Finite Group Databasebeta

← #26224124

Subgroups — #26224124

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253170C211yesmaximal, characteristic
2#20251813C211yesmaximal, characteristic
3#20244333C211yesmaximal, characteristic, complemented
4#20244161C211yesmaximal, characteristic, complemented
5#20243984C211yesmaximal, characteristic, complemented
6#20243984C211yesmaximal, characteristic, complemented
7#20243662C211yesmaximal, characteristic
8#20243662C211yesmaximal, characteristic
9#20243405C211yesmaximal, characteristic
10#20243273C211yesmaximal, characteristic, complemented
11#20243268C211yesmaximal, characteristic, complemented
12#20243260C211yesmaximal, characteristic, complemented
13#20243234C211yesmaximal, characteristic
14#20243227C211yesmaximal, characteristic
15C47×#2961C211yesmaximal, characteristic, complemented
16C2×#13094030C2211yescharacteristic
17C2×#13094030C2211yescharacteristic
18C4×#10625350C2211yescharacteristic
19#15689427C411yescharacteristic, complemented
20#15689427C411yescharacteristic, complemented
21#15689420C411yescharacteristic, complemented
22#15689420C411yescharacteristic, complemented
23#15689415C411yescharacteristic, complemented
24#15689410C411yescharacteristic, complemented
25#15689405C411yescharacteristic, complemented
26#15689400C411yescharacteristic, complemented
27C2×#13093959C2211yescharacteristic
28C2×#13093959C2211yescharacteristic
29#15689159C2211yescharacteristic
30#15689159C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093950C2211yescharacteristic
33C2×#13093950C2211yescharacteristic
34#15689117C2211yescharacteristic
35#15689117C2211yescharacteristic
36#15689080—21no—
37#15689080—21no—
38#15689078C2211yescharacteristic
39#15689078C2211yescharacteristic
40C4×#10625329C2211yescharacteristic
41#15689075—21no—
42C2×#13093934C2211yescharacteristic
43#97×D47—21no—
44C2×C8×Dic47C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46#15688887C2211yescharacteristic
47#15688887C2211yescharacteristic
48#15688884C2211yescharacteristic
49#15688884C2211yescharacteristic
50#15688882C2211yescharacteristic
51#15688882C2211yescharacteristic
52#15688882C2211yescharacteristic
53#15688882C2211yescharacteristic
54#15688877C2211yescharacteristic
55#15688877C2211yescharacteristic
56C47×#533C2211yescharacteristic
57C47×#446—21no—
58C47×#446—21no—
59C47×#446—21no—
60C47×#446—21no—
61C47×#424C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C47×#423C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C47×#405C2211yescharacteristic
66C2×#97×C47C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094030—22no—
69#13094030—22no—
70#13094030—22no—
71#13094030Q814yescomplemented
72C2×#10625329C2311yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C2×C8×D47—21no—
79C2×C8×D47—21no—
80C4×Dic94C2×C411yescharacteristic
81C4×Dic94C2×C411yescharacteristic
82C4×D188C2×C411yescharacteristic
83C4×D188C2×C411yescharacteristic
84C4×C22⋊D47—21no—
85C4×C22⋊D47—21no—
86#13093983C2311yescharacteristic
87#13093981—21no—
88C2×C4⋊Dic47—21no—
89C2×C4×Dic47C2311yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47—21no—
92#13093959—22no—
93#13093959—22no—
94#13093957C2×C411yescharacteristic
95#13093957C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101#13093955C2×C411yescharacteristic
102C4⋊(C47⋊C8)C2×C411yescharacteristic
103C4⋊(C47⋊C8)C2×C411yescharacteristic
104C4⋊(C47⋊C8)C2×C411yescharacteristic
105C4⋊(C47⋊C8)C2×C411yescharacteristic
106#13093950—22no—
107#13093950—22no—
108#13093947C2×C411yescharacteristic
109#13093947C2×C411yescharacteristic
110#13093947C2×C411yescharacteristic
111#13093947C2×C411yescharacteristic
112#13093944C2×C411yescharacteristic
113#13093944C2×C411yescharacteristic
114#13093944C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116#13093935—21no—
117#13093934—21no—
118#13093934—21no—
119#13093934—22no—
120C4×C47⋊C8—21no—
121C8×Dic47—21no—
122C8×Dic47—21no—
123C8×Dic47—22no—
124C47⋊#95—21no—
125C2×M16×C47C2311yescharacteristic
126C2×M16×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C4⋊Q8×C47C2×C411yescharacteristic
130C4⋊Q8×C47C2×C411yescharacteristic
131#125×C47C2×C411yescharacteristic
132#125×C47C2×C411yescharacteristic
133C22⋊Q8×C47—21no—
134C22⋊Q8×C47—21no—
135C4×Q8×C47—21no—
136C4×Q8×C47—21no—
137#117×C47C2311yescharacteristic
138#117×C47C2311yescharacteristic
139C2×C42×C47C2311yescharacteristic
140C4⋊C8×C47—21no—
141C4⋊C8×C47—21no—
142C4⋊C8×C47—21no—
143C4⋊C8×C47—21no—
144C4⋊C8×C47—21no—
145C4⋊C8×C47—21no—
146#97×C47—21no—
147#97×C47—21no—
148#97×C47D411yescharacteristic
149#97×C47D411yescharacteristic
150#97×C47D411yescharacteristic
151#97×C47D411yescharacteristic
152C4×C8×C47—21no—
153C4×C8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C22×C4×C47#4111yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×C4×C47C2411yescharacteristic
159C2×C22⋊D47—21no—
160C22×Dic47—21no—
161C22×Dic47—21no—
162#10625350—21no—
163#10625350—21no—
164#10625350C2×Q812yes—
165#10625350#4112yes—
166C2×D188C22×C411yescharacteristic
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×Dic94C22×C411yescharacteristic
171M16×C47—21no—
172M16×C47—21no—
173M16×C47—21no—
174M16×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×Q812yes—
184C2×C8×C47#4112yes—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47C22×C411yescharacteristic
192C4⋊C4×C47C22×C411yescharacteristic
193C4⋊C4×C47C22×C411yescharacteristic
194C4⋊C4×C47C22×C411yescharacteristic
195C22⋊C4×C47—21no—
196C22⋊C4×C47—21no—
197C42×C47—21no—
198C42×C47—21no—
199C42×C47C22×C411yescharacteristic
200C42×C47C22×C411yescharacteristic
201C42×C47C2×D411yescharacteristic
202C42×C47C2×D411yescharacteristic
203C22⋊Dic47—21no—
204(C2×D47)⋊C4—21no—
205(C2×D47)⋊C4—21no—
206C4⋊Dic47—42no—
207C4⋊Dic47C22×C411yescharacteristic
208C4⋊Dic47C22×C411yescharacteristic
209Dic47⋊C4—21no—
210Dic47⋊C4—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
214C4×Dic47—21no—
215C4×Dic47—21no—
216C4×Dic47—21no—
217C4×Dic47—21no—
218#10625329—21no—
219#10625329—21no—
220#10625329C2×Q812yes—
221#10625329#4112yes—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8C22×C411yescharacteristic
229C2×C47⋊C8C22×C411yescharacteristic
230C2×C47⋊C8C22×C411yescharacteristic
231C2×C47⋊C8C22×C411yescharacteristic
232#10625324—24no—
233#10625324—24no—
234C8×D47—24no—
235C8×D47—24no—
236C23×C47C2×#4111yescharacteristic
237C22×D47—21no—
238Q8×C47—81no—
239Q8×C47—81no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C4×D411yescharacteristic
247C2×C4×C47C4×D411yescharacteristic
248C2×C4×C47C4×D411yescharacteristic
249C2×C4×C47C4×D411yescharacteristic
250C2×C4×C47C23×C411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47C22×Q811yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C22⋊D47—22no—
257C22⋊D47—22no—
258C2×Dic47—21no—
259C2×Dic47—22no—
260C2×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267D188—21no—
268D188C4×Q812yes—
269C4×D47—22no—
270C4×D47—22no—
271C4×D47—81no—
272C4×D47—81no—
273Dic94—21no—
274Dic94C4×Q812yes—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—41no—
278C8×C47—41no—
279C8×C47C22⋊Q812yes—
280C8×C47C22⋊Q812yes—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—21no—
284C47⋊C8—21no—
285C47⋊C8—22no—
286C47⋊C8—22no—
287#21629—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47C2×C4×D411yescharacteristic
291C22×C47#52911yescharacteristic
292C22×C47#53311yescharacteristic
293C2×D47—22no—
294C2×D47—41no—
295C2×D47—41no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47C2×C4×Q811yescharacteristic
305C4×C47C4×#4111yescharacteristic
306C4×C47C2×C22⋊Q811yescharacteristic
307C4×C47#52511yescharacteristic
308Dic47—22no—
309Dic47—42no—
310Dic47—41no—
311Dic47—41no—
312Dic47—81no—
313#3076—471no—
314#2961D4711yescharacteristic, complemented
315#2875—471no—
316#1986—471no—
317#1950—471no—
318#1922—471no—
319#1922—471no—
320#1866—471no—
321#1866—471no—
322#1806—471no—
323#1773—471no—
324#1772—471no—
325#1771—471no—
326#1765—471no—
327#1764—471no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47C4×C22⋊Q811yescharacteristic
331C2×C47#295611yescharacteristic
332C2×C47#295711yescharacteristic
333D47—42no—
334C2×#131—471no—
335C2×#131—471no—
336#533C2×D4711yescharacteristic
337C4×#41—471no—
338#479—471no—
339#479—471no—
340#478—471no—
341#478—471no—
342#477—471no—
343#476—471no—
344#475—471no—
345#474—471no—
346#446—21no—
347#446—21no—
348#446—21no—
349#446—21no—
350C2×#108—471no—
351C2×#108—471no—
352#427—471no—
353#427—471no—
354#424C2×D4711yescharacteristic
355#424C2×D4711yescharacteristic
356#423C2×D4711yescharacteristic
357C2×C4⋊C8—471no—
358C2×#104—471no—
359C2×#104—471no—
360#416—471no—
361#416—471no—
362#405—471no—
363#405—471no—
364#405—941no—
365#405—941no—
366#405C2×D4711yescharacteristic
367#405C2×D4711yescharacteristic
368C4×M16—471no—
369C4×M16—941no—
370C2×#97—471no—
371C2×#97—941no—
372C2×#97C2×D4711yescharacteristic
373C2×C4×C8—471no—
374C4×C4⋊C4—471no—
375#341—471no—
376#341—471no—
377#339—471no—
378#339—471no—
379#339—471no—
380#339—471no—
381#339—471no—
382#339—471no—
383#336—471no—
384#336—471no—
385C47#2162911yescharacteristic, complemented, Sylow
386C2×#41—471no—
387#131—474no—
388#131—942no—
389#131—942no—
390#131—942no—
391C2×M16—471no—
392C2×M16—471no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16C22×D4711yescharacteristic
396C2×M16C22×D4711yescharacteristic
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—941no—
400C22×C8—941no—
401C22×C8C22×D4711yescharacteristic
402C22×C8C22×D4711yescharacteristic
403C4⋊Q8C4×D4711yescharacteristic
404C4⋊Q8C4×D4711yescharacteristic
405#125C4×D4711yescharacteristic
406#125C4×D4711yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—471no—
412C4×Q8—471no—
413C4×D4—471no—
414C4×D4—471no—
415C4×D4—941no—
416C4×D4—941no—
417#117—471no—
418#117—941no—
419#117C22×D4711yescharacteristic
420#117C22×D4711yescharacteristic
421C2×C4⋊C4—941no—
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—941no—
425C2×C42C22×D4711yescharacteristic
426#108—942no—
427#108—942no—
428#107—471no—
429#107—471no—
430#107—471no—
431#107—471no—
432#106—471no—
433#106—471no—
434#106—471no—
435#106—471no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—471no—
443C4⋊C8—471no—
444C4⋊C8—471no—
445C4⋊C8—471no—
446#104—942no—
447#104—942no—
448#103—471no—
449#103—471no—
450#103—471no—
451#103—471no—
452#102—471no—
453#102—471no—
454#102—471no—
455#102—471no—
456#97—21no—
457#97—21no—
458#97—942no—
459#97—941no—
460#97—941no—
461#97—941no—
462#97C22⋊D4711yescharacteristic
463#97C22⋊D4711yescharacteristic
464#97C22⋊D4711yescharacteristic
465#97C22⋊D4711yescharacteristic
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—942no—
469C4×C8—941no—
470C4×C8—941no—
471C4×C8—941no—
472#95—941no—
473#41—472no—
474#41—472no—
475#41—941no—
476#41—941no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—471no—
480C2×D4—471no—
481C2×D4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4#1062535011yescharacteristic
488C22×C4#1062535011yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—472no—
495M16—472no—
496M16—944no—
497M16—941no—
498M16—941no—
499M16—944no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—471no—
505C2×C8—471no—
506C2×C8—471no—
507C2×C8—471no—
508C2×C8—944no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—944no—
516C2×C8Q8×D4712yes—
517C2×C8#1062535412yes—
518C2×C8C2×C22⋊D4711yescharacteristic
519C2×C8C2×C22⋊D4711yescharacteristic
520C2×C8C2×C22⋊D4711yescharacteristic
521C2×C8C2×C22⋊D4711yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—471no—
529C4⋊C4—471no—
530C4⋊C4—941no—
531C4⋊C4—941no—
532C4⋊C4—1882no—
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C4⋊C4C2×C4×D4711yescharacteristic
536C4⋊C4C2×C4×D4711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C42—21no—
543C42—21no—
544C42—941no—
545C42—941no—
546C42—941no—
547C42—941no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42C2×C4×D4711yescharacteristic
552C42C2×C4×D4711yescharacteristic
553C42C2×C22⋊D4711yescharacteristic
554C42C2×C22⋊D4711yescharacteristic
555C23—941no—
556C23C2×#1062535011yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—472no—
560Q8—941no—
561D4—472no—
562D4—942no—
563D4—942no—
564D4—941no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—941no—
572C2×C4—942no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—3761no—
578C2×C4—3761no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4C4×C22⋊D4711yescharacteristic
585C2×C4C4×C22⋊D4711yescharacteristic
586C2×C4C4×C22⋊D4711yescharacteristic
587C2×C4C4×C22⋊D4711yescharacteristic
588C2×C4C22×C4×D4711yescharacteristic
589C2×C4C22×C22⋊D4711yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4C2×#1062535411yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—941no—
599C8—941no—
600C8—941no—
601C8—941no—
602C8—942no—
603C8—942no—
604C8#1309400012yes—
605C8#1309400012yes—
606C22—21no—
607C22—21no—
608C22—942no—
609C22—1881no—
610C22—1881no—
611C22C2×C4×C22⋊D4711yescharacteristic
612C22#1568966011yescharacteristic
613C22#1568967711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—942no—
623C4—3761no—
624C4—1882no—
625C4—1881no—
626C4—1881no—
627C4C4×Q8×D4711yescharacteristic
628C4C4×#1062535411yescharacteristic
629C4C2×#1309400011yescharacteristic
630C4#1568963011yescharacteristic
631C2—21no—
632C2—21no—
633C2—1882no—
634C2C4×#1309400011yescharacteristic
635C2#2025229511yescharacteristic
636C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2961C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#2961D47
hypocenterC47#21629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2961

Complements

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

NH ≅ G/Ntype
3. #20244333C2semidirect
4. #20244161C2semidirect
5. #20243984C2semidirect
6. #20243984C2semidirect
10. #20243273C2semidirect
11. #20243268C2semidirect
12. #20243260C2semidirect
15. C47×#2961C2semidirect
19. #15689427C4semidirect
20. #15689427C4semidirect
21. #15689420C4semidirect
22. #15689420C4semidirect
23. #15689415C4semidirect
24. #15689410C4semidirect
25. #15689405C4semidirect
26. #15689400C4semidirect
71. #13094030Q8semidirect
314. #2961D47semidirect
385. C47#21629semidirect

Maximal subgroups

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

subgroupindex
#202531702
#202518132
#202443332
#202441612
#202439842
#202436622
#202434052
#202432732
#202432682
#202432602
#202432342
#202432272
C47×#29612
#2162947