Finite Group Databasebeta

← #26319372

Subgroups — #26319372

Order 12032.

746 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251770C211yesmaximal, characteristic, complemented
2#20244890C211yesmaximal, characteristic, complemented
3#20244780C211yesmaximal, characteristic, complemented
4#20244776C211yesmaximal, characteristic
5#20244705C211yesmaximal, characteristic
6#20244241C211yesmaximal, characteristic
7#20244118C211yesmaximal, characteristic, complemented
8#20244074C211yesmaximal, characteristic
9#20244063C211yesmaximal, characteristic, complemented
10#20244029C211yesmaximal, characteristic, complemented
11#20243966C211yesmaximal, characteristic, complemented
12#20243722C211yesmaximal, characteristic
13#20243635C211yesmaximal, characteristic
14C4×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C47×#2293C211yesmaximal, characteristic
16C22×#10625335C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093947C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×C4×C47⋊C8C2211yescharacteristic
29C2×C4×C47⋊C8C2211yescharacteristic
30#15689029C2211yescharacteristic
31#15689029C2211yescharacteristic
32#15689029C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689021C2211yescharacteristic
36#15689007—21no—
37#15689007—21no—
38#15689007—21no—
39#15688991—21no—
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47C2211yescharacteristic
49C2×#117×C47—21no—
50C47×#390C2211yescharacteristic
51C47×#390C2211yescharacteristic
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#388—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47—21no—
58C43×C47C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C2×#10625335—22no—
61C2×#10625335—22no—
62C2×#10625335—41no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73#13093957—22no—
74#13093957—41no—
75#13093955—22no—
76C4⋊(C47⋊C8)—22no—
77C4⋊(C47⋊C8)—22no—
78#13093947—22no—
79#13093947—22no—
80#13093947—41no—
81#13093945—22no—
82#13093945—22no—
83#13093945—41no—
84C4×C47⋊C8—41no—
85C4×C47⋊C8—41no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C22×D4×C47C2311yescharacteristic
96C23×C4×C47—21no—
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99#117×C47—44no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47D411yescharacteristic
112C2×C42×C47D411yescharacteristic
113C2×C42×C47D411yescharacteristic
114C2×C42×C47D411yescharacteristic
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117C2×C42×C47C2311yescharacteristic
118#95×C47—21no—
119#95×C47—21no—
120#95×C47—21no—
121C24×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47#4112yes—
128C22×C4×C47—24no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—42no—
133C22×C4×C47—42no—
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2411yescharacteristic
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—21no—
145C2×Dic94—21no—
146C2×Dic94—21no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—42no—
157C4⋊C4×C47—42no—
158C4⋊C4×C47#4112yes—
159C22⋊C4×C47—24no—
160C22⋊C4×C47—42no—
161C22⋊C4×C47—42no—
162C22⋊C4×C47—42no—
163C22⋊C4×C47—42no—
164C42×C47—22no—
165C42×C47—22no—
166C42×C47—22no—
167C42×C47—22no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—42no—
175#10625335—44no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182Dic47⋊C4—42no—
183Dic47⋊C4—42no—
184Dic47⋊C4—42no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8#4112yes—
196C2×C47⋊C8#4112yes—
197C23×C47—22no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47C22×D411yescharacteristic
205D4×C47—22no—
206D4×C47—22no—
207D4×C47—41no—
208D4×C47—41no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—48no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47#13512yes—
234C2×C4×C47#13512yes—
235C2×C4×C47AGL(1,ℤ/8)12yes—
236C2×C4×C47#13712yes—
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C47C2×#4111yescharacteristic
241C2×C4×C47H(5,𝔽2)11yescharacteristic
242C2×C4×C472−1+411yescharacteristic
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255Dic94—41no—
256Dic94—41no—
257Dic94—41no—
258Dic94—41no—
259C47⋊C8—22no—
260C47⋊C8—22no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263#29433—471nomaximal, Sylow
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—81no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47#52511yescharacteristic
272C22×C47#53211yescharacteristic
273C22×C47#53711yescharacteristic
274C22×C47C2×#13511yescharacteristic
275C22×C47C2×#13511yescharacteristic
276C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C47C2×#13711yescharacteristic
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—22no—
282C4×C47—42no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47—81no—
286C4×C47—81no—
287C4×C47#55111yescharacteristic
288C4×C47#55211yescharacteristic
289C4×C47#55311yescharacteristic
290C4×C47#55611yescharacteristic
291Dic47—81no—
292Dic47—81no—
293Dic47—81no—
294Dic47—81no—
295#2863—471no—
296#2293D4711yescharacteristic
297#2088—471no—
298#2068—471no—
299#2067—471no—
300#2055—471no—
301#1968—471no—
302#1942—471no—
303#1934—471no—
304#1933—471no—
305#1928—471no—
306#1919—471no—
307#1877—471no—
308#1862—471no—
309C4×C4⋊C8—471no—
310C2×C47—82no—
311C2×C47#260111yescharacteristic
312C2×C47#310511yescharacteristic
313C2×C47#310711yescharacteristic
314C2×C47#316811yescharacteristic
315C2×C47#318211yescharacteristic
316C2×C47#324711yescharacteristic
317C2×C47#324811yescharacteristic
318C22×SD16—471no—
319C2×C4×D4C2×D4711yescharacteristic
320C2×#117—21no—
321C2×#107—471no—
322C2×#107—471no—
323C2×#106—471no—
324C2×C4⋊C8—471no—
325C2×C4⋊C8—471no—
326C2×#103—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×#102—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×C4×C8—471no—
333C2×C4×C8—471no—
334#391—471no—
335#391—471no—
336#391—471no—
337#390C2×D4711yescharacteristic
338#390C2×D4711yescharacteristic
339#389—471no—
340#389—471no—
341#389—471no—
342#389C2×D4711yescharacteristic
343#389C2×D4711yescharacteristic
344#388—21no—
345#388—21no—
346#387—941no—
347#387—941no—
348#387—941no—
349#383—941no—
350C4×C4⋊C4C2×D4711yescharacteristic
351C4×C22⋊C4—21no—
352C43C2×D4711yescharacteristic
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#340—471no—
359#336—471no—
360#336—471no—
361C47#2943311yescharacteristic, complemented, Sylow
362C22×Q8—471no—
363C22×D4C22×D4711yescharacteristic
364C23×C4—21no—
365C2×SD16—942no—
366C2×SD16—942no—
367C2×SD16—1881no—
368C22×C8—471no—
369C22×C8—471no—
370C22×C8—471no—
371C22×C8—471no—
372C4×D4—22no—
373C4×D4—22no—
374#117—44no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—471no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—471no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4—941no—
383C2×C4⋊C4C22×D4711yescharacteristic
384C2×C4⋊C4C22×D4711yescharacteristic
385C2×C4⋊C4C22×D4711yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42C22⋊D4711yescharacteristic
393C2×C42C22⋊D4711yescharacteristic
394C2×C42C22⋊D4711yescharacteristic
395C2×C42C22⋊D4711yescharacteristic
396C2×C42C22×D4711yescharacteristic
397C2×C42C22×D4711yescharacteristic
398C2×C42C22×D4711yescharacteristic
399#107—942no—
400#107—1881no—
401#106—942no—
402C4⋊C8—942no—
403C4⋊C8—942no—
404#103—942no—
405#103—942no—
406#103—1881no—
407#102—942no—
408#102—942no—
409#102—1881no—
410C4×C8—1881no—
411C4×C8—1881no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—941no—
416#95—941no—
417#95—941no—
418#95—941no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95—941no—
424C24—21no—
425C2×Q8—941no—
426C2×Q8—941no—
427C2×Q8—941no—
428C2×Q8—941no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4#1062535012yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4C2×C22⋊D4711yescharacteristic
448C22×C4C2×C22⋊D4711yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450C22×C4C2×C22⋊D4711yescharacteristic
451C22×C4C2×C22⋊D4711yescharacteristic
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C23×D4711yescharacteristic
454SD16—1884no—
455C2×C8—472no—
456C2×C8—472no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—941no—
461C2×C8—941no—
462C2×C8—941no—
463C2×C8—941no—
464C2×C8—941no—
465C2×C8—941no—
466C2×C8—941no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—1882no—
481C4⋊C4—1882no—
482C4⋊C4—1882no—
483C4⋊C4#1062535012yes—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D4711yescharacteristic
508Q8—1881no—
509Q8—1881no—
510Q8—1881no—
511Q8—1881no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—48no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4#1309404412yes—
553C2×C4#1309404412yes—
554C2×C4#1309405012yes—
555C2×C4#1309405412yes—
556C2×C4#41×D4711yescharacteristic
557C2×C4#41×D4711yescharacteristic
558C2×C4C2×#1062535011yescharacteristic
559C2×C4C2×#1062535011yescharacteristic
560C2×C4#1309407011yescharacteristic
561C2×C4#1309407111yescharacteristic
562C8—942no—
563C8—942no—
564C8—1881no—
565C8—1881no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1568963411yescharacteristic
574C22#1568966911yescharacteristic
575C22#1568970111yescharacteristic
576C22C2×#1309404411yescharacteristic
577C22C2×#1309404411yescharacteristic
578C22C2×#1309405011yescharacteristic
579C22C2×#1309405411yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—3761no—
590C4—3761no—
591C4—3761no—
592C4—3761no—
593C4#1568979711yescharacteristic
594C4#1568980611yescharacteristic
595C4#1568981711yescharacteristic
596C4#1568984111yescharacteristic
597C2—82no—
598C2#2024898511yescharacteristic
599C2#2025343511yescharacteristic
600C2#2025345911yescharacteristic
601C2#2025395211yescharacteristic
602C2#2025410211yescharacteristic
603C2#2025470811yescharacteristic
604C2#2025472511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2293C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2293D47
hypocenterC47#29433
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20251770C2semidirect
2. #20244890C2semidirect
3. #20244780C2semidirect
7. #20244118C2semidirect
9. #20244063C2semidirect
10. #20244029C2semidirect
11. #20243966C2semidirect
14. C4×C4⋊(C47⋊C8)C2semidirect
361. C47#29433semidirect

Maximal subgroups

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

subgroupindex
#202517702
#202448902
#202447802
#202447762
#202447052
#202442412
#202441182
#202440742
#202440632
#202440292
#202439662
#202437222
#202436352
C4×C4⋊(C47⋊C8)2
C47×#22932
#2943347