Finite Group Databasebeta

← #26215945

Subgroups — #26215945

Order 12032.

1308 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic
2C2×#15689171C211yesmaximal, characteristic, complemented
3#20251977C211yesmaximal, characteristic, complemented
4C2×#15689141C211yesmaximal, characteristic
5C2×#15689139C211yesmaximal, characteristic
6#20243441C218yesmaximal, complemented
7C2×#15688895C211yesmaximal, characteristic, complemented
8C2×C47×#344C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889C414yescomplemented
13#15689889C414yescomplemented
14C2×#13094032C2214yes—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19C2×#13093983C2211yescharacteristic
20#15689171—22no—
21#15689171—22no—
22C2×#13093959C2214yescomplemented
23#15689166—22no—
24#15689163—22no—
25#15689159C2214yescomplemented
26#15689141—22no—
27#15689141C2214yes—
28#15689139—22no—
29#15689139C2214yes—
30C2×#13093952—22no—
31C2×#13093950—22no—
32#15688895C2214yescomplemented
33C22×M16×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C47×#344C2214yescomplemented
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350C2×C412yes—
44C2×#10625350C2×C412yes—
45C2×#10625350D412yes—
46C2×#10625350D412yes—
47C2×#10625350Q812yes—
48C2×#10625350C2312yes—
49C22×Dic94Q811yescharacteristic
50C22×D188Q811yescharacteristic
51C22×C22⋊D47—21no—
52C22×C4×D47—21no—
53#13094032—28no—
54#13094032C2×C4116yescomplemented
55#13094030—28no—
56#13094030—28no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329C2×C412yes—
63C2×#10625329C2×C412yes—
64C2×#10625329D412yes—
65C2×#10625329D412yes—
66C2×#10625329D412yes—
67C2×#10625329D412yes—
68C2×#10625329C2312yes—
69C2×#10625324—24no—
70M16×D47—28no—
71M16×D47—28no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8C2312yes—
74C2×C8×D47—24no—
75#13093983—21no—
76#13093983—21no—
77#13093983—21no—
78#13093983C2312yes—
79C2×C4⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×C4×Dic47—21no—
82#13093959—28no—
83#13093957—24no—
84#13093955—24no—
85#13093952—28no—
86#13093950—28no—
87C23×C4×C47C2311yescharacteristic
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47C2×C412yes—
97C2×M16×C47C2×C412yes—
98C2×M16×C47C2312yes—
99C2×M16×C47C2312yes—
100C22×C8×C47—21no—
101C22×C8×C47—21no—
102#117×C47—21no—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47C2312yes—
106C2×C4⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C42×C47—21no—
109C24×C47#4111yescharacteristic
110C23×D47—21no—
111C22×C4×C47—41no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×Q811yescharacteristic
121C22×C4×C47C2×Q811yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47C2411yescharacteristic
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C2×C22⋊D47—22no—
130C2×C22⋊D47—22no—
131C2×C22⋊D47—22no—
132C22×Dic47—21no—
133C22×Dic47—41no—
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—
144#10625350—22no—
145#10625350—22no—
146#10625350C4⋊C414yes—
147#10625350C4⋊C414yes—
148#10625350C22×C414yes—
149#10625350C2×D414yes—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188C4⋊C412yes—
154C2×D188C4⋊C412yes—
155C2×D188C2×Q812yes—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94C4⋊C412yes—
166C2×Dic94C4⋊C412yes—
167C2×Dic94C2×Q812yes—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—22no—
173M16×C47—41no—
174M16×C47—41no—
175M16×C47C22×C414yes—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
180C2×C8×C47—41no—
181C2×C8×C47—41no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47—41no—
184C22⋊C4×C47—22no—
185C22⋊C4×C47—41no—
186C42×C47—22no—
187C42×C47—41no—
188C22⋊Dic47—22no—
189C22⋊Dic47—41no—
190C4⋊Dic47—22no—
191C4⋊Dic47—41no—
192C4×Dic47—22no—
193C4×Dic47—41no—
194#10625329—22no—
195#10625329—22no—
196#10625329—41no—
197#10625329—41no—
198#10625329C22⋊C414yes—
199#10625329C22⋊C414yes—
200#10625329C22⋊C414yes—
201#10625329C22⋊C414yes—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—41no—
204C2×C47⋊C8—41no—
205C2×C47⋊C8C22×C414yes—
206C2×C47⋊C8C2×D414yes—
207C2×C47⋊C8C2×D414yes—
208#10625324—216no—
209C8×D47—216no—
210C23×C47—81no—
211C23×C47#11711yescharacteristic
212C23×C47#11711yescharacteristic
213C23×C47#12111yescharacteristic
214C23×C47#12111yescharacteristic
215C23×C47C22⋊Q811yescharacteristic
216C23×C47C22⋊Q811yescharacteristic
217C23×C47C2×#4111yescharacteristic
218C22×D47—22no—
219C22×D47—22no—
220C22×D47—22no—
221C22×D47—82no—
222C2×C4×C47—42no—
223C2×C4×C47—82no—
224C2×C4×C47C2×C22⋊C411yescharacteristic
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C2×C22⋊C411yescharacteristic
227C2×C4×C47C2×C22⋊C411yescharacteristic
228C2×C4×C47C2×C4⋊C411yescharacteristic
229C2×C4×C47C2×C4⋊C411yescharacteristic
230C2×C4×C47C2×C4⋊C411yescharacteristic
231C2×C4×C47C2×C4⋊C411yescharacteristic
232C2×C4×C47#11711yescharacteristic
233C2×C4×C47#11711yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47#12111yescharacteristic
237C2×C4×C47#12111yescharacteristic
238C2×C4×C47#12111yescharacteristic
239C2×C4×C47#12111yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47C22⋊Q811yescharacteristic
242C2×C4×C47C22⋊Q811yescharacteristic
243C2×C4×C47C22⋊Q811yescharacteristic
244C2×C4×C47C22⋊Q811yescharacteristic
245C2×C4×C47C22⋊Q811yescharacteristic
246C2×C4×C47C23×C411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C22×D411yescharacteristic
249C2×C4×C47C22×D411yescharacteristic
250C2×C4×C47C22×Q811yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C22⋊D47—24no—
253C22⋊D47—24no—
254C22⋊D47—24no—
255C22⋊D47—24no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—42no—
260C2×Dic47—82no—
261D188—22no—
262D188—22no—
263D188—22no—
264D188C2×C4⋊C414yes—
265C4×D47—24no—
266C4×D47—24no—
267C4×D47—24no—
268C4×D47—24no—
269Dic94—22no—
270Dic94—22no—
271Dic94—22no—
272Dic94C2×C4⋊C414yes—
273C8×C47—24no—
274C8×C47—42no—
275C47⋊C8—42no—
276C47⋊C8C2×C22⋊C418yes—
277#20675—471nomaximal, Sylow
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47#38011yescharacteristic
286C22×C47#38011yescharacteristic
287C22×C47#38011yescharacteristic
288C22×C47#38011yescharacteristic
289C22×C47C2×#11711yescharacteristic
290C22×C47C2×#12111yescharacteristic
291C22×C47C2×C22⋊Q811yescharacteristic
292C2×D47—24no—
293C2×D47—44no—
294C2×D47—82no—
295C2×D47—82no—
296C4×C47—82no—
297C4×C47#38011yescharacteristic
298C4×C47#38011yescharacteristic
299C4×C47#38011yescharacteristic
300C4×C47#38011yescharacteristic
301C4×C47C22×C22⋊C411yescharacteristic
302C4×C47C22×C4⋊C411yescharacteristic
303C4×C47C2×#12111yescharacteristic
304C4×C47C2×C22⋊Q811yescharacteristic
305Dic47—24no—
306Dic47—82no—
307C2×#568—471no—
308C2×#430—471no—
309#2911—471no—
310C2×#421—471no—
311C2×#421—471no—
312#1814—478no—
313C2×#344—471no—
314C2×#344D4711yescharacteristic, complemented
315C2×C47—21no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—21no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47C2×#38011yescharacteristic
323D47—44no—
324C22×#41—471no—
325#568—474no—
326#568—474no—
327#568—942no—
328#568—942no—
329C2×#131—474no—
330C2×#131—942no—
331C22×M16—471no—
332C22×M16—471no—
333C22×M16—942no—
334C22×M16C2×D4711yescharacteristic
335C22×M16C2×D4711yescharacteristic
336C2×#117—471no—
337C2×#117C2×D4711yescharacteristic
338#430—942no—
339#430—942no—
340C2×#108—474no—
341#428—942no—
342#428—942no—
343#427—474no—
344#421—474no—
345#421—474no—
346#421—942no—
347#421—942no—
348C2×#104—942no—
349C2×#104—942no—
350#344—474no—
351#344C2×D4714yescomplemented
352C47#2067511yescharacteristic, complemented, Sylow
353C2×#41—472no—
354C2×#41—472no—
355C2×#41—472no—
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—472no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C22×Q8—471no—
366C22×D4—471no—
367C22×D4—941no—
368C23×C4—941no—
369C23×C4C22×D4711yescharacteristic
370#131—4716no—
371#131—948no—
372#131—948no—
373#131—948no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—472no—
383C2×M16—472no—
384C2×M16—472no—
385C2×M16—472no—
386C2×M16—472no—
387C2×M16—472no—
388C2×M16—472no—
389C2×M16—944no—
390C2×M16—948no—
391C2×M16—948no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16—941no—
396C2×M16—941no—
397C2×M16C4×D4712yes—
398C2×M16C4×D4712yes—
399C2×M16C22×D4712yes—
400C2×M16C22×D4712yes—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—472no—
404C22×C8—944no—
405C22×C8—941no—
406#117—21no—
407#117—21no—
408#117—21no—
409#117—472no—
410#117—941no—
411#117—941no—
412#117—941no—
413#117C22×D4712yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—941no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—941no—
418C2×C42—21no—
419C2×C42—941no—
420#108—948no—
421#107—944no—
422#106—944no—
423#104—948no—
424#104—948no—
425C24—941no—
426C24#1062535011yescharacteristic
427#41—474no—
428#41—474no—
429#41—474no—
430#41—474no—
431#41—942no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443C2×Q8—472no—
444C2×Q8—472no—
445C2×Q8—472no—
446C2×Q8—941no—
447C2×Q8—941no—
448C2×Q8—941no—
449C2×D4—472no—
450C2×D4—472no—
451C2×D4—472no—
452C2×D4—942no—
453C2×D4—942no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C22×C4—41no—
462C22×C4—941no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—1881no—
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4#1062535011yescharacteristic
473C22×C4#1062535011yescharacteristic
474C22×C4#1062535011yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4D4×D4711yescharacteristic
477C22×C4D4×D4711yescharacteristic
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4711yescharacteristic
480C22×C4D4×D4711yescharacteristic
481C22×C4Q8×D4711yescharacteristic
482C22×C4Q8×D4711yescharacteristic
483C22×C4C23×D4711yescharacteristic
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—41no—
490M16—41no—
491M16—474no—
492M16—474no—
493M16—474no—
494M16—474no—
495M16—9416no—
496M16—942no—
497M16—942no—
498M16—1881no—
499M16—1881no—
500M16C2×C4×D4714yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—474no—
508C2×C8—474no—
509C2×C8—474no—
510C2×C8—9416no—
511C2×C8—942no—
512C2×C8—1881no—
513C2×C8—1881no—
514C4⋊C4—22no—
515C4⋊C4—41no—
516C4⋊C4—942no—
517C4⋊C4—1881no—
518C22⋊C4—22no—
519C22⋊C4—41no—
520C22⋊C4—942no—
521C22⋊C4—1881no—
522C42—22no—
523C42—41no—
524C42—942no—
525C42—1881no—
526C23—81no—
527C23—942no—
528C23—942no—
529C23—942no—
530C23—3762no—
531C23#1309398111yescharacteristic
532C23#1309398111yescharacteristic
533C23#1309399711yescharacteristic
534C23#1309399711yescharacteristic
535C23#1309400211yescharacteristic
536C23#1309400211yescharacteristic
537C23C2×#1062535011yescharacteristic
538Q8—474no—
539Q8—942no—
540Q8—942no—
541Q8—942no—
542D4—474no—
543D4—944no—
544D4—944no—
545D4—944no—
546D4—944no—
547D4—942no—
548D4—942no—
549D4—942no—
550C2×C4—42no—
551C2×C4—82no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—944no—
556C2×C4—944no—
557C2×C4—944no—
558C2×C4—944no—
559C2×C4—3762no—
560C2×C4—1882no—
561C2×C4C22⋊C4×D4711yescharacteristic
562C2×C4C22⋊C4×D4711yescharacteristic
563C2×C4C22⋊C4×D4711yescharacteristic
564C2×C4C22⋊C4×D4711yescharacteristic
565C2×C4C4⋊C4×D4711yescharacteristic
566C2×C4C4⋊C4×D4711yescharacteristic
567C2×C4C4⋊C4×D4711yescharacteristic
568C2×C4C4⋊C4×D4711yescharacteristic
569C2×C4#1309398111yescharacteristic
570C2×C4#1309398111yescharacteristic
571C2×C4#1309399711yescharacteristic
572C2×C4#1309399711yescharacteristic
573C2×C4#1309399711yescharacteristic
574C2×C4#1309399711yescharacteristic
575C2×C4#1309399711yescharacteristic
576C2×C4#1309399711yescharacteristic
577C2×C4#1309400211yescharacteristic
578C2×C4#1309400211yescharacteristic
579C2×C4#1309400211yescharacteristic
580C2×C4#1309400211yescharacteristic
581C2×C4#1309400211yescharacteristic
582C2×C4#1309400211yescharacteristic
583C2×C4C22×C4×D4711yescharacteristic
584C2×C4C2×D4×D4711yescharacteristic
585C2×C4C2×D4×D4711yescharacteristic
586C2×C4C2×D4×D4711yescharacteristic
587C2×C4C2×Q8×D4711yescharacteristic
588C2×C4C2×#1062535011yescharacteristic
589C8—24no—
590C8—42no—
591C8—478no—
592C8—1882no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—944no—
601C22—3762no—
602C22—3762no—
603C22—1884no—
604C22#1568898211yescharacteristic
605C22#1568898211yescharacteristic
606C22#1568898211yescharacteristic
607C22#1568898211yescharacteristic
608C22C2×#1309398111yescharacteristic
609C22C2×#1309399711yescharacteristic
610C22C2×#1309400211yescharacteristic
611C4—82no—
612C4—944no—
613C4—3762no—
614C4#1568898211yescharacteristic
615C4#1568898211yescharacteristic
616C4#1568898211yescharacteristic
617C4#1568898211yescharacteristic
618C4C2×C22⋊C4×D4711yescharacteristic
619C4C2×C4⋊C4×D4711yescharacteristic
620C4C2×#1309399711yescharacteristic
621C4C2×#1309400211yescharacteristic
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—21no—
629C2—1884no—
630C2C2×#1568898211yescharacteristic
subgroupG/H
centerC4C2×#13093997
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#344C2
socleC2×C47C2×#380
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#344D47
hypocenterC47#20675
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
2. C2×#15689171C2semidirect
3. #20251977C2semidirect
6. #20243441C2semidirect
7. C2×#15688895C2semidirect
8. C2×C47×#344C2semidirect
12. #15689889C4semidirect
13. #15689889C4semidirect
22. C2×#13093959C22semidirect
25. #15689159C22semidirect
32. #15688895C22semidirect
36. C47×#344C22semidirect
54. #13094032C2×C4semidirect
314. C2×#344D47semidirect
351. #344C2×D47semidirect
352. C47#20675semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156891712
#202519772
C2×#156891412
C2×#156891392
#202434412
C2×#156888952
C2×C47×#3442
#2067547