Finite Group Databasebeta

← #26123642

Subgroups — #26123642

Order 12032.

852 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689139C211yesmaximal, characteristic
2C2×#15689139C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4C2×#15688894C211yesmaximal, characteristic, complemented
5#20243126C211yesmaximal, characteristic, complemented
6#20243099C211yesmaximal, characteristic, complemented
7C2×C47×#430C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689139—22no—
13#15689139—22no—
14#15689139—22no—
15#15689139C414yescomplemented
16C2×#13093950—22no—
17C2×#13093950—22no—
18#15689091—22no—
19#15689089—22no—
20#15689086—22no—
21#15688894—22no—
22#15688891—22no—
23#15688884—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—
45C22×C4×D47—21no—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329D412yes—
52C22×C47⋊C8—21no—
53#13093983—21no—
54#13093983—21no—
55#13093983—21no—
56#13093983—21no—
57#13093983—21no—
58#13093983—21no—
59#13093983—21no—
60#13093983C2×C412yes—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C22⋊Dic47—21no—
64C2×C22⋊Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47D412yes—
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—21no—
116C22×Dic47—22no—
117C22×Dic47—41no—
118#10625350—22no—
119#10625350—22no—
120#10625350—22no—
121#10625350—22no—
122#10625350—22no—
123#10625350—22no—
124#10625350—22no—
125#10625350—22no—
126#10625350—41no—
127#10625350—41no—
128#10625350—41no—
129#10625350—41no—
130#10625350—41no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134C2×D188—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188C4⋊C412yes—
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—41no—
143C2×C4×D47—41no—
144C2×C4×D47—41no—
145C2×C4×D47—41no—
146C2×Dic94—21no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94C4⋊C412yes—
152M16×C47—22no—
153M16×C47—22no—
154M16×C47—22no—
155M16×C47—22no—
156M16×C47—22no—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—41no—
160M16×C47—41no—
161M16×C47—41no—
162M16×C47—41no—
163M16×C47C22⋊C414yes—
164C2×C8×C47—22no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C2×C8×C47—41no—
172C2×C8×C47—41no—
173C22⋊Dic47—22no—
174C22⋊Dic47—41no—
175C22⋊Dic47—41no—
176C22⋊Dic47—41no—
177C4⋊Dic47—22no—
178C4⋊Dic47—41no—
179C4⋊Dic47—41no—
180C4⋊Dic47—41no—
181C4×Dic47—22no—
182C4×Dic47—22no—
183C4×Dic47—22no—
184C4×Dic47—41no—
185#10625329—22no—
186#10625329—22no—
187#10625329—41no—
188#10625329—41no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C23×C47—81no—
193C23×C47C4×D411yescharacteristic
194C23×C47#12111yescharacteristic
195C23×C47C22⋊Q811yescharacteristic
196C23×C47#12311yescharacteristic
197C23×C47#12411yescharacteristic
198C23×C47#12411yescharacteristic
199C23×C47#12611yescharacteristic
200C22×D47—22no—
201C22×D47—41no—
202C22×D47—41no—
203C22×D47—82no—
204C2×C4×C47C2×C22⋊C411yescharacteristic
205C2×C4×C47C2×C4⋊C411yescharacteristic
206C2×C4×C47#11711yescharacteristic
207C2×C4×C47C4×D411yescharacteristic
208C2×C4×C47C4×D411yescharacteristic
209C2×C4×C47C4×D411yescharacteristic
210C2×C4×C47#12011yescharacteristic
211C2×C4×C47#12011yescharacteristic
212C2×C4×C47#12011yescharacteristic
213C2×C4×C47#12111yescharacteristic
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×C47C22⋊Q811yescharacteristic
221C2×C4×C47C22⋊Q811yescharacteristic
222C2×C4×C47C22⋊Q811yescharacteristic
223C2×C4×C47C22⋊Q811yescharacteristic
224C2×C4×C47C22⋊Q811yescharacteristic
225C2×C4×C47#12311yescharacteristic
226C2×C4×C47#12311yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12411yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12711yescharacteristic
232C22⋊D47—42no—
233C22⋊D47—42no—
234C22⋊D47—42no—
235C22⋊D47—42no—
236C2×Dic47—22no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—82no—
242C2×Dic47—82no—
243D188—22no—
244D188—22no—
245D188—41no—
246D188—41no—
247C4×D47—42no—
248C4×D47—42no—
249C4×D47—42no—
250C4×D47—42no—
251Dic94—22no—
252Dic94—22no—
253Dic94—41no—
254Dic94—41no—
255C8×C47—24no—
256C8×C47—42no—
257C8×C47—42no—
258C47⋊C8—42no—
259#11118—471nomaximal, Sylow
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47#38511yescharacteristic
268C22×C47#38811yescharacteristic
269C22×C47#39011yescharacteristic
270C22×C47#39311yescharacteristic
271C22×C47#39411yescharacteristic
272C22×C47#39611yescharacteristic
273C22×C47#39711yescharacteristic
274C2×D47—44no—
275C2×D47—42no—
276C2×D47—82no—
277C2×D47—82no—
278C4×C47#38011yescharacteristic
279C4×C47#38511yescharacteristic
280C4×C47#38611yescharacteristic
281C4×C47#38811yescharacteristic
282C4×C47#39211yescharacteristic
283C4×C47#39411yescharacteristic
284C4×C47#39611yescharacteristic
285C4×C47#39911yescharacteristic
286Dic47—42no—
287Dic47—82no—
288Dic47—82no—
289C2×#430D4711yescharacteristic, complemented
290C2×#421—471no—
291C2×#421—471no—
292#2879—471no—
293C2×#344—471no—
294#1742—471no—
295#1733—471no—
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—21no—
300C2×C47—21no—
301C2×C47—21no—
302C2×C47—21no—
303C2×C47#143911yescharacteristic
304D47—82no—
305C22×#41—471no—
306C22×M16—471no—
307C22×M16C2×D4711yescharacteristic
308C22×M16C2×D4711yescharacteristic
309C22×M16C2×D4711yescharacteristic
310C2×#117—471no—
311C2×#117—471no—
312#430—22no—
313#430—22no—
314C2×#108—22no—
315#421—474no—
316#421—942no—
317#421—942no—
318#421—942no—
319C2×#104—942no—
320C2×#104—942no—
321#408—942no—
322#408—942no—
323#407—942no—
324#344—942no—
325#343—942no—
326#339—942no—
327C47#1111811yescharacteristic, complemented, Sylow
328C2×#41—472no—
329C2×#41—472no—
330C2×#41—941no—
331C2×#41—941no—
332C2×#41—941no—
333C2×#41—941no—
334C2×#41—941no—
335C2×#41—941no—
336C2×#41—941no—
337C2×#41—941no—
338C2×#41—941no—
339C2×#41—941no—
340C22×Q8—471no—
341C22×D4—471no—
342C22×D4—941no—
343C23×C4—941no—
344C23×C4C22×D4711yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
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—472no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16C4×D4712yes—
365C2×M16D18812yes—
366C2×M16C22⋊D4712yes—
367C2×M16C22⋊D4712yes—
368C2×M16C22⋊D4712yes—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—941no—
373#117—472no—
374#117—941no—
375#117—941no—
376#117—941no—
377#117—941no—
378#117—941no—
379#117—941no—
380#117—941no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C42—472no—
386C2×C42—941no—
387#108—28no—
388#104—948no—
389#104—948no—
390C22⋊C8—948no—
391C24—941no—
392C24#1062535411yescharacteristic
393#41—942no—
394#41—942no—
395#41—942no—
396#41—942no—
397#41—942no—
398#41—942no—
399#41—942no—
400#41—942no—
401#41—1881no—
402#41—1881no—
403#41—1881no—
404#41—1881no—
405#41—1881no—
406#41—1881no—
407#41—1881no—
408#41—1881no—
409C2×Q8—472no—
410C2×Q8—941no—
411C2×Q8—941no—
412C2×Q8—941no—
413C2×Q8—941no—
414C2×Q8—941no—
415C2×D4—472no—
416C2×D4—942no—
417C2×D4—942no—
418C2×D4—941no—
419C2×D4—941no—
420C2×D4—941no—
421C2×D4—941no—
422C2×D4—941no—
423C2×D4—1881no—
424C2×D4—1881no—
425C2×D4—1881no—
426C2×D4—1881no—
427C22×C4—941no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—1881no—
432C22×C4—1881no—
433C22×C4—1881no—
434C22×C4—1881no—
435C22×C4—1881no—
436C22×C4C2×C4×D4711yescharacteristic
437C22×C4C2×D18811yescharacteristic
438C22×C4#1062535011yescharacteristic
439C22×C4#1062535011yescharacteristic
440C22×C4D4×D4711yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4D4×D4711yescharacteristic
443C22×C4#1062535211yescharacteristic
444C22×C4Q8×D4711yescharacteristic
445C22×C4#1062535411yescharacteristic
446C22×C4#1062535411yescharacteristic
447C22×C4C2×C22⋊D4711yescharacteristic
448C22×C4C2×C22⋊D4711yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450M16—22no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—41no—
458M16—41no—
459M16—41no—
460M16—41no—
461M16—942no—
462M16—942no—
463M16—1881no—
464M16—1881no—
465M16(C2×D47)⋊C414yes—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—942no—
476C2×C8—1881no—
477C2×C8—1881no—
478C4⋊C4—942no—
479C4⋊C4—1881no—
480C4⋊C4—1881no—
481C4⋊C4—1881no—
482C22⋊C4—942no—
483C22⋊C4—1881no—
484C22⋊C4—1881no—
485C22⋊C4—1881no—
486C42—942no—
487C42—942no—
488C42—942no—
489C42—1881no—
490C23—81no—
491C23—942no—
492C23—3762no—
493C23—1881no—
494C23—1881no—
495C23#1309398611yescharacteristic
496C23#1309399911yescharacteristic
497C23#1309400011yescharacteristic
498C23#1309400911yescharacteristic
499C23#1309401311yescharacteristic
500C23#1309401311yescharacteristic
501C23#1309401911yescharacteristic
502Q8—942no—
503Q8—942no—
504Q8—1881no—
505Q8—1881no—
506D4—942no—
507D4—942no—
508D4—1882no—
509D4—1882no—
510D4—1882no—
511D4—1882no—
512D4—1881no—
513D4—1881no—
514C2×C4—942no—
515C2×C4—3762no—
516C2×C4—3762no—
517C2×C4—1882no—
518C2×C4—1882no—
519C2×C4—1881no—
520C2×C4—1881no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4C2×(C2×D47)⋊C411yescharacteristic
526C2×C4C4⋊C4×D4711yescharacteristic
527C2×C4#1309398211yescharacteristic
528C2×C4C4×C22⋊D4711yescharacteristic
529C2×C4C4×C22⋊D4711yescharacteristic
530C2×C4#1309398611yescharacteristic
531C2×C4#1309399211yescharacteristic
532C2×C4#1309399211yescharacteristic
533C2×C4#1309399311yescharacteristic
534C2×C4#1309399511yescharacteristic
535C2×C4#1309399611yescharacteristic
536C2×C4#1309399611yescharacteristic
537C2×C4#1309399811yescharacteristic
538C2×C4#1309399811yescharacteristic
539C2×C4#1309399911yescharacteristic
540C2×C4#1309399911yescharacteristic
541C2×C4#1309400011yescharacteristic
542C2×C4#1309400011yescharacteristic
543C2×C4#1309400211yescharacteristic
544C2×C4#1309400211yescharacteristic
545C2×C4#1309400411yescharacteristic
546C2×C4#1309400711yescharacteristic
547C2×C4#1309400911yescharacteristic
548C2×C4#1309400911yescharacteristic
549C2×C4#1309400911yescharacteristic
550C2×C4#1309401311yescharacteristic
551C2×C4#1309401911yescharacteristic
552C2×C4#1309402011yescharacteristic
553C8—24no—
554C8—42no—
555C8—42no—
556C8—1882no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—3762no—
565C22—3762no—
566C22—1884no—
567C22—1882no—
568C22#1568899411yescharacteristic
569C22#1568901311yescharacteristic
570C22#1568902411yescharacteristic
571C22#1568903411yescharacteristic
572C22#1568904011yescharacteristic
573C22#1568904511yescharacteristic
574C22#1568904911yescharacteristic
575C4—3762no—
576C4—3762no—
577C4—1882no—
578C4#1568898011yescharacteristic
579C4#1568899411yescharacteristic
580C4#1568900211yescharacteristic
581C4#1568901311yescharacteristic
582C4#1568903111yescharacteristic
583C4#1568904011yescharacteristic
584C4#1568904511yescharacteristic
585C4#1568905811yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—3762no—
594C2#2024163011yescharacteristic
subgroupG/H
centerC4#15689031
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#430C2
socleC2×C47#1439
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#430D47
hypocenterC47#11118
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
4. C2×#15688894C2semidirect
5. #20243126C2semidirect
6. #20243099C2semidirect
7. C2×C47×#430C2semidirect
15. #15689139C4semidirect
289. C2×#430D47semidirect
327. C47#11118semidirect

Maximal subgroups

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

subgroupindex
C2×#156891392
#202518322
C2×#156888942
#202431262
#202430992
C2×C47×#4302
#1111847