Finite Group Databasebeta

← #403879

Subgroups — #403879

Order 512.

1112 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2330C211yesmaximal, characteristic
2C2×#2100C211yesmaximal, characteristic
3C2×#2099C211yesmaximal, characteristic
4#14277C211yesmaximal, characteristic
5#11385C212yesmaximal
6#11267C212yesmaximal
7#11208C211yesmaximal, characteristic
8#11208C211yesmaximal, characteristic
9#10885C212yesmaximal
10#10884C212yesmaximal
11#10796C211yesmaximal, characteristic
12C22×#125C2211yescharacteristic
13#2330—24no—
14#2330—24no—
15C2×#389—21no—
16C2×#389—21no—
17C2×#389C2212yes—
18C2×#389C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#387—21no—
21C2×#387—21no—
22C2×#384C2211yescharacteristic
23C2×#384C2211yescharacteristic
24C2×#382C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×#376C2211yescharacteristic
28#2100—24no—
29#2099—24no—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#336C2212yes—
39C2×#336C2212yes—
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42#1444—21no—
43#1444—21no—
44#1442—21no—
45#1442—21no—
46C4⋊#95C2212yes—
47C23×C8C2312yes—
48C23×C8C2312yes—
49C2×#125—22no—
50C2×#125—22no—
51C2×#125—22no—
52C2×#125—22no—
53C2×#125—22no—
54C2×#125Q814yes—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4C2312yes—
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2312yes—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C42—21no—
71C22×C42—21no—
72C22×C42C2311yescharacteristic
73C22×C42C2311yescharacteristic
74C22×C42C2311yescharacteristic
75#389—28no—
76#389—28no—
77#389—22no—
78#389—22no—
79#389—24no—
80#389—24no—
81#389D414yes—
82#389D414yes—
83#387—28no—
84#387—28no—
85#384—22no—
86#384—22no—
87#384—22no—
88#384—22no—
89#382—24no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—22no—
94#376—22no—
95#376—22no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95D411yescharacteristic
106C2×#95D411yescharacteristic
107C2×#95D411yescharacteristic
108C2×#95D411yescharacteristic
109#340—24no—
110#340—24no—
111#340—24no—
112#340—24no—
113#340—24no—
114#340—24no—
115#340—24no—
116#340—24no—
117#336—22no—
118#336—22no—
119#336—24no—
120#336—24no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C23×C4C2411yescharacteristic
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148#125—28no—
149#125—28no—
150#125—28no—
151#125—28no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4—82no—
191C2×C4⋊C4—82no—
192C2×C4⋊C4—82no—
193C2×C4⋊C4—82no—
194C2×C4⋊C4—82no—
195C2×C4⋊C4—82no—
196C2×C4⋊C4C2×D412yes—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4C2×Q812yes—
201C2×C4⋊C4C2×Q812yes—
202C2×C4⋊C4#4114yes—
203C2×C4⋊C4#4112yes—
204C2×C4⋊C4#4112yes—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—24no—
215C2×C42—24no—
216C2×C42—82no—
217C2×C42—82no—
218C2×C42C2×D412yes—
219C2×C42C2×D412yes—
220C2×C42C2×Q812yes—
221C2×C42#4112yes—
222C2×C42#4114yes—
223#95—24no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—24no—
228#95—24no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95—22no—
233#95—44no—
234#95—82no—
235#95—82no—
236C24C22×D411yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4#12012yes—
296C22×C4#12012yes—
297C22×C4C22⋊Q812yes—
298C22×C4C22⋊Q812yes—
299C22×C4#12412yes—
300C22×C4#12412yes—
301C22×C4C22×D411yescharacteristic
302C22×C4C22×D411yescharacteristic
303C22×C4C22×Q811yescharacteristic
304C22×C4C2×#4111yescharacteristic
305C22×C4C2×#4111yescharacteristic
306C22×C4C2×#4111yescharacteristic
307C22×C4C2×#4112yes—
308C22×C4C2×#4112yes—
309C22×C42−1+412yes—
310C22×C42−1+412yes—
311C2×C8—42no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C4⋊C4—216no—
326C4⋊C4—216no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—84no—
346C4⋊C4—84no—
347C4⋊C4—88no—
348C4⋊C4—84no—
349C4⋊C4—84no—
350C4⋊C4—84no—
351C4⋊C4—84no—
352C4⋊C4C22⋊Q814yes—
353C4⋊C4C22⋊Q814yes—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—24no—
359C42—24no—
360C42—24no—
361C42—24no—
362C42—84no—
363C42—84no—
364C23C2×#12011yescharacteristic
365C23C2×C22⋊Q811yescharacteristic
366C23#52511yescharacteristic
367C23#52511yescharacteristic
368C23C2×#12411yescharacteristic
369C23#53611yescharacteristic
370C23#53611yescharacteristic
371C23#57612yes—
372C23#57712yes—
373C23#57712yes—
374C23#57812yes—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4C2×C22⋊Q811yescharacteristic
440C2×C4C2×C22⋊Q811yescharacteristic
441C2×C4#52511yescharacteristic
442C2×C4#52511yescharacteristic
443C2×C4#52912yes—
444C2×C4#52912yes—
445C2×C4#54112yes—
446C2×C4#54112yes—
447C2×C4#54712yes—
448C2×C4#54712yes—
449C2×C4#54812yes—
450C2×C4#54812yes—
451C2×C4#55612yes—
452C2×C4#55612yes—
453C2×C4#55712yes—
454C2×C4#55712yes—
455C8—82no—
456C8—82no—
457C22#239811yescharacteristic
458C22#240611yescharacteristic
459C22#243611yescharacteristic
460C22#256811yescharacteristic
461C22#258111yescharacteristic
462C22#263411yescharacteristic
463C22#284811yescharacteristic
464C22#300811yescharacteristic
465C22#300911yescharacteristic
466C22#301011yescharacteristic
467C22#301111yescharacteristic
468C22#308312yes—
469C22#308412yes—
470C22#311912yes—
471C22#312012yes—
472C22#312412yes—
473C22#312512yes—
474C22#313612yes—
475C22#313712yes—
476C22#324112yes—
477C22#324112yes—
478C22#324212yes—
479C22#324212yes—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—44no—
486C4—42no—
487C4—44no—
488C4—82no—
489C4—82no—
490C4—84no—
491C4—162no—
492C4#245312yes—
493C4#245312yes—
494C4#246912yes—
495C4#246912yes—
496C2#1488411yescharacteristic
497C2#2383212yes—
498C2#2406911yescharacteristic
499C2#2407111yescharacteristic
500C2#2591411yescharacteristic
501C2#2591511yescharacteristic
502C2#2922812yes—
503C2#2928512yes—
504C2#3010412yes—
505C2#3296311yescharacteristic
506C2#3296511yescharacteristic
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×#23302
C2×#21002
C2×#20992
#142772
#113852
#112672
#112082
#108852
#108842
#107962