Finite Group Databasebeta

← #26236158

Subgroups — #26236158

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689221C211yesmaximal, characteristic
2#20246335C211yesmaximal, characteristic
3#20244272C211yesmaximal, characteristic
4#20244245C211yesmaximal, characteristic
5#20244026C211yesmaximal, characteristic, complemented
6#20244019C211yesmaximal, characteristic, complemented
7#20244015C211yesmaximal, characteristic
8#20244008C211yesmaximal, characteristic
9#20243557C211yesmaximal, characteristic, complemented
10#20243395C211yesmaximal, characteristic
11#20243393C211yesmaximal, characteristic, complemented
12#20243286C211yesmaximal, characteristic, complemented
13C4×#13093957C211yesmaximal, characteristic, complemented
14#20243263C211yesmaximal, characteristic, complemented
15C47×#2356C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093982—21no—
19#15689221C418yescomplemented
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093944C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689025C2211yescharacteristic
37#15689015—21no—
38#15689015—21no—
39#15688993C2211yescharacteristic
40#15688980—21no—
41C4×C4⋊Dic47C2211yescharacteristic
42C4×C4⋊Dic47C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49C2×C4×Q8×C47C2211yescharacteristic
50C47×#391C2211yescharacteristic
51C47×#391C2211yescharacteristic
52C47×#387—21no—
53C47×#387—21no—
54C47×#383—21no—
55C47×#382C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C47×#376—21no—
60C22×D188C2311yescharacteristic
61C22×C4×D47—21no—
62C2×#10625336—22no—
63C2×#10625336—22no—
64C2×#10625336C2×C414yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C4×D188—22no—
70C4×D188C2×C414yes—
71#13093982—44no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
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—
83C2×C4×Dic47—21no—
84#13093957—22no—
85#13093957—41no—
86#13093957C2×C414yes—
87#13093955—22no—
88#13093955—41no—
89C4⋊(C47⋊C8)—22no—
90#13093948—41no—
91#13093948—41no—
92#13093948C2×C414yes—
93#13093944—41no—
94#13093944—41no—
95#13093944C2×C414yes—
96#13093935—22no—
97#13093935C2×C414yes—
98C4×C47⋊C8—22no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C22×Q8×C47C2311yescharacteristic
102C4×Q8×C47—22no—
103C4×Q8×C47C2×C414yes—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47D411yescharacteristic
106C2×C4⋊C4×C47D411yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C42×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×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47D411yescharacteristic
125#95×C47D411yescharacteristic
126C23×D47—21no—
127C2×Q8×C47—21no—
128C2×Q8×C47—21no—
129C2×Q8×C47—21no—
130C2×Q8×C47—21no—
131C2×Q8×C47—21no—
132C2×Q8×C47C22×C412yes—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2411yescharacteristic
144C22×Dic47—21no—
145C22×Dic47—21no—
146C22×Dic47—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188C22×C412yes—
153C2×C4×D47—24no—
154C2×C4×D47—42no—
155C2×C4×D47—42no—
156C4⋊C4×C47—24no—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47C22×C412yes—
165C42×C47—24no—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—42no—
171C42×C47—42no—
172C42×C47C22×C412yes—
173C42×C47#4112yes—
174#10625336—28no—
175(C2×D47)⋊C4—24no—
176(C2×D47)⋊C4—42no—
177(C2×D47)⋊C4—42no—
178(C2×D47)⋊C4—81no—
179(C2×D47)⋊C4—81no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—42no—
186C4⋊Dic47—81no—
187C4⋊Dic47C22×C412yes—
188C4×Dic47—42no—
189C4×Dic47—42no—
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⋊C8C22×C412yes—
199C2×C47⋊C8C22×C412yes—
200C2×C47⋊C8#4112yes—
201C2×C47⋊C8#4112yes—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210Q8×C47—22no—
211Q8×C47—22no—
212Q8×C47—41no—
213Q8×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—22no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
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—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×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47C4×D412yes—
242C2×C4×C47C4×D412yes—
243C2×C4×C47AGL(1,ℤ/8)12yes—
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47H(5,𝔽2)11yescharacteristic
249C2×C4×C472−1+411yescharacteristic
250C2×Dic47—22no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259D188—22no—
260D188—22no—
261D188—41no—
262D188—41no—
263C4×D47—48no—
264C47⋊C8—22no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8#11714yescomplemented
268#22820—471nomaximal, Sylow
269C22×C47C2×C4×D411yescharacteristic
270C22×C47#54711yescharacteristic
271C22×C47#55011yescharacteristic
272C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C47#57511yescharacteristic
274C22×C47#57711yescharacteristic
275C22×C47#57811yescharacteristic
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C2×D47—81no—
283C4×C47—22no—
284C4×C47—22no—
285C4×C47—22no—
286C4×C47—41no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—42no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47C2×#11711yescharacteristic
294C4×C47#52011yescharacteristic
295C4×C47#55511yescharacteristic
296C4×C47#55611yescharacteristic
297Dic47—42no—
298Dic47—81no—
299Dic47—81no—
300C2×#440—471no—
301#2356D4711yescharacteristic, complemented
302#2354—471no—
303#1973—471no—
304#1968—471no—
305#1928—471no—
306#1927—471no—
307#1926—471no—
308#1925—471no—
309#1847—471no—
310#1804—471no—
311#1803—471no—
312#1776—471no—
313C4×#107—471no—
314#1771—471no—
315C2×C47#235411yescharacteristic
316C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C47#294711yescharacteristic
318C2×C47#334311yescharacteristic
319C2×C47#334811yescharacteristic
320C2×C47#339711yescharacteristic
321C2×C47#340211yescharacteristic
322D47—82no—
323C22×SD16—471no—
324C2×C4×Q8C2×D4711yescharacteristic
325C2×C4×D4—471no—
326C2×#117—941no—
327#440—478no—
328C2×#107—471no—
329C2×#107—471no—
330C2×#107—471no—
331C2×#106—471no—
332C2×#106—471no—
333C2×C4⋊C8—471no—
334C2×#103—471no—
335C2×#103—471no—
336C2×#103—471no—
337C2×#102—471no—
338C2×#102—471no—
339C2×#102—471no—
340C2×#97—471no—
341C2×#97—471no—
342C2×C4×C8—471no—
343#391C2×D4711yescharacteristic
344#391C2×D4711yescharacteristic
345#390—471no—
346#390—471no—
347#388—941no—
348#388—941no—
349#387—21no—
350#387—21no—
351#384—471no—
352#383—21no—
353#382C2×D4711yescharacteristic
354#380—941no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4—471no—
357C4×C4⋊C4C2×D4711yescharacteristic
358C4×C4⋊C4C2×D4711yescharacteristic
359C4×C4⋊C4C2×D4711yescharacteristic
360#376—21no—
361#340—471no—
362#340—471no—
363#340—471no—
364#340—471no—
365#336—471no—
366#336—471no—
367C47#2282011yescharacteristic, complemented, Sylow
368C22×Q8C22×D4711yescharacteristic
369C22×D4—471no—
370C23×C4—941no—
371C2×SD16—474no—
372C2×SD16—942no—
373C2×SD16—942no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—471no—
377C22×C8—471no—
378C4×Q8—22no—
379C4×Q8C4×D4714yes—
380C4×D4—474no—
381C4×D4—942no—
382#117—1884no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—471no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
389C2×C4⋊C4C22⋊D4711yescharacteristic
390C2×C4⋊C4C22⋊D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C4⋊C4C22×D4711yescharacteristic
393C2×C4⋊C4C22×D4711yescharacteristic
394C2×C22⋊C4—941no—
395C2×C22⋊C4—941no—
396C2×C22⋊C4—941no—
397C2×C22⋊C4—941no—
398C2×C22⋊C4—941no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—941no—
403C2×C42—941no—
404C2×C42C22×D4711yescharacteristic
405C2×C42C22×D4711yescharacteristic
406C2×C42C22×D4711yescharacteristic
407#107—474no—
408#107—942no—
409#107—1881no—
410#106—942no—
411#106—1881no—
412C4⋊C8—942no—
413#103—474no—
414#103—1881no—
415#103—1881no—
416#102—474no—
417#102—1881no—
418#102—1881no—
419#97—474no—
420#97—942no—
421C4×C8—942no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—941no—
431#95—941no—
432#95C22⋊D4711yescharacteristic
433#95C22⋊D4711yescharacteristic
434C24—941no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8C2×C4×D4712yes—
441C2×D4—472no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—941no—
446C2×D4—941no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—941no—
452C22×C4—944no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—1882no—
456C22×C4—1882no—
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C23×D4711yescharacteristic
464SD16—948no—
465C2×C8—472no—
466C2×C8—472no—
467C2×C8—472no—
468C2×C8—472no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—472no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—3761no—
492C4⋊C4—1882no—
493C4⋊C4C2×C4×D4712yes—
494C22⋊C4—944no—
495C22⋊C4—3761no—
496C22⋊C4—3761no—
497C22⋊C4—1882no—
498C22⋊C4—1882no—
499C42—24no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—42no—
506C42—1882no—
507C42—1882no—
508C42C2×C4×D4712yes—
509C42#1062535012yes—
510C23—942no—
511C23—1881no—
512C23—1881no—
513C23—1881no—
514C23—1881no—
515C23—1881no—
516C23—1881no—
517C23C22×C22⋊D4711yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—942no—
523D4—942no—
524D4—1881no—
525D4—1881no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
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—942no—
554C2×C4—1888no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4C4×C22⋊D4712yes—
564C2×C4C4×C22⋊D4712yes—
565C2×C4#1309404912yes—
566C2×C4C22×C4×D4711yescharacteristic
567C2×C4#41×D4711yescharacteristic
568C2×C4#41×D4711yescharacteristic
569C2×C4C2×#1062535011yescharacteristic
570C2×C4#1309407011yescharacteristic
571C2×C4#1309407111yescharacteristic
572C8—474no—
573C8—942no—
574C8—1881no—
575C8—1881no—
576C22—3761no—
577C22—3761no—
578C22—3761no—
579C22—3761no—
580C22—1882no—
581C22—1882no—
582C22—1882no—
583C22C2×C4×C22⋊D4711yescharacteristic
584C22#1568977211yescharacteristic
585C22#1568979211yescharacteristic
586C22C2×#1309404911yescharacteristic
587C22#1568992111yescharacteristic
588C22#1568993111yescharacteristic
589C22#1568993811yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—42no—
594C4—42no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—3761no—
601C4—3761no—
602C4—1882no—
603C4#117×D4711yescharacteristic
604C4#1568960311yescharacteristic
605C4#1568983611yescharacteristic
606C4#1568984111yescharacteristic
607C2—3762no—
608C2#2024633811yescharacteristic
609C2C4×#1309404911yescharacteristic
610C2#2025223111yescharacteristic
611C2#2025582811yescharacteristic
612C2#2025589711yescharacteristic
613C2#2025640811yescharacteristic
614C2#2025646311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2356C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenter#2356D47
hypocenterC47#22820
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2356

Complements

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

NH ≅ G/Ntype
5. #20244026C2semidirect
6. #20244019C2semidirect
9. #20243557C2semidirect
11. #20243393C2semidirect
12. #20243286C2semidirect
13. C4×#13093957C2semidirect
14. #20243263C2semidirect
15. C47×#2356C2semidirect
19. #15689221C4semidirect
267. C47⋊C8#117semidirect
301. #2356D47semidirect
367. C47#22820semidirect

Maximal subgroups

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

subgroupindex
C2×#156892212
#202463352
#202442722
#202442452
#202440262
#202440192
#202440152
#202440082
#202435572
#202433952
#202433932
#202432862
C4×#130939572
#202432632
C47×#23562
#2282047