Finite Group Databasebeta

← #26121719

Subgroups — #26121719

Order 12032.

1180 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689096C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4#20243099C211yesmaximal, characteristic, complemented
5#20243098C211yesmaximal, characteristic, complemented
6#20243097C211yesmaximal, characteristic, complemented
7C47×#1733C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9#15689889—22no—
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13C2×#13094032—22no—
14C2×#13094030—22no—
15C22×#10625329C2211yescharacteristic
16C2×M16×D47C414yescomplemented
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#15689096—22no—
20#15689096—22no—
21#15689096C414yescomplemented
22#15689096C414yescomplemented
23C2×#13093938—22no—
24C2×#13093938—22no—
25#15688884—22no—
26#15688883—22no—
27#15688882—22no—
28C22×M16×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic
31C47×#339—22no—
32C2×#10625350—21no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350C2×C412yes—
41C2×#10625350C2×C412yes—
42C2×#10625350D412yes—
43C2×#10625350D412yes—
44C22×Dic94Q811yescharacteristic
45C22×D188Q811yescharacteristic
46C22×C22⋊D47D412yes—
47C22×C4×D47C2×C412yes—
48#13094032—28no—
49#13094032—28no—
50#13094030—28no—
51#13094030—28no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329C2×C412yes—
56C2×#10625329D412yes—
57C2×#10625329D412yes—
58C2×#10625324—24no—
59M16×D47—28no—
60M16×D47—28no—
61C22×C47⋊C8—21no—
62C2×C8×D47—24no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983C2×C412yes—
70#13093983C2×C412yes—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C22⋊Dic47—21no—
74C2×C22⋊Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77#13093938—28no—
78#13093938—28no—
79C23×C4×C47C2311yescharacteristic
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47C2×C412yes—
84C2×M16×C47D412yes—
85C2×M16×C47D412yes—
86C22×C8×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47—21no—
93#117×C47C2×C412yes—
94#117×C47C2×C412yes—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C22⋊C4×C47—21no—
98C2×C22⋊C4×C47—21no—
99C2×C42×C47—21no—
100C2×C42×C47—21no—
101C24×C47C2×D411yescharacteristic
102C23×D47C4⋊C412yes—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47C22×C411yescharacteristic
106C22×C4×C47C22×C411yescharacteristic
107C22×C4×C47C22×C411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×Q811yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C2×C22⋊D47—22no—
120C2×C22⋊D47—22no—
121C2×C22⋊D47—22no—
122C2×C22⋊D47—22no—
123C2×C22⋊D47C22⋊C414yes—
124C2×C22⋊D47C22⋊C414yes—
125C22×Dic47—41no—
126C22×Dic47—41no—
127C22×Dic47C4⋊C412yes—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—22no—
143#10625350—22no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188C4⋊C412yes—
149C2×D188C4⋊C412yes—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47C4214yes—
155C2×C4×D47C22⋊C414yes—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94C4⋊C412yes—
161C2×Dic94C4⋊C412yes—
162M16×C47—22no—
163M16×C47—22no—
164M16×C47—22no—
165M16×C47C22⋊C414yes—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—41no—
172C4⋊C4×C47—41no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47—41no—
177C42×C47—22no—
178C42×C47—22no—
179C42×C47—41no—
180C42×C47—41no—
181C22⋊Dic47—22no—
182C22⋊Dic47—22no—
183C22⋊Dic47—41no—
184C22⋊Dic47—41no—
185C4⋊Dic47—22no—
186C4⋊Dic47—22no—
187C4⋊Dic47—41no—
188C4⋊Dic47—41no—
189C4×Dic47—22no—
190C4×Dic47—22no—
191C4×Dic47—41no—
192C4×Dic47—41no—
193#10625329—22no—
194#10625329—22no—
195#10625329—22no—
196#10625329C22⋊C414yes—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200#10625324—216no—
201C8×D47—216no—
202C23×C47—81no—
203C23×C47C2×C22⋊C411yescharacteristic
204C23×C47C2×C22⋊C411yescharacteristic
205C23×C47C2×C4⋊C411yescharacteristic
206C23×C47#12111yescharacteristic
207C23×C47#12111yescharacteristic
208C23×C47#12111yescharacteristic
209C23×C47#12111yescharacteristic
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—82no—
213C22×D47#9514yes—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—82no—
217C2×C4×C47—82no—
218C2×C4×C47C2×C4211yescharacteristic
219C2×C4×C47C2×C22⋊C411yescharacteristic
220C2×C4×C47C2×C22⋊C411yescharacteristic
221C2×C4×C47C2×C22⋊C411yescharacteristic
222C2×C4×C47C2×C4⋊C411yescharacteristic
223C2×C4×C47C2×C4⋊C411yescharacteristic
224C2×C4×C47#11711yescharacteristic
225C2×C4×C47#11711yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47#12011yescharacteristic
235C2×C4×C47#12011yescharacteristic
236C2×C4×C47#12011yescharacteristic
237C2×C4×C47#12011yescharacteristic
238C2×C4×C47C22⋊Q811yescharacteristic
239C2×C4×C47C22⋊Q811yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47C22⋊Q811yescharacteristic
242C2×C4×C47#12311yescharacteristic
243C2×C4×C47#12311yescharacteristic
244C2×C4×C47#12311yescharacteristic
245C2×C4×C47#12311yescharacteristic
246C22⋊D47—24no—
247C22⋊D47—24no—
248C22⋊D47—24no—
249C22⋊D47—24no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—82no—
255C2×Dic47—82no—
256C2×Dic47#9514yes—
257D188—22no—
258D188—22no—
259D188—22no—
260D188—22no—
261C4×D47—24no—
262C4×D47—24no—
263C4×D47—24no—
264C4×D47—24no—
265Dic94—22no—
266Dic94—22no—
267Dic94—22no—
268Dic94—22no—
269C8×C47—24no—
270C47⋊C8—24no—
271#10766—471nomaximal, Sylow
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47C2×#9511yescharacteristic
280C22×C47#38011yescharacteristic
281C22×C47#38011yescharacteristic
282C22×C47#38611yescharacteristic
283C22×C47#38611yescharacteristic
284C22×C47#38611yescharacteristic
285C22×C47#38611yescharacteristic
286C2×D47—24no—
287C2×D47—44no—
288C2×D47—82no—
289C2×D47—82no—
290C4×C47—82no—
291C4×C47—82no—
292C4×C47C4×C22⋊C411yescharacteristic
293C4×C47C4×C22⋊C411yescharacteristic
294C4×C47#37911yescharacteristic
295C4×C47#38111yescharacteristic
296C4×C47#38511yescharacteristic
297C4×C47#38511yescharacteristic
298C4×C47#38511yescharacteristic
299C4×C47#38511yescharacteristic
300Dic47—24no—
301Dic47—82no—
302Dic47—82no—
303C2×#568—471no—
304C2×#410—471no—
305C2×#410—471no—
306#1733—471no—
307#1733—471no—
308#1733—471no—
309#1733D4711yescharacteristic, complemented
310C2×C47—21no—
311C2×C47—21no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—21no—
315C2×C47—21no—
316C2×C47—21no—
317C2×C47C22⋊#9511yescharacteristic
318D47—44no—
319C22×#41—471no—
320#568—942no—
321#568—942no—
322#568—942no—
323#568—942no—
324C2×#131—942no—
325C2×#131—942no—
326C22×M16—471no—
327C22×M16—474no—
328C22×M16C2×D4711yescharacteristic
329C2×#117—471no—
330C2×#117—471no—
331C2×#117C2×D4711yescharacteristic
332C2×#117C2×D4711yescharacteristic
333#410—474no—
334#410—474no—
335#410—942no—
336#410—942no—
337C2×#99—942no—
338C2×#99—942no—
339#339—22no—
340#339—942no—
341#339—942no—
342#339—942no—
343C47#1076611yescharacteristic, complemented, Sylow
344C2×#41—472no—
345C2×#41—472no—
346C2×#41—472no—
347C2×#41—472no—
348C2×#41—941no—
349C2×#41—941no—
350C2×#41—941no—
351C2×#41—941no—
352C2×#41—941no—
353C2×#41—941no—
354C2×#41—941no—
355C2×#41—941no—
356C22×Q8—471no—
357C22×D4—472no—
358C22×D4—471no—
359C23×C4—472no—
360C23×C4C22×D4711yescharacteristic
361#131—948no—
362#131—948no—
363#131—948no—
364#131—948no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—472no—
369C2×M16—472no—
370C2×M16—472no—
371C2×M16—944no—
372C2×M16—948no—
373C2×M16—941no—
374C2×M16—941no—
375C2×M16—941no—
376C2×M16—948no—
377C2×M16C4×D4712yes—
378C2×M16D18812yes—
379C2×M16C22⋊D4712yes—
380C22×C8—21no—
381C22×C8—944no—
382C22×C8—941no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—472no—
390#117—472no—
391#117—941no—
392#117—941no—
393#117—941no—
394#117—941no—
395#117—941no—
396#117—941no—
397#117C4×D4712yes—
398#117C4×D4712yes—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—941no—
406C2×C22⋊C4—941no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—941no—
410C2×C42—941no—
411#99—948no—
412#99—948no—
413C24—472no—
414C24D4×D4711yescharacteristic
415#41—942no—
416#41—942no—
417#41—942no—
418#41—942no—
419#41—942no—
420#41—942no—
421#41—942no—
422#41—942no—
423#41—942no—
424#41—942no—
425#41—942no—
426#41—942no—
427#41—942no—
428#41—942no—
429#41—942no—
430#41—942no—
431C2×Q8—472no—
432C2×Q8—472no—
433C2×Q8—941no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×D4—474no—
438C2×D4—474no—
439C2×D4—472no—
440C2×D4—472no—
441C2×D4—942no—
442C2×D4—942no—
443C2×D4—942no—
444C2×D4—942no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—941no—
448C2×D4—941no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—472no—
452C22×C4—474no—
453C22×C4—474no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4C2×D18811yescharacteristic
464C22×C4#1062535011yescharacteristic
465C22×C4#1062535011yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4D4×D4711yescharacteristic
468C22×C4D4×D4711yescharacteristic
469C22×C4D4×D4711yescharacteristic
470C22×C4#1062535211yescharacteristic
471C22×C4Q8×D4711yescharacteristic
472C22×C4#1062535411yescharacteristic
473C22×C4C2×C22⋊D4711yescharacteristic
474M16—22no—
475M16—22no—
476M16—22no—
477M16—474no—
478M16—9416no—
479M16—942no—
480M16—942no—
481M16—942no—
482M16(C2×D47)⋊C414yes—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—9416no—
487C2×C8—942no—
488C2×C8—942no—
489C2×C8—942no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—1881no—
497C4⋊C4—1881no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—942no—
503C22⋊C4—942no—
504C22⋊C4—1881no—
505C22⋊C4—1881no—
506C42—22no—
507C42—22no—
508C42—41no—
509C42—41no—
510C42—942no—
511C42—942no—
512C42—1881no—
513C42—1881no—
514C23—81no—
515C23—474no—
516C23—942no—
517C23—942no—
518C23—3762no—
519C23C22⋊C4×D4711yescharacteristic
520C23C22⋊C4×D4711yescharacteristic
521C23C4⋊C4×D4711yescharacteristic
522C23#1309399511yescharacteristic
523C23#1309399711yescharacteristic
524C23#1309399711yescharacteristic
525C23#1309399911yescharacteristic
526Q8—942no—
527Q8—942no—
528Q8—942no—
529Q8—942no—
530D4—944no—
531D4—944no—
532D4—944no—
533D4—944no—
534D4—942no—
535D4—942no—
536D4—942no—
537D4—942no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—474no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—3762no—
550C2×C4—3762no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4C42×D4711yescharacteristic
554C2×C4C22⋊C4×D4711yescharacteristic
555C2×C4C22⋊C4×D4711yescharacteristic
556C2×C4C2×(C2×D47)⋊C411yescharacteristic
557C2×C4C4⋊C4×D4711yescharacteristic
558C2×C4C4⋊C4×D4711yescharacteristic
559C2×C4#1309398111yescharacteristic
560C2×C4#1309398211yescharacteristic
561C2×C4(C22⋊D47)⋊C411yescharacteristic
562C2×C4(C22⋊D47)⋊C411yescharacteristic
563C2×C4C4×C22⋊D4711yescharacteristic
564C2×C4C4×C22⋊D4711yescharacteristic
565C2×C4#1309398611yescharacteristic
566C2×C4#1309398611yescharacteristic
567C2×C4C4×D18811yescharacteristic
568C2×C4C4×D18811yescharacteristic
569C2×C4#1309399211yescharacteristic
570C2×C4#1309399211yescharacteristic
571C2×C4#1309399411yescharacteristic
572C2×C4#1309399411yescharacteristic
573C2×C4#1309400011yescharacteristic
574C2×C4#1309400211yescharacteristic
575C2×C4#1309400211yescharacteristic
576C2×C4#1309400411yescharacteristic
577C2×C4#1309400611yescharacteristic
578C2×C4#1309400611yescharacteristic
579C2×C4#1309400911yescharacteristic
580C2×C4#1309400911yescharacteristic
581C8—24no—
582C8—944no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—944no—
591C22—3762no—
592C22—3762no—
593C22—1884no—
594C22#95×D4711yescharacteristic
595C22#1568898011yescharacteristic
596C22#1568898211yescharacteristic
597C22#1568899911yescharacteristic
598C22#1568899911yescharacteristic
599C22#1568900111yescharacteristic
600C22#1568900111yescharacteristic
601C4—82no—
602C4—82no—
603C4—944no—
604C4—3762no—
605C4—3762no—
606C4#1568897011yescharacteristic
607C4C4×(C2×D47)⋊C411yescharacteristic
608C4#1568897811yescharacteristic
609C4#1568898511yescharacteristic
610C4#1568899411yescharacteristic
611C4#1568899411yescharacteristic
612C4#1568899711yescharacteristic
613C4#1568899711yescharacteristic
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—1884no—
622C2(C2×D47)⋊#9511yescharacteristic
subgroupG/H
centerC4#15688978
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1733C2
socleC2×C47C22⋊#95
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1733D47
hypocenterC47#10766
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #20243099C2semidirect
5. #20243098C2semidirect
6. #20243097C2semidirect
7. C47×#1733C2semidirect
16. C2×M16×D47C4semidirect
21. #15689096C4semidirect
22. #15689096C4semidirect
309. #1733D47semidirect
343. C47#10766semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156890962
#202430992
#202430982
#202430972
C47×#17332
#1076647