Finite Group Databasebeta

← #26224530

Subgroups — #26224530

Order 12032.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094019C211yesmaximal, characteristic
2#20244002C211yesmaximal, characteristic
3#20243999C211yesmaximal, characteristic
4#20243993C211yesmaximal, characteristic
5#20243954C211yesmaximal, characteristic, complemented
6#20243949C211yesmaximal, characteristic, complemented
7#20243944C211yesmaximal, characteristic, complemented
8#20243530C211yesmaximal, characteristic, complemented
9#20243256C211yesmaximal, characteristic, complemented
10C8×C4⋊Dic47C211yesmaximal, characteristic, complemented
11#20243173C211yesmaximal, characteristic
12#20243173C211yesmaximal, characteristic
13#20243171C211yesmaximal, characteristic
14#97×Dic47C211yesmaximal, characteristic, complemented
15C47×#1771C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17C2×#13094019C411yescharacteristic
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×Dic47⋊C8C2211yescharacteristic
20C2×(C2×D47)⋊C8C2211yescharacteristic
21C2×(C2×D47)⋊C8C2211yescharacteristic
22C2×(C2×D47)⋊C8C2211yescharacteristic
23C2×#13093935C2211yescharacteristic
24C2×#13093934C2211yescharacteristic
25C2×#13093934C2211yescharacteristic
26C2×C8×Dic47C2211yescharacteristic
27C2×C8×Dic47C2211yescharacteristic
28C2×C8×Dic47C2211yescharacteristic
29#15689015C411yescharacteristic
30#15689013C411yescharacteristic
31#15689012C411yescharacteristic
32#15689009C411yescharacteristic
33#15689006C411yescharacteristic
34#15689004C411yescharacteristic
35#15688990C411yescharacteristic
36C4×Dic47⋊C4C2211yescharacteristic
37C4×C4⋊Dic47C2211yescharacteristic
38C4×(C2×D47)⋊C4C2211yescharacteristic
39C4×(C2×D47)⋊C4C2211yescharacteristic
40C4×(C2×D47)⋊C4C2211yescharacteristic
41C42×Dic47C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C2×#97×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×C4×D47C2311yescharacteristic
60C2×#10625324—22no—
61C2×#10625324—22no—
62C2×#10625324—22no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094019—24no—
68C2×C4⋊Dic47C2×C411yescharacteristic
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×Dic47⋊C4C2×C411yescharacteristic
71C2×Dic47⋊C4C2×C411yescharacteristic
72C2×(C2×D47)⋊C4C2×C411yescharacteristic
73C2×(C2×D47)⋊C4C2×C411yescharacteristic
74C2×(C2×D47)⋊C4C2×C411yescharacteristic
75C2×(C2×D47)⋊C4C2×C411yescharacteristic
76C2×(C2×D47)⋊C4C2×C411yescharacteristic
77C2×(C2×D47)⋊C4C2×C411yescharacteristic
78C2×C4×Dic47C2×C411yescharacteristic
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47C2×C411yescharacteristic
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83C2×C4×Dic47C2311yescharacteristic
84C2×C4×Dic47C2311yescharacteristic
85C4⋊(C47⋊C8)—22no—
86Dic47⋊C8—22no—
87(C2×D47)⋊C8—22no—
88(C2×D47)⋊C8—22no—
89(C2×D47)⋊C8—22no—
90#13093935—22no—
91#13093934—22no—
92#13093934—22no—
93C8×Dic47—22no—
94C8×Dic47—22no—
95C8×Dic47—22no—
96C47⋊#95C2×C411yescharacteristic
97C47⋊#95C2×C411yescharacteristic
98C47⋊#95C2×C411yescharacteristic
99C47⋊#95C2×C411yescharacteristic
100C47⋊#95C2×C411yescharacteristic
101C47⋊#95C2×C411yescharacteristic
102C47⋊#95C2×C411yescharacteristic
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C22×C8×C47C2311yescharacteristic
108C22×C8×C47C2311yescharacteristic
109C22×C8×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2×C411yescharacteristic
111C2×C4⋊C4×C47C2×C411yescharacteristic
112C2×C42×C47C2311yescharacteristic
113C2×C42×C47C2311yescharacteristic
114C2×C42×C47C2311yescharacteristic
115C4⋊C8×C47—22no—
116#97×C47—22no—
117#97×C47—22no—
118C4×C8×C47—22no—
119#95×C47C2×C411yescharacteristic
120#95×C47C2×C411yescharacteristic
121C23×D47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C22×C411yescharacteristic
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C2411yescharacteristic
129C22×Dic47C22×C411yescharacteristic
130C22×Dic47C22×C411yescharacteristic
131C22×Dic47C22×C411yescharacteristic
132C22×Dic47C22×C411yescharacteristic
133C22×Dic47C22×C411yescharacteristic
134C22×Dic47C22×C411yescharacteristic
135C22×Dic47C22×C411yescharacteristic
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—21no—
141C2×C4×D47—21no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47#4112yes—
151C2×C8×C47#4112yes—
152C2×C8×C47#4112yes—
153C2×C8×C47#4112yes—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—41no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162(C2×D47)⋊C4—22no—
163(C2×D47)⋊C4—22no—
164(C2×D47)⋊C4—22no—
165(C2×D47)⋊C4—22no—
166(C2×D47)⋊C4—41no—
167(C2×D47)⋊C4—41no—
168C4⋊Dic47—22no—
169C4⋊Dic47M1614yescomplemented
170Dic47⋊C4—22no—
171Dic47⋊C4—41no—
172C4×Dic47—21no—
173C4×Dic47—21no—
174C4×Dic47—21no—
175C4×Dic47—21no—
176C4×Dic47—21no—
177C4×Dic47—21no—
178C4×Dic47—22no—
179C4×Dic47—22no—
180C4×Dic47—41no—
181C4×Dic47—41no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
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#4112yes—
193C2×C47⋊C8#4112yes—
194#10625324—44no—
195C23×C47C23×C411yescharacteristic
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—21no—
201C22×D47—21no—
202C22×D47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
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×C47C2×M1612yes—
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C2×C4×C47C2×#4111yescharacteristic
225C2×C4×C47C2×#4111yescharacteristic
226C2×C4×C47C2×#4111yescharacteristic
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47C2×M1612yes—
246C2×Dic47C2×M1612yes—
247C2×Dic47#13112yes—
248C4×D47—41no—
249C4×D47—41no—
250C4×D47—41no—
251C4×D47—41no—
252C8×C47—22no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47#12614yescomplemented
256C47⋊C8—22no—
257C47⋊C8—22no—
258C47⋊C8—41no—
259C47⋊C8—41no—
260#21667—471nomaximal, Sylow
261C22×C47C4×#4111yescharacteristic
262C22×C47C4×#4111yescharacteristic
263C22×C47C4×#4111yescharacteristic
264C22×C47C22×M1611yescharacteristic
265C22×C47C2×#13111yescharacteristic
266C22×C47#56811yescharacteristic
267C22×C47#56811yescharacteristic
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C2×D47—41no—
272C2×D47—41no—
273C2×D47—41no—
274C2×D47—41no—
275C4×C47—22no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47C2×#12611yescharacteristic
282C4×C47#52911yescharacteristic
283C4×C47#52911yescharacteristic
284C4×C47#52911yescharacteristic
285Dic47—22no—
286Dic47—22no—
287Dic47—22no—
288Dic47—41no—
289Dic47—41no—
290Dic47—41no—
291Dic47—41no—
292C4×#126—471no—
293#1924—471no—
294#1924—471no—
295#1923—471no—
296#1917—471no—
297#1917—471no—
298#1916—471no—
299#1839—471no—
300#1771D4711yescharacteristic, complemented
301#1770—471no—
302C8×C4⋊C4—471no—
303#1753—471no—
304#1753—471no—
305#1753—471no—
306C4×#97—471no—
307C2×C47C4×#12611yescharacteristic
308C2×C47#296511yescharacteristic
309C2×C47#296711yescharacteristic
310C2×C47#296811yescharacteristic
311C2×C47#296911yescharacteristic
312C2×C47#297011yescharacteristic
313C2×C47#297111yescharacteristic
314D47—81no—
315C22×M16—471no—
316C2×#126—471no—
317C2×C4⋊C8—471no—
318C2×C4⋊C8—471no—
319C2×C4⋊C8C2×D4711yescharacteristic
320C2×C22⋊C8—471no—
321C2×C22⋊C8—471no—
322C2×C22⋊C8—471no—
323C2×#97—471no—
324C2×#97—471no—
325C2×#97—471no—
326C2×#97C2×D4711yescharacteristic
327C2×#97C2×D4711yescharacteristic
328C2×C4×C8—471no—
329C2×C4×C8—471no—
330C2×C4×C8—471no—
331C2×C4×C8C2×D4711yescharacteristic
332#388—471no—
333#388—471no—
334#388—471no—
335#387—471no—
336#387—471no—
337#387—471no—
338#383—471no—
339C4×C4⋊C4—471no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4C2×D4711yescharacteristic
342C4×C22⋊C4—471no—
343C4×C22⋊C4—471no—
344C4×C22⋊C4—471no—
345C43—471no—
346#336—471no—
347#336—471no—
348#336—471no—
349#336—471no—
350#336—471no—
351#336—471no—
352#336—471no—
353#336—471no—
354#336—471no—
355#336—471no—
356#336C2×D4711yescharacteristic
357#336C2×D4711yescharacteristic
358C47#2166711yescharacteristic, complemented, Sylow
359C23×C4—471no—
360C2×M16—942no—
361C2×M16—942no—
362C2×M16—942no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—471no—
366C22×C8—471no—
367C22×C8C22×D4711yescharacteristic
368C22×C8C22×D4711yescharacteristic
369C22×C8C22×D4711yescharacteristic
370C22×C8C22×D4711yescharacteristic
371#126—944no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4C4×D4711yescharacteristic
377C2×C4⋊C4C4×D4711yescharacteristic
378C2×C22⋊C4—471no—
379C2×C22⋊C4—471no—
380C2×C22⋊C4—471no—
381C2×C22⋊C4—471no—
382C2×C22⋊C4—471no—
383C2×C22⋊C4—471no—
384C2×C42—471no—
385C2×C42—471no—
386C2×C42—471no—
387C2×C42—471no—
388C2×C42—471no—
389C2×C42—471no—
390C2×C42—471no—
391C2×C42C22×D4711yescharacteristic
392C2×C42C22×D4711yescharacteristic
393C2×C42C22×D4711yescharacteristic
394C4⋊C8—22no—
395C4⋊C8—942no—
396C4⋊C8—942no—
397C22⋊C8—942no—
398C22⋊C8—942no—
399C22⋊C8—942no—
400#97—22no—
401#97—22no—
402#97—942no—
403#97—942no—
404#97—942no—
405C4×C8—22no—
406C4×C8—942no—
407C4×C8—942no—
408C4×C8—942no—
409#95—471no—
410#95—471no—
411#95—471no—
412#95—471no—
413#95—471no—
414#95—471no—
415#95—471no—
416#95—471no—
417#95—471no—
418#95—471no—
419#95C4×D4711yescharacteristic
420#95C4×D4711yescharacteristic
421C24—471no—
422C22×C4—471no—
423C22×C4—471no—
424C22×C4—471no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4C2×C4×D4711yescharacteristic
436C22×C4C2×C4×D4711yescharacteristic
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4C2×C4×D4711yescharacteristic
440C22×C4C2×C4×D4711yescharacteristic
441C22×C4C23×D4711yescharacteristic
442M16—1884no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—472no—
452C2×C8—472no—
453C2×C8—941no—
454C2×C8—941no—
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#1062535012yes—
464C2×C8#1062535012yes—
465C2×C8#1062535212yes—
466C2×C8#1062535412yes—
467C4⋊C4—22no—
468C4⋊C4—41no—
469C4⋊C4—474no—
470C4⋊C4—942no—
471C4⋊C4—942no—
472C4⋊C4—1881no—
473C22⋊C4—942no—
474C22⋊C4—942no—
475C22⋊C4—942no—
476C22⋊C4—942no—
477C22⋊C4—1881no—
478C22⋊C4—1881no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—942no—
486C42—942no—
487C42—941no—
488C42—941no—
489C42—941no—
490C42—941no—
491C42—941no—
492C42—941no—
493C42—1881no—
494C42—1881no—
495C23—941no—
496C23—941no—
497C23—941no—
498C23—941no—
499C23—941no—
500C23—941no—
501C23—941no—
502C23C22×C4×D4711yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—472no—
521C2×C4—472no—
522C2×C4—472no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4M16×D4712yes—
546C2×C4#41×D4711yescharacteristic
547C2×C4#41×D4711yescharacteristic
548C2×C4C2×#1062535211yescharacteristic
549C2×C4C2×#1062535011yescharacteristic
550C2×C4C2×#1062535011yescharacteristic
551C2×C4C2×#1062535411yescharacteristic
552C8—22no—
553C8—41no—
554C8—41no—
555C8—942no—
556C8—942no—
557C8—1881no—
558C8—1881no—
559C8#1309401914yescomplemented
560C22—1881no—
561C22—1881no—
562C22—1881no—
563C22—1881no—
564C22—1881no—
565C22—1881no—
566C22—1881no—
567C22C4×#1062535211yescharacteristic
568C22C4×#1062535011yescharacteristic
569C22C4×#1062535411yescharacteristic
570C22C2×M16×D4711yescharacteristic
571C22#131×D4711yescharacteristic
572C22#1568988811yescharacteristic
573C22#1568988911yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—942no—
581C4—942no—
582C4—942no—
583C4—1881no—
584C4—1881no—
585C4—1881no—
586C4—1881no—
587C4C2×#1309401911yescharacteristic
588C4#1568965111yescharacteristic
589C4#1568965311yescharacteristic
590C4#1568966011yescharacteristic
591C2—3761no—
592C2C4×#1309401911yescharacteristic
593C2#2025234811yescharacteristic
594C2#2025236711yescharacteristic
595C2#2025238111yescharacteristic
596C2#2025238811yescharacteristic
597C2#2025240111yescharacteristic
598C2#2025240611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1771C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1771D47
hypocenterC47#21667
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
5. #20243954C2semidirect
6. #20243949C2semidirect
7. #20243944C2semidirect
8. #20243530C2semidirect
9. #20243256C2semidirect
10. C8×C4⋊Dic47C2semidirect
14. #97×Dic47C2semidirect
15. C47×#1771C2semidirect
169. C4⋊Dic47M16semidirect
255. C8×C47#126semidirect
300. #1771D47semidirect
358. C47#21667semidirect
559. C8#13094019semidirect

Maximal subgroups

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

subgroupindex
C4×#130940192
#202440022
#202439992
#202439932
#202439542
#202439492
#202439442
#202435302
#202432562
C8×C4⋊Dic472
#202431732
#202431712
#97×Dic472
C47×#17712
#2166747