Finite Group Databasebeta

← #26289051

Subgroups — #26289051

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246424C211yesmaximal, characteristic
2#20244802C211yesmaximal, characteristic, complemented
3#20244773C211yesmaximal, characteristic, complemented
4#20244577C211yesmaximal, characteristic
5#20244570C211yesmaximal, characteristic
6#20244154C211yesmaximal, characteristic, complemented
7#20244118C211yesmaximal, characteristic, complemented
8#20243996C211yesmaximal, characteristic, complemented
9#20243973C211yesmaximal, characteristic, complemented
10#20243970C211yesmaximal, characteristic, complemented
11#20243648C211yesmaximal, characteristic, complemented
12#20243585C211yesmaximal, characteristic, complemented
13#20243480C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C47×#2495C211yesmaximal, characteristic, complemented
16C2×#13093998C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093955C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×#13093944C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689023—21no—
33#15689021C2211yescharacteristic
34#15689012—21no—
35#15688999—21no—
36C4×C4⋊Dic47C2211yescharacteristic
37#15688970—21no—
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C47×#400—21no—
49C47×#397—21no—
50C47×#389C2211yescharacteristic
51C47×#389C2211yescharacteristic
52C47×#388—21no—
53C47×#383—21no—
54C47×#382C2211yescharacteristic
55C47×#380C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C22⋊D47—21no—
61C22×C4×D47—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093998—22no—
67#13093998—22no—
68C4×D188—22no—
69C4×D188—41no—
70#13093983—22no—
71#13093983—41no—
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×C22⋊Dic47—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—
83#13093957—22no—
84#13093957—41no—
85#13093955—22no—
86#13093955—22no—
87C4⋊(C47⋊C8)—22no—
88#13093944—22no—
89#13093944—22no—
90#13093944—22no—
91#13093944—41no—
92C22⋊(C47⋊C8)—22no—
93C22⋊(C47⋊C8)—41no—
94C4×C47⋊C8—41no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C23×C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47D411yescharacteristic
107C2×C22⋊C4×C47D411yescharacteristic
108C2×C42×C47—21no—
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47—21no—
117#95×C47—21no—
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C24×C47C2×D411yescharacteristic
121C23×D47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
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×C47C2411yescharacteristic
138C2×C22⋊D47—24no—
139C2×C22⋊D47—81no—
140C2×C22⋊D47—81no—
141C22×Dic47—21no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188#4112yes—
150C2×C4×D47—42no—
151C2×C4×D47—42no—
152C2×C4×D47—81no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—81no—
162C4⋊C4×C47—81no—
163C22⋊C4×C47—22no—
164C22⋊C4×C47—41no—
165C22⋊C4×C47—42no—
166C22⋊C4×C47—81no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C42×C47—42no—
172C22⋊Dic47—42no—
173(C2×D47)⋊C4—24no—
174(C2×D47)⋊C4—42no—
175(C2×D47)⋊C4—42no—
176(C2×D47)⋊C4—81no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47#4112yes—
182C4⋊Dic47#4112yes—
183Dic47⋊C4—81no—
184C4×Dic47—42no—
185C4×Dic47—81no—
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#4112yes—
198C23×C47—21no—
199C23×C47—21no—
200C23×C47—21no—
201C23×C47—21no—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47C22×D411yescharacteristic
206C22×D47—22no—
207C22×D47—41no—
208C22×D47—41no—
209C22×D47—41no—
210C22×D47—41no—
211C22×D47—41no—
212C22×D47—41no—
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—21no—
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×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47#13512yes—
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47C2×#4111yescharacteristic
247C2×C4×C47C2×#4111yescharacteristic
248C2×C4×C47H(5,𝔽2)11yescharacteristic
249C2×C4×C472−1+411yescharacteristic
250C22⋊D47—84no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260D188—22no—
261D188—22no—
262D188—41no—
263D188—41no—
264C4×D47—84no—
265C47⋊C8—22no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268C47⋊C8—41no—
269#27038—471nomaximal, Sylow
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47#52511yescharacteristic
278C22×C47#54611yescharacteristic
279C22×C47#54711yescharacteristic
280C22×C47C2×#13511yescharacteristic
281C22×C47#57511yescharacteristic
282C22×C47#57611yescharacteristic
283C22×C47#57711yescharacteristic
284C2×D47—42no—
285C2×D47—42no—
286C2×D47—42no—
287C2×D47—81no—
288C2×D47—81no—
289C2×D47—81no—
290C2×D47—81no—
291C4×C47—22no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47—81no—
297C4×C47—81no—
298C4×C47—81no—
299C4×C47—81no—
300C4×C47#52911yescharacteristic
301C4×C47#53911yescharacteristic
302C4×C47#55311yescharacteristic
303C4×C47#55611yescharacteristic
304Dic47—42no—
305Dic47—42no—
306Dic47—81no—
307#2495D4711yescharacteristic, complemented
308#2363—471no—
309#2073—471no—
310#2067—471no—
311#2034—471no—
312#2033—471no—
313#1949—471no—
314#1942—471no—
315#1923—471no—
316#1920—471no—
317#1920—471no—
318#1864—471no—
319#1854—471no—
320#1825—471no—
321C4×#102—471no—
322C2×C47—81no—
323C2×C47#246611yescharacteristic
324C2×C47#310211yescharacteristic
325C2×C47#311811yescharacteristic
326C2×C47#329611yescharacteristic
327C2×C47#330911yescharacteristic
328C2×C47#334111yescharacteristic
329C2×C47#335111yescharacteristic
330D47—82no—
331C2×#121—471no—
332C2×C4×D4—471no—
333C2×#117—471no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#106—471no—
337C2×#106—471no—
338C2×C4⋊C8—471no—
339C2×#102—471no—
340C2×#102—471no—
341C2×#102—471no—
342C2×#102—471no—
343C2×C22⋊C8—471no—
344C2×C22⋊C8—471no—
345C2×C4×C8—471no—
346#400—21no—
347#397—21no—
348#390—471no—
349#390—941no—
350#389—471no—
351#389C2×D4711yescharacteristic
352#389C2×D4711yescharacteristic
353#388—21no—
354#388—941no—
355#386—941no—
356#383—21no—
357#382C2×D4711yescharacteristic
358#380C2×D4711yescharacteristic
359#380C2×D4711yescharacteristic
360C4×C4⋊C4—471no—
361C4×C4⋊C4C2×D4711yescharacteristic
362C4×C22⋊C4—941no—
363C4×C22⋊C4C2×D4711yescharacteristic
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#340—471no—
369#340—471no—
370#340—471no—
371#340—471no—
372#336—471no—
373#336—471no—
374C47#2703811yescharacteristic, complemented, Sylow
375C22×D4—471no—
376C22×D4—941no—
377C23×C4—941no—
378C23×C4C22×D4711yescharacteristic
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382C22×C8—471no—
383#121—942no—
384#121—942no—
385C4×D4—942no—
386C4×D4—1881no—
387#117—942no—
388#117—1881no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4C22×D4711yescharacteristic
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4—941no—
404C2×C22⋊C4—941no—
405C2×C22⋊C4—941no—
406C2×C22⋊C4C22⋊D4711yescharacteristic
407C2×C22⋊C4C22⋊D4711yescharacteristic
408C2×C42—21no—
409C2×C42—941no—
410C2×C42—941no—
411C2×C42C22×D4711yescharacteristic
412C2×C42C22×D4711yescharacteristic
413#107—942no—
414#107—1881no—
415#106—942no—
416#106—942no—
417C4⋊C8—942no—
418#102—942no—
419#102—942no—
420#102—942no—
421#102—1881no—
422C22⋊C8—942no—
423C22⋊C8—1881no—
424C4×C8—1881no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—941no—
433#95—941no—
434#95C22⋊D4711yescharacteristic
435#95C22⋊D4711yescharacteristic
436C24—941no—
437C24C2×C22⋊D4711yescharacteristic
438C2×D4—472no—
439C2×D4—944no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C2×D4—3761no—
446C2×D4—3761no—
447C22×C4—21no—
448C22×C4—21no—
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—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—3761no—
461C22×C4—1882no—
462C22×C4—1882no—
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C23×D4711yescharacteristic
469C2×C8—472no—
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—
479C2×C8—941no—
480C2×C8—941no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—81no—
490C4⋊C4—81no—
491C4⋊C4—472no—
492C4⋊C4—472no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—3761no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—42no—
501C22⋊C4—81no—
502C22⋊C4—944no—
503C22⋊C4—3761no—
504C22⋊C4—1882no—
505C22⋊C4—1882no—
506C22⋊C4—1882no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—3761no—
513C42—1882no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—942no—
522C23—1881no—
523C23—1881no—
524C23—1881no—
525C23—1881no—
526C23—1881no—
527C23—1881no—
528C23C22×C22⋊D4711yescharacteristic
529D4—942no—
530D4—942no—
531D4—3764no—
532D4—1881no—
533D4—1881no—
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—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
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—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—3764no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4—1881no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1881no—
574C2×C4#1309404412yes—
575C2×C4#41×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C2×C4#41×D4711yescharacteristic
578C2×C4#41×D4711yescharacteristic
579C2×C4#1309407011yescharacteristic
580C2×C4#1309407111yescharacteristic
581C8—942no—
582C8—1881no—
583C8—1881no—
584C8—1881no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—3761no—
593C22—3761no—
594C22—3761no—
595C22—3761no—
596C22—1882no—
597C22—1882no—
598C22—1882no—
599C22#1568963011yescharacteristic
600C22#1568976111yescharacteristic
601C22#1568977211yescharacteristic
602C22C2×#1309404411yescharacteristic
603C22#1568992111yescharacteristic
604C22#1568992611yescharacteristic
605C22#1568993111yescharacteristic
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4—3761no—
616C4—1882no—
617C4—1882no—
618C4#1568965611yescharacteristic
619C4#1568971411yescharacteristic
620C4#1568982411yescharacteristic
621C4#1568984011yescharacteristic
622C2—81no—
623C2—3762no—
624C2#2024742011yescharacteristic
625C2#2025340011yescharacteristic
626C2#2025356611yescharacteristic
627C2#2025521711yescharacteristic
628C2#2025538811yescharacteristic
629C2#2025580611yescharacteristic
630C2#2025594811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2495C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenter#2495D47
hypocenterC47#27038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2495

Complements

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

NH ≅ G/Ntype
2. #20244802C2semidirect
3. #20244773C2semidirect
6. #20244154C2semidirect
7. #20244118C2semidirect
8. #20243996C2semidirect
9. #20243973C2semidirect
10. #20243970C2semidirect
11. #20243648C2semidirect
12. #20243585C2semidirect
13. #20243480C2semidirect
14. C4×#13093944C2semidirect
15. C47×#2495C2semidirect
307. #2495D47semidirect
374. C47#27038semidirect

Maximal subgroups

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

subgroupindex
#202464242
#202448022
#202447732
#202445772
#202445702
#202441542
#202441182
#202439962
#202439732
#202439702
#202436482
#202435852
#202434802
C4×#130939442
C47×#24952
#2703847