Finite Group Databasebeta

← #26123614

Subgroups — #26123614

Order 12032.

898 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689139C211yesmaximal, characteristic
2C22×#13093950C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5C2×#15688884C211yesmaximal, characteristic, complemented
6#20243081C211yesmaximal, characteristic, complemented
7C2×C47×#430C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C22×C4×Dic47C2211yescharacteristic
12#15689139—22no—
13#15689139—22no—
14C2×#13093950—22no—
15C2×#13093950—22no—
16C2×#13093950—22no—
17C2×#13093950C414yescomplemented
18#15689091—22no—
19#15689089—22no—
20#15689086—22no—
21#15688895—22no—
22#15688884—22no—
23#15688877—22no—
24C22×M16×C47C2211yescharacteristic
25C22×M16×C47C2211yescharacteristic
26C22×M16×C47C2211yescharacteristic
27C47×#430—22no—
28C47×#430—22no—
29C2×#108×C47—22no—
30C2×#10625350—21no—
31C2×#10625350—21no—
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×#10625350D412yes—
42C22×Dic94Q811yescharacteristic
43C22×D188Q811yescharacteristic
44C22×C22⋊D47—21no—
45C23×Dic47—21no—
46C22×C4×D47—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C22×C47⋊C8D412yes—
54#13093983—21no—
55#13093983—21no—
56#13093983—21no—
57#13093983D412yes—
58C2×C4⋊Dic47—21no—
59C2×C22⋊Dic47—21no—
60C2×C4×Dic47—21no—
61C2×C4×Dic47—21no—
62C2×C4×Dic47—21no—
63C2×C4×Dic47—21no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47C2×C412yes—
67#13093950—28no—
68#13093950—28no—
69(C2×D47)⋊C8—28no—
70C23×C4×C47C2311yescharacteristic
71C2×M16×C47—21no—
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C2×M16×C47C2×C412yes—
85C2×M16×C47D412yes—
86C2×M16×C47D412yes—
87C2×M16×C47D412yes—
88C2×M16×C47D412yes—
89C22×C8×C47—21no—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92#108×C47—28no—
93C24×C47#4111yescharacteristic
94C23×D47—21no—
95C22×C4×C47C22×C411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×Q811yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C2×C22⋊D47—22no—
110C2×C22⋊D47—22no—
111C2×C22⋊D47—41no—
112C2×C22⋊D47—41no—
113C2×C22⋊D47—41no—
114C2×C22⋊D47—41no—
115C22×Dic47—22no—
116C22×Dic47—21no—
117C22×Dic47—44no—
118C22×Dic47—41no—
119C22×Dic47—41no—
120C22×Dic47—41no—
121#10625350—22no—
122#10625350—22no—
123#10625350—22no—
124#10625350—22no—
125#10625350—22no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—41no—
130#10625350—41no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188C4⋊C412yes—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—41no—
146C2×C4×D47—41no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94C4⋊C412yes—
155M16×C47—22no—
156M16×C47—22no—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—41no—
163M16×C47—41no—
164M16×C47—41no—
165M16×C47—41no—
166M16×C47C22⋊C414yes—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—41no—
173C2×C8×C47—41no—
174C2×C8×C47—41no—
175C2×C8×C47—41no—
176C22⋊Dic47—22no—
177C22⋊Dic47—41no—
178C4⋊Dic47—22no—
179C4⋊Dic47—41no—
180C4×Dic47—22no—
181C4×Dic47—22no—
182C4×Dic47—22no—
183C4×Dic47—41no—
184C4×Dic47—41no—
185C4×Dic47—41no—
186#10625329—41no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C23×C47—42no—
194C23×C47C4×D411yescharacteristic
195C23×C47#12111yescharacteristic
196C23×C47C22⋊Q811yescharacteristic
197C23×C47#12311yescharacteristic
198C23×C47#12411yescharacteristic
199C23×C47#12411yescharacteristic
200C23×C47#12611yescharacteristic
201C22×D47—22no—
202C22×D47—41no—
203C22×D47—41no—
204C22×D47—82no—
205C2×C4×C47C2×C22⋊C411yescharacteristic
206C2×C4×C47C2×C4⋊C411yescharacteristic
207C2×C4×C47#11711yescharacteristic
208C2×C4×C47C4×D411yescharacteristic
209C2×C4×C47C4×D411yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47#12011yescharacteristic
212C2×C4×C47#12011yescharacteristic
213C2×C4×C47#12011yescharacteristic
214C2×C4×C47#12111yescharacteristic
215C2×C4×C47#12111yescharacteristic
216C2×C4×C47#12111yescharacteristic
217C2×C4×C47#12111yescharacteristic
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12111yescharacteristic
220C2×C4×C47#12111yescharacteristic
221C2×C4×C47C22⋊Q811yescharacteristic
222C2×C4×C47C22⋊Q811yescharacteristic
223C2×C4×C47C22⋊Q811yescharacteristic
224C2×C4×C47C22⋊Q811yescharacteristic
225C2×C4×C47C22⋊Q811yescharacteristic
226C2×C4×C47#12311yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12311yescharacteristic
230C2×C4×C47#12411yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12711yescharacteristic
233C22⋊D47—42no—
234C22⋊D47—42no—
235C22⋊D47—42no—
236C22⋊D47—42no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—42no—
240C2×Dic47—44no—
241C2×Dic47—44no—
242C2×Dic47—42no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—42no—
246C2×Dic47—82no—
247D188—22no—
248D188—22no—
249D188—41no—
250D188—41no—
251C4×D47—42no—
252C4×D47—42no—
253C4×D47—42no—
254C4×D47—42no—
255Dic94—22no—
256Dic94—22no—
257Dic94—41no—
258Dic94—41no—
259C8×C47—24no—
260C8×C47—42no—
261C8×C47—42no—
262C47⋊C8—42no—
263#11114—471nomaximal, Sylow
264C22×C47—22no—
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47#38511yescharacteristic
272C22×C47#38811yescharacteristic
273C22×C47#39011yescharacteristic
274C22×C47#39311yescharacteristic
275C22×C47#39411yescharacteristic
276C22×C47#39611yescharacteristic
277C22×C47#39711yescharacteristic
278C2×D47—44no—
279C2×D47—42no—
280C2×D47—82no—
281C2×D47—82no—
282C4×C47#38011yescharacteristic
283C4×C47#38511yescharacteristic
284C4×C47#38611yescharacteristic
285C4×C47#38811yescharacteristic
286C4×C47#39211yescharacteristic
287C4×C47#39411yescharacteristic
288C4×C47#39611yescharacteristic
289C4×C47#39911yescharacteristic
290Dic47—44no—
291Dic47—42no—
292Dic47—82no—
293C2×#430D4711yescharacteristic, complemented
294C2×#421—471no—
295C22×#104—471no—
296#2879—471no—
297C2×#344—471no—
298C2×#339—471no—
299#1728—471no—
300C2×C47—21no—
301C2×C47—21no—
302C2×C47—21no—
303C2×C47—21no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47#143911yescharacteristic
307C2×C47#186112yes—
308D47—82no—
309C22×#41—471no—
310C22×M16—471no—
311C22×M16C2×D4711yescharacteristic
312C22×M16C2×D4711yescharacteristic
313C22×M16C2×D4711yescharacteristic
314C2×#117—471no—
315C22×C42—471no—
316#430—22no—
317#430—22no—
318C2×#108—22no—
319#421—942no—
320#421—942no—
321C2×#104—474no—
322C2×#104—942no—
323C2×#104—942no—
324C2×#104—942no—
325#408—942no—
326#408—942no—
327#407—942no—
328#344—942no—
329#339—942no—
330#336—942no—
331C47#1111411yescharacteristic, complemented, Sylow
332C2×#41—472no—
333C2×#41—472no—
334C2×#41—941no—
335C2×#41—941no—
336C2×#41—941no—
337C2×#41—941no—
338C2×#41—941no—
339C2×#41—941no—
340C2×#41—941no—
341C2×#41—941no—
342C2×#41—941no—
343C2×#41—941no—
344C22×Q8—471no—
345C22×D4—471no—
346C22×D4—941no—
347C23×C4—941no—
348C23×C4—941no—
349C23×C4C22×D4711yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16C4×D4712yes—
370C2×M16D18812yes—
371C2×M16C22⋊D4712yes—
372C2×M16C22⋊D4712yes—
373C2×M16C22⋊D4712yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—472no—
378#117—472no—
379#117—941no—
380#117—941no—
381#117—941no—
382C2×C4⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C42—472no—
385C2×C42—941no—
386C2×C42—941no—
387C2×C42—941no—
388C2×C42—941no—
389C2×C42—941no—
390C2×C42—941no—
391#108—28no—
392#104—948no—
393#104—948no—
394C22⋊C8—948no—
395C24—941no—
396C24#1062535411yescharacteristic
397#41—942no—
398#41—942no—
399#41—942no—
400#41—942no—
401#41—942no—
402#41—942no—
403#41—942no—
404#41—942no—
405#41—1881no—
406#41—1881no—
407#41—1881no—
408#41—1881no—
409#41—1881no—
410#41—1881no—
411#41—1881no—
412#41—1881no—
413C2×Q8—472no—
414C2×Q8—941no—
415C2×Q8—941no—
416C2×Q8—941no—
417C2×Q8—941no—
418C2×Q8—941no—
419C2×D4—472no—
420C2×D4—942no—
421C2×D4—942no—
422C2×D4—941no—
423C2×D4—941no—
424C2×D4—941no—
425C2×D4—941no—
426C2×D4—941no—
427C2×D4—1881no—
428C2×D4—1881no—
429C2×D4—1881no—
430C2×D4—1881no—
431C22×C4—942no—
432C22×C4—941no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—1884no—
436C22×C4—1881no—
437C22×C4—1881no—
438C22×C4—1881no—
439C22×C4—1881no—
440C22×C4—1881no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4C2×C4×D4711yescharacteristic
444C22×C4C2×D18811yescharacteristic
445C22×C4#1062535011yescharacteristic
446C22×C4#1062535011yescharacteristic
447C22×C4D4×D4711yescharacteristic
448C22×C4D4×D4711yescharacteristic
449C22×C4D4×D4711yescharacteristic
450C22×C4#1062535211yescharacteristic
451C22×C4Q8×D4711yescharacteristic
452C22×C4#1062535411yescharacteristic
453C22×C4#1062535411yescharacteristic
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—1881no—
469M16—1881no—
470M16—1881no—
471M16—1881no—
472M16(C2×D47)⋊C414yes—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—942no—
483C2×C8—942no—
484C2×C8—942no—
485C4⋊C4—942no—
486C4⋊C4—1881no—
487C22⋊C4—942no—
488C22⋊C4—1881no—
489C42—942no—
490C42—942no—
491C42—942no—
492C42—1881no—
493C42—1881no—
494C42—1881no—
495C23—42no—
496C23—942no—
497C23—3762no—
498C23—1881no—
499C23—1881no—
500C23#1309398611yescharacteristic
501C23#1309399911yescharacteristic
502C23#1309400011yescharacteristic
503C23#1309400911yescharacteristic
504C23#1309401311yescharacteristic
505C23#1309401311yescharacteristic
506C23#1309401911yescharacteristic
507Q8—942no—
508Q8—942no—
509Q8—1881no—
510Q8—1881no—
511D4—942no—
512D4—942no—
513D4—1882no—
514D4—1882no—
515D4—1882no—
516D4—1882no—
517D4—1881no—
518D4—1881no—
519C2×C4—944no—
520C2×C4—942no—
521C2×C4—3762no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1884no—
525C2×C4—1884no—
526C2×C4—1882no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4C2×(C2×D47)⋊C411yescharacteristic
534C2×C4C4⋊C4×D4711yescharacteristic
535C2×C4#1309398211yescharacteristic
536C2×C4C4×C22⋊D4711yescharacteristic
537C2×C4C4×C22⋊D4711yescharacteristic
538C2×C4#1309398611yescharacteristic
539C2×C4#1309399211yescharacteristic
540C2×C4#1309399211yescharacteristic
541C2×C4#1309399311yescharacteristic
542C2×C4#1309399511yescharacteristic
543C2×C4#1309399611yescharacteristic
544C2×C4#1309399611yescharacteristic
545C2×C4#1309399811yescharacteristic
546C2×C4#1309399811yescharacteristic
547C2×C4#1309399911yescharacteristic
548C2×C4#1309399911yescharacteristic
549C2×C4#1309400011yescharacteristic
550C2×C4#1309400011yescharacteristic
551C2×C4#1309400211yescharacteristic
552C2×C4#1309400211yescharacteristic
553C2×C4#1309400411yescharacteristic
554C2×C4#1309400711yescharacteristic
555C2×C4#1309400911yescharacteristic
556C2×C4#1309400911yescharacteristic
557C2×C4#1309400911yescharacteristic
558C2×C4#1309401311yescharacteristic
559C2×C4#1309401911yescharacteristic
560C2×C4#1309402011yescharacteristic
561C8—24no—
562C8—42no—
563C8—42no—
564C8—1882no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—3762no—
573C22—3762no—
574C22—1884no—
575C22—1882no—
576C22#1568899411yescharacteristic
577C22#1568901311yescharacteristic
578C22#1568902411yescharacteristic
579C22#1568903411yescharacteristic
580C22#1568904011yescharacteristic
581C22#1568904511yescharacteristic
582C22#1568904911yescharacteristic
583C4—3762no—
584C4—1884no—
585C4—1882no—
586C4#1568898011yescharacteristic
587C4#1568899411yescharacteristic
588C4#1568900211yescharacteristic
589C4#1568901311yescharacteristic
590C4#1568903111yescharacteristic
591C4#1568904011yescharacteristic
592C4#1568904511yescharacteristic
593C4#1568905811yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—3762no—
601C2#2024163011yescharacteristic
602C2#2024362512yes—
subgroupG/H
centerC2×C4#13093992
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#430C2
socleC22×C47#385
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#430D47
hypocenterC47#11114
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. C2×#15688884C2semidirect
6. #20243081C2semidirect
7. C2×C47×#430C2semidirect
17. C2×#13093950C4semidirect
293. C2×#430D47semidirect
331. C47#11114semidirect

Maximal subgroups

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

subgroupindex
C2×#156891392
C22×#130939502
#202518322
C2×#156888952
C2×#156888842
#202430812
C2×C47×#4302
#1111447