Finite Group Databasebeta

← #26238363

Subgroups — #26238363

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#20253170C211yesmaximal, characteristic
2#20251953C211yesmaximal, characteristic
3#20244370C211yesmaximal, characteristic, complemented
4#20244163C211yesmaximal, characteristic, complemented
5#20244138C211yesmaximal, characteristic, complemented
6#20244133C211yesmaximal, characteristic, complemented
7#20243987C211yesmaximal, characteristic, complemented
8#20243987C211yesmaximal, characteristic, complemented
9#20243662C211yesmaximal, characteristic
10#20243662C211yesmaximal, characteristic
11#20243247C211yesmaximal, characteristic, complemented
12#20243234C211yesmaximal, characteristic
13#20243227C211yesmaximal, characteristic
14#20243201C211yesmaximal, characteristic
15C47×#2962C211yesmaximal, 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
31#15689149C2211yescharacteristic
32#15689149C2211yescharacteristic
33#15689148—21no—
34#15689148—21no—
35#15689147C2211yescharacteristic
36#15689145—21no—
37C2×C4⋊(C47⋊C8)C2211yescharacteristic
38C4⋊C8×D47—21no—
39C2×#13093950C2211yescharacteristic
40C2×#13093950C2211yescharacteristic
41#15689117C2211yescharacteristic
42#15689117C2211yescharacteristic
43C2×#13093934C2211yescharacteristic
44C2×C8×Dic47C2211yescharacteristic
45#15688969C2211yescharacteristic
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—
60C8×Q8×C47—21no—
61C47×#424C2211yescharacteristic
62C47×#424C2211yescharacteristic
63C2×C4⋊C8×C47C2211yescharacteristic
64C47×#405C2211yescharacteristic
65C47×#405C2211yescharacteristic
66C4×M16×C47C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094030—22no—
69#13094030—22no—
70#13094030—41no—
71#13094030—41no—
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×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C42×D47—21no—
91#13093959—41no—
92#13093959—41no—
93#13093957C2×C411yescharacteristic
94#13093957C2×C411yescharacteristic
95#13093957C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)—21no—
103C4⋊(C47⋊C8)C2×C411yescharacteristic
104C4⋊(C47⋊C8)C2×C411yescharacteristic
105C4⋊(C47⋊C8)C2×C411yescharacteristic
106C4⋊(C47⋊C8)C2×C411yescharacteristic
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109Dic47⋊C8—21no—
110Dic47⋊C8—21no—
111#13093950—22no—
112#13093950Q814yescomplemented
113#13093947C2×C411yescharacteristic
114#13093947C2×C411yescharacteristic
115#13093947C2×C411yescharacteristic
116#13093947C2×C411yescharacteristic
117#13093944C2×C411yescharacteristic
118#13093944C2×C411yescharacteristic
119#13093944C2×C411yescharacteristic
120#13093944C2×C411yescharacteristic
121#13093934—41no—
122C8×Dic47—41no—
123C47⋊#95—21no—
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×C47D411yescharacteristic
145C4⋊C8×C47D411yescharacteristic
146C4⋊C8×C47D411yescharacteristic
147C4⋊C8×C47D411yescharacteristic
148#97×C47—21no—
149#97×C47—21no—
150#97×C47—21no—
151C4×C8×C47—21no—
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×C47C2×Q812yes—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—21no—
178C2×C8×C47—21no—
179C2×C8×C47—21no—
180C2×C8×C47—21no—
181C2×C8×C47C2×D411yescharacteristic
182C2×C8×C47C2×D411yescharacteristic
183C2×C8×C47C2×D411yescharacteristic
184C2×C8×C47C2×D411yescharacteristic
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⋊Dic47C22×C411yescharacteristic
207C4⋊Dic47C22×C411yescharacteristic
208Dic47⋊C4—21no—
209Dic47⋊C4—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
214C4×Dic47—21no—
215C4×Dic47—21no—
216C4×Dic47C2×Q812yes—
217#10625329—21no—
218#10625329—21no—
219#10625329—21no—
220#10625329—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8C22×C411yescharacteristic
228C2×C47⋊C8C22×C411yescharacteristic
229C2×C47⋊C8C22×C411yescharacteristic
230C2×C47⋊C8C22×C411yescharacteristic
231#10625324—42no—
232#10625324—42no—
233C8×D47—42no—
234C8×D47—42no—
235C23×C47C2×#4111yescharacteristic
236C22×D47—21no—
237Q8×C47—42no—
238Q8×C47—81no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47C4×D411yescharacteristic
246C2×C4×C47C4×D411yescharacteristic
247C2×C4×C47C4×D411yescharacteristic
248C2×C4×C47C4×D411yescharacteristic
249C2×C4×C47C23×C411yescharacteristic
250C2×C4×C47C22×D411yescharacteristic
251C2×C4×C47C22×Q811yescharacteristic
252C2×C4×C47C2×#4111yescharacteristic
253C2×C4×C47H(5,𝔽2)11yescharacteristic
254C2×C4×C472−1+411yescharacteristic
255C22⋊D47—22no—
256C22⋊D47—22no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—22no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266D188—21no—
267D188C4×Q812yes—
268C4×D47—22no—
269C4×D47—22no—
270C4×D47—42no—
271C4×D47—81no—
272Dic94—21no—
273Dic94C4×Q812yes—
274C8×C47—21no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—22no—
279C8×C47—41no—
280C47⋊C8—21no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—21no—
284C47⋊C8—41no—
285C47⋊C8—41no—
286#22984—471nomaximal, Sylow
287C22×C47—21no—
288C22×C47—21no—
289C22×C47C2×C4×D411yescharacteristic
290C22×C47#55211yescharacteristic
291C22×C47#55411yescharacteristic
292C2×D47—22no—
293C2×D47—41no—
294C2×D47—41no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—41no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47C2×C4×Q811yescharacteristic
304C4×C47#52011yescharacteristic
305C4×C47#54611yescharacteristic
306C4×C47D4×Q811yescharacteristic
307Dic47—22no—
308Dic47—42no—
309Dic47—41no—
310Dic47—41no—
311Dic47—81no—
312#3076—471no—
313#2962D4711yescharacteristic, complemented
314#2906—471no—
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#236011yescharacteristic
330C2×C47#295511yescharacteristic
331C2×C47#295711yescharacteristic
332D47—42no—
333C2×#131—471no—
334C2×#131—471no—
335#533C2×D4711yescharacteristic
336C4×#41—471no—
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—21no—
346#446—21no—
347#446—21no—
348C8×Q8—21no—
349C2×#108—471no—
350C2×#108—471no—
351#427—471no—
352#427—471no—
353#424—471no—
354#424—471no—
355#424—941no—
356#424—941no—
357#424C2×D4711yescharacteristic
358#424C2×D4711yescharacteristic
359#423—471no—
360#423—941no—
361C2×C4⋊C8—471no—
362C2×C4⋊C8—941no—
363C2×C4⋊C8C2×D4711yescharacteristic
364C2×#104—471no—
365C2×#104—471no—
366#416—471no—
367#416—471no—
368#405C2×D4711yescharacteristic
369#405C2×D4711yescharacteristic
370C4×M16C2×D4711yescharacteristic
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×#41—471no—
386#131—942no—
387#131—942no—
388#131—1881no—
389#131—1881no—
390C2×M16—471no—
391C2×M16—471no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16C22×D4711yescharacteristic
395C2×M16C22×D4711yescharacteristic
396C22×C8—471no—
397C22×C8—471no—
398C22×C8—941no—
399C22×C8—941no—
400C22×C8C22×D4711yescharacteristic
401C22×C8C22×D4711yescharacteristic
402C4⋊Q8C4×D4711yescharacteristic
403C4⋊Q8C4×D4711yescharacteristic
404#125C4×D4711yescharacteristic
405#125C4×D4711yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—471no—
411C4×Q8—471no—
412C4×D4—471no—
413C4×D4—471no—
414C4×D4—941no—
415C4×D4—941no—
416#117—471no—
417#117—941no—
418#117C22×D4711yescharacteristic
419#117C22×D4711yescharacteristic
420C2×C42—471no—
421C2×C42—471no—
422C2×C42—941no—
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—471no—
439C4⋊C8—471no—
440C4⋊C8—471no—
441C4⋊C8—471no—
442C4⋊C8—941no—
443C4⋊C8—941no—
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—21no—
463#97—21no—
464#97—21no—
465#97—1881no—
466C4×C8—21no—
467C4×C8—21no—
468C4×C8—21no—
469C4×C8—1881no—
470#95—941no—
471#95—941no—
472#41—472no—
473#41—472no—
474#41—941no—
475#41—941no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—471no—
479C2×D4—471no—
480C2×D4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4#1062535011yescharacteristic
487C22×C4#1062535011yescharacteristic
488C22×C4C23×D4711yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—941no—
493M16—941no—
494M16—941no—
495M16—941no—
496M16—1882no—
497M16—1882no—
498M16Q8×D4712yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—471no—
506C2×C8—471no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—1882no—
516C2×C8—1882no—
517C2×C8C2×C22⋊D4711yescharacteristic
518C2×C8C2×C22⋊D4711yescharacteristic
519C2×C8C2×C22⋊D4711yescharacteristic
520C2×C8C2×C22⋊D4711yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
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—941no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C42—21no—
541C42—21no—
542C42—472no—
543C42—941no—
544C42—941no—
545C42—941no—
546C42—941no—
547C42—941no—
548C42—941no—
549C42C2×C4×D4711yescharacteristic
550C42C2×C4×D4711yescharacteristic
551C42C2×C22⋊D4711yescharacteristic
552C42C2×C22⋊D4711yescharacteristic
553C23—941no—
554C23C2×#1062535011yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—472no—
558Q8—941no—
559D4—472no—
560D4—942no—
561D4—942no—
562D4—941no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—941no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—942no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—3761no—
576C2×C4—1882no—
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×C4#41×D4711yescharacteristic
590C2×C4#1309407011yescharacteristic
591C2×C4#1309407211yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—22no—
597C8—41no—
598C8—941no—
599C8—941no—
600C8—941no—
601C8—941no—
602C8—1881no—
603C8—1881no—
604C22—21no—
605C22—21no—
606C22—942no—
607C22—1881no—
608C22—1881no—
609C22C2×C4×C22⋊D4711yescharacteristic
610C22#1568981411yescharacteristic
611C22#1568983311yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—942no—
621C4—3761no—
622C4—1882no—
623C4—1881no—
624C4—1881no—
625C4C4×Q8×D4711yescharacteristic
626C4#1568960511yescharacteristic
627C4#1568976111yescharacteristic
628C4Q8×C22⋊D4711yescharacteristic
629C2—21no—
630C2—21no—
631C2—1882no—
632C2#2024638911yescharacteristic
633C2#2025228911yescharacteristic
634C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2962C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#2962D47
hypocenterC47#22984
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #20244370C2semidirect
4. #20244163C2semidirect
5. #20244138C2semidirect
6. #20244133C2semidirect
7. #20243987C2semidirect
8. #20243987C2semidirect
11. #20243247C2semidirect
15. C47×#2962C2semidirect
19. #15689427C4semidirect
20. #15689427C4semidirect
21. #15689420C4semidirect
22. #15689420C4semidirect
23. #15689415C4semidirect
24. #15689410C4semidirect
25. #15689405C4semidirect
26. #15689400C4semidirect
112. #13093950Q8semidirect
313. #2962D47semidirect
384. C47#22984semidirect

Maximal subgroups

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

subgroupindex
#202531702
#202519532
#202443702
#202441632
#202441382
#202441332
#202439872
#202436622
#202432472
#202432342
#202432272
#202432012
C47×#29622
#2298447