Finite Group Databasebeta

← #417031

Subgroups — #417031

Order 512.

860 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14348C211yesmaximal, characteristic
2#14276C211yesmaximal, characteristic
3#11316C212yesmaximal
4#11315C212yesmaximal
5#11293C212yesmaximal
6#11292C212yesmaximal
7#10843C211yesmaximal, characteristic
8#10843C211yesmaximal, characteristic
9#10842C211yesmaximal, characteristic
10#10841C211yesmaximal, characteristic
11#10694C211yesmaximal, characteristic
12C22×#97C2211yescharacteristic
13C22×C4×C8C2211yescharacteristic
14C2×#389C2212yes—
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#382C2211yescharacteristic
18C2×#382C2211yescharacteristic
19C2×#376C2211yescharacteristic
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31C2×#336C2211yescharacteristic
32#1442—22no—
33#1442—22no—
34#1441—22no—
35#1441—22no—
36C4⋊#95C2212yes—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C23×C8C2311yescharacteristic
40C23×C8C2311yescharacteristic
41C23×C8C2311yescharacteristic
42C23×C8C2311yescharacteristic
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C42C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C2×#97—22no—
54C2×#97—22no—
55C2×#97—22no—
56C2×C4×C8—22no—
57C2×C4×C8—22no—
58C2×C4×C8—22no—
59#389—42no—
60#389—42no—
61#384—22no—
62#384—22no—
63#384—22no—
64#384Q814yes—
65#382—22no—
66#382—22no—
67#382—22no—
68#382—22no—
69#376—22no—
70#376—22no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95D412yes—
81C2×#95D412yes—
82#340—24no—
83#340—24no—
84#340—24no—
85#340—24no—
86#340—42no—
87#340—42no—
88#340—42no—
89#340—42no—
90#336—22no—
91#336—22no—
92#336—22no—
93#336—22no—
94C23×C4—22no—
95C23×C4—22no—
96C23×C4—22no—
97C23×C4—22no—
98C23×C4C2×D412yes—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D412yes—
102C23×C4C2411yescharacteristic
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—21no—
107C22×C8—21no—
108C22×C8—21no—
109C22×C8—21no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—21no—
113C22×C8—21no—
114C22×C8—21no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—21no—
120C22×C8—21no—
121C22×C8—21no—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—21no—
125C22×C8—21no—
126C22×C8—21no—
127C22×C8#4112yes—
128C22×C8#4112yes—
129C22×C8#4112yes—
130C22×C8#4112yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
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—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—28no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—82no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4—82no—
162C2×C4⋊C4—82no—
163C2×C4⋊C4C2×Q814yes—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42C2×Q812yes—
177C2×C42#4112yes—
178C2×C42#4112yes—
179C2×C42#4112yes—
180C2×C42#4112yes—
181C2×C42#4112yes—
182#97—44no—
183C4×C8—44no—
184#95—24no—
185#95—24no—
186#95—44no—
187#95—44no—
188#95—44no—
189#95—82no—
190#95—82no—
191#95—82no—
192#95—82no—
193#95—82no—
194#95—82no—
195C24C22×D411yescharacteristic
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
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—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4C22⋊Q814yes—
246C22×C4#12314yes—
247C22×C4#12414yes—
248C22×C4C22×Q811yescharacteristic
249C22×C4C2×#4111yescharacteristic
250C22×C4C2×#4111yescharacteristic
251C22×C4C2×#4111yescharacteristic
252C22×C4C2×#4111yescharacteristic
253C22×C4C2×#4111yescharacteristic
254C22×C4C2×#4111yescharacteristic
255C22×C4C2×#4111yescharacteristic
256C22×C4C2×#4111yescharacteristic
257C22×C4C2×#4111yescharacteristic
258C22×C4H(5,𝔽2)11yescharacteristic
259C22×C4H(5,𝔽2)11yescharacteristic
260C22×C42−1+411yescharacteristic
261C22×C42−1+411yescharacteristic
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C4⋊C4—24no—
291C4⋊C4—24no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—88no—
307C4⋊C4—88no—
308C4⋊C4—88no—
309C42—41no—
310C42—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42#12514yes—
318C42#12514yes—
319C42#12614yes—
320C42#12614yes—
321C23C2×C22⋊Q811yescharacteristic
322C23C2×#12311yescharacteristic
323C23C2×#12411yescharacteristic
324C23#53211yescharacteristic
325C23#53211yescharacteristic
326C23#53511yescharacteristic
327C23#53611yescharacteristic
328C23#57612yes—
329C23#57712yes—
330C23#57712yes—
331C23#57812yes—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4#40018yes—
384C2×C4C2×#12511yescharacteristic
385C2×C4C2×#12511yescharacteristic
386C2×C4C2×#12611yescharacteristic
387C2×C4C2×#12611yescharacteristic
388C2×C4#52911yescharacteristic
389C2×C4#52911yescharacteristic
390C2×C4#52911yescharacteristic
391C2×C4#52911yescharacteristic
392C2×C4#54211yescharacteristic
393C2×C4#54211yescharacteristic
394C2×C4#54211yescharacteristic
395C2×C4#54211yescharacteristic
396C2×C4#55211yescharacteristic
397C2×C4#55211yescharacteristic
398C2×C4#55211yescharacteristic
399C2×C4#55211yescharacteristic
400C2×C4#55311yescharacteristic
401C2×C4#55311yescharacteristic
402C2×C4#55311yescharacteristic
403C2×C4#55311yescharacteristic
404C2×C4#55411yescharacteristic
405C2×C4#55411yescharacteristic
406C2×C4#55511yescharacteristic
407C2×C4#55511yescharacteristic
408C2×C4#55611yescharacteristic
409C2×C4#55611yescharacteristic
410C2×C4#55711yescharacteristic
411C2×C4#55711yescharacteristic
412C8—42no—
413C8—42no—
414C8—42no—
415C8—42no—
416C22C2×#40011yescharacteristic
417C22#249911yescharacteristic
418C22#250011yescharacteristic
419C22#256511yescharacteristic
420C22#256611yescharacteristic
421C22#264011yescharacteristic
422C22#286111yescharacteristic
423C22#308112yes—
424C22#308212yes—
425C22#309812yes—
426C22#309912yes—
427C22#313612yes—
428C22#313712yes—
429C22#317411yescharacteristic
430C22#317411yescharacteristic
431C22#317611yescharacteristic
432C22#317711yescharacteristic
433C22#317812yes—
434C22#317912yes—
435C22#322412yes—
436C22#322512yes—
437C22#324312yes—
438C22#324412yes—
439C4—28no—
440C4—82no—
441C4—84no—
442C4—81no—
443C4—81no—
444C4—162no—
445C4—162no—
446C4—162no—
447C4#249411yescharacteristic
448C4#249411yescharacteristic
449C4#249511yescharacteristic
450C4#249511yescharacteristic
451C4#250811yescharacteristic
452C4#250811yescharacteristic
453C4#250911yescharacteristic
454C4#250911yescharacteristic
455C2#1523911yescharacteristic
456C2#2374912yes—
457C2#2788411yescharacteristic
458C2#2788511yescharacteristic
459C2#2790412yes—
460C2#2918912yes—
461C2#2920111yescharacteristic
462C2#2920211yescharacteristic
463C2#3021112yes—
464C2#3328411yescharacteristic
465C2#3328511yescharacteristic
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
#143482
#142762
#113162
#113152
#112932
#112922
#108432
#108422
#108412
#106942