Finite Group Databasebeta

← #26316200

Subgroups — #26316200

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246099C211yesmaximal, characteristic
2#20244536C211yesmaximal, characteristic, complemented
3#20244531C211yesmaximal, characteristic
4#20244526C211yesmaximal, characteristic, complemented
5#20244521C211yesmaximal, characteristic
6#20244202C211yesmaximal, characteristic
7#20244197C211yesmaximal, characteristic
8#20243521C211yesmaximal, characteristic, complemented
9#20243515C211yesmaximal, characteristic, complemented
10#20243400C211yesmaximal, characteristic, complemented
11#20243395C211yesmaximal, characteristic
12#20243390C211yesmaximal, characteristic, complemented
13#20243385C211yesmaximal, characteristic
14#20243245C211yesmaximal, characteristic, complemented
15C47×#2660C211yesmaximal, characteristic, complemented
16C2×#13094012C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×#13093947C2211yescharacteristic
22C2×#13093947C2211yescharacteristic
23C2×#13093947C2211yescharacteristic
24C2×#13093947C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689029C2211yescharacteristic
32#15689025C2211yescharacteristic
33#15689015—21no—
34#15689015—21no—
35#15688997—21no—
36#15688997—21no—
37#15688993C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4⋊Q8×C47C2211yescharacteristic
49C2×#125×C47C2211yescharacteristic
50C47×#398—21no—
51C47×#398—21no—
52C47×#395—21no—
53C47×#395—21no—
54C47×#384C2211yescharacteristic
55C47×#384C2211yescharacteristic
56C47×#382C2211yescharacteristic
57C47×#382C2211yescharacteristic
58C47×#376C2211yescharacteristic
59C22×Dic94C2311yescharacteristic
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13094012—22no—
67#13094012Q814yescomplemented
68C4×Dic94—22no—
69C4×Dic94—22no—
70C4×D188—22no—
71C4×D188—22no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×Dic47⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×(C2×D47)⋊C4—21no—
82C2×C4×Dic47—21no—
83C4⋊(C47⋊C8)—22no—
84C4⋊(C47⋊C8)—22no—
85#13093947—41no—
86#13093947—41no—
87#13093947—41no—
88#13093947—41no—
89#13093944—41no—
90#13093944—41no—
91#13093944—41no—
92#13093944—41no—
93#13093935—22no—
94C4×C47⋊C8—22no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×Q8×C47—21no—
98C4⋊Q8×C47—41no—
99C4⋊Q8×C47—41no—
100#125×C47—41no—
101#125×C47—41no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47—21no—
120#95×C47D411yescharacteristic
121#95×C47D411yescharacteristic
122#95×C47D411yescharacteristic
123#95×C47D411yescharacteristic
124C23×D47—21no—
125C2×Q8×C47—42no—
126C2×Q8×C47—81no—
127C2×Q8×C47—81no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2411yescharacteristic
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188C2×Q812yes—
148C2×C4×D47—42no—
149C2×C4×D47—81no—
150C2×C4×D47—81no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94C2×Q812yes—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—42no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—42no—
168C4⋊C4×C47—81no—
169C4⋊C4×C47—81no—
170C4⋊C4×C47—81no—
171C4⋊C4×C47—81no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47C2×Q812yes—
175C42×C47#4112yes—
176C42×C47#4112yes—
177C42×C47#4112yes—
178(C2×D47)⋊C4—24no—
179(C2×D47)⋊C4—24no—
180(C2×D47)⋊C4—42no—
181(C2×D47)⋊C4—81no—
182(C2×D47)⋊C4—81no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—81no—
188C4⋊Dic47—81no—
189Dic47⋊C4—42no—
190C4×Dic47—42no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C23×C47C22×D411yescharacteristic
204C22×D47—22no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
211Q8×C47—84no—
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—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
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—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47C22⋊Q812yes—
239C2×C4×C47C22⋊Q812yes—
240C2×C4×C47#12412yes—
241C2×C4×C47#12412yes—
242C2×C4×C47C22×Q811yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C2×C4×C47H(5,𝔽2)11yescharacteristic
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257D188—22no—
258D188—22no—
259D188—41no—
260D188—41no—
261C4×D47—84no—
262Dic94—22no—
263Dic94—22no—
264Dic94—41no—
265Dic94—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268C47⋊C8—41no—
269C47⋊C8—41no—
270#29151—471nomaximal, Sylow
271C22×C47C2×C22⋊Q811yescharacteristic
272C22×C47C2×#12411yescharacteristic
273C22×C47#53511yescharacteristic
274C22×C47#57611yescharacteristic
275C22×C47#57711yescharacteristic
276C22×C47#57711yescharacteristic
277C22×C47#57811yescharacteristic
278C2×D47—42no—
279C2×D47—42no—
280C2×D47—42no—
281C2×D47—81no—
282C2×D47—81no—
283C2×D47—81no—
284C2×D47—81no—
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—22no—
288C4×C47—22no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47—81no—
295C4×C47#55411yescharacteristic
296C4×C47#55411yescharacteristic
297C4×C47#55511yescharacteristic
298C4×C47#55511yescharacteristic
299Dic47—42no—
300Dic47—81no—
301Dic47—81no—
302#2660D4711yescharacteristic, complemented
303#2326—471no—
304#2026—471no—
305#2025—471no—
306#2024—471no—
307#2023—471no—
308#1959—471no—
309#1958—471no—
310#1836—471no—
311#1834—471no—
312#1805—471no—
313#1804—471no—
314#1803—471no—
315#1802—471no—
316#1768—471no—
317C2×C47#256311yescharacteristic
318C2×C47#308311yescharacteristic
319C2×C47#308411yescharacteristic
320C2×C47#313611yescharacteristic
321C2×C47#313711yescharacteristic
322C2×C47#322411yescharacteristic
323C2×C47#322511yescharacteristic
324D47—82no—
325C2×C4⋊Q8C2×D4711yescharacteristic
326C2×#125C2×D4711yescharacteristic
327C2×#124—471no—
328C2×C4×Q8—471no—
329C2×C4×D4—471no—
330C2×C4⋊C8—471no—
331C2×C4⋊C8—471no—
332C2×#103—471no—
333C2×#103—471no—
334C2×#103—471no—
335C2×#103—471no—
336C2×#102—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#102—471no—
340C2×#97—471no—
341C2×C4×C8—471no—
342#398—21no—
343#398—21no—
344#395—21no—
345#395—21no—
346#391—471no—
347#390—471no—
348#388—941no—
349#388—941no—
350#385—941no—
351#385—941no—
352#384—471no—
353#384C2×D4711yescharacteristic
354#384C2×D4711yescharacteristic
355#382C2×D4711yescharacteristic
356#382C2×D4711yescharacteristic
357#376C2×D4711yescharacteristic
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#336—471no—
367#336—471no—
368C47#2915111yescharacteristic, complemented, Sylow
369C22×Q8—21no—
370C22×Q8—471no—
371C22×D4—471no—
372C23×C4—941no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—471no—
377C4⋊Q8—41no—
378C4⋊Q8—41no—
379#125—41no—
380#125—41no—
381#124—474no—
382#124—942no—
383C4×Q8—942no—
384C4×Q8—942no—
385C4×D4—942no—
386C4×D4—942no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C4⋊C4C22×D4711yescharacteristic
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—941no—
406C2×C22⋊C4—941no—
407C2×C22⋊C4—941no—
408C2×C42—941no—
409C2×C42C22×D4711yescharacteristic
410C2×C42C22×D4711yescharacteristic
411C2×C42C22×D4711yescharacteristic
412C4⋊C8—942no—
413C4⋊C8—942no—
414#103—1881no—
415#103—1881no—
416#103—1881no—
417#103—1881no—
418#102—1881no—
419#102—1881no—
420#102—1881no—
421#102—1881no—
422#97—942no—
423C4×C8—942no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—941no—
429#95—941no—
430#95C22⋊D4711yescharacteristic
431#95C22⋊D4711yescharacteristic
432#95C22⋊D4711yescharacteristic
433#95C22⋊D4711yescharacteristic
434C24—941no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8—472no—
439C2×Q8—941no—
440C2×Q8—941no—
441C2×Q8—941no—
442C2×Q8—941no—
443C2×Q8—941no—
444C2×D4—472no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—941no—
448C2×D4—941no—
449C2×D4—941no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4—941no—
457C22×C4—3761no—
458C22×C4—3761no—
459C22×C4—1882no—
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C23×D4711yescharacteristic
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—81no—
493C4⋊C4—81no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—3761no—
499C4⋊C4—3761no—
500C4⋊C4—1882no—
501C22⋊C4—944no—
502C22⋊C4—944no—
503C22⋊C4—3761no—
504C22⋊C4—3761no—
505C22⋊C4—1882no—
506C42—21no—
507C42—21no—
508C42—1882no—
509C42Q8×D4712yes—
510C42#1062535412yes—
511C42#1062535412yes—
512C42#1062535412yes—
513C23—942no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23—1881no—
518C23—1881no—
519C23—1881no—
520C23C22×C22⋊D4711yescharacteristic
521Q8—84no—
522Q8—942no—
523Q8—942no—
524Q8—1881no—
525Q8—1881no—
526D4—942no—
527D4—942no—
528D4—1881no—
529D4—1881no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—942no—
557C2×C4—3764no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4#1309400012yes—
567C2×C4#1309400012yes—
568C2×C4#1309401312yes—
569C2×C4#1309401312yes—
570C2×C4C2×Q8×D4711yescharacteristic
571C2×C4C2×#1062535411yescharacteristic
572C2×C4C2×#1062535411yescharacteristic
573C2×C4C2×#1062535411yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309406911yescharacteristic
576C8—1881no—
577C8—1881no—
578C8—1881no—
579C8—1881no—
580C22—3761no—
581C22—3761no—
582C22—3761no—
583C22—3761no—
584C22—1882no—
585C22—1882no—
586C22—1882no—
587C22C2×#1309400011yescharacteristic
588C22C2×#1309401311yescharacteristic
589C22#1568969011yescharacteristic
590C22#1568992611yescharacteristic
591C22#1568993111yescharacteristic
592C22#1568993411yescharacteristic
593C22#1568993811yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—3761no—
605C4—3761no—
606C4—1882no—
607C4#1568983411yescharacteristic
608C4#1568983411yescharacteristic
609C4#1568983911yescharacteristic
610C4#1568983911yescharacteristic
611C2—3762no—
612C2#2024856211yescharacteristic
613C2#2025323511yescharacteristic
614C2#2025324611yescharacteristic
615C2#2025374711yescharacteristic
616C2#2025375811yescharacteristic
617C2#2025448211yescharacteristic
618C2#2025449711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2660C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2660D47
hypocenterC47#29151
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2660

Complements

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

NH ≅ G/Ntype
2. #20244536C2semidirect
4. #20244526C2semidirect
8. #20243521C2semidirect
9. #20243515C2semidirect
10. #20243400C2semidirect
12. #20243390C2semidirect
14. #20243245C2semidirect
15. C47×#2660C2semidirect
67. #13094012Q8semidirect
302. #2660D47semidirect
368. C47#29151semidirect

Maximal subgroups

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

subgroupindex
#202460992
#202445362
#202445312
#202445262
#202445212
#202442022
#202441972
#202435212
#202435152
#202434002
#202433952
#202433902
#202433852
#202432452
C47×#26602
#2915147