Finite Group Databasebeta

← #26289094

Subgroups — #26289094

Order 12032.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247821C211yesmaximal, characteristic, complemented
2#20244791C211yesmaximal, characteristic, complemented
3#20244776C211yesmaximal, characteristic, complemented
4#20244567C211yesmaximal, characteristic
5#20244567C211yesmaximal, characteristic
6#20244146C211yesmaximal, characteristic, complemented
7#20244118C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic, complemented
9#20243977C211yesmaximal, characteristic, complemented
10#20243966C211yesmaximal, characteristic, complemented
11#20243649C211yesmaximal, characteristic, complemented
12#20243587C211yesmaximal, characteristic, complemented
13#20243483C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C47×#2363C211yesmaximal, characteristic
16C2×#13093957C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×#13093945C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C4×C47⋊C8C2211yescharacteristic
28#15689065—21no—
29#15689046—21no—
30#15689021C2211yescharacteristic
31#15689021C2211yescharacteristic
32#15689016—21no—
33#15689010—21no—
34#15688993C2211yescharacteristic
35#15688983C2211yescharacteristic
36#15688983C2211yescharacteristic
37C4×C4⋊Dic47C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#121×C47C2211yescharacteristic
49C2×C4×D4×C47C2211yescharacteristic
50C2×#117×C47C2211yescharacteristic
51C47×#390—21no—
52C47×#390C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#386—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C22⋊C4×C47—21no—
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2311yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×Dic47⋊C4—21no—
70C2×Dic47⋊C4—21no—
71C2×C22⋊Dic47—21no—
72C2×C22⋊Dic47—21no—
73C2×C4×Dic47—21no—
74#13093957—22no—
75#13093957—22no—
76#13093957—41no—
77#13093955—22no—
78C4⋊(C47⋊C8)—22no—
79#13093945—22no—
80#13093945—22no—
81#13093945—22no—
82#13093945—41no—
83C22⋊(C47⋊C8)—22no—
84C22⋊(C47⋊C8)—41no—
85C4×C47⋊C8—41no—
86C47⋊#95—21no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C22×D4×C47—21no—
92C22×D4×C47C2311yescharacteristic
93C23×C4×C47—21no—
94C23×C4×C47C2311yescharacteristic
95#121×C47—22no—
96#121×C47—22no—
97C4×D4×C47—22no—
98C4×D4×C47—41no—
99#117×C47—22no—
100#117×C47—41no—
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×C22⋊C4×C47D411yescharacteristic
111C2×C22⋊C4×C47D411yescharacteristic
112C2×C42×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116#95×C47—21no—
117#95×C47—21no—
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47—21no—
121C24×C47C2×D411yescharacteristic
122C2×D4×C47—24no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—81no—
129C2×D4×C47—81no—
130C2×D4×C47#4112yes—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—81no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2411yescharacteristic
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—81no—
158C4⋊C4×C47#4112yes—
159C4⋊C4×C47#4112yes—
160C22⋊C4×C47—24no—
161C22⋊C4×C47—22no—
162C22⋊C4×C47—22no—
163C22⋊C4×C47—42no—
164C22⋊C4×C47—42no—
165C22⋊C4×C47—42no—
166C22⋊C4×C47—81no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—42no—
172C42×C47—81no—
173C22⋊Dic47—81no—
174C22⋊Dic47—81no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—81no—
184C4⋊Dic47—81no—
185Dic47⋊C4—42no—
186Dic47⋊C4—81no—
187C4×Dic47—81no—
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—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8#4112yes—
200C23×C47—22no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—41no—
213C23×C47—41no—
214C23×C47C22×D411yescharacteristic
215D4×C47—22no—
216D4×C47—22no—
217D4×C47—41no—
218D4×C47—41no—
219D4×C47—84no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—22no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—84no—
247C2×C4×C47#13512yes—
248C2×C4×C47#13712yes—
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47H(5,𝔽2)11yescharacteristic
254C2×C4×C472−1+411yescharacteristic
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C47⋊C8—22no—
268C47⋊C8—41no—
269C47⋊C8—41no—
270C47⋊C8—41no—
271#27041—471nomaximal, Sylow
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—42no—
276C22×C47—41no—
277C22×C47—42no—
278C22×C47—41no—
279C22×C47—42no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—81no—
283C22×C47—81no—
284C22×C47—81no—
285C22×C47—81no—
286C22×C47#52511yescharacteristic
287C22×C47#54611yescharacteristic
288C22×C47#54711yescharacteristic
289C22×C47C2×#13511yescharacteristic
290C22×C47C2×#13711yescharacteristic
291C22×C47#57611yescharacteristic
292C22×C47#57611yescharacteristic
293C4×C47—22no—
294C4×C47—22no—
295C4×C47—41no—
296C4×C47—42no—
297C4×C47—41no—
298C4×C47—41no—
299C4×C47—42no—
300C4×C47—81no—
301C4×C47#52911yescharacteristic
302C4×C47#53911yescharacteristic
303C4×C47#55311yescharacteristic
304C4×C47#55611yescharacteristic
305Dic47—81no—
306Dic47—81no—
307Dic47—81no—
308Dic47—81no—
309#2497—471no—
310#2363D4711yescharacteristic
311#2071—471no—
312#2067—471no—
313#2033—471no—
314#2033—471no—
315#1947—471no—
316#1942—471no—
317#1923—471no—
318#1921—471no—
319#1919—471no—
320#1864—471no—
321#1854—471no—
322#1825—471no—
323C4×#102—471no—
324C2×C47—81no—
325C2×C47—82no—
326C2×C47#246611yescharacteristic
327C2×C47#310711yescharacteristic
328C2×C47#312211yescharacteristic
329C2×C47#330511yescharacteristic
330C2×C47#331411yescharacteristic
331C2×C47#333911yescharacteristic
332C2×C47#335711yescharacteristic
333C2×#121C2×D4711yescharacteristic
334C2×C4×D4C2×D4711yescharacteristic
335C2×#117C2×D4711yescharacteristic
336C2×#107—471no—
337C2×#107—471no—
338C2×#107—471no—
339C2×#106—471no—
340C2×C4⋊C8—471no—
341C2×#102—471no—
342C2×#102—471no—
343C2×#102—471no—
344C2×#102—471no—
345C2×C22⋊C8—471no—
346C2×C22⋊C8—471no—
347C2×C4×C8—471no—
348#400—941no—
349#396—941no—
350#390—21no—
351#390C2×D4711yescharacteristic
352#389—471no—
353#389—471no—
354#389C2×D4711yescharacteristic
355#388—21no—
356#388—941no—
357#387—941no—
358#386—21no—
359#384—471no—
360#380—471no—
361#380—471no—
362C4×C4⋊C4—471no—
363C4×C4⋊C4C2×D4711yescharacteristic
364C4×C22⋊C4—21no—
365C4×C22⋊C4C2×D4711yescharacteristic
366#340—471no—
367#340—471no—
368#340—471no—
369#340—471no—
370#340—471no—
371#340—471no—
372#340—471no—
373#340—471no—
374#336—471no—
375#336—471no—
376C47#2704111yescharacteristic, complemented, Sylow
377C22×D4—21no—
378C22×D4C22×D4711yescharacteristic
379C23×C4—21no—
380C23×C4C22×D4711yescharacteristic
381C22×C8—471no—
382C22×C8—471no—
383C22×C8—471no—
384C22×C8—471no—
385#121—22no—
386#121—22no—
387C4×D4—22no—
388C4×D4—41no—
389#117—22no—
390#117—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4C22×D4711yescharacteristic
401C2×C4⋊C4C22×D4711yescharacteristic
402C2×C4⋊C4C22×D4711yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C22⋊C4C22⋊D4711yescharacteristic
411C2×C22⋊C4C22⋊D4711yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—941no—
415C2×C42C22×D4711yescharacteristic
416C2×C42C22×D4711yescharacteristic
417#107—942no—
418#107—942no—
419#107—1881no—
420#106—942no—
421C4⋊C8—942no—
422#102—942no—
423#102—942no—
424#102—942no—
425#102—1881no—
426C22⋊C8—942no—
427C22⋊C8—1881no—
428C4×C8—1881no—
429#95—21no—
430#95—21no—
431#95—941no—
432#95—941no—
433#95—941no—
434#95—941no—
435#95—941no—
436#95C22⋊D4711yescharacteristic
437#95C22⋊D4711yescharacteristic
438C24—21no—
439C24C2×C22⋊D4711yescharacteristic
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4#1062535012yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—81no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C23×D4711yescharacteristic
471C2×C8—472no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—81no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—3761no—
497C4⋊C4—3761no—
498C4⋊C4—3761no—
499C4⋊C4—1882no—
500C4⋊C4#1062535012yes—
501C4⋊C4#1062535212yes—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—81no—
509C22⋊C4—3761no—
510C22⋊C4—3761no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—81no—
517C42—3761no—
518C23—21no—
519C23—21no—
520C23—22no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×C22⋊D4711yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—84no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4—1881no—
575C2×C4—1881no—
576C2×C4—1881no—
577C2×C4#1309404412yes—
578C2×C4#1309405412yes—
579C2×C4#41×D4711yescharacteristic
580C2×C4C2×#1062535211yescharacteristic
581C2×C4C2×#1062535011yescharacteristic
582C2×C4C2×#1062535011yescharacteristic
583C2×C4#1309406911yescharacteristic
584C2×C4#1309407111yescharacteristic
585C8—942no—
586C8—1881no—
587C8—1881no—
588C8—1881no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—41no—
597C22—42no—
598C22—41no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1568963411yescharacteristic
604C22#1568976711yescharacteristic
605C22#1568977211yescharacteristic
606C22C2×#1309404411yescharacteristic
607C22C2×#1309405411yescharacteristic
608C22#1568992611yescharacteristic
609C22#1568992611yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—3761no—
619C4—3761no—
620C4—3761no—
621C4—3761no—
622C4#1568965311yescharacteristic
623C4#1568971511yescharacteristic
624C4#1568982311yescharacteristic
625C4#1568984311yescharacteristic
626C2—81no—
627C2—82no—
628C2#2024741811yescharacteristic
629C2#2025345911yescharacteristic
630C2#2025363111yescharacteristic
631C2#2025533811yescharacteristic
632C2#2025546911yescharacteristic
633C2#2025578411yescharacteristic
634C2#2025600811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2363C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenter#2363D47
hypocenterC47#27041
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #20247821C2semidirect
2. #20244791C2semidirect
3. #20244776C2semidirect
6. #20244146C2semidirect
7. #20244118C2semidirect
8. #20243996C2semidirect
9. #20243977C2semidirect
10. #20243966C2semidirect
11. #20243649C2semidirect
12. #20243587C2semidirect
13. #20243483C2semidirect
14. C4×#13093945C2semidirect
376. C47#27041semidirect

Maximal subgroups

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

subgroupindex
#202478212
#202447912
#202447762
#202445672
#202441462
#202441182
#202439962
#202439772
#202439662
#202436492
#202435872
#202434832
C4×#130939452
C47×#23632
#2704147