Finite Group Databasebeta

← #26233890

Subgroups — #26233890

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252042C211yesmaximal, characteristic
2#20251977C211yesmaximal, characteristic
3#20244138C211yesmaximal, characteristic, complemented
4#20244133C211yesmaximal, characteristic, complemented
5#20243987C211yesmaximal, characteristic, complemented
6#20243987C211yesmaximal, characteristic, complemented
7#20243984C211yesmaximal, characteristic, complemented
8#20243984C211yesmaximal, characteristic, complemented
9#20243487C211yesmaximal, characteristic
10#20243485C211yesmaximal, characteristic
11#20243428C211yesmaximal, characteristic
12#20243273C211yesmaximal, characteristic, complemented
13#20243268C211yesmaximal, characteristic, complemented
14#20243174C211yesmaximal, characteristic
15C47×#2924C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18#15689181—21no—
19#15689181—21no—
20#15689177—21no—
21#15689173—21no—
22C2×#13093959C2211yescharacteristic
23C2×#13093959C2211yescharacteristic
24#15689166C411yescharacteristic, complemented
25#15689166C411yescharacteristic, complemented
26#15689166C411yescharacteristic, complemented
27#15689166C411yescharacteristic, complemented
28#15689163C411yescharacteristic, complemented
29#15689163C411yescharacteristic, complemented
30#15689163C411yescharacteristic, complemented
31#15689163C411yescharacteristic, complemented
32#15689159C2211yescharacteristic
33#15689159C2211yescharacteristic
34#15689159C2211yescharacteristic
35#15689159C2211yescharacteristic
36#15689149C2211yescharacteristic
37#15689149C2211yescharacteristic
38#15689087C2211yescharacteristic
39#15689078C2211yescharacteristic
40#15689078C2211yescharacteristic
41C2×#13093934C2211yescharacteristic
42C2×C8×Dic47C2211yescharacteristic
43C4×C22⋊Dic47C2211yescharacteristic
44#15688887C2211yescharacteristic
45#15688887C2211yescharacteristic
46#15688884C2211yescharacteristic
47#15688884C2211yescharacteristic
48#15688884C2211yescharacteristic
49#15688884C2211yescharacteristic
50#15688882C2211yescharacteristic
51#15688882C2211yescharacteristic
52#15688882C2211yescharacteristic
53#15688882C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C2×#117×C47C2211yescharacteristic
57C47×#433—21no—
58C47×#433—21no—
59C47×#432—21no—
60C47×#431—21no—
61C47×#424C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C47×#407C2211yescharacteristic
64C2×C22⋊C8×C47C2211yescharacteristic
65C47×#405C2211yescharacteristic
66C47×#405C2211yescharacteristic
67C2×#10625329—22no—
68C2×#10625329—22no—
69C2×#10625329C2×C411yescharacteristic
70C2×#10625329C2×C411yescharacteristic
71C2×#10625329C2×C411yescharacteristic
72C2×#10625329C2×C411yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625329C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13093983—21no—
78#13093983—21no—
79#13093983C2×C411yescharacteristic
80#13093983C2×C411yescharacteristic
81#13093983C2311yescharacteristic
82#13093983C2311yescharacteristic
83C2×C4⋊Dic47C2×C411yescharacteristic
84C2×C4⋊Dic47C2×C411yescharacteristic
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C4×Dic47—21no—
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90#13093959—22no—
91#13093959—22no—
92#13093957C2×C411yescharacteristic
93#13093957C2×C411yescharacteristic
94#13093957C2×C411yescharacteristic
95#13093957C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093957C2×C411yescharacteristic
99#13093957C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101#13093955C2×C411yescharacteristic
102#13093955C2×C411yescharacteristic
103#13093955C2×C411yescharacteristic
104#13093955C2×C411yescharacteristic
105#13093955C2×C411yescharacteristic
106#13093955C2×C411yescharacteristic
107#13093955C2×C411yescharacteristic
108Dic47⋊C8—21no—
109Dic47⋊C8—21no—
110Dic47⋊C8—21no—
111Dic47⋊C8—21no—
112C22⋊(C47⋊C8)—21no—
113C22⋊(C47⋊C8)—21no—
114#13093934—21no—
115#13093934—21no—
116#13093934—22no—
117C8×Dic47—21no—
118C8×Dic47—21no—
119C8×Dic47—22no—
120C47⋊#95—21no—
121C23×C4×C47C2311yescharacteristic
122C2×M16×C47C2311yescharacteristic
123C2×M16×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C22×C8×C47C2311yescharacteristic
126#117×C47—21no—
127#117×C47—21no—
128#117×C47C2×C411yescharacteristic
129#117×C47C2×C411yescharacteristic
130#117×C47C2311yescharacteristic
131#117×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2×C411yescharacteristic
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C22⋊C4×C47—21no—
135C2×C42×C47—21no—
136C4⋊C8×C47—21no—
137C4⋊C8×C47—21no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141C22⋊C8×C47—21no—
142C22⋊C8×C47D411yescharacteristic
143C22⋊C8×C47D411yescharacteristic
144C22⋊C8×C47D411yescharacteristic
145C22⋊C8×C47D411yescharacteristic
146#97×C47—21no—
147#97×C47—21no—
148C4×C8×C47—21no—
149C4×C8×C47—21no—
150C24×C47#4111yescharacteristic
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47#4111yescharacteristic
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167M16×C47—21no—
168M16×C47—21no—
169M16×C47—21no—
170M16×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47C22×C411yescharacteristic
184C4⋊C4×C47C22×C411yescharacteristic
185C4⋊C4×C47C22×C411yescharacteristic
186C4⋊C4×C47C22×C411yescharacteristic
187C22⋊C4×C47—21no—
188C22⋊C4×C47—21no—
189C22⋊C4×C47—21no—
190C22⋊C4×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C22⋊Dic47—21no—
196C22⋊Dic47—21no—
197C22⋊Dic47—21no—
198C22⋊Dic47—21no—
199C22⋊Dic47—42no—
200C4⋊Dic47—21no—
201C4⋊Dic47—21no—
202C4⋊Dic47C22×C411yescharacteristic
203C4⋊Dic47C22×C411yescharacteristic
204C4⋊Dic47C22×C411yescharacteristic
205C4⋊Dic47C22×C411yescharacteristic
206C4×Dic47—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
214#10625329—22no—
215#10625329—22no—
216#10625329—22no—
217#10625329—22no—
218#10625329—21no—
219#10625329—21no—
220#10625329—21no—
221#10625329—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8C22×C411yescharacteristic
227C2×C47⋊C8C22×C411yescharacteristic
228C2×C47⋊C8C22×C411yescharacteristic
229C2×C47⋊C8C22×C411yescharacteristic
230C2×C47⋊C8#4112yes—
231C2×C47⋊C8#4112yes—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47C4×D411yescharacteristic
237C23×C47C4×D411yescharacteristic
238C23×C47C2×#4111yescharacteristic
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—42no—
254C2×C4×C47—81no—
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47C23×C411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C472−1+411yescharacteristic
262C2×C4×C472−1+411yescharacteristic
263C2×Dic47—22no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267C2×Dic47—21no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—81no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C8×C47—41no—
280C8×C47—41no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—41no—
284C47⋊C8—41no—
285C47⋊C8#11712yes—
286C47⋊C8#11712yes—
287#22608—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—21no—
292C22×C47—21no—
293C22×C47—21no—
294C22×C47—21no—
295C22×C47—21no—
296C22×C47—81no—
297C22×C47—81no—
298C22×C47C2×C4×D411yescharacteristic
299C22×C47#55211yescharacteristic
300C22×C47#55211yescharacteristic
301C4×C47—21no—
302C4×C47—21no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47C2×#11711yescharacteristic
308C4×C47#51911yescharacteristic
309C4×C47#54711yescharacteristic
310C4×C47#54711yescharacteristic
311Dic47—42no—
312Dic47—41no—
313Dic47—41no—
314Dic47—41no—
315Dic47—41no—
316Dic47—81no—
317#2924—471no—
318#2924D4711yescharacteristic
319#2911—471no—
320#1946—471no—
321#1945—471no—
322#1922—471no—
323#1922—471no—
324#1922—471no—
325#1922—471no—
326#1826—471no—
327#1826—471no—
328#1811—471no—
329#1773—471no—
330#1772—471no—
331#1753—471no—
332C2×C47—21no—
333C2×C47—21no—
334C2×C47—41no—
335C2×C47—41no—
336C2×C47#234411yescharacteristic
337C2×C47#295511yescharacteristic
338C2×C47#295611yescharacteristic
339C22×M16—471no—
340C2×#117—471no—
341C2×#117C2×D4711yescharacteristic
342#433—21no—
343#433—21no—
344#433—941no—
345#433—941no—
346#432—21no—
347#432—941no—
348#431—21no—
349#431—941no—
350C2×#108—471no—
351C2×#108—471no—
352#428—471no—
353#428—471no—
354#428—471no—
355#428—471no—
356#428—471no—
357#428—471no—
358#428—471no—
359#428—471no—
360#427—471no—
361#427—471no—
362#427—471no—
363#427—471no—
364#424—471no—
365#424—471no—
366#424C2×D4711yescharacteristic
367#424C2×D4711yescharacteristic
368#407—471no—
369#407C2×D4711yescharacteristic
370C2×C22⋊C8C2×D4711yescharacteristic
371#405—471no—
372#405—471no—
373#405C2×D4711yescharacteristic
374#405C2×D4711yescharacteristic
375C2×#97—471no—
376C2×C4×C8—471no—
377C4×C22⋊C4—471no—
378#341—471no—
379#341—471no—
380#339—471no—
381#339—471no—
382#339—471no—
383#339—471no—
384#339—471no—
385#339—471no—
386#339—471no—
387#339—471no—
388#336—471no—
389#336—471no—
390C47#2260811yescharacteristic, complemented, Sylow
391C23×C4C22×D4711yescharacteristic
392C2×M16—471no—
393C2×M16—471no—
394C2×M16—471no—
395C2×M16—471no—
396C2×M16—471no—
397C2×M16—471no—
398C2×M16—942no—
399C2×M16—942no—
400C2×M16C22×D4711yescharacteristic
401C2×M16C22×D4711yescharacteristic
402C22×C8—471no—
403C22×C8—471no—
404C22×C8C22×D4711yescharacteristic
405C22×C8C22×D4711yescharacteristic
406#117—21no—
407#117—21no—
408#117—471no—
409#117—471no—
410#117—471no—
411#117—471no—
412#117—941no—
413#117—941no—
414#117C4×D4711yescharacteristic
415#117C4×D4711yescharacteristic
416#117C22×D4711yescharacteristic
417#117C22×D4711yescharacteristic
418C2×C4⋊C4—471no—
419C2×C4⋊C4—471no—
420C2×C4⋊C4C4×D4711yescharacteristic
421C2×C4⋊C4C4×D4711yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C42—21no—
426C2×C42—471no—
427C2×C42—471no—
428C2×C42—941no—
429#108—942no—
430#108—942no—
431#107—471no—
432#107—471no—
433#107—471no—
434#107—471no—
435#107—471no—
436#107—471no—
437#107—471no—
438#107—471no—
439#106—471no—
440#106—471no—
441#106—471no—
442#106—471no—
443#106—471no—
444#106—471no—
445#106—471no—
446#106—471no—
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—941no—
452C4⋊C8—941no—
453C4⋊C8—941no—
454C4⋊C8—941no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—941no—
458C22⋊C8—941no—
459C22⋊C8C22⋊D4711yescharacteristic
460C22⋊C8C22⋊D4711yescharacteristic
461C22⋊C8C22⋊D4711yescharacteristic
462C22⋊C8C22⋊D4711yescharacteristic
463#97—21no—
464#97—21no—
465#97—942no—
466#97—941no—
467#97—941no—
468C4×C8—21no—
469C4×C8—21no—
470C4×C8—942no—
471C4×C8—941no—
472C4×C8—941no—
473#95—941no—
474C24#1062535011yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4C2×C4×D4711yescharacteristic
487C22×C4#1062535011yescharacteristic
488C22×C4C2×C22⋊D4711yescharacteristic
489C22×C4C2×C22⋊D4711yescharacteristic
490C22×C4C23×D4711yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—942no—
496M16—942no—
497M16—942no—
498M16—942no—
499M16—941no—
500M16—941no—
501M16—941no—
502M16—941no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—472no—
512C2×C8—472no—
513C2×C8—471no—
514C2×C8—471no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8C2×C22⋊D4711yescharacteristic
520C2×C8C2×C22⋊D4711yescharacteristic
521C2×C8C2×C22⋊D4711yescharacteristic
522C2×C8C2×C22⋊D4711yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—471no—
526C4⋊C4—471no—
527C4⋊C4—471no—
528C4⋊C4—471no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4C2×C4×D4711yescharacteristic
532C4⋊C4C2×C4×D4711yescharacteristic
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C22⋊C4—941no—
543C22⋊C4—1882no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42—941no—
552C42—941no—
553C42—941no—
554C42—941no—
555C42—941no—
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23C4×C22⋊D4711yescharacteristic
561C23C4×C22⋊D4711yescharacteristic
562C23C2×#1062535011yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—42no—
578C2×C4—81no—
579C2×C4—942no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—941no—
583C2×C4—941no—
584C2×C4—3761no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1882no—
590C2×C4—1881no—
591C2×C4C4×C22⋊D4711yescharacteristic
592C2×C4C4×C22⋊D4711yescharacteristic
593C2×C4C22×C4×D4711yescharacteristic
594C2×C4C22×C22⋊D4711yescharacteristic
595C2×C4#41×D4711yescharacteristic
596C2×C4#41×D4711yescharacteristic
597C2×C4#1309407111yescharacteristic
598C2×C4#1309407111yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—472no—
606C8—472no—
607C8—941no—
608C8—941no—
609C8—1881no—
610C8—1881no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—81no—
620C22—81no—
621C22C2×C4×C22⋊D4711yescharacteristic
622C22#1568980611yescharacteristic
623C22#1568980611yescharacteristic
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—3761no—
631C4—1882no—
632C4—1881no—
633C4—1881no—
634C4—1881no—
635C4—1881no—
636C4#117×D4711yescharacteristic
637C4#1568960011yescharacteristic
638C4#1568977211yescharacteristic
639C4#1568977211yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#2024625811yescharacteristic
645C2#2025228911yescharacteristic
646C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C2×C4×D4
prime radicalC24×C47#41
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#22608
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #20244138C2semidirect
4. #20244133C2semidirect
5. #20243987C2semidirect
6. #20243987C2semidirect
7. #20243984C2semidirect
8. #20243984C2semidirect
12. #20243273C2semidirect
13. #20243268C2semidirect
24. #15689166C4semidirect
25. #15689166C4semidirect
26. #15689166C4semidirect
27. #15689166C4semidirect
28. #15689163C4semidirect
29. #15689163C4semidirect
30. #15689163C4semidirect
31. #15689163C4semidirect
390. C47#22608semidirect

Maximal subgroups

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

subgroupindex
#202520422
#202519772
#202441382
#202441332
#202439872
#202439842
#202434872
#202434852
#202434282
#202432732
#202432682
#202431742
C47×#29242
#2260847