Finite Group Databasebeta

← #26284918

Subgroups — #26284918

Order 12032.

732 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247904C211yesmaximal, characteristic, complemented
2#20244791C211yesmaximal, characteristic
3#20244762C211yesmaximal, characteristic
4#20244624C211yesmaximal, characteristic
5#20244624C211yesmaximal, characteristic
6#20244067C211yesmaximal, characteristic, complemented
7#20244019C211yesmaximal, characteristic, complemented
8#20243980C211yesmaximal, characteristic, complemented
9#20243973C211yesmaximal, characteristic, complemented
10#20243947C211yesmaximal, characteristic, complemented
11#20243642C211yesmaximal, characteristic, complemented
12#20243635C211yesmaximal, characteristic
13#20243393C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic
15C47×#2367C211yesmaximal, characteristic
16C2×#13094014—21no—
17C2×#13093957C2211yescharacteristic
18C2×#13093955C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×#13093948C2211yescharacteristic
21C2×#13093948C2211yescharacteristic
22C2×#13093948C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×C4×C47⋊C8C2211yescharacteristic
29#15689063—21no—
30#15689053—21no—
31#15689021C2211yescharacteristic
32#15689021C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689008—21no—
36#15688993C2211yescharacteristic
37C4×C4⋊Dic47C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#124×C47C2211yescharacteristic
49C2×C4×Q8×C47C2211yescharacteristic
50C2×C4×D4×C47C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#388—21no—
54C47×#388—21no—
55C47×#385—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47—21no—
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63#13094014—44no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×C4×Dic47—21no—
75#13093957—22no—
76#13093955—22no—
77C4⋊(C47⋊C8)—41no—
78#13093948—22no—
79#13093948—22no—
80#13093948—22no—
81#13093948—41no—
82#13093945—22no—
83#13093945—22no—
84#13093945—22no—
85#13093945—41no—
86C4×C47⋊C8—41no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C22×Q8×C47C2311yescharacteristic
93C22×D4×C47C2311yescharacteristic
94C23×C4×C47—21no—
95#124×C47—22no—
96#124×C47—22no—
97C4×Q8×C47—22no—
98C4×Q8×C47—41no—
99C4×D4×C47—22no—
100C4×D4×C47—41no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C22⋊C4×C47—21no—
111C2×C42×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C2×C42×C47C2311yescharacteristic
116#95×C47—21no—
117#95×C47—21no—
118#95×C47—21no—
119#95×C47D411yescharacteristic
120#95×C47D411yescharacteristic
121C24×C47—21no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C2×Q8×C47#4112yes—
128C2×D4×C47—21no—
129C2×D4×C47—21no—
130C2×D4×C47—21no—
131C2×D4×C47—21no—
132C2×D4×C47—21no—
133C2×D4×C47#4112yes—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—81no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2411yescharacteristic
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—42no—
157C4⋊C4×C47#4112yes—
158C22⋊C4×C47—24no—
159C22⋊C4×C47—24no—
160C22⋊C4×C47—42no—
161C22⋊C4×C47—42no—
162C22⋊C4×C47—81no—
163C42×C47—21no—
164C42×C47—21no—
165C42×C47—21no—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—42no—
170C42×C47—81no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47—21no—
178C4⋊Dic47—42no—
179C4⋊Dic47—42no—
180C4⋊Dic47#4112yes—
181Dic47⋊C4—42no—
182Dic47⋊C4—42no—
183Dic47⋊C4—42no—
184Dic47⋊C4—42no—
185C4×Dic47—42no—
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—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C23×C47—22no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—41no—
202C23×C47—41no—
203C23×C47—41no—
204C23×C47—41no—
205C23×C47C22×D411yescharacteristic
206Q8×C47—22no—
207Q8×C47—22no—
208Q8×C47—41no—
209Q8×C47—41no—
210D4×C47—22no—
211D4×C47—22no—
212D4×C47—41no—
213D4×C47—41no—
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—22no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—22no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
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×C47—41no—
239C2×C4×C47—84no—
240C2×C4×C47#13512yes—
241C2×C4×C47AGL(1,ℤ/8)12yes—
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C2×C4×C472−1+411yescharacteristic
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—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264#26761—471nomaximal, Sylow
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—81no—
269C22×C47—81no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47#52511yescharacteristic
273C22×C47#54611yescharacteristic
274C22×C47#54811yescharacteristic
275C22×C47C2×#13511yescharacteristic
276C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C47#57711yescharacteristic
278C22×C47#57811yescharacteristic
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—42no—
284C4×C47—41no—
285C4×C47—41no—
286C4×C47—42no—
287C4×C47—81no—
288C4×C47#52911yescharacteristic
289C4×C47#53911yescharacteristic
290C4×C47#55211yescharacteristic
291C4×C47#55311yescharacteristic
292Dic47—42no—
293Dic47—81no—
294Dic47—81no—
295Dic47—81no—
296#2506—471no—
297#2367D4711yescharacteristic
298#2071—471no—
299#2065—471no—
300#2042—471no—
301#2042—471no—
302#1933—471no—
303#1927—471no—
304#1921—471no—
305#1920—471no—
306#1916—471no—
307#1863—471no—
308#1862—471no—
309#1803—471no—
310C4×#102—471no—
311C2×C47—82no—
312C2×C47#246011yescharacteristic
313C2×C47#310611yescharacteristic
314C2×C47#312011yescharacteristic
315C2×C47#330011yescharacteristic
316C2×C47#330611yescharacteristic
317C2×C47#336511yescharacteristic
318C2×C47#336711yescharacteristic
319C2×#125—941no—
320C2×#124C2×D4711yescharacteristic
321C2×C4×Q8C2×D4711yescharacteristic
322C2×C4×D4C2×D4711yescharacteristic
323C2×#107—471no—
324C2×#106—471no—
325C2×C4⋊C8—471no—
326C2×#103—471no—
327C2×#103—471no—
328C2×#103—471no—
329C2×#103—471no—
330C2×#102—471no—
331C2×#102—471no—
332C2×#102—471no—
333C2×#102—471no—
334C2×C4×C8—471no—
335#400—941no—
336#398—941no—
337#391C2×D4711yescharacteristic
338#390C2×D4711yescharacteristic
339#389—471no—
340#389—471no—
341#389—471no—
342#389—471no—
343#388—21no—
344#388—21no—
345#387—941no—
346#385—21no—
347#384—471no—
348C4×C4⋊C4—471no—
349C4×C4⋊C4C2×D4711yescharacteristic
350C4×C4⋊C4C2×D4711yescharacteristic
351C4×C22⋊C4—21no—
352#340—471no—
353#340—471no—
354#340—471no—
355#340—471no—
356#340—471no—
357#340—471no—
358#336—471no—
359#336—471no—
360#336—471no—
361#336—471no—
362C47#2676111yescharacteristic, complemented, Sylow
363C22×Q8C22×D4711yescharacteristic
364C22×D4C22×D4711yescharacteristic
365C23×C4—21no—
366C22×C8—471no—
367C22×C8—471no—
368C22×C8—471no—
369C22×C8—471no—
370#125—1884no—
371#124—22no—
372#124—22no—
373C4×Q8—22no—
374C4×Q8—41no—
375C4×D4—22no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—471no—
379C2×C4⋊C4—471no—
380C2×C4⋊C4—471no—
381C2×C4⋊C4—471no—
382C2×C4⋊C4—941no—
383C2×C4⋊C4—941no—
384C2×C4⋊C4—941no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4C22⋊D4711yescharacteristic
389C2×C4⋊C4C22⋊D4711yescharacteristic
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—941no—
400C2×C42C22×D4711yescharacteristic
401C2×C42C22×D4711yescharacteristic
402C2×C42C22×D4711yescharacteristic
403#107—942no—
404#106—942no—
405C4⋊C8—1881no—
406#103—942no—
407#103—942no—
408#103—942no—
409#103—1881no—
410#102—942no—
411#102—942no—
412#102—942no—
413#102—1881no—
414C4×C8—1881no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—941no—
419#95—941no—
420#95—941no—
421#95—941no—
422#95—941no—
423#95C22⋊D4711yescharacteristic
424#95C22⋊D4711yescharacteristic
425C24—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8#1062535012yes—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4#1062535012yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—81no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4C2×C22⋊D4711yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450C22×C4C2×C22⋊D4711yescharacteristic
451C22×C4C2×C22⋊D4711yescharacteristic
452C22×C4C2×C22⋊D4711yescharacteristic
453C22×C4C2×C22⋊D4711yescharacteristic
454C22×C4C23×D4711yescharacteristic
455C2×C8—941no—
456C2×C8—941no—
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—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—472no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—941no—
477C4⋊C4—941no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—1882no—
482C4⋊C4—1882no—
483C4⋊C4—1882no—
484C4⋊C4—1882no—
485C4⋊C4—1882no—
486C4⋊C4—1882no—
487C4⋊C4#1062535212yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—81no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—81no—
501C42—1882no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C22×C22⋊D4711yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—84no—
544C2×C4—942no—
545C2×C4—1881no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4#1309404412yes—
557C2×C4#1309404912yes—
558C2×C4#41×D4711yescharacteristic
559C2×C4C2×#1062535211yescharacteristic
560C2×C4C2×#1062535011yescharacteristic
561C2×C4C2×#1062535011yescharacteristic
562C2×C4#1309406911yescharacteristic
563C2×C4#1309407111yescharacteristic
564C8—1881no—
565C8—1881no—
566C8—1881no—
567C8—1881no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#1568963411yescharacteristic
576C22#1568976711yescharacteristic
577C22#1568978011yescharacteristic
578C22C2×#1309404411yescharacteristic
579C22C2×#1309404911yescharacteristic
580C22#1568993411yescharacteristic
581C22#1568993811yescharacteristic
582C4—22no—
583C4—22no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—42no—
589C4—41no—
590C4—81no—
591C4—3761no—
592C4—3761no—
593C4—3761no—
594C4—1882no—
595C4#1568965311yescharacteristic
596C4#1568971511yescharacteristic
597C4#1568981311yescharacteristic
598C4#1568982211yescharacteristic
599C2—82no—
600C2#2024733411yescharacteristic
601C2#2025344811yescharacteristic
602C2#2025360211yescharacteristic
603C2#2025527511yescharacteristic
604C2#2025534911yescharacteristic
605C2#2025608011yescharacteristic
606C2#2025610211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2367C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#2367D47
hypocenterC47#26761
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #20247904C2semidirect
6. #20244067C2semidirect
7. #20244019C2semidirect
8. #20243980C2semidirect
9. #20243973C2semidirect
10. #20243947C2semidirect
11. #20243642C2semidirect
13. #20243393C2semidirect
362. C47#26761semidirect

Maximal subgroups

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

subgroupindex
#202479042
#202447912
#202447622
#202446242
#202440672
#202440192
#202439802
#202439732
#202439472
#202436422
#202436352
#202433932
C4×#130939452
C47×#23672
#2676147