Finite Group Databasebeta

← #410790

Subgroups — #410790

Order 512.

908 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2100C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3#14277C211yesmaximal, characteristic
4#13779C211yesmaximal, characteristic
5#11357C212yesmaximal
6#11268C212yesmaximal
7#11208C211yesmaximal, characteristic
8#11208C211yesmaximal, characteristic
9#10807C212yesmaximal
10#10806C212yesmaximal
11#10796C211yesmaximal, characteristic
12C2×#389C2211yescharacteristic
13C2×#389C2211yescharacteristic
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#382C2211yescharacteristic
17C2×#382C2211yescharacteristic
18C2×C4×C4⋊C4C2212yes—
19C2×#376C2211yescharacteristic
20#2100—24no—
21#2099—24no—
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#1444—22no—
35#1442—22no—
36#1436—22no—
37#1436—22no—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C23×C8C2312yes—
42C23×C8C2312yes—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2311yescharacteristic
53C22×C4⋊C4C2311yescharacteristic
54C22×C42—22no—
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58#389—22no—
59#389—22no—
60#389—22no—
61#389—22no—
62#384—22no—
63#384—24no—
64#384D414yes—
65#382—22no—
66#382—22no—
67#382—24no—
68C4×C4⋊C4—24no—
69C4×C4⋊C4—24no—
70#376—24no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95D412yes—
82C2×#95D412yes—
83#340—24no—
84#340—24no—
85#340—24no—
86#340—24no—
87#340—24no—
88#340—24no—
89#340—24no—
90#340—24no—
91#336—22no—
92#336—22no—
93#336—24no—
94#336—24no—
95C23×C4—22no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4—22no—
99C23×C4—21no—
100C23×C4—21no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D412yes—
104C23×C4C2×D412yes—
105C23×C4C2411yescharacteristic
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
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—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—44no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4—82no—
155C2×C4⋊C4—82no—
156C2×C4⋊C4—82no—
157C2×C4⋊C4—82no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4C2×D414yes—
160C2×C4⋊C4#4114yes—
161C2×C4⋊C4#4112yes—
162C2×C4⋊C4#4112yes—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—22no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—44no—
172C2×C42—82no—
173C2×C42—82no—
174C2×C42C2×D412yes—
175C2×C42#4112yes—
176C2×C42#4114yes—
177C2×C42#4114yes—
178#95—24no—
179#95—24no—
180#95—28no—
181#95—24no—
182#95—24no—
183#95—42no—
184#95—42no—
185#95—44no—
186#95—82no—
187#95—82no—
188#95—82no—
189#95—82no—
190C24C22×D411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4#12112yes—
246C22×C4#12112yes—
247C22×C4#12314yes—
248C22×C4#12414yes—
249C22×C4C22×D411yescharacteristic
250C22×C4C2×#4112yes—
251C22×C4C2×#4112yes—
252C22×C4C2×#4111yescharacteristic
253C22×C4C2×#4111yescharacteristic
254C22×C4C2×#4111yescharacteristic
255C22×C4C2×#4112yes—
256C22×C42−1+412yes—
257C22×C42−1+411yescharacteristic
258C22×C42−1+411yescharacteristic
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—84no—
294C4⋊C4—84no—
295C4⋊C4—88no—
296C4⋊C4—84no—
297C4⋊C4—84no—
298C42—24no—
299C42—24no—
300C42—24no—
301C42—24no—
302C42—24no—
303C42—24no—
304C42—88no—
305C23C2×#12111yescharacteristic
306C23C2×#12311yescharacteristic
307C23#52511yescharacteristic
308C23#52511yescharacteristic
309C23C2×#12411yescharacteristic
310C23#53611yescharacteristic
311C23#53611yescharacteristic
312C23#57612yes—
313C23#57712yes—
314C23#57712yes—
315C23#57812yes—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—24no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4#52912yes—
375C2×C4#52912yes—
376C2×C4#52912yes—
377C2×C4#53212yes—
378C2×C4#54112yes—
379C2×C4#54112yes—
380C2×C4#54712yes—
381C2×C4#54811yescharacteristic
382C2×C4#54811yescharacteristic
383C2×C4#55212yes—
384C2×C4#55212yes—
385C2×C4#55212yes—
386C2×C4#55212yes—
387C2×C4#55211yescharacteristic
388C2×C4#55211yescharacteristic
389C2×C4#55612yes—
390C8—82no—
391C8—82no—
392C22#239811yescharacteristic
393C22#248411yescharacteristic
394C22#250311yescharacteristic
395C22#253611yescharacteristic
396C22#254711yescharacteristic
397C22#263411yescharacteristic
398C22#285411yescharacteristic
399C22#304111yescharacteristic
400C22#304211yescharacteristic
401C22#304311yescharacteristic
402C22#304411yescharacteristic
403C22#309612yes—
404C22#309712yes—
405C22#311912yes—
406C22#312012yes—
407C22#312412yes—
408C22#312512yes—
409C22#313612yes—
410C22#313712yes—
411C22#324112yes—
412C22#324212yes—
413C22#324312yes—
414C22#324412yes—
415C4—44no—
416C4—42no—
417C4—42no—
418C4—44no—
419C4—84no—
420C4—82no—
421C4—82no—
422C4—84no—
423C4—161no—
424C4—161no—
425C4#251912yes—
426C4#251912yes—
427C4#253312yes—
428C4#253312yes—
429C2#1509011yescharacteristic
430C2#2383212yes—
431C2#2762212yes—
432C2#2797112yes—
433C2#2821111yescharacteristic
434C2#2821211yescharacteristic
435C2#2872811yescharacteristic
436C2#2872911yescharacteristic
437C2#3010312yes—
438C2#3311811yescharacteristic
439C2#3311911yescharacteristic
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×#21002
C2×#20992
#142772
#137792
#113572
#112682
#112082
#108072
#108062
#107962