Finite Group Databasebeta

← #411547

Subgroups — #411547

Order 512.

882 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1942C211yesmaximal, characteristic
2C2×#1746C211yesmaximal, characteristic
3#14266C212yesmaximal
4#11377C211yesmaximal, characteristic
5#11377C211yesmaximal, characteristic
6#11328C211yesmaximal, characteristic
7#11315C212yesmaximal
8#11292C212yesmaximal
9#11256C211yesmaximal, characteristic
10#10881C212yesmaximal
11#10820C211yesmaximal, characteristic
12C22×#107C2211yescharacteristic
13C22×#107C2211yescharacteristic
14C22×#97C2211yescharacteristic
15C22×C4×C8C2211yescharacteristic
16C2×#389C2212yes—
17C2×#389C2212yes—
18C2×#376C2211yescharacteristic
19#1942—24no—
20#1746—24no—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2211yescharacteristic
28C2×#340C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31C2×#336C2211yescharacteristic
32C2×#336C2211yescharacteristic
33#1445—22no—
34#1443—22no—
35#1442—22no—
36#1441—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2212yes—
40C4⋊#95C2212yes—
41C23×C8C2311yescharacteristic
42C23×C8C2311yescharacteristic
43C23×C8C2311yescharacteristic
44C23×C8C2311yescharacteristic
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C2×#107—22no—
55C2×#107—24no—
56C2×#107—22no—
57C2×#107—22no—
58C2×#107—22no—
59C2×#97—22no—
60C2×#97—22no—
61C2×#97—22no—
62C2×C4×C8—22no—
63C2×C4×C8—22no—
64C2×C4×C8D414yes—
65#389—24no—
66#389—24no—
67#389—24no—
68#389—24no—
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×#95—22no—
81C2×#95D411yescharacteristic
82C2×#95D411yescharacteristic
83C2×#95D411yescharacteristic
84C2×#95D411yescharacteristic
85#340—24no—
86#340—22no—
87#340—24no—
88#340—24no—
89#340—22no—
90#340—24no—
91#340—24no—
92#340—24no—
93#336—22no—
94#336—22no—
95#336—22no—
96#336—22no—
97C23×C4—22no—
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4C2411yescharacteristic
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—21no—
111C22×C8—21no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—21no—
116C22×C8—21no—
117C22×C8—21no—
118C22×C8—21no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8C2×D412yes—
123C22×C8C2×D412yes—
124C22×C8#4112yes—
125C22×C8#4112yes—
126C22×C8#4112yes—
127C22×C8#4112yes—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
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—28no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—82no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4—82no—
155C2×C4⋊C4—82no—
156C2×C4⋊C4#4114yes—
157C2×C4⋊C4#4114yes—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42C2×D412yes—
171C2×C42#4112yes—
172#107—28no—
173#107—44no—
174#97—28no—
175C4×C8—28no—
176#95—28no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—44no—
182#95—82no—
183#95—82no—
184#95—82no—
185#95—82no—
186#95—82no—
187#95—82no—
188#95—82no—
189#95—82no—
190C24C22×D411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—24no—
207C22×C4—24no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
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×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4#12112yes—
250C22×C4#12112yes—
251C22×C4C22×D411yescharacteristic
252C22×C4C2×#4111yescharacteristic
253C22×C4C2×#4111yescharacteristic
254C22×C4C2×#4111yescharacteristic
255C22×C4C2×#4112yes—
256C22×C4C2×#4111yescharacteristic
257C22×C4C2×#4111yescharacteristic
258C22×C4C2×#4112yes—
259C22×C42−1+412yes—
260C22×C42−1+412yes—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—24no—
264C2×C8—24no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8#12314yes—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—88no—
298C4⋊C4—88no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—41no—
304C42—42no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42—42no—
309C23C2×#12111yescharacteristic
310C23#52512yes—
311C23#53211yescharacteristic
312C23#53211yescharacteristic
313C23#53612yes—
314C23#57611yescharacteristic
315C23#57612yes—
316C23#57712yes—
317C23#57811yescharacteristic
318C23#57811yescharacteristic
319C23#57811yescharacteristic
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
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×C4C2×#12311yescharacteristic
381C2×C4#52511yescharacteristic
382C2×C4#52511yescharacteristic
383C2×C4#52911yescharacteristic
384C2×C4#52912yes—
385C2×C4#52911yescharacteristic
386C2×C4#53211yescharacteristic
387C2×C4#53611yescharacteristic
388C2×C4#53611yescharacteristic
389C2×C4#54112yes—
390C2×C4#55212yes—
391C2×C4#55212yes—
392C2×C4#55212yes—
393C2×C4#55212yes—
394C2×C4#55212yes—
395C2×C4#55212yes—
396C2×C4#55612yes—
397C2×C4#55612yes—
398C8—24no—
399C8—42no—
400C8—42no—
401C8—42no—
402C22#239211yescharacteristic
403C22#260412yes—
404C22#261112yes—
405C22#262111yescharacteristic
406C22#285411yescharacteristic
407C22#305811yescharacteristic
408C22#305911yescharacteristic
409C22#306011yescharacteristic
410C22#306111yescharacteristic
411C22#312012yes—
412C22#312112yes—
413C22#312212yes—
414C22#312412yes—
415C22#317511yescharacteristic
416C22#317511yescharacteristic
417C22#317711yescharacteristic
418C22#317711yescharacteristic
419C22#317912yes—
420C22#317912yes—
421C22#324112yes—
422C22#324212yes—
423C22#324312yes—
424C22#324312yes—
425C4—42no—
426C4—42no—
427C4—84no—
428C4—81no—
429C4—84no—
430C4—81no—
431C4—81no—
432C4—81no—
433C4—162no—
434C4—162no—
435C4#248411yescharacteristic
436C4#249911yescharacteristic
437C4#252812yes—
438C4#253312yes—
439C4#259911yescharacteristic
440C4#261111yescharacteristic
441C2#1512211yescharacteristic
442C2#2370311yescharacteristic
443C2#2370411yescharacteristic
444C2#2952712yes—
445C2#2953112yes—
446C2#2958512yes—
447C2#2958612yes—
448C2#2988011yescharacteristic
449C2#2988211yescharacteristic
450C2#3313211yescharacteristic
451C2#3313911yescharacteristic
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×#19422
C2×#17462
#142662
#113772
#113282
#113152
#112922
#112562
#108812
#108202