Finite Group Databasebeta

← #468895

Subgroups — #468895

Order 512.

968 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2C2×#2101C212yesmaximal
3#14276C211yesmaximal, characteristic
4#11293C212yesmaximal
5#11292C212yesmaximal
6#11208C212yesmaximal
7#11207C212yesmaximal
8#11207C212yesmaximal
9#10796C211yesmaximal, characteristic
10#2647—28no—
11C2×#400—22no—
12C2×#398—22no—
13C2×#389C2212yes—
14C2×#389C2212yes—
15C2×#389C2212yes—
16C2×#384C2211yescharacteristic
17C2×#384C2211yescharacteristic
18C2×#382C2211yescharacteristic
19C2×#382C2211yescharacteristic
20C2×#376C2211yescharacteristic
21#2101—28no—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2212yes—
31C2×#336C2212yes—
32C2×#336C2211yescharacteristic
33C2×#336C2211yescharacteristic
34#1441—22no—
35#1441—22no—
36C4⋊#95C2212yes—
37C23×C8C2312yes—
38C23×C8C2312yes—
39C22×C4⋊C4—22no—
40C22×C4⋊C4—22no—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C42C2311yescharacteristic
50C22×C42C2311yescharacteristic
51C22×C42C2311yescharacteristic
52#400—216no—
53#398—216no—
54#389—24no—
55#389—24no—
56#389—24no—
57#389—24no—
58#389—24no—
59#389D418yes—
60#384—24no—
61#384—24no—
62#382—24no—
63#382—24no—
64#376—24no—
65C2×#95—22no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95D412yes—
74C2×#95D412yes—
75#340—24no—
76#340—24no—
77#340—24no—
78#340—24no—
79#340—24no—
80#340—24no—
81#340—42no—
82#340—42no—
83#336—24no—
84#336—24no—
85#336—41no—
86#336—41no—
87C23×C4—22no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4C2×D412yes—
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4C2×D412yes—
95C23×C4C2411yescharacteristic
96C22×C8—22no—
97C22×C8—22no—
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—24no—
132C2×C4⋊C4—24no—
133C2×C4⋊C4—28no—
134C2×C4⋊C4—28no—
135C2×C4⋊C4—28no—
136C2×C4⋊C4—44no—
137C2×C4⋊C4—82no—
138C2×C4⋊C4—82no—
139C2×C4⋊C4—82no—
140C2×C4⋊C4—82no—
141C2×C4⋊C4—82no—
142C2×C4⋊C4—82no—
143C2×C4⋊C4—82no—
144C2×C4⋊C4—82no—
145C2×C4⋊C4—82no—
146C2×C4⋊C4—82no—
147C2×C4⋊C4C2×D414yes—
148C2×C4⋊C4C2×D414yes—
149C2×C4⋊C4#4114yes—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—22no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—22no—
160C2×C42C2×D414yes—
161C2×C42#4114yes—
162#95—28no—
163#95—28no—
164#95—28no—
165#95—24no—
166#95—24no—
167#95—42no—
168#95—42no—
169#95—44no—
170#95—82no—
171#95—82no—
172C24C22×D411yescharacteristic
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—24no—
189C22×C4—24no—
190C22×C4—24no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
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—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4#12012yes—
223C22×C4#12012yes—
224C22×C4#12414yes—
225C22×C4C22×D412yes—
226C22×C4C2×#4112yes—
227C22×C4C2×#4112yes—
228C22×C4H(5,𝔽2)11yescharacteristic
229C22×C42−1+411yescharacteristic
230C22×C42−1+412yes—
231C22×C42−1+411yescharacteristic
232C22×C42−1+411yescharacteristic
233C22×C42−1+411yescharacteristic
234C22×C42−1+411yescharacteristic
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—88no—
266C4⋊C4—88no—
267C4⋊C4—84no—
268C4⋊C4—84no—
269C4⋊C4—88no—
270C4⋊C4—88no—
271C42—24no—
272C42—24no—
273C42—24no—
274C42—24no—
275C42—42no—
276C42—42no—
277C23C2×#12011yescharacteristic
278C23#52511yescharacteristic
279C23C2×#12411yescharacteristic
280C23#53611yescharacteristic
281C23#53611yescharacteristic
282C23#53611yescharacteristic
283C23#53711yescharacteristic
284C23#57612yes—
285C23#57712yes—
286C23#57712yes—
287C23#57812yes—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4#53612yes—
341C2×C4#53712yes—
342C2×C4#54112yes—
343C2×C4#54112yes—
344C2×C4#54112yes—
345C2×C4#54112yes—
346C2×C4#54712yes—
347C2×C4#54712yes—
348C2×C4#54812yes—
349C2×C4#54812yes—
350C2×C4#55212yes—
351C2×C4#55312yes—
352C2×C4#56311yescharacteristic
353C2×C4#56311yescharacteristic
354C2×C4#56411yescharacteristic
355C2×C4#56411yescharacteristic
356C8—82no—
357C8—82no—
358C22#240611yescharacteristic
359C22#243611yescharacteristic
360C22#256211yescharacteristic
361C22#261611yescharacteristic
362C22#263411yescharacteristic
363C22#264211yescharacteristic
364C22#282211yescharacteristic
365C22#301212yes—
366C22#301312yes—
367C22#312211yescharacteristic
368C22#312311yescharacteristic
369C22#312611yescharacteristic
370C22#312711yescharacteristic
371C22#313612yes—
372C22#313712yes—
373C22#324112yes—
374C22#324212yes—
375C22#324312yes—
376C22#324312yes—
377C22#324412yes—
378C22#324412yes—
379C22#325712yes—
380C22#325812yes—
381C4—42no—
382C4—42no—
383C4—44no—
384C4—84no—
385C4—82no—
386C4—84no—
387C4—84no—
388C4—162no—
389C4#271912yes—
390C4#271912yes—
391C4#272512yes—
392C4#272512yes—
393C2#1663411yescharacteristic
394C2#2407011yescharacteristic
395C2#2407211yescharacteristic
396C2#2591612yes—
397C2#2913311yescharacteristic
398C2#2913511yescharacteristic
399C2#2970212yes—
400C2#3010111yescharacteristic
401C2#3010211yescharacteristic
402C2#3023212yes—
403C2#3285412yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#26472
C2×#21012
#142762
#112932
#112922
#112082
#112072
#107962