Finite Group Databasebeta

← #26123744

Subgroups — #26123744

Order 12032.

864 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251978C211yesmaximal, characteristic, complemented
2C2×#15689139C211yesmaximal, characteristic
3#20251908C211yesmaximal, characteristic
4C2×#15689096C211yesmaximal, characteristic
5#20243121C211yesmaximal, characteristic, complemented
6C2×#15688880C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C2×#13093983C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689165—22no—
13#15689165—22no—
14#15689161—22no—
15#15689139—22no—
16#15689139—22no—
17C2×#13093950—22no—
18#15689133C412yescomplemented
19#15689129C412yescomplemented
20#15689125—22no—
21#15689120—22no—
22#15689096—22no—
23#15689096—22no—
24C2×#13093938—22no—
25#15688890—22no—
26#15688880—22no—
27C22×M16×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C47×#344—22no—
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×#10625350—21no—
41C2×#10625350D412yes—
42C2×#10625350Q812yes—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47—21no—
46C22×C4×D47—21no—
47#13093983—21no—
48#13093983—21no—
49#13093983—21no—
50#13093983—21no—
51#13093983—21no—
52#13093983—21no—
53#13093983—21no—
54#13093983—21no—
55#13093983—21no—
56#13093983C2×C412yes—
57#13093983D412yes—
58#13093983D412yes—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C22⋊Dic47—21no—
63C2×C22⋊Dic47—21no—
64C2×C22⋊Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68#13093958—24no—
69#13093956—24no—
70#13093950—28no—
71#13093949—24no—
72#13093946—24no—
73#13093938—28no—
74C23×C4×C47C2311yescharacteristic
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—
87C22×C8×C47—21no—
88C22×C8×C47D412yes—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C22⋊C4×C47D412yes—
95C2×C42×C47—21no—
96C24×C47C2×D411yescharacteristic
97C23×D47—21no—
98C22×C4×C47—22no—
99C22×C4×C47C22×C411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×Q811yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C2×C22⋊D47—22no—
114C2×C22⋊D47—22no—
115C2×C22⋊D47—41no—
116C2×C22⋊D47—41no—
117C2×C22⋊D47—41no—
118C2×C22⋊D47—41no—
119C22×Dic47—21no—
120C22×Dic47—41no—
121C22×Dic47—41no—
122C22×Dic47—41no—
123#10625350—22no—
124#10625350—22no—
125#10625350—22no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188C4⋊C412yes—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×C4×D47—41no—
150C2×C4×D47—41no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94C4⋊C412yes—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47—22no—
163M16×C47—41no—
164M16×C47—41no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47C22⋊C414yes—
171C4⋊C4×C47—41no—
172C4⋊C4×C47—41no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—22no—
175C42×C47—41no—
176C42×C47—41no—
177C22⋊Dic47—22no—
178C22⋊Dic47—22no—
179C22⋊Dic47—22no—
180C22⋊Dic47—41no—
181C22⋊Dic47—41no—
182C22⋊Dic47—41no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47—22no—
186C4⋊Dic47—41no—
187C4⋊Dic47—41no—
188C4⋊Dic47—41no—
189C4×Dic47—22no—
190C4×Dic47—22no—
191C4×Dic47—22no—
192C4×Dic47—41no—
193C4×Dic47—41no—
194C4×Dic47—41no—
195C23×C47—81no—
196C23×C47C4×D411yescharacteristic
197C23×C47#12011yescharacteristic
198C23×C47#12111yescharacteristic
199C23×C47#12111yescharacteristic
200C23×C47C22⋊Q811yescharacteristic
201C23×C47#12311yescharacteristic
202C23×C47#12711yescharacteristic
203C22×D47—22no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—82no—
207C2×C4×C47—42no—
208C2×C4×C47—82no—
209C2×C4×C47C2×C22⋊C411yescharacteristic
210C2×C4×C47C2×C4⋊C411yescharacteristic
211C2×C4×C47#11711yescharacteristic
212C2×C4×C47C4×D411yescharacteristic
213C2×C4×C47C4×D411yescharacteristic
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47#12011yescharacteristic
216C2×C4×C47#12011yescharacteristic
217C2×C4×C47#12111yescharacteristic
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12111yescharacteristic
220C2×C4×C47#12111yescharacteristic
221C2×C4×C47#12111yescharacteristic
222C2×C4×C47#12111yescharacteristic
223C2×C4×C47C22⋊Q811yescharacteristic
224C2×C4×C47C22⋊Q811yescharacteristic
225C2×C4×C47C22⋊Q811yescharacteristic
226C2×C4×C47C22⋊Q811yescharacteristic
227C2×C4×C47C22⋊Q811yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12311yescharacteristic
230C2×C4×C47#12311yescharacteristic
231C2×C4×C47#12311yescharacteristic
232C2×C4×C47#12411yescharacteristic
233C2×C4×C47#12411yescharacteristic
234C2×C4×C47#12411yescharacteristic
235C2×C4×C47#12611yescharacteristic
236C2×C4×C47#12611yescharacteristic
237C22⋊D47—42no—
238C22⋊D47—42no—
239C22⋊D47—42no—
240C22⋊D47—42no—
241C2×Dic47—22no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—82no—
248C2×Dic47—82no—
249C2×Dic47—82no—
250D188—22no—
251D188—22no—
252D188—41no—
253D188—41no—
254C4×D47—42no—
255C4×D47—42no—
256C4×D47—42no—
257C4×D47—42no—
258Dic94—22no—
259Dic94—22no—
260Dic94—41no—
261Dic94—41no—
262C8×C47—24no—
263C8×C47—42no—
264#11132—471nomaximal, Sylow
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47#38511yescharacteristic
273C22×C47#38811yescharacteristic
274C22×C47#39011yescharacteristic
275C22×C47#39211yescharacteristic
276C22×C47#39411yescharacteristic
277C22×C47#39611yescharacteristic
278C22×C47#39911yescharacteristic
279C2×D47—42no—
280C2×D47—82no—
281C2×D47—82no—
282C2×D47—82no—
283C4×C47—82no—
284C4×C47#38011yescharacteristic
285C4×C47#38511yescharacteristic
286C4×C47#38611yescharacteristic
287C4×C47#38811yescharacteristic
288C4×C47#39311yescharacteristic
289C4×C47#39411yescharacteristic
290C4×C47#39611yescharacteristic
291C4×C47#39711yescharacteristic
292Dic47—42no—
293Dic47—82no—
294Dic47—82no—
295Dic47—82no—
296#2911—471no—
297C2×#421—471no—
298#2896—471no—
299C2×#410—471no—
300C2×#344D4711yescharacteristic, complemented
301#1740—471no—
302C2×H(3,ℤ/4)—471no—
303C2×C47—21no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47—21no—
307C2×C47—21no—
308C2×C47—21no—
309C2×C47—21no—
310C2×C47#143911yescharacteristic
311D47—82no—
312C22×#41—471no—
313C22×M16C2×D4711yescharacteristic
314C22×M16C2×D4711yescharacteristic
315C2×#117—471no—
316C2×#117—471no—
317C2×#117—471no—
318C2×#117C2×D4711yescharacteristic
319#428—942no—
320#428—942no—
321#427—942no—
322#421—942no—
323#421—942no—
324C2×#104—942no—
325#419—472no—
326#418—472no—
327#417—942no—
328#416—942no—
329#410—942no—
330#410—942no—
331C2×#99—942no—
332#344—22no—
333#342—942no—
334H(3,ℤ/4)—942no—
335C47#1113211yescharacteristic, complemented, Sylow
336C2×#41—472no—
337C2×#41—472no—
338C2×#41—941no—
339C2×#41—941no—
340C2×#41—941no—
341C2×#41—941no—
342C2×#41—941no—
343C2×#41—941no—
344C2×#41—941no—
345C2×#41—941no—
346C2×#41—941no—
347C2×#41—941no—
348C22×Q8—471no—
349C22×D4—471no—
350C22×D4—941no—
351C23×C4—941no—
352C23×C4C22×D4711yescharacteristic
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×M16C4×D4712yes—
363C2×M16D18812yes—
364C2×M16C22⋊D4712yes—
365C22×C8—21no—
366C22×C8D18812yes—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—472no—
372#117—472no—
373#117—472no—
374#117—941no—
375#117—941no—
376#117—941no—
377#117—941no—
378#117—941no—
379#117—941no—
380#117—941no—
381#117—941no—
382#117—941no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—941no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—941no—
387C2×C22⋊C4—941no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—941no—
390C2×C22⋊C4D18812yes—
391C2×C42—21no—
392C2×C42—941no—
393C2×C42—941no—
394C2×C42—941no—
395#107—944no—
396#106—944no—
397#104—948no—
398#103—944no—
399#102—944no—
400#99—948no—
401C24—941no—
402C24C2×D18811yescharacteristic
403#41—942no—
404#41—942no—
405#41—942no—
406#41—942no—
407#41—942no—
408#41—942no—
409#41—942no—
410#41—942no—
411#41—1881no—
412#41—1881no—
413#41—1881no—
414#41—1881no—
415#41—1881no—
416#41—1881no—
417#41—1881no—
418#41—1881no—
419C2×Q8—472no—
420C2×Q8—941no—
421C2×Q8—941no—
422C2×Q8—941no—
423C2×Q8—941no—
424C2×Q8—941no—
425C2×D4—472no—
426C2×D4—942no—
427C2×D4—942no—
428C2×D4—941no—
429C2×D4—941no—
430C2×D4—941no—
431C2×D4—941no—
432C2×D4—941no—
433C2×D4—1881no—
434C2×D4—1881no—
435C2×D4—1881no—
436C2×D4—1881no—
437C22×C4—22no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4—1881no—
447C22×C4—1881no—
448C22×C4C2×C4×D4711yescharacteristic
449C22×C4C2×D18811yescharacteristic
450C22×C4C2×D18811yescharacteristic
451C22×C4#1062535011yescharacteristic
452C22×C4#1062535011yescharacteristic
453C22×C4D4×D4711yescharacteristic
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4#1062535211yescharacteristic
457C22×C4#1062535211yescharacteristic
458C22×C4#1062535211yescharacteristic
459C22×C4Q8×D4711yescharacteristic
460C22×C4#1062535411yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8(C2×D47)⋊C414yes—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—942no—
479C4⋊C4—942no—
480C4⋊C4—942no—
481C4⋊C4—1881no—
482C4⋊C4—1881no—
483C4⋊C4—1881no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—942no—
487C22⋊C4—942no—
488C22⋊C4—942no—
489C22⋊C4—1881no—
490C22⋊C4—1881no—
491C22⋊C4—1881no—
492C42—41no—
493C42—41no—
494C42—942no—
495C42—942no—
496C42—942no—
497C42—1881no—
498C42—1881no—
499C42—1881no—
500C23—81no—
501C23—942no—
502C23—3762no—
503C23—1881no—
504C23—1881no—
505C23C4×D18811yescharacteristic
506C23#1309399411yescharacteristic
507C23#1309399811yescharacteristic
508C23#1309399911yescharacteristic
509C23#1309400411yescharacteristic
510C23#1309400811yescharacteristic
511C23#1309402111yescharacteristic
512Q8—942no—
513Q8—942no—
514Q8—1881no—
515Q8—1881no—
516D4—942no—
517D4—942no—
518D4—1882no—
519D4—1882no—
520D4—1882no—
521D4—1882no—
522D4—1881no—
523D4—1881no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—942no—
527C2×C4—3762no—
528C2×C4—3762no—
529C2×C4—3762no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4—1882no—
539C2×C4C2×(C2×D47)⋊C411yescharacteristic
540C2×C4C4⋊C4×D4711yescharacteristic
541C2×C4#1309398211yescharacteristic
542C2×C4(C22⋊D47)⋊C411yescharacteristic
543C2×C4(C22⋊D47)⋊C411yescharacteristic
544C2×C4C4×D18811yescharacteristic
545C2×C4#1309399411yescharacteristic
546C2×C4#1309399411yescharacteristic
547C2×C4#1309399511yescharacteristic
548C2×C4#1309399611yescharacteristic
549C2×C4#1309399611yescharacteristic
550C2×C4#1309399811yescharacteristic
551C2×C4#1309399911yescharacteristic
552C2×C4#1309399911yescharacteristic
553C2×C4#1309400011yescharacteristic
554C2×C4#1309400211yescharacteristic
555C2×C4#1309400211yescharacteristic
556C2×C4#1309400411yescharacteristic
557C2×C4#1309400411yescharacteristic
558C2×C4#1309400611yescharacteristic
559C2×C4#1309400611yescharacteristic
560C2×C4#1309400811yescharacteristic
561C2×C4#1309400811yescharacteristic
562C2×C4#1309401011yescharacteristic
563C2×C4#1309401011yescharacteristic
564C2×C4#1309401211yescharacteristic
565C2×C4#1309401911yescharacteristic
566C2×C4#1309401911yescharacteristic
567C8—24no—
568C8—42no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—3762no—
577C22—3762no—
578C22—3762no—
579C22—1882no—
580C22#1568899711yescharacteristic
581C22#1568901511yescharacteristic
582C22#1568902511yescharacteristic
583C22#1568903311yescharacteristic
584C22#1568903911yescharacteristic
585C22#1568904511yescharacteristic
586C22#1568906011yescharacteristic
587C4—82no—
588C4—3762no—
589C4—3762no—
590C4—3762no—
591C4—1882no—
592C4#1568898011yescharacteristic
593C4#1568899711yescharacteristic
594C4#1568900011yescharacteristic
595C4#1568901511yescharacteristic
596C4#1568903611yescharacteristic
597C4#1568903911yescharacteristic
598C4#1568904511yescharacteristic
599C4#1568905011yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—3762no—
608C2#2024163411yescharacteristic
subgroupG/H
centerC4#15689050
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC2×C47#1439
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#11132
LCSG ▷ C22×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
1. #20251978C2semidirect
5. #20243121C2semidirect
6. C2×#15688880C2semidirect
7. C2×C47×#344C2semidirect
18. #15689133C4semidirect
19. #15689129C4semidirect
300. C2×#344D47semidirect
335. C47#11132semidirect

Maximal subgroups

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

subgroupindex
#202519782
C2×#156891392
#202519082
C2×#156890962
#202431212
C2×#156888802
C2×C47×#3442
#1113247