Finite Group Databasebeta

← #351113

Subgroups — #351113

Order 512.

621 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33200C211yesmaximal, characteristic
2#33196C211yesmaximal, characteristic
3#30220C211yesmaximal, characteristic
4#20569C211yesmaximal, characteristic
5#9900C211yesmaximal, characteristic
6#9694C211yesmaximal, characteristic
7#9562C212yesmaximal
8#9561C212yesmaximal
9#9220C212yesmaximal
10#9220C212yesmaximal
11#8787C211yesmaximal, characteristic
12C2×#479—21no—
13C2×#475C2212yes—
14C2×C8×Q8C2212yes—
15#2868C2211yescharacteristic
16#2859C2211yescharacteristic
17C42×Q8C2211yescharacteristic
18#2043—21no—
19#2043—21no—
20#2043—22no—
21#1989—21no—
22#1988C2212yes—
23#1956C2212yes—
24#1956C2212yes—
25#1949—21no—
26#1948—21no—
27#1948—21no—
28#1948C2211yescharacteristic
29#1947C2211yescharacteristic
30#1842C2211yescharacteristic
31#1842C2211yescharacteristic
32#1805—21no—
33#1803—21no—
34#1803—21no—
35#1803C2211yescharacteristic
36#1803C2211yescharacteristic
37C8×C4⋊C4—22no—
38C8×C4⋊C4C2212yes—
39C4×C4⋊C8—21no—
40C4×C4⋊C8C2211yescharacteristic
41#1744—21no—
42#1744C2211yescharacteristic
43C2×#332C2212yes—
44C2×#332C2212yes—
45#1296C2212yes—
46#1296C2212yes—
47#1277C2212yes—
48#1277C2212yes—
49C2×C4⋊Q8—21no—
50C2×C4⋊Q8—21no—
51C2×C4⋊Q8C2312yes—
52C2×#125—21no—
53C2×C4×Q8D411yescharacteristic
54C2×C4×Q8D411yescharacteristic
55C2×C4×Q8C2311yescharacteristic
56#479—44no—
57#475—24no—
58#475—24no—
59C8×Q8—24no—
60C8×Q8—24no—
61C2×#107—21no—
62C2×#106—22no—
63C2×#106—21no—
64C2×C4⋊C8—22no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8C2312yes—
70C2×C4⋊C8C2311yescharacteristic
71C2×C4⋊C8C2311yescharacteristic
72C2×C4⋊C8C2312yes—
73C2×#103—22no—
74C2×#103—21no—
75C2×#103—21no—
76C2×#103—22no—
77C2×#103—22no—
78C2×#103—22no—
79C2×#103—22no—
80C2×C4×C8—22no—
81C2×C4×C8—22no—
82C2×C4×C8—21no—
83C2×C4×C8C2312yes—
84#389—21no—
85#389—21no—
86#389—21no—
87#389—21no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384—21no—
92#384C2311yescharacteristic
93#384C2311yescharacteristic
94#382—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4D411yescharacteristic
99C4×C4⋊C4D411yescharacteristic
100C4×C4⋊C4C2311yescharacteristic
101C43—21no—
102C43C2311yescharacteristic
103#340—22no—
104#340—22no—
105#340—21no—
106#340—21no—
107#340—21no—
108#340—21no—
109#336—22no—
110#336—21no—
111#336D411yescharacteristic
112#336D411yescharacteristic
113#336D412yes—
114#332—24no—
115#332—24no—
116C22×Q8—22no—
117C22×Q8C2×D411yescharacteristic
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8C2×D412yes—
123C22×C8C2×D412yes—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—81no—
129C4⋊Q8—82no—
130C4⋊Q8—81no—
131#125—42no—
132#125—42no—
133C4×Q8—22no—
134C4×Q8—22no—
135C4×Q8—22no—
136C4×Q8SD1614yes—
137C4×Q8Q1614yes—
138C4×Q8#4114yes—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4C2×D411yescharacteristic
157C2×C4⋊C4C2×D411yescharacteristic
158C2×C4⋊C4C2×D411yescharacteristic
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42C2×D411yescharacteristic
169C2×C42#4111yescharacteristic
170C2×C42#4111yescharacteristic
171C2×C42C2411yescharacteristic
172#107—42no—
173#106—44no—
174#106—42no—
175C4⋊C8—28no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—22no—
181C4⋊C8—42no—
182C4⋊C8—42no—
183C4⋊C8—42no—
184C4⋊C8—42no—
185C4⋊C8#4114yes—
186#103—44no—
187#103—42no—
188#103—42no—
189#103—82no—
190#103—82no—
191#103—82no—
192#103—82no—
193C4×C8—28no—
194C4×C8—22no—
195C4×C8—22no—
196C4×C8—81no—
197C4×C8—82no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—41no—
202#95—41no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—21no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8#12412yes—
213C2×Q8C2×SD1612yes—
214C2×Q8C2×Q1612yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—42no—
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4C22×D411yescharacteristic
227C22×C4C22×D411yescharacteristic
228C22×C4C2×#4111yescharacteristic
229C2×C8—22no—
230C2×C8—22no—
231C2×C8—24no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—41no—
246C2×C8—41no—
247C4⋊C4—24no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—82no—
267C4⋊C4—82no—
268C4⋊C4—82no—
269C4⋊C4—82no—
270C4⋊C4—82no—
271C4⋊C4—82no—
272C4⋊C4#12412yes—
273C4⋊C4C2×SD1612yes—
274C4⋊C4C2×Q1612yes—
275C42—24no—
276C42—21no—
277C42—22no—
278C42—21no—
279C42—24no—
280C42—24no—
281C42—41no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—81no—
286C42—81no—
287C42C2×SD1612yes—
288C42C2×Q1612yes—
289C42#13512yes—
290C42#13512yes—
291C42C2×#4112yes—
292C42C2×#4112yes—
293C23C2×#12111yescharacteristic
294Q8—22no—
295Q8—22no—
296Q8—22no—
297Q8—82no—
298Q8—82no—
299Q8—82no—
300Q8—82no—
301Q8#48714yes—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—82no—
325C2×C4—81no—
326C2×C4—82no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4#46512yes—
334C2×C4#46512yes—
335C2×C4#46712yes—
336C2×C4#46712yes—
337C2×C4#52512yes—
338C2×C4C2×#12411yescharacteristic
339C2×C4#52912yes—
340C2×C4#53211yescharacteristic
341C2×C4C22×SD1611yescharacteristic
342C2×C4C22×Q1611yescharacteristic
343C2×C4C2×#13511yescharacteristic
344C2×C4C2×#13511yescharacteristic
345C2×C4#57611yescharacteristic
346C2×C4#57712yes—
347C2×C4#57711yescharacteristic
348C8—42no—
349C8—44no—
350C8—42no—
351C8—82no—
352C8—81no—
353C8—81no—
354C22#285011yescharacteristic
355C22#304311yescharacteristic
356C22#304511yescharacteristic
357C22C2×#46511yescharacteristic
358C22C2×#46711yescharacteristic
359C22#306911yescharacteristic
360C22#306911yescharacteristic
361C4—24no—
362C4—22no—
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—42no—
368C4—42no—
369C4—42no—
370C4—162no—
371C4—161no—
372C4—161no—
373C4#311912yes—
374C4#312612yes—
375C4C2×#48711yescharacteristic
376C4#313111yescharacteristic
377C4#316711yescharacteristic
378C4#317011yescharacteristic
379C2#1939711yescharacteristic
380C2#1939911yescharacteristic
381C2#1940811yescharacteristic
382C2#1941111yescharacteristic
383C2#3303911yescharacteristic
384C2#3304311yescharacteristic
385C2#3306511yescharacteristic
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
#332002
#331962
#302202
#205692
#99002
#96942
#95622
#95612
#92202
#87872