387—21no—
80#387—21no—
81#384—21no—
82#384—21no—
83#384—21no—
84#384—21no—
85#384—21no—
86#384—21no—
87#384C2312yes—
88#384C2312yes—
89C4×C4⋊C4—21no—
90C4×C4⋊C4C2311yescharacteristic
91#376—21no—
92C43C2311yescharacteristic
93#340—22no—
94#340—22no—
95#340—22no—
96#340—22no—
97#340—22no—
98#340—22no—
99#340—22no—
100#340—22no—
101#336—21no—
102#336—21no—
103#336—21no—
104#336—21no—
105#336—21no—
106#336—21no—
107#336—21no—
108#336—21no—
109#336—21no—
110#336—21no—
111#336—21no—
112C22×Q8—41no—
113C22×Q8—41no—
114C22×Q8C2×D411yescharacteristic
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8C2×D411yescharacteristic
120C22×C8C2×D411yescharacteristic
121C22×C8C2×D411yescharacteristic
122C22×C8C2×D411yescharacteristic
123C4⋊Q8—42no—
124C4⋊Q8—42no—
125C4⋊Q8—42no—
126C4⋊Q8—42no—
127C4⋊Q8—82no—
128C4⋊Q8—82no—
129C4⋊Q8—82no—
130C4⋊Q8—82no—
131C4×Q8—21no—
132C4×Q8—21no—
133C4×Q8—21no—
134C4×Q8—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—41no—
147C2×C4⋊C4—41no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4C2×D411yescharacteristic
151C2×C4⋊C4C2×D411yescharacteristic
152C2×C4⋊C4C2×D411yescharacteristic
153C2×C42—21no—
154C2×C42—21no—
155C2×C42C2×D411yescharacteristic
156C2×C42C2×D411yescharacteristic
157C2×C42C2×D411yescharacteristic
158C2×C42C2×D411yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C2×C42C2411yescharacteristic
162#107—82no—
163#106—82no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—42no—
173C4⋊C8—42no—
174#103—82no—
175#103—82no—
176#97—42no—
177C4×C8—22no—
178C4×C8—22no—
179C4×C8—21no—
180C4×C8—21no—
181C4×C8—21no—
182C4×C8—21no—
183C4×C8—41no—
184C4×C8—41no—
185#95—21no—
186#95—21no—
187#95—21no—
188#95—21no—
189#95—21no—
190#95—21no—
191#95—21no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—82no—
197C2×Q8—82no—
198C2×Q8—82no—
199C2×Q8—82no—
200C2×Q8—82no—
201C2×Q8—82no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4#12111yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4C22×D411yescharacteristic
213C22×C4C22×D411yescharacteristic
214C22×C4C2×#4111yescharacteristic
215C2×C8—21no—
216C2×C8—21no—
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×C8—21no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—22no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—82no—
256C4⋊C4—82no—
257C4⋊C4—82no—
258C4⋊C4—82no—
259C4⋊C4—82no—
260C4⋊C4—82no—
261C4⋊C4—82no—
262C4⋊C4—82no—
263C42—21no—
264C42—21no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42#13512yes—
274C42#13712yes—
275C422−1+411yescharacteristic
276C422−1+411yescharacteristic
277C422−1+411yescharacteristic
278C422−1+411yescharacteristic
279C23C2×#12111yescharacteristic
280Q8—42no—
281Q8—42no—
282Q8—164no—
283Q8—164no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4#46412yes—
313C2×C4#46412yes—
314C2×C4#47112yes—
315C2×C4#47112yes—
316C2×C4#53611yescharacteristic
317C2×C4#53611yescharacteristic
318C2×C4#53611yescharacteristic
319C2×C4#53611yescharacteristic
320C2×C4#54111yescharacteristic
321C2×C4#54111yescharacteristic
322C2×C4C2×#13511yescharacteristic
323C2×C4C2×#13711yescharacteristic
324C2×C4#57511yescharacteristic
325C2×C4#57511yescharacteristic
326C2×C4#57612yes—
327C2×C4#57812yes—
328C8—41no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—81no—
333C8—81no—
334C8—82no—
335C8—82no—
336C22#262111yescharacteristic
337C22C2×#46411yescharacteristic
338C22#304011yescharacteristic
339C22#305811yescharacteristic
340C22#305911yescharacteristic
341C22C2×#47111yescharacteristic
342C22C2×#47111yescharacteristic
343C4—22no—
344C4—22no—
345C4—22no—
346C4—22no—
347C4—21no—
348C4—21no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—162no—
354C4—162no—
355C4#323311yescharacteristic
356C4#323311yescharacteristic
357C4#323711yescharacteristic
358C4#323711yescharacteristic
359C4#324312yes—
360C4#324312yes—
361C2#1921411yescharacteristic
362C2#1921511yescharacteristic
363C2#1936411yescharacteristic
364C2#1936511yescharacteristic
365C2#2986711yescharacteristic
366C2#2988011yescharacteristic
367C2#2988711yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#121
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#332892
#299842
#299832
#213412
#106562
#106552
#106242
#106232
#99052
#99032
#87852