Finite Group Databasebeta

← #26238369

Subgroups — #26238369

Order 12032.

692 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#20253176C211yesmaximal, characteristic
2#20252331C211yesmaximal, characteristic, complemented
3#20244368C211yesmaximal, characteristic, complemented
4#20244161C211yesmaximal, characteristic, complemented
5#20244138C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20243984C211yesmaximal, characteristic, complemented
8#20243984C211yesmaximal, characteristic, complemented
9#20243663C211yesmaximal, characteristic
10#20243663C211yesmaximal, characteristic
11#20243247C211yesmaximal, characteristic, complemented
12#20243230C211yesmaximal, characteristic
13#20243223C211yesmaximal, characteristic
14#20243198C211yesmaximal, characteristic
15C47×#2906C211yesmaximal, characteristic
16#15689680C2211yescharacteristic
17#15689430C411yescharacteristic, complemented
18#15689430C411yescharacteristic, complemented
19#15689423C411yescharacteristic, complemented
20#15689423C411yescharacteristic, complemented
21#15689418C411yescharacteristic, complemented
22#15689413C411yescharacteristic, complemented
23#15689408C411yescharacteristic, complemented
24#15689403C411yescharacteristic, complemented
25#15689252—21no—
26#15689252—21no—
27#15689250—21no—
28#15689247—21no—
29C2×#13093959C2211yescharacteristic
30C2×#13093959C2211yescharacteristic
31#15689159C2211yescharacteristic
32#15689159C2211yescharacteristic
33#15689149C2211yescharacteristic
34#15689149C2211yescharacteristic
35C2×C4⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093951C2211yescharacteristic
37C2×#13093951C2211yescharacteristic
38#15689119C2211yescharacteristic
39#15689119C2211yescharacteristic
40#15689078C2211yescharacteristic
41#15689078C2211yescharacteristic
42C4×#10625329C2211yescharacteristic
43C2×#13093934C2211yescharacteristic
44C2×C8×Dic47C2211yescharacteristic
45#15688969C2211yescharacteristic
46#15688887C2211yescharacteristic
47#15688887C2211yescharacteristic
48#15688884C2211yescharacteristic
49#15688884C2211yescharacteristic
50#15688884C2211yescharacteristic
51#15688884C2211yescharacteristic
52#15688882C2211yescharacteristic
53#15688882C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×#131×C47C2211yescharacteristic
57C2×#131×C47C2211yescharacteristic
58C4×#41×C47C2211yescharacteristic
59C47×#424—21no—
60C47×#424—21no—
61C47×#424C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C47×#423—21no—
64C47×#423C2211yescharacteristic
65C2×C4⋊C8×C47—21no—
66C2×C4⋊C8×C47C2211yescharacteristic
67C2×#10625329C2311yescharacteristic
68C2×#10625329C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71#13094024C2×C411yescharacteristic
72#13094024C2×C411yescharacteristic
73#13094016C2×C411yescharacteristic
74#13094016C2×C411yescharacteristic
75#13094003—21no—
76#13094003—21no—
77C4×Dic94—21no—
78C4×Dic94—21no—
79#13093983C2311yescharacteristic
80#13093983C2311yescharacteristic
81C2×C4×Dic47C2311yescharacteristic
82C2×C4×Dic47C2311yescharacteristic
83#13093959—41no—
84#13093959—41no—
85#13093957C2×C411yescharacteristic
86#13093957C2×C411yescharacteristic
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92#13093955C2×C411yescharacteristic
93C4⋊(C47⋊C8)C2×C411yescharacteristic
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2×C411yescharacteristic
96C4⋊(C47⋊C8)C2×C411yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101#13093951—22no—
102#13093951Q814yescomplemented
103#13093948C2×C411yescharacteristic
104#13093948C2×C411yescharacteristic
105#13093948C2×C411yescharacteristic
106#13093948C2×C411yescharacteristic
107#13093945C2×C411yescharacteristic
108#13093945C2×C411yescharacteristic
109#13093945C2×C411yescharacteristic
110#13093945C2×C411yescharacteristic
111#13093935—21no—
112#13093934—21no—
113#13093934—21no—
114#13093934—41no—
115C4×C47⋊C8—21no—
116C8×Dic47—21no—
117C8×Dic47—21no—
118C8×Dic47—41no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C2×#41×C47C2311yescharacteristic
122#131×C47—22no—
123#131×C47—22no—
124#131×C47—41no—
125#131×C47—41no—
126C2×M16×C47—21no—
127C2×M16×C47—21no—
128C2×M16×C47C2311yescharacteristic
129C2×M16×C47C2311yescharacteristic
130C22×C8×C47—21no—
131C22×C8×C47—21no—
132C22×C8×C47C2311yescharacteristic
133C22×C8×C47C2311yescharacteristic
134C4×Q8×C47C2×C411yescharacteristic
135C4×Q8×C47C2×C411yescharacteristic
136C4×D4×C47—21no—
137C4×D4×C47—21no—
138C4×D4×C47C2×C411yescharacteristic
139C4×D4×C47C2×C411yescharacteristic
140#117×C47—21no—
141#117×C47C2311yescharacteristic
142C2×C42×C47—21no—
143C2×C42×C47C2311yescharacteristic
144C4⋊C8×C47—21no—
145C4⋊C8×C47—21no—
146C4⋊C8×C47—21no—
147C4⋊C8×C47—21no—
148C4⋊C8×C47—21no—
149C4⋊C8×C47—21no—
150C4⋊C8×C47D411yescharacteristic
151C4⋊C8×C47D411yescharacteristic
152C4⋊C8×C47D411yescharacteristic
153C4⋊C8×C47D411yescharacteristic
154#41×C47—21no—
155#41×C47—21no—
156#41×C47C2×Q812yes—
157#41×C47#4112yes—
158C2×Q8×C47C22×C411yescharacteristic
159C2×D4×C47—21no—
160C2×D4×C47C22×C411yescharacteristic
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47#4111yescharacteristic
165C22×C4×C47#4111yescharacteristic
166C22×C4×C47C2411yescharacteristic
167C22×Dic47—21no—
168C22×Dic47—21no—
169C2×Dic94—21no—
170C2×Dic94—21no—
171M16×C47—21no—
172M16×C47—21no—
173M16×C47—21no—
174M16×C47—21no—
175M16×C47—42no—
176M16×C47—42no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47—21no—
182C2×C8×C47—21no—
183C2×C8×C47—42no—
184C2×C8×C47—42no—
185C2×C8×C47C2×D411yescharacteristic
186C2×C8×C47C2×D411yescharacteristic
187C2×C8×C47C2×D411yescharacteristic
188C2×C8×C47C2×D411yescharacteristic
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22×C411yescharacteristic
192C4⋊C4×C47C22×C411yescharacteristic
193C22⋊C4×C47—21no—
194C22⋊C4×C47—21no—
195C22⋊C4×C47—21no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47C22×C411yescharacteristic
200C42×C47C22×C411yescharacteristic
201C42×C47C2×D411yescharacteristic
202C42×C47C2×D411yescharacteristic
203C22⋊Dic47—21no—
204C22⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47C22×C411yescharacteristic
208C4⋊Dic47C22×C411yescharacteristic
209C4⋊Dic47C22×C411yescharacteristic
210C4⋊Dic47C22×C411yescharacteristic
211Dic47⋊C4—21no—
212Dic47⋊C4—21no—
213Dic47⋊C4—21no—
214Dic47⋊C4—21no—
215C4×Dic47—21no—
216C4×Dic47—21no—
217C4×Dic47—21no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47C2×Q812yes—
221#10625329—21no—
222#10625329—21no—
223#10625329—21no—
224#10625329C2×Q812yes—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8C22×C411yescharacteristic
232C2×C47⋊C8C22×C411yescharacteristic
233C2×C47⋊C8C22×C411yescharacteristic
234C2×C47⋊C8C22×C411yescharacteristic
235C23×C47—21no—
236C23×C47C2×#4111yescharacteristic
237Q8×C47—21no—
238Q8×C47C4×Q812yes—
239D4×C47—22no—
240D4×C47—22no—
241D4×C47—21no—
242D4×C47C4×Q812yes—
243C2×C4×C47—21no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—42no—
251C2×C4×C47—81no—
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C23×C411yescharacteristic
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×Q811yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47H(5,𝔽2)11yescharacteristic
261C2×C4×C472−1+411yescharacteristic
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—22no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272Dic94—42no—
273Dic94—81no—
274C8×C47—21no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—41no—
279C8×C47—41no—
280C47⋊C8—21no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—21no—
284C47⋊C8—22no—
285C47⋊C8—41no—
286#22984—471nomaximal, Sylow
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—22no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47C2×C4×D411yescharacteristic
293C22×C47#55211yescharacteristic
294C22×C47#55411yescharacteristic
295C4×C47—22no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47C2×C4×Q811yescharacteristic
303C4×C47#52011yescharacteristic
304C4×C47#54611yescharacteristic
305C4×C47D4×Q811yescharacteristic
306Dic47—42no—
307Dic47—41no—
308Dic47—41no—
309Dic47—41no—
310Dic47—41no—
311Dic47—81no—
312#3076—471no—
313#2962—471no—
314#2906D4711yescharacteristic
315#1995—471no—
316#1950—471no—
317#1946—471no—
318#1945—471no—
319#1922—471no—
320#1922—471no—
321#1866—471no—
322#1866—471no—
323#1768—471no—
324#1765—471no—
325#1764—471no—
326#1759—471no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47—42no—
330C2×C47#236011yescharacteristic
331C2×C47#295511yescharacteristic
332C2×C47#295711yescharacteristic
333C2×#131C2×D4711yescharacteristic
334C2×#131C2×D4711yescharacteristic
335#533—471no—
336C4×#41C2×D4711yescharacteristic
337#479—471no—
338#479—471no—
339#478—471no—
340#478—471no—
341#477—471no—
342#476—471no—
343#475—471no—
344#474—471no—
345#446—941no—
346#446—941no—
347#446—941no—
348C8×Q8—941no—
349C2×#108—471no—
350C2×#108—471no—
351#427—471no—
352#427—471no—
353#424—21no—
354#424—21no—
355#424—471no—
356#424—471no—
357#424C2×D4711yescharacteristic
358#424C2×D4711yescharacteristic
359#423—21no—
360#423C2×D4711yescharacteristic
361C2×C4⋊C8—21no—
362C2×C4⋊C8—471no—
363C2×C4⋊C8C2×D4711yescharacteristic
364C2×#104—471no—
365C2×#104—471no—
366#416—471no—
367#416—471no—
368#405—471no—
369#405—471no—
370C4×M16—471no—
371C2×#97—471no—
372C2×C4×C8—471no—
373#376—471no—
374#341—471no—
375#341—471no—
376#339—471no—
377#339—471no—
378#339—471no—
379#339—471no—
380#339—471no—
381#339—471no—
382#336—471no—
383#336—471no—
384C47#2298411yescharacteristic, complemented, Sylow
385C2×#41C22×D4711yescharacteristic
386#131—22no—
387#131—22no—
388#131—41no—
389#131—41no—
390C2×M16—21no—
391C2×M16—21no—
392C2×M16—471no—
393C2×M16—471no—
394C2×M16C22×D4711yescharacteristic
395C2×M16C22×D4711yescharacteristic
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—471no—
399C22×C8—471no—
400C22×C8C22×D4711yescharacteristic
401C22×C8C22×D4711yescharacteristic
402C4⋊Q8—471no—
403C4⋊Q8—471no—
404#125—471no—
405#125—471no—
406C22⋊Q8—941no—
407C22⋊Q8—941no—
408C4×Q8—941no—
409C4×Q8—941no—
410C4×Q8C4×D4711yescharacteristic
411C4×Q8C4×D4711yescharacteristic
412C4×D4—21no—
413C4×D4—21no—
414C4×D4C4×D4711yescharacteristic
415C4×D4C4×D4711yescharacteristic
416#117—21no—
417#117—471no—
418#117—471no—
419#117C22×D4711yescharacteristic
420C2×C42—21no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42C22×D4711yescharacteristic
424#108—1881no—
425#108—1881no—
426#107—471no—
427#107—471no—
428#107—471no—
429#107—471no—
430#106—471no—
431#106—471no—
432#106—471no—
433#106—471no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—471no—
441C4⋊C8—471no—
442C4⋊C8—471no—
443C4⋊C8—471no—
444C4⋊C8—941no—
445C4⋊C8—941no—
446C4⋊C8—941no—
447C4⋊C8—941no—
448C4⋊C8C22⋊D4711yescharacteristic
449C4⋊C8C22⋊D4711yescharacteristic
450C4⋊C8C22⋊D4711yescharacteristic
451C4⋊C8C22⋊D4711yescharacteristic
452#104—474no—
453#104—942no—
454#103—471no—
455#103—471no—
456#103—471no—
457#103—471no—
458#102—471no—
459#102—471no—
460#102—471no—
461#102—471no—
462#97—941no—
463#97—941no—
464#97—941no—
465#97—1881no—
466C4×C8—941no—
467C4×C8—941no—
468C4×C8—941no—
469C4×C8—1881no—
470#95—941no—
471#95—941no—
472#41—21no—
473#41—21no—
474#41#1062535212yes—
475#41Q8×D4712yes—
476C2×Q8—941no—
477C2×Q8—941no—
478C2×Q8C2×C4×D4711yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D4711yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4#1062535011yescharacteristic
487C22×C4#1062535011yescharacteristic
488C22×C4C23×D4711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—42no—
494M16—42no—
495M16—472no—
496M16—941no—
497M16—941no—
498M16—941no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8C2×C22⋊D4711yescharacteristic
518C2×C8C2×C22⋊D4711yescharacteristic
519C2×C8C2×C22⋊D4711yescharacteristic
520C2×C8C2×C22⋊D4711yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—471no—
524C4⋊C4—471no—
525C4⋊C4—471no—
526C4⋊C4—471no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—941no—
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—472no—
544C42—941no—
545C42—941no—
546C42—941no—
547C42—941no—
548C42—941no—
549C42C2×C4×D4711yescharacteristic
550C42C2×C4×D4711yescharacteristic
551C42C2×C22⋊D4711yescharacteristic
552C42C2×C22⋊D4711yescharacteristic
553C23—21no—
554C23C2×#1062535011yescharacteristic
555Q8—21no—
556Q8—3761no—
557Q8—1882no—
558Q8#1309398912yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4#1309398912yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—942no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—1881no—
578C2×C4—1881no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4C4×C22⋊D4711yescharacteristic
583C2×C4C4×C22⋊D4711yescharacteristic
584C2×C4C4×C22⋊D4711yescharacteristic
585C2×C4C4×C22⋊D4711yescharacteristic
586C2×C4C22×C4×D4711yescharacteristic
587C2×C4C22×C22⋊D4711yescharacteristic
588C2×C4C2×Q8×D4711yescharacteristic
589C2×C4C2×#1062535211yescharacteristic
590C2×C4#1309406911yescharacteristic
591C2×C4#1309407211yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—942no—
599C8—941no—
600C8—941no—
601C8—941no—
602C8—941no—
603C8—1881no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22C2×C4×C22⋊D4711yescharacteristic
610C22#1568980811yescharacteristic
611C22#1568982811yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—3761no—
620C4—1882no—
621C4—1881no—
622C4—1881no—
623C4—1881no—
624C4—1881no—
625C4C2×#1309398911yescharacteristic
626C4#1568960411yescharacteristic
627C4#1568976711yescharacteristic
628C4Q8×C22⋊D4711yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#2024639311yescharacteristic
633C2#2025228911yescharacteristic
634C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2906C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×C47C23
cosocleC22×C4×C47C24
hypercenter#2906D47
hypocenterC47#22984
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #20252331C2semidirect
3. #20244368C2semidirect
4. #20244161C2semidirect
5. #20244138C2semidirect
6. #20244133C2semidirect
7. #20243984C2semidirect
8. #20243984C2semidirect
11. #20243247C2semidirect
17. #15689430C4semidirect
18. #15689430C4semidirect
19. #15689423C4semidirect
20. #15689423C4semidirect
21. #15689418C4semidirect
22. #15689413C4semidirect
23. #15689408C4semidirect
24. #15689403C4semidirect
102. #13093951Q8semidirect
384. C47#22984semidirect

Maximal subgroups

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

subgroupindex
#202531762
#202523312
#202443682
#202441612
#202441382
#202441332
#202439842
#202436632
#202432472
#202432302
#202432232
#202431982
C47×#29062
#2298447