Finite Group Databasebeta

← #26183971

Subgroups — #26183971

Order 12032.

930 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#20257140C211yesmaximal, characteristic
2#20252046C211yesmaximal, characteristic, complemented
3#20241963C212yesmaximal, complemented
4#20241959C211yesmaximal, characteristic, complemented
5#20241938C212yesmaximal, complemented
6#20241929C211yesmaximal, characteristic
7#20241911C212yesmaximal, complemented
8#20241907C211yesmaximal, characteristic, complemented
9#20241886C212yesmaximal, complemented
10#20241877C211yesmaximal, characteristic
11C47×#2347C211yesmaximal, characteristic, complemented
12#15689841—21no—
13#15689828—21no—
14#15689812—21no—
15#15689808—21no—
16#15689806—22no—
17#15689799—22no—
18#15689751C411yescharacteristic, complemented
19#15689744C412yescomplemented
20#15689735C412yescomplemented
21#15689699C411yescharacteristic, complemented
22#15689680C2212yes—
23#15689657C2212yes—
24#15689634C2211yescharacteristic
25C2×#13094003C2211yescharacteristic
26#15689603C411yescharacteristic, complemented
27#15689600C411yescharacteristic, complemented
28#15689184—22no—
29#15689180C2212yes—
30#15689176C2212yes—
31#15689150—21no—
32#15689087C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34#15689079—21no—
35#15688859C2212yes—
36#15688859C2211yescharacteristic
37#15688859C2212yes—
38#15688859C2212yes—
39#15688859C2212yes—
40#15688859C2211yescharacteristic
41#15688859C2212yes—
42#15688856C2212yes—
43#15688856C2211yescharacteristic
44#15688856C2211yescharacteristic
45C2×#117×C47C2211yescharacteristic
46C47×#389—21no—
47C47×#388—22no—
48C47×#383C2212yes—
49C47×#380C2211yescharacteristic
50C4×C4⋊C4×C47—21no—
51C4×C4⋊C4×C47C2212yes—
52C4×C22⋊C4×C47C2211yescharacteristic
53C2×#10625350C2×C411yescharacteristic
54C22×Dic94C2×C411yescharacteristic
55C2×#10625329—21no—
56C22×C47⋊C8—21no—
57#13094024C2×C412yes—
58#13094024C2×C412yes—
59#13094023—21no—
60#13094019—22no—
61#13094018—22no—
62#13094017—22no—
63#13094017—22no—
64#13094016—22no—
65#13094016C2×C412yes—
66#13094015—21no—
67#13094014—22no—
68#13094014—22no—
69#13094012C2×C412yes—
70#13094010—22no—
71#13094008—22no—
72#13094007—22no—
73#13094007—21no—
74#13094006—22no—
75#13094004—21no—
76#13094004—21no—
77#13094003—22no—
78#13094003—21no—
79#13094003—21no—
80#13094003C2×C411yescharacteristic
81#13094003C2×C412yes—
82#13094003C2312yes—
83#13094003C2311yescharacteristic
84#13094002—22no—
85#13094001—22no—
86#13093998C2×C411yescharacteristic
87#13093998C2311yescharacteristic
88#13093993—21no—
89C4×Dic94—22no—
90C4×Dic94C2×C412yes—
91C4×Dic94C2×C412yes—
92C4×Dic94C2×C412yes—
93#13093989—21no—
94#13093989—21no—
95C4×D188C2×C412yes—
96C4×C22⋊D47—22no—
97C4×C22⋊D47—21no—
98C4×C22⋊D47—21no—
99(C22⋊D47)⋊C4—22no—
100#13093983—22no—
101#13093983C2×C411yescharacteristic
102#13093982—21no—
103#13093981—22no—
104#13093980—22no—
105C2×C4⋊Dic47C2×C411yescharacteristic
106C2×Dic47⋊C4—21no—
107C4⋊C4×D47—21no—
108C2×C22⋊Dic47—21no—
109C4⋊(C47⋊C8)—22no—
110C4⋊(C47⋊C8)—22no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)C2311yescharacteristic
114C22⋊(C47⋊C8)C2311yescharacteristic
115C22⋊(C47⋊C8)C2312yes—
116#13093935—22no—
117C4×C47⋊C8—22no—
118C23×C4×C47C2311yescharacteristic
119#117×C47C2×C412yes—
120#117×C47C2×C411yescharacteristic
121#117×C47C2×C411yescharacteristic
122#117×C47D412yes—
123#117×C47D411yescharacteristic
124#117×C47D411yescharacteristic
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—22no—
127C2×C4⋊C4×C47D411yescharacteristic
128C2×C4⋊C4×C47D411yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47D412yes—
132C2×C42×C47—21no—
133C2×C42×C47—22no—
134C2×C42×C47C2312yes—
135#95×C47—22no—
136#95×C47—22no—
137#95×C47C2311yescharacteristic
138#95×C47C2311yescharacteristic
139#95×C47C2312yes—
140C24×C47C2×D411yescharacteristic
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—42no—
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2411yescharacteristic
153C2×C22⋊D47—21no—
154C2×C22⋊D47—21no—
155C2×C22⋊D47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158#10625350—42no—
159C2×D188C22×C411yescharacteristic
160C2×C4×D47—21no—
161C2×C4×D47—22no—
162C2×Dic94—21no—
163C2×Dic94—22no—
164C2×Dic94—42no—
165C2×Dic94C22×C412yes—
166C2×Dic94C22×C411yescharacteristic
167C4⋊C4×C47—42no—
168C4⋊C4×C47—44no—
169C4⋊C4×C47C22⋊C411yescharacteristic
170C4⋊C4×C47C22⋊C411yescharacteristic
171C4⋊C4×C47C22⋊C412yes—
172C4⋊C4×C47C22⋊C411yescharacteristic
173C4⋊C4×C47C22⋊C411yescharacteristic
174C4⋊C4×C47C22⋊C412yes—
175C22⋊C4×C47—42no—
176C22⋊C4×C47—81no—
177C22⋊C4×C47C22⋊C412yes—
178C22⋊C4×C47C22⋊C412yes—
179C22⋊C4×C47C22⋊C412yes—
180C22⋊C4×C47C22⋊C412yes—
181C42×C47—42no—
182C42×C47—82no—
183C42×C47C22×C412yes—
184C42×C47C22×C412yes—
185C42×C47C2×D412yes—
186C42×C47C2×D412yes—
187C22⋊Dic47—22no—
188C22⋊Dic47—21no—
189C22⋊Dic47—21no—
190C22⋊Dic47—22no—
191C22⋊Dic47—21no—
192(C2×D47)⋊C4—22no—
193(C2×D47)⋊C4—22no—
194(C2×D47)⋊C4—21no—
195(C2×D47)⋊C4—22no—
196(C2×D47)⋊C4—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—22no—
199C4⋊Dic47—22no—
200C4⋊Dic47—22no—
201C4⋊Dic47C22×C412yes—
202C4⋊Dic47C22×C411yescharacteristic
203C4⋊Dic47C22×C411yescharacteristic
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—21no—
211Dic47⋊C4—22no—
212Dic47⋊C4—21no—
213C4×Dic47—22no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C4×Dic47—21no—
217#10625329—42no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—22no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—42no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47C2×C22⋊C411yescharacteristic
227C23×C47C2×C22⋊C411yescharacteristic
228C23×C47C22×D411yescharacteristic
229C22×D47—21no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—42no—
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—42no—
245C2×C4×C47—42no—
246C2×C4×C47—42no—
247C2×C4×C47—41no—
248C2×C4×C47C2×C22⋊C412yes—
249C2×C4×C47C2×C22⋊C412yes—
250C2×C4×C47C2×C22⋊C411yescharacteristic
251C2×C4×C47C2×C22⋊C412yes—
252C2×C4×C47C2×C22⋊C412yes—
253C2×C4×C47C2×C22⋊C411yescharacteristic
254C2×C4×C47C23×C411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C22⋊D47—42no—
257C22⋊D47—41no—
258C22⋊D47—41no—
259C22⋊D47—81no—
260C2×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—42no—
266C2×Dic47—81no—
267D188—41no—
268C4×D47—42no—
269C4×D47—82no—
270Dic94—42no—
271Dic94—42no—
272Dic94—41no—
273Dic94—82no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276C47⋊C8—42no—
277#17612—471nomaximal, Sylow
278C22×C47—21no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47—21no—
283C22×C47—21no—
284C22×C47—21no—
285C22×C47—21no—
286C22×C47—81no—
287C22×C47—81no—
288C22×C47C22×C22⋊C411yescharacteristic
289C22×C47#57711yescharacteristic
290C22×C47#57811yescharacteristic
291C2×D47—41no—
292C2×D47—41no—
293C2×D47—41no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—22no—
298C4×C47—22no—
299C4×C47—22no—
300C4×C47—22no—
301C4×C47—42no—
302C4×C47—82no—
303C4×C47—81no—
304C4×C47#41012yes—
305Dic47—42no—
306Dic47—41no—
307Dic47—41no—
308Dic47—41no—
309Dic47—42no—
310#3495—471no—
311#2924—471no—
312#2347D4711yescharacteristic, complemented
313#1521—472no—
314#1520—471no—
315#1515—472no—
316#1513—471no—
317#1509—472no—
318#1508—471no—
319#1503—472no—
320#1501—471no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—41no—
324C2×C47—41no—
325C2×C47C2×#41011yescharacteristic
326C2×C47#289811yescharacteristic
327C2×C47#290111yescharacteristic
328D47—81no—
329#556—941no—
330#554—941no—
331#552—942no—
332#552—941no—
333#552—941no—
334#551—942no—
335#544—471no—
336#542—472no—
337#541—472no—
338#536—471no—
339#533—472no—
340#529—472no—
341#525—471no—
342C2×C22⋊Q8—471no—
343#520—471no—
344#519—471no—
345C2×#117C2×D4711yescharacteristic
346#433—942no—
347#432—472no—
348#431—472no—
349#424—941no—
350#407—471no—
351C2×C22⋊C8—471no—
352#405—941no—
353#389—21no—
354#388—22no—
355#383C2×D4712yes—
356#380C2×D4711yescharacteristic
357C4×C4⋊C4—21no—
358C4×C4⋊C4C2×D4712yes—
359C4×C22⋊C4C2×D4711yescharacteristic
360#328—471no—
361#328—471no—
362#328—472no—
363#328—472no—
364#328—472no—
365#328—472no—
366#328—472no—
367#327—471no—
368#327—471no—
369#327—472no—
370C47#1761211yescharacteristic, complemented, Sylow
371C2×#41—471no—
372C22×Q8—471no—
373C23×C4C22×D4711yescharacteristic
374C2×M16—941no—
375C22×C8—941no—
376C4⋊Q8—472no—
377C4⋊Q8—472no—
378C4⋊Q8—941no—
379#126—942no—
380#126—942no—
381#126—942no—
382#126—942no—
383#125—472no—
384#125—942no—
385#125—942no—
386#125—941no—
387#125—942no—
388#124—472no—
389#124—942no—
390#123—941no—
391#123—942no—
392#123—942no—
393#123—942no—
394C22⋊Q8—472no—
395C22⋊Q8—471no—
396C22⋊Q8—472no—
397C22⋊Q8—471no—
398C22⋊Q8—941no—
399C22⋊Q8—941no—
400C22⋊Q8—942no—
401C22⋊Q8—941no—
402C22⋊Q8—941no—
403C22⋊Q8—942no—
404C22⋊Q8—942no—
405#121—471no—
406#121—471no—
407#120—941no—
408C4×Q8—472no—
409C4×Q8—472no—
410C4×Q8—472no—
411C4×Q8—941no—
412C4×Q8—941no—
413C4×Q8—942no—
414C4×D4—472no—
415C4×D4—941no—
416C4×D4—941no—
417C4×D4—942no—
418C4×D4—942no—
419#117—471no—
420#117—942no—
421#117—941no—
422#117—942no—
423#117—942no—
424#117C4×D4711yescharacteristic
425#117C4×D4711yescharacteristic
426#117C4×D4712yes—
427#117D18811yescharacteristic
428#117D18812yes—
429#117D18811yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—471no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4C22⋊D4711yescharacteristic
436C2×C4⋊C4C22⋊D4711yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4C22⋊D4712yes—
441C2×C42—21no—
442C2×C42—22no—
443C2×C42C22×D4712yes—
444C4⋊C8—942no—
445C4⋊C8—942no—
446C22⋊C8—471no—
447C22⋊C8—471no—
448C22⋊C8—472no—
449C22⋊C8—941no—
450C22⋊C8—941no—
451#97—942no—
452C4×C8—942no—
453#95—22no—
454#95—22no—
455#95C22×D4711yescharacteristic
456#95C22×D4711yescharacteristic
457#95C22×D4712yes—
458C24C2×C22⋊D4711yescharacteristic
459#41—1882no—
460C2×Q8—472no—
461C2×Q8—471no—
462C2×Q8—942no—
463C2×Q8—941no—
464C2×Q8—1882no—
465C2×D4—471no—
466C2×D4—941no—
467C2×D4—941no—
468C2×D4—941no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—42no—
473C22×C4—941no—
474C22×C4—941no—
475C22×C4—942no—
476C22×C4—941no—
477C22×C4C2×C4×D4711yescharacteristic
478C22×C4C2×C4×D4711yescharacteristic
479C22×C4C2×D18811yescharacteristic
480C22×C4C2×D18811yescharacteristic
481C22×C4C2×C22⋊D4712yes—
482C22×C4C2×C22⋊D4711yescharacteristic
483C22×C4C2×C22⋊D4712yes—
484C22×C4C23×D4711yescharacteristic
485M16—1882no—
486C2×C8—941no—
487C2×C8—942no—
488C2×C8—941no—
489C2×C8—1882no—
490C4⋊C4—42no—
491C4⋊C4—44no—
492C4⋊C4—472no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—942no—
500C4⋊C4—941no—
501C4⋊C4—942no—
502C4⋊C4—941no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—941no—
508C4⋊C4(C2×D47)⋊C411yescharacteristic
509C4⋊C4(C2×D47)⋊C411yescharacteristic
510C4⋊C4(C2×D47)⋊C412yes—
511C4⋊C4(C2×D47)⋊C411yescharacteristic
512C4⋊C4(C2×D47)⋊C411yescharacteristic
513C4⋊C4(C2×D47)⋊C412yes—
514C22⋊C4—42no—
515C22⋊C4—81no—
516C22⋊C4—942no—
517C22⋊C4—941no—
518C22⋊C4—941no—
519C22⋊C4—942no—
520C22⋊C4—941no—
521C22⋊C4—942no—
522C22⋊C4—942no—
523C22⋊C4—941no—
524C22⋊C4—942no—
525C22⋊C4—941no—
526C22⋊C4(C2×D47)⋊C412yes—
527C22⋊C4(C2×D47)⋊C412yes—
528C22⋊C4(C2×D47)⋊C412yes—
529C22⋊C4(C2×D47)⋊C412yes—
530C42—42no—
531C42—82no—
532C42—941no—
533C42—942no—
534C42—942no—
535C42—942no—
536C42C2×C4×D4712yes—
537C42C2×C4×D4712yes—
538C42C2×D18812yes—
539C42C2×D18812yes—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—941no—
545C23C2×(C2×D47)⋊C411yescharacteristic
546C23C2×(C2×D47)⋊C411yescharacteristic
547C23C22×C22⋊D4711yescharacteristic
548Q8—3762no—
549Q8—1882no—
550Q8—1881no—
551Q8—1882no—
552D4—3761no—
553D4—1881no—
554D4—1882no—
555D4—1881no—
556D4—1881no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—942no—
578C2×C4—941no—
579C2×C4—942no—
580C2×C4—3762no—
581C2×C4—3761no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4C2×(C2×D47)⋊C412yes—
585C2×C4C2×(C2×D47)⋊C412yes—
586C2×C4C2×(C2×D47)⋊C412yes—
587C2×C4C2×(C2×D47)⋊C412yes—
588C2×C4C2×(C2×D47)⋊C411yescharacteristic
589C2×C4C2×(C2×D47)⋊C411yescharacteristic
590C2×C4C22×C4×D4711yescharacteristic
591C2×C4C22×D18811yescharacteristic
592C8—1881no—
593C8—1881no—
594C8—1882no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—1881no—
606C22—1881no—
607C22—1881no—
608C22C22×(C2×D47)⋊C411yescharacteristic
609C22#1568993411yescharacteristic
610C22#1568993811yescharacteristic
611C4—22no—
612C4—22no—
613C4—22no—
614C4—22no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—82no—
620C4—81no—
621C4—1881no—
622C4—1882no—
623C4—1881no—
624C4—1881no—
625C4—1882no—
626C4#1568909612yes—
627C2—21no—
628C2—21no—
629C2—41no—
630C2—41no—
631C2—3761no—
632C2C2×#1568909611yescharacteristic
633C2#2025191811yescharacteristic
634C2#2025193611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2347C2
socleC22×C47C22×C22⋊C4
prime radical#15689634C22
cosocleC22×C4×C47C24
hypercenter#2347D47
hypocenterC47#17612
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #20252046C2semidirect
3. #20241963C2semidirect
4. #20241959C2semidirect
5. #20241938C2semidirect
7. #20241911C2semidirect
8. #20241907C2semidirect
9. #20241886C2semidirect
11. C47×#2347C2semidirect
18. #15689751C4semidirect
19. #15689744C4semidirect
20. #15689735C4semidirect
21. #15689699C4semidirect
26. #15689603C4semidirect
27. #15689600C4semidirect
312. #2347D47semidirect
370. C47#17612semidirect

Maximal subgroups

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

subgroupindex
#202571402
#202520462
#202419632
#202419592
#202419382
#202419292
#202419112
#202419072
#202418862
#202418772
C47×#23472
#1761247