Finite Group Databasebeta

← #26226856

Subgroups — #26226856

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689179C211yesmaximal, characteristic
2#20245794C211yesmaximal, characteristic
3#20245784C211yesmaximal, characteristic
4#20244158C211yesmaximal, characteristic, complemented
5#20244156C211yesmaximal, characteristic, complemented
6#20244154C211yesmaximal, characteristic, complemented
7#20243590C211yesmaximal, characteristic
8#20243588C211yesmaximal, characteristic
9#20243586C211yesmaximal, characteristic
10#20243584C211yesmaximal, characteristic
11#20243555C211yesmaximal, characteristic, complemented
12#20243553C211yesmaximal, characteristic, complemented
13#20243520C211yesmaximal, characteristic, complemented
14#20243520C211yesmaximal, characteristic, complemented
15C47×#1949C211yesmaximal, characteristic, complemented
16C2×#13093982C2211yescharacteristic
17C2×#13093982C2211yescharacteristic
18C2×C42×D47C2211yescharacteristic
19#15689179C418yescomplemented
20C2×#13093958C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×(C2×D47)⋊C8C2211yescharacteristic
29C2×#13093934C2211yescharacteristic
30C2×#13093934C2211yescharacteristic
31#15688992C2211yescharacteristic
32#15688992C2211yescharacteristic
33#15688990—21no—
34#15688989C2211yescharacteristic
35#15688988C2211yescharacteristic
36#15688988C2211yescharacteristic
37#15688985—21no—
38#15688982—21no—
39#15688982—21no—
40#15688980C2211yescharacteristic
41#15688980C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688974—21no—
44#15688974—21no—
45C4×(C2×D47)⋊C4—21no—
46#15688969—21no—
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53C2×#107×C47C2211yescharacteristic
54C2×#106×C47C2211yescharacteristic
55C2×C4⋊C8×C47C2211yescharacteristic
56C47×#382C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C22×C4×D47D411yescharacteristic
61C22×C4×D47D411yescharacteristic
62C22×C4×D47C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13093982—41no—
66#13093982—41no—
67#13093982—41no—
68#13093982—41no—
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×Dic47⋊C4—21no—
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×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47D411yescharacteristic
85C2×C4×Dic47D411yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C42×D47C2×C414yes—
88C42×D47Q814yes—
89#13093958—41no—
90#13093957—41no—
91#13093957—41no—
92#13093956—41no—
93#13093955—41no—
94#13093955—41no—
95C4⋊(C47⋊C8)C2×C414yes—
96(C2×D47)⋊C8C2×C414yes—
97(C2×D47)⋊C8C2×C414yes—
98#13093934C2×C414yes—
99#13093934C2×C414yes—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C22×C8×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C42×C47—21no—
116C2×C42×C47C2311yescharacteristic
117#107×C47—41no—
118#106×C47—41no—
119C4⋊C8×C47C2×C414yes—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123C23×D47C2×D411yescharacteristic
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47C2×D411yescharacteristic
136C22×Dic47C2×D411yescharacteristic
137C22×Dic47C2×D411yescharacteristic
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—21no—
141C2×C4×D47—21no—
142C2×C4×D47—41no—
143C2×C4×D47—41no—
144C2×C4×D47—41no—
145C2×C4×D47—41no—
146C2×C4×D47C4⋊C414yes—
147C2×C4×D47C4⋊C414yes—
148C2×C4×D47C22×C412yes—
149C2×C4×D47C2×Q812yes—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47C22×C412yes—
155C2×C8×C47C22×C412yes—
156C4⋊C4×C47—21no—
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—
164C42×C47—42no—
165C42×C47C22×C412yes—
166C42×C47C2×Q812yes—
167(C2×D47)⋊C4—42no—
168(C2×D47)⋊C4—42no—
169(C2×D47)⋊C4—42no—
170(C2×D47)⋊C4—42no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179Dic47⋊C4—42no—
180Dic47⋊C4—42no—
181Dic47⋊C4—42no—
182Dic47⋊C4—42no—
183C4×Dic47—42no—
184C4×Dic47—42no—
185C4×Dic47—42no—
186C4×Dic47C4⋊C414yes—
187C4×Dic47C4⋊C414yes—
188C4×Dic47C22×C412yes—
189C4×Dic47C2×Q812yes—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8C22×C412yes—
195C2×C47⋊C8C22×C412yes—
196C23×C47C22×D411yescharacteristic
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—21no—
201C22×D47—21no—
202C22×D47—21no—
203C22×D47C2×C4⋊C412yes—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47C2×C4⋊C412yes—
221C2×C4×C47C2×C4⋊C412yes—
222C2×C4×C47C23×C411yescharacteristic
223C2×C4×C47C22×Q811yescharacteristic
224C2×C4×C47H(5,𝔽2)11yescharacteristic
225C2×C4×C47H(5,𝔽2)11yescharacteristic
226C2×C4×C472−1+411yescharacteristic
227C2×C4×C472−1+411yescharacteristic
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—41no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47C2×C4⋊C412yes—
247C2×Dic47C2×C4⋊C412yes—
248C2×Dic47C2×C4⋊C412yes—
249C4×D47—22no—
250C4×D47—22no—
251C4×D47—22no—
252C4×D47—22no—
253C4×D47—44no—
254C4×D47—44no—
255C8×C47—22no—
256C8×C47—22no—
257C47⋊C8—22no—
258C47⋊C8—22no—
259#21989—471nomaximal, Sylow
260C22×C47C22×C4⋊C411yescharacteristic
261C22×C47#53511yescharacteristic
262C22×C47#53611yescharacteristic
263C22×C47#57511yescharacteristic
264C22×C47#57511yescharacteristic
265C22×C47#57511yescharacteristic
266C22×C47#57511yescharacteristic
267C2×D47—22no—
268C2×D47—22no—
269C2×D47—22no—
270C2×D47—41no—
271C2×D47—41no—
272C2×D47—41no—
273C2×D47—41no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—81no—
277C4×C47—81no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47#52011yescharacteristic
281C4×C47#52011yescharacteristic
282C4×C47#54411yescharacteristic
283C4×C47#54411yescharacteristic
284Dic47—22no—
285Dic47—22no—
286Dic47—22no—
287Dic47—81no—
288Dic47—81no—
289Dic47—81no—
290Dic47—81no—
291C2×#432—471no—
292#2285—471no—
293#2283—471no—
294#1949—471no—
295#1949—471no—
296#1949—471no—
297#1949D4711yescharacteristic, complemented
298#1854—471no—
299#1854—471no—
300#1854—471no—
301#1854—471no—
302#1847—471no—
303#1847—471no—
304#1836—471no—
305#1836—471no—
306C2×C47#231711yescharacteristic
307C2×C47#291111yescharacteristic
308C2×C47#291111yescharacteristic
309C2×C47#321911yescharacteristic
310C2×C47#321911yescharacteristic
311C2×C47#324011yescharacteristic
312C2×C47#324011yescharacteristic
313D47—42no—
314C2×#117—471no—
315C2×#117—471no—
316C22×C42—471no—
317#432—478no—
318C2×#107—471no—
319C2×#107—471no—
320C2×#107—471no—
321C2×#107C2×D4711yescharacteristic
322C2×#106—471no—
323C2×#106—471no—
324C2×#106—471no—
325C2×#106C2×D4711yescharacteristic
326C2×C4⋊C8—471no—
327C2×C4⋊C8C2×D4711yescharacteristic
328C2×C22⋊C8—471no—
329C2×C22⋊C8—471no—
330C2×#97—471no—
331C2×#97—471no—
332#384—471no—
333#384—471no—
334#383—941no—
335#382—471no—
336#382—471no—
337#382—471no—
338#382C2×D4711yescharacteristic
339#381—941no—
340#380—471no—
341#380—471no—
342#380—941no—
343#380—941no—
344C4×C4⋊C4—471no—
345C4×C4⋊C4—941no—
346C4×C4⋊C4—941no—
347C4×C4⋊C4C2×D4711yescharacteristic
348C4×C22⋊C4—941no—
349#376—941no—
350#340—471no—
351#340—471no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340C2×D4711yescharacteristic
357#340C2×D4711yescharacteristic
358C47#2198911yescharacteristic, complemented, Sylow
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—471no—
362C22×C8—471no—
363C22×C8—471no—
364C22×C8C22×D4711yescharacteristic
365C22×C8C22×D4711yescharacteristic
366#117—1881no—
367#117—1881no—
368#117—1881no—
369#117—1881no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C4⋊C4C22×D4711yescharacteristic
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C42—21no—
387C2×C42—471no—
388C2×C42—471no—
389C2×C42—471no—
390C2×C42—474no—
391C2×C42—474no—
392C2×C42—941no—
393C2×C42—941no—
394C2×C42—941no—
395C2×C42C22×D4711yescharacteristic
396#107—41no—
397#107—1881no—
398#107—1881no—
399#107—1881no—
400#106—41no—
401#106—1881no—
402#106—1881no—
403#106—1881no—
404C4⋊C8—474no—
405C4⋊C8C4×D4714yes—
406C22⋊C8—474no—
407C22⋊C8—474no—
408#97—474no—
409#97—474no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—941no—
414#95—941no—
415#95—941no—
416#95—941no—
417#95—941no—
418#95—941no—
419#95—941no—
420#95—941no—
421#95—941no—
422C24—471no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—471no—
430C22×C4—472no—
431C22×C4—472no—
432C22×C4—474no—
433C22×C4—474no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4D4×D4711yescharacteristic
447C22×C4D4×D4711yescharacteristic
448C22×C4C23×D4711yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—472no—
454C2×C8—472no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8C2×C4×D4712yes—
460C2×C8C2×C4×D4712yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—1882no—
478C4⋊C4—1882no—
479C4⋊C4—1882no—
480C4⋊C4—1882no—
481C22⋊C4—1882no—
482C22⋊C4—1882no—
483C22⋊C4—1882no—
484C22⋊C4—1882no—
485C42—42no—
486C42—474no—
487C42—474no—
488C42—472no—
489C42—472no—
490C42—1882no—
491C42—1882no—
492C42—1882no—
493C42C2×C4×D4712yes—
494C42Q8×D4712yes—
495C23—472no—
496C23—941no—
497C23—941no—
498C23—941no—
499C23—941no—
500C23—941no—
501C23—941no—
502C23C2×D4×D4711yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—472no—
520C2×C4—472no—
521C2×C4—472no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—1884no—
533C2×C4—1884no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4C4⋊C4×D4712yes—
547C2×C4C4⋊C4×D4712yes—
548C2×C4C22×C4×D4711yescharacteristic
549C2×C4C2×Q8×D4711yescharacteristic
550C2×C4#1309406911yescharacteristic
551C2×C4#1309407011yescharacteristic
552C2×C4#1309407111yescharacteristic
553C2×C4#1309407211yescharacteristic
554C8—22no—
555C8—22no—
556C8—942no—
557C8—942no—
558C22—942no—
559C22—942no—
560C22—942no—
561C22—1881no—
562C22—1881no—
563C22—1881no—
564C22—1881no—
565C22C2×C4⋊C4×D4711yescharacteristic
566C22#1568968911yescharacteristic
567C22#1568969611yescharacteristic
568C22#1568991911yescharacteristic
569C22#1568992011yescharacteristic
570C22#1568992011yescharacteristic
571C22#1568992211yescharacteristic
572C4—22no—
573C4—22no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—942no—
579C4—942no—
580C4—942no—
581C4—3761no—
582C4—3761no—
583C4—3761no—
584C4—3761no—
585C4#1568960211yescharacteristic
586C4#1568960511yescharacteristic
587C4#1568975011yescharacteristic
588C4#1568975311yescharacteristic
589C2—1882no—
590C2#2024601011yescharacteristic
591C2#2025197511yescharacteristic
592C2#2025197611yescharacteristic
593C2#2025442411yescharacteristic
594C2#2025443011yescharacteristic
595C2#2025462711yescharacteristic
596C2#2025463311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1949C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
cosocleC22×C4×C47C24
hypercenter#1949D47
hypocenterC47#21989
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #20244158C2semidirect
5. #20244156C2semidirect
6. #20244154C2semidirect
11. #20243555C2semidirect
12. #20243553C2semidirect
13. #20243520C2semidirect
14. #20243520C2semidirect
15. C47×#1949C2semidirect
19. #15689179C4semidirect
297. #1949D47semidirect
358. C47#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#156891792
#202457942
#202457842
#202441582
#202441562
#202441542
#202435902
#202435882
#202435862
#202435842
#202435552
#202435532
#202435202
C47×#19492
#2198947