Finite Group Databasebeta

← #26123691

Subgroups — #26123691

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093950C211yesmaximal, characteristic
2C2×#15689120C211yesmaximal, characteristic
3C2×#15689091C211yesmaximal, characteristic
4C2×#15688884C211yesmaximal, characteristic, complemented
5#20243086C211yesmaximal, characteristic, complemented
6C2×#15688877C211yesmaximal, characteristic, complemented
7C22×#108×C47C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C22×C4×Dic47C2211yescharacteristic
12C2×#13093950—22no—
13C2×#13093950—22no—
14C2×#13093950—22no—
15#15689120—22no—
16#15689120—22no—
17C2×#13093949C411yescharacteristic, complemented
18C2×#13093949C411yescharacteristic, complemented
19C2×#13093946C411yescharacteristic, complemented
20C2×#13093946C411yescharacteristic, complemented
21#15689091—22no—
22#15689091—22no—
23C2×(C2×D47)⋊C8—22no—
24#15688884—22no—
25#15688877—22no—
26#15688877—22no—
27C22×M16×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C23×C8×C47C2211yescharacteristic
30C2×#108×C47—22no—
31C2×#108×C47—22no—
32C2×#108×C47—22no—
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×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350D412yes—
44C2×#10625350Q812yes—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47—21no—
48C23×Dic47—21no—
49C22×C4×D47—21no—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8—21no—
55C22×C47⋊C8—21no—
56C22×C47⋊C8D412yes—
57#13093983—21no—
58#13093983—21no—
59#13093983—21no—
60#13093983—21no—
61C2×C4⋊Dic47C2×C411yescharacteristic
62C2×C4⋊Dic47C2×C411yescharacteristic
63C2×C22⋊Dic47—21no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47—21no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—21no—
70C2×C4×Dic47D412yes—
71#13093950—28no—
72#13093949—22no—
73#13093949—22no—
74#13093946—22no—
75#13093946—22no—
76(C2×D47)⋊C8—28no—
77C23×C4×C47C2311yescharacteristic
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×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47D412yes—
89C2×M16×C47D412yes—
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C22×C8×C47—21no—
93C22×C8×C47—21no—
94C22×C8×C47—21no—
95C22×C8×C47—21no—
96C22×C8×C47C2×C411yescharacteristic
97C22×C8×C47C2×C411yescharacteristic
98C22×C8×C47D412yes—
99C22×C8×C47D412yes—
100#108×C47—28no—
101C24×C47#4111yescharacteristic
102C23×D47—21no—
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
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
117C2×C22⋊D47—22no—
118C2×C22⋊D47—22no—
119C2×C22⋊D47—41no—
120C2×C22⋊D47—41no—
121C2×C22⋊D47—41no—
122C2×C22⋊D47—41no—
123C22×Dic47—24no—
124C22×Dic47—21no—
125C22×Dic47—22no—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—42no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131#10625350—22no—
132#10625350—22no—
133#10625350—22no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—41no—
140#10625350—41no—
141#10625350—41no—
142#10625350—41no—
143#10625350—41no—
144#10625350—41no—
145#10625350—41no—
146#10625350—41no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188C4⋊C412yes—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—41no—
156C2×C4×D47—41no—
157C2×C4×D47—41no—
158C2×C4×D47—41no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94C4⋊C412yes—
165M16×C47—22no—
166M16×C47—22no—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—41no—
170M16×C47—41no—
171M16×C47—41no—
172M16×C47—41no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C2×C8×C47—22no—
183C2×C8×C47—41no—
184C2×C8×C47—41no—
185C2×C8×C47—41no—
186C2×C8×C47—41no—
187C2×C8×C47C22⋊C412yes—
188C2×C8×C47C22⋊C412yes—
189C22⋊Dic47—41no—
190C22⋊Dic47—41no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4×Dic47—22no—
196C4×Dic47—22no—
197C4×Dic47—41no—
198C4×Dic47—41no—
199C4×Dic47—41no—
200C4×Dic47—41no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—41no—
205C2×C47⋊C8—41no—
206C2×C47⋊C8—41no—
207C2×C47⋊C8—41no—
208C23×C47—22no—
209C23×C47—22no—
210C23×C47C4×D411yescharacteristic
211C23×C47#12111yescharacteristic
212C23×C47C22⋊Q811yescharacteristic
213C23×C47#12311yescharacteristic
214C23×C47#12411yescharacteristic
215C23×C47#12411yescharacteristic
216C23×C47#12611yescharacteristic
217C22×D47—22no—
218C22×D47—41no—
219C22×D47—41no—
220C22×D47—42no—
221C22×D47—42no—
222C2×C4×C47C2×C22⋊C411yescharacteristic
223C2×C4×C47C2×C4⋊C411yescharacteristic
224C2×C4×C47#11711yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47#12011yescharacteristic
229C2×C4×C47#12011yescharacteristic
230C2×C4×C47#12011yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12111yescharacteristic
236C2×C4×C47#12111yescharacteristic
237C2×C4×C47#12111yescharacteristic
238C2×C4×C47C22⋊Q811yescharacteristic
239C2×C4×C47C22⋊Q811yescharacteristic
240C2×C4×C47C22⋊Q811yescharacteristic
241C2×C4×C47C22⋊Q811yescharacteristic
242C2×C4×C47C22⋊Q811yescharacteristic
243C2×C4×C47#12311yescharacteristic
244C2×C4×C47#12311yescharacteristic
245C2×C4×C47#12311yescharacteristic
246C2×C4×C47#12311yescharacteristic
247C2×C4×C47#12411yescharacteristic
248C2×C4×C47#12611yescharacteristic
249C2×C4×C47#12711yescharacteristic
250C22⋊D47—42no—
251C22⋊D47—42no—
252C22⋊D47—42no—
253C22⋊D47—42no—
254C2×Dic47—24no—
255C2×Dic47—22no—
256C2×Dic47—44no—
257C2×Dic47—44no—
258C2×Dic47—42no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—42no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266D188—22no—
267D188—22no—
268D188—41no—
269D188—41no—
270C4×D47—42no—
271C4×D47—42no—
272C4×D47—42no—
273C4×D47—42no—
274Dic94—22no—
275Dic94—22no—
276Dic94—41no—
277Dic94—41no—
278C8×C47—22no—
279C8×C47—22no—
280C8×C47—42no—
281C8×C47—42no—
282C47⋊C8—42no—
283#11125—471nomaximal, Sylow
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—21no—
292C22×C47#38511yescharacteristic
293C22×C47#38811yescharacteristic
294C22×C47#39011yescharacteristic
295C22×C47#39311yescharacteristic
296C22×C47#39411yescharacteristic
297C22×C47#39611yescharacteristic
298C22×C47#39711yescharacteristic
299C22×C47#44312yes—
300C22×C47#44412yes—
301C2×D47—44no—
302C2×D47—42no—
303C2×D47—82no—
304C2×D47—81no—
305C2×D47—81no—
306C4×C47#38011yescharacteristic
307C4×C47#38511yescharacteristic
308C4×C47#38611yescharacteristic
309C4×C47#38811yescharacteristic
310C4×C47#39211yescharacteristic
311C4×C47#39411yescharacteristic
312C4×C47#39611yescharacteristic
313C4×C47#39911yescharacteristic
314Dic47—44no—
315Dic47—42no—
316Dic47—81no—
317Dic47—81no—
318C22×#108D4711yescharacteristic, complemented
319C22×#104—471no—
320C2×#416—471no—
321C2×#408—471no—
322C2×#339—471no—
323#1729—471no—
324C2×#336—471no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47—21no—
328C2×C47—21no—
329C2×C47#143911yescharacteristic
330C2×C47#186612yes—
331C2×C47#192912yes—
332C2×C47#197411yescharacteristic
333C2×C47#197511yescharacteristic
334D47—82no—
335C22×#41—471no—
336C22×M16C2×D4711yescharacteristic
337C22×M16C2×D4711yescharacteristic
338C23×C8—471no—
339C23×C8C2×D4711yescharacteristic
340C2×#117—471no—
341C22×C42—471no—
342C2×#108—22no—
343C2×#108—22no—
344C2×#108—22no—
345C2×#104—942no—
346C2×#104—942no—
347C2×#104—942no—
348#416—942no—
349#416—942no—
350C2×#103—471no—
351C2×#103—471no—
352C2×#102—471no—
353C2×#102—471no—
354#408—942no—
355#408—942no—
356C2×C22⋊C8—942no—
357#339—942no—
358#336—942no—
359#336—942no—
360C47#1112511yescharacteristic, complemented, Sylow
361C2×#41—472no—
362C2×#41—472no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C2×#41—941no—
371C2×#41—941no—
372C2×#41—941no—
373C22×Q8—471no—
374C22×D4—471no—
375C22×D4—941no—
376C23×C4—941no—
377C23×C4—941no—
378C23×C4C22×D4711yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16C22⋊D4712yes—
390C2×M16C22⋊D4712yes—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8—21no—
396C22×C8—21no—
397C22×C8—472no—
398C22×C8—941no—
399C22×C8—941no—
400C22×C8—941no—
401C22×C8—941no—
402C22×C8—941no—
403C22×C8—941no—
404C22×C8C4×D4711yescharacteristic
405C22×C8C4×D4711yescharacteristic
406C22×C8D18812yes—
407C22×C8C22⋊D4712yes—
408#117—941no—
409#117—941no—
410#117—941no—
411#117—941no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C22⋊C4—941no—
415C2×C42—472no—
416C2×C42—941no—
417C2×C42—941no—
418C2×C42—941no—
419C2×C42—941no—
420C2×C42—941no—
421C2×C42—941no—
422#108—28no—
423#104—948no—
424#103—942no—
425#103—942no—
426#102—942no—
427#102—942no—
428C22⋊C8—948no—
429C24—941no—
430C24#1062535411yescharacteristic
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—1881no—
440#41—1881no—
441#41—1881no—
442#41—1881no—
443#41—1881no—
444#41—1881no—
445#41—1881no—
446#41—1881no—
447C2×Q8—472no—
448C2×Q8—941no—
449C2×Q8—941no—
450C2×Q8—941no—
451C2×Q8—941no—
452C2×Q8—941no—
453C2×D4—472no—
454C2×D4—942no—
455C2×D4—942no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—941no—
460C2×D4—941no—
461C2×D4—1881no—
462C2×D4—1881no—
463C2×D4—1881no—
464C2×D4—1881no—
465C22×C4—944no—
466C22×C4—941no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—941no—
471C22×C4—941no—
472C22×C4—1882no—
473C22×C4—1881no—
474C22×C4—1881no—
475C22×C4—1881no—
476C22×C4—1881no—
477C22×C4—1881no—
478C22×C4—1881no—
479C22×C4C2×C4×D4711yescharacteristic
480C22×C4C2×D18811yescharacteristic
481C22×C4#1062535011yescharacteristic
482C22×C4#1062535011yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4#1062535211yescharacteristic
487C22×C4Q8×D4711yescharacteristic
488C22×C4#1062535411yescharacteristic
489C22×C4#1062535411yescharacteristic
490C22×C4C2×C22⋊D4711yescharacteristic
491C22×C4C2×C22⋊D4711yescharacteristic
492C22×C4C2×C22⋊D4711yescharacteristic
493M16—22no—
494M16—22no—
495M16—22no—
496M16—22no—
497M16—41no—
498M16—41no—
499M16—41no—
500M16—41no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—942no—
516C2×C8—942no—
517C2×C8—942no—
518C2×C8—1881no—
519C2×C8—1881no—
520C2×C8—1881no—
521C2×C8—1881no—
522C2×C8(C2×D47)⋊C412yes—
523C2×C8(C2×D47)⋊C412yes—
524C4⋊C4—941no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C22⋊C4—1881no—
529C22⋊C4—1881no—
530C42—942no—
531C42—942no—
532C42—1881no—
533C42—1881no—
534C42—1881no—
535C42—1881no—
536C23—22no—
537C23—22no—
538C23—942no—
539C23—1882no—
540C23—1882no—
541C23—1881no—
542C23—1881no—
543C23#1309398611yescharacteristic
544C23#1309399911yescharacteristic
545C23#1309400011yescharacteristic
546C23#1309400911yescharacteristic
547C23#1309401311yescharacteristic
548C23#1309401311yescharacteristic
549C23#1309401911yescharacteristic
550Q8—942no—
551Q8—942no—
552Q8—1881no—
553Q8—1881no—
554D4—942no—
555D4—942no—
556D4—1882no—
557D4—1882no—
558D4—1882no—
559D4—1882no—
560D4—1881no—
561D4—1881no—
562C2×C4—944no—
563C2×C4—942no—
564C2×C4—1882no—
565C2×C4—1882no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1882no—
569C2×C4—1884no—
570C2×C4—1884no—
571C2×C4—1881no—
572C2×C4—1881no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4—1882no—
576C2×C4—1882no—
577C2×C4—1882no—
578C2×C4C2×(C2×D47)⋊C411yescharacteristic
579C2×C4C4⋊C4×D4711yescharacteristic
580C2×C4#1309398211yescharacteristic
581C2×C4C4×C22⋊D4711yescharacteristic
582C2×C4C4×C22⋊D4711yescharacteristic
583C2×C4#1309398611yescharacteristic
584C2×C4#1309399211yescharacteristic
585C2×C4#1309399211yescharacteristic
586C2×C4#1309399311yescharacteristic
587C2×C4#1309399511yescharacteristic
588C2×C4#1309399611yescharacteristic
589C2×C4#1309399611yescharacteristic
590C2×C4#1309399811yescharacteristic
591C2×C4#1309399811yescharacteristic
592C2×C4#1309399911yescharacteristic
593C2×C4#1309399911yescharacteristic
594C2×C4#1309400011yescharacteristic
595C2×C4#1309400011yescharacteristic
596C2×C4#1309400211yescharacteristic
597C2×C4#1309400211yescharacteristic
598C2×C4#1309400411yescharacteristic
599C2×C4#1309400711yescharacteristic
600C2×C4#1309400911yescharacteristic
601C2×C4#1309400911yescharacteristic
602C2×C4#1309400911yescharacteristic
603C2×C4#1309401311yescharacteristic
604C2×C4#1309401911yescharacteristic
605C2×C4#1309402011yescharacteristic
606C8—22no—
607C8—22no—
608C8—42no—
609C8—42no—
610C8—1882no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—3761no—
620C22—3761no—
621C22—3762no—
622C22—1884no—
623C22—1882no—
624C22#1568899411yescharacteristic
625C22#1568901311yescharacteristic
626C22#1568902411yescharacteristic
627C22#1568903411yescharacteristic
628C22#1568904011yescharacteristic
629C22#1568904511yescharacteristic
630C22#1568904911yescharacteristic
631C22#1568923912yes—
632C22#1568924412yes—
633C4—3761no—
634C4—3761no—
635C4—1884no—
636C4—1882no—
637C4#1568898011yescharacteristic
638C4#1568899411yescharacteristic
639C4#1568900211yescharacteristic
640C4#1568901311yescharacteristic
641C4#1568903111yescharacteristic
642C4#1568904011yescharacteristic
643C4#1568904511yescharacteristic
644C4#1568905811yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—3762no—
650C2#2024163011yescharacteristic
651C2#2024366012yes—
652C2#2024403512yes—
653C2#2024427411yescharacteristic
654C2#2024427911yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC22×#108×C47C2
socleC23×C47C4×D4
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC22×#108D47
hypocenterC47#11125
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#108

Complements

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

NH ≅ G/Ntype
4. C2×#15688884C2semidirect
5. #20243086C2semidirect
6. C2×#15688877C2semidirect
7. C22×#108×C47C2semidirect
17. C2×#13093949C4semidirect
18. C2×#13093949C4semidirect
19. C2×#13093946C4semidirect
20. C2×#13093946C4semidirect
318. C22×#108D47semidirect
360. C47#11125semidirect

Maximal subgroups

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

subgroupindex
C22×#130939502
C2×#156891202
C2×#156890912
C2×#156888842
#202430862
C2×#156888772
C22×#108×C472
#1112547