Finite Group Databasebeta

← #26123290

Subgroups — #26123290

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093952C211yesmaximal, characteristic
2#20251905C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5#20243097C211yesmaximal, characteristic, complemented
6C2×#15688883C211yesmaximal, characteristic, complemented
7C47×#2296C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12C2×#13093952—22no—
13C2×#13093952—22no—
14C2×#13093952—22no—
15#15689131C412yescomplemented
16#15689127C412yescomplemented
17#15689122—22no—
18#15689117—22no—
19#15689096—22no—
20#15689096—22no—
21C2×#13093938—22no—
22#15688893—22no—
23#15688883—22no—
24#15688882—22no—
25C2×#117×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C22×C42×C47C2211yescharacteristic
28C47×#389—22no—
29C47×#385—22no—
30C4×C4⋊C4×C47—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—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329C2×C412yes—
58C2×#10625329D412yes—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983D412yes—
65C2×C4⋊Dic47—21no—
66C2×C22⋊Dic47—21no—
67C2×C4×Dic47—21no—
68#13093952—28no—
69#13093947—24no—
70#13093944—24no—
71#13093938—28no—
72C23×C4×C47—21no—
73C23×C4×C47C2311yescharacteristic
74#117×C47—21no—
75#117×C47—21no—
76#117×C47—21no—
77#117×C47—21no—
78#117×C47—21no—
79#117×C47—21no—
80#117×C47C2×C412yes—
81#117×C47D412yes—
82C2×C4⋊C4×C47—24no—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47D412yes—
85C2×C22⋊C4×C47—21no—
86C2×C22⋊C4×C47D412yes—
87C2×C42×C47—21no—
88C2×C42×C47—21no—
89C2×C42×C47—21no—
90C2×C42×C47—21no—
91C2×C42×C47—21no—
92C2×C42×C47—21no—
93C2×C42×C47—21no—
94C2×C42×C47D412yes—
95#95×C47—24no—
96C24×C47C2×D411yescharacteristic
97C23×D47—21no—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—44no—
102C22×C4×C47—41no—
103C22×C4×C47—41no—
104C22×C4×C47C22×C411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×Q811yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C2×C22⋊D47—22no—
119C2×C22⋊D47—22no—
120C2×C22⋊D47—41no—
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C2×C22⋊D47—41no—
124C22×Dic47—21no—
125C22×Dic47—41no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×D188C4⋊C412yescomplemented
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—41no—
151C2×C4×D47—41no—
152C2×C4×D47—41no—
153C2×C4×D47—41no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159C2×Dic94C4⋊C412yescomplemented
160C4⋊C4×C47—22no—
161C4⋊C4×C47—48no—
162C4⋊C4×C47—41no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47C22⋊C414yes—
165C22⋊C4×C47—22no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47—22no—
168C22⋊C4×C47—22no—
169C42×C47—22no—
170C42×C47—22no—
171C42×C47—22no—
172C42×C47—22no—
173C42×C47—41no—
174C42×C47—41no—
175C42×C47—41no—
176C42×C47—41no—
177C22⋊Dic47—22no—
178C22⋊Dic47—41no—
179C4⋊Dic47—22no—
180C4⋊Dic47—41no—
181C4×Dic47—22no—
182C4×Dic47—41no—
183#10625329—22no—
184#10625329—22no—
185#10625329—22no—
186#10625329—22no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190#10625329—41no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C23×C47—42no—
198C23×C47C4×D411yescharacteristic
199C23×C47#12011yescharacteristic
200C23×C47#12011yescharacteristic
201C23×C47#12111yescharacteristic
202C23×C47#12111yescharacteristic
203C23×C47C22⋊Q811yescharacteristic
204C23×C47#12411yescharacteristic
205C22×D47—22no—
206C22×D47—41no—
207C22×D47—41no—
208C22×D47—82no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—44no—
212C2×C4×C47—42no—
213C2×C4×C47—44no—
214C2×C4×C47—44no—
215C2×C4×C47—42no—
216C2×C4×C47—44no—
217C2×C4×C47—42no—
218C2×C4×C47C2×C22⋊C411yescharacteristic
219C2×C4×C47C2×C4⋊C411yescharacteristic
220C2×C4×C47#11711yescharacteristic
221C2×C4×C47C4×D411yescharacteristic
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47#12011yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47#12111yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47C22⋊Q811yescharacteristic
232C2×C4×C47C22⋊Q811yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47#12311yescharacteristic
237C2×C4×C47#12311yescharacteristic
238C2×C4×C47#12311yescharacteristic
239C2×C4×C47#12311yescharacteristic
240C2×C4×C47#12311yescharacteristic
241C2×C4×C47#12411yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12611yescharacteristic
244C2×C4×C47#12611yescharacteristic
245C2×C4×C47#12711yescharacteristic
246C22⋊D47—42no—
247C22⋊D47—42no—
248C22⋊D47—42no—
249C22⋊D47—42no—
250C2×Dic47—22no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—42no—
254C2×Dic47—82no—
255D188—22no—
256D188—22no—
257D188—41no—
258D188—41no—
259C4×D47—42no—
260C4×D47—42no—
261C4×D47—42no—
262C4×D47—42no—
263Dic94—22no—
264Dic94—22no—
265Dic94—41no—
266Dic94—41no—
267C47⋊C8—42no—
268C47⋊C8—42no—
269#11060—471nomaximal, Sylow
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47#38511yescharacteristic
278C22×C47#38611yescharacteristic
279C22×C47#38811yescharacteristic
280C22×C47#39211yescharacteristic
281C22×C47#39311yescharacteristic
282C22×C47#39411yescharacteristic
283C22×C47#39611yescharacteristic
284C2×D47—42no—
285C2×D47—82no—
286C2×D47—82no—
287C2×D47—82no—
288C4×C47—44no—
289C4×C47—44no—
290C4×C47—82no—
291C4×C47#38011yescharacteristic
292C4×C47#38511yescharacteristic
293C4×C47#38811yescharacteristic
294C4×C47#39011yescharacteristic
295C4×C47#39411yescharacteristic
296C4×C47#39611yescharacteristic
297C4×C47#39711yescharacteristic
298C4×C47#39911yescharacteristic
299Dic47—42no—
300Dic47—82no—
301C22×#104—471no—
302#2896—471no—
303C2×#410—471no—
304#2296D4711yescharacteristic, complemented
305C2×#344—471no—
306#1733—471no—
307C2×#339—471no—
308C2×C47—21no—
309C2×C47—21no—
310C2×C47—21no—
311C2×C47—21no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47#143911yescharacteristic
315C2×C47#190612yes—
316D47—82no—
317C22×#41—471no—
318C22×M16—471no—
319C22×M16—471no—
320C2×#117—471no—
321C2×#117C2×D4711yescharacteristic
322C2×#117C2×D4711yescharacteristic
323C22×C42C2×D4711yescharacteristic
324C2×#104—942no—
325C2×#104—942no—
326C2×#104—942no—
327#419—472no—
328#418—472no—
329#417—942no—
330#416—942no—
331#410—942no—
332#410—942no—
333C2×#99—942no—
334#389—22no—
335#385—22no—
336C4×C4⋊C4—22no—
337#344—942no—
338#339—942no—
339#339—942no—
340C47#1106011yescharacteristic, complemented, Sylow
341C2×#41—472no—
342C2×#41—472no—
343C2×#41—941no—
344C2×#41—941no—
345C2×#41—941no—
346C2×#41—941no—
347C2×#41—941no—
348C2×#41—941no—
349C2×#41—941no—
350C2×#41—941no—
351C2×#41—941no—
352C2×#41—941no—
353C22×Q8—471no—
354C22×D4—471no—
355C22×D4—941no—
356C23×C4—21no—
357C23×C4—941no—
358C23×C4C22×D4711yescharacteristic
359C2×M16—472no—
360C2×M16—472no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16—941no—
371C22×C8—941no—
372C22×C8—941no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—472no—
380#117—941no—
381#117—941no—
382#117—941no—
383#117C4×D4712yes—
384#117D18812yes—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4C22⋊D4712yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—941no—
391C2×C22⋊C4C22⋊D4712yes—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—941no—
400C2×C42C22⋊D4712yes—
401#104—948no—
402#103—944no—
403#102—944no—
404#99—948no—
405#95—24no—
406C24—941no—
407C24C2×C22⋊D4711yescharacteristic
408#41—942no—
409#41—942no—
410#41—942no—
411#41—942no—
412#41—942no—
413#41—942no—
414#41—942no—
415#41—942no—
416#41—1881no—
417#41—1881no—
418#41—1881no—
419#41—1881no—
420#41—1881no—
421#41—1881no—
422#41—1881no—
423#41—1881no—
424C2×Q8—472no—
425C2×Q8—941no—
426C2×Q8—941no—
427C2×Q8—941no—
428C2×Q8—941no—
429C2×Q8—941no—
430C2×D4—472no—
431C2×D4—942no—
432C2×D4—942no—
433C2×D4—941no—
434C2×D4—941no—
435C2×D4—941no—
436C2×D4—941no—
437C2×D4—941no—
438C2×D4—1881no—
439C2×D4—1881no—
440C2×D4—1881no—
441C2×D4—1881no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—941no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—1881no—
452C22×C4—1881no—
453C22×C4—1881no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4#1062535011yescharacteristic
459C22×C4#1062535011yescharacteristic
460C22×C4D4×D4711yescharacteristic
461C22×C4D4×D4711yescharacteristic
462C22×C4D4×D4711yescharacteristic
463C22×C4#1062535211yescharacteristic
464C22×C4Q8×D4711yescharacteristic
465C22×C4#1062535411yescharacteristic
466C22×C4#1062535411yescharacteristic
467C22×C4#1062535411yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470M16—942no—
471M16—942no—
472M16—942no—
473M16—942no—
474M16—1881no—
475M16—1881no—
476M16—1881no—
477M16—1881no—
478C2×C8—942no—
479C2×C8—942no—
480C2×C8—1881no—
481C2×C8—1881no—
482C2×C8—1881no—
483C2×C8—1881no—
484C4⋊C4—22no—
485C4⋊C4—48no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—942no—
489C4⋊C4—1881no—
490C4⋊C4(C2×D47)⋊C414yes—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—942no—
496C22⋊C4—1881no—
497C42—22no—
498C42—22no—
499C42—22no—
500C42—22no—
501C42—41no—
502C42—41no—
503C42—41no—
504C42—41no—
505C42—942no—
506C42—1881no—
507C23—42no—
508C23—942no—
509C23—3762no—
510C23—1881no—
511C23—1881no—
512C23C4×C22⋊D4711yescharacteristic
513C23#1309399211yescharacteristic
514C23#1309399311yescharacteristic
515C23#1309399611yescharacteristic
516C23#1309399811yescharacteristic
517C23#1309400011yescharacteristic
518C23#1309401311yescharacteristic
519Q8—942no—
520Q8—942no—
521Q8—1881no—
522Q8—1881no—
523D4—942no—
524D4—942no—
525D4—1882no—
526D4—1882no—
527D4—1882no—
528D4—1882no—
529D4—1881no—
530D4—1881no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—942no—
541C2×C4—3762no—
542C2×C4—1882no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4C2×(C2×D47)⋊C411yescharacteristic
550C2×C4C4⋊C4×D4711yescharacteristic
551C2×C4#1309398211yescharacteristic
552C2×C4C4×C22⋊D4711yescharacteristic
553C2×C4#1309398611yescharacteristic
554C2×C4#1309398611yescharacteristic
555C2×C4#1309399211yescharacteristic
556C2×C4#1309399511yescharacteristic
557C2×C4#1309399611yescharacteristic
558C2×C4#1309399811yescharacteristic
559C2×C4#1309399911yescharacteristic
560C2×C4#1309399911yescharacteristic
561C2×C4#1309399911yescharacteristic
562C2×C4#1309400011yescharacteristic
563C2×C4#1309400011yescharacteristic
564C2×C4#1309400211yescharacteristic
565C2×C4#1309400211yescharacteristic
566C2×C4#1309400411yescharacteristic
567C2×C4#1309400711yescharacteristic
568C2×C4#1309400911yescharacteristic
569C2×C4#1309400911yescharacteristic
570C2×C4#1309400911yescharacteristic
571C2×C4#1309400911yescharacteristic
572C2×C4#1309401311yescharacteristic
573C2×C4#1309401311yescharacteristic
574C2×C4#1309401911yescharacteristic
575C2×C4#1309401911yescharacteristic
576C2×C4#1309402011yescharacteristic
577C8—1882no—
578C8—1882no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—3762no—
587C22—3762no—
588C22—3762no—
589C22—1882no—
590C22#1568899411yescharacteristic
591C22#1568900211yescharacteristic
592C22#1568901311yescharacteristic
593C22#1568903111yescharacteristic
594C22#1568903411yescharacteristic
595C22#1568904011yescharacteristic
596C22#1568904511yescharacteristic
597C4—44no—
598C4—44no—
599C4—82no—
600C4—3762no—
601C4—1882no—
602C4#1568898011yescharacteristic
603C4#1568899411yescharacteristic
604C4#1568901311yescharacteristic
605C4#1568902411yescharacteristic
606C4#1568904011yescharacteristic
607C4#1568904511yescharacteristic
608C4#1568904911yescharacteristic
609C4#1568905811yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—3762no—
617C2#2024163011yescharacteristic
618C2#2024388912yes—
subgroupG/H
centerC2×C4#13093998
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2296C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#2296D47
hypocenterC47#11060
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. #20243097C2semidirect
6. C2×#15688883C2semidirect
7. C47×#2296C2semidirect
15. #15689131C4semidirect
16. #15689127C4semidirect
147. C2×D188C4⋊C4semidirect
159. C2×Dic94C4⋊C4semidirect
304. #2296D47semidirect
340. C47#11060semidirect

Maximal subgroups

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

subgroupindex
C22×#130939522
#202519052
C2×#156890962
C2×#156888932
#202430972
C2×#156888832
C47×#22962
#1106047