Finite Group Databasebeta

← #26243713

Subgroups — #26243713

Order 12032.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256793C211yesmaximal, characteristic, complemented
2C2×#15689139C211yesmaximal, characteristic
3C2×#15689139C211yesmaximal, characteristic
4C2×#15689096C211yesmaximal, characteristic
5#20244563C218yesmaximal, complemented
6#20243099C211yesmaximal, characteristic, complemented
7C2×#15688880C211yesmaximal, characteristic, complemented
8C2×C47×#344C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689754—22no—
11#15689751—22no—
12#15689751—22no—
13#15689749—22no—
14#15689680—22no—
15#15689676—22no—
16#15689676C2214yescomplemented
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#15689139—22no—
21#15689139—22no—
22#15689139—22no—
23#15689139C2214yes—
24C2×#13093950—22no—
25C2×#13093950C2214yes—
26#15689096—22no—
27#15689096C2214yes—
28C2×#13093938—22no—
29#15688884C2214yescomplemented
30#15688880C2214yescomplemented
31C22×M16×C47C2211yescharacteristic
32C22×M16×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C47×#344C2214yescomplemented
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×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350Q812yescomplemented
46C2×#10625350C2312yes—
47C22×Dic94Q811yescharacteristic, complemented
48C22×D188Q811yescharacteristic, complemented
49C22×C22⋊D47—21no—
50C22×C4×D47—21no—
51#13094024—24no—
52#13094023—24no—
53#13094023—24no—
54#13094016—24no—
55#13094015—24no—
56#13094015—24no—
57#13094003—28no—
58#13094001—28no—
59#13094001—28no—
60C4×Dic94—28no—
61#13093983—21no—
62#13093983—21no—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983—21no—
68#13093983D412yes—
69#13093983D412yes—
70#13093983D412yes—
71#13093983C2312yes—
72#13093983C2312yes—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47D412yes—
81C2×C4×Dic47C2312yes—
82#13093950—28no—
83#13093950—28no—
84#13093938—28no—
85C23×C4×C47C2311yescharacteristic
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47C2312yes—
97C2×M16×C47C2312yes—
98C22×C8×C47—21no—
99C22×C8×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102#117×C47D412yes—
103#117×C47C2312yes—
104C2×C4⋊C4×C47—21no—
105C2×C22⋊C4×C47D412yes—
106C2×C42×C47—21no—
107C24×C47C2×D411yescharacteristic
108C23×D47—21no—
109C22×C4×C47—22no—
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×Q811yescharacteristic
116C22×C4×C47C2×Q811yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C22×C4×C47#4111yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47C2411yescharacteristic
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47—41no—
127C2×C22⋊D47—41no—
128C2×C22⋊D47—41no—
129C2×C22⋊D47—41no—
130C22×Dic47—21no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—41no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—41no—
143#10625350—41no—
144#10625350—41no—
145#10625350—41no—
146#10625350—41no—
147#10625350—41no—
148#10625350—41no—
149#10625350—41no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188C2×Q812yes—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—41no—
159C2×C4×D47—41no—
160C2×C4×D47—41no—
161C2×C4×D47—41no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94—28no—
168C2×Dic94C2×Q812yes—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—22no—
173M16×C47—41no—
174M16×C47—41no—
175M16×C47—41no—
176M16×C47—41no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—41no—
180C2×C8×C47—41no—
181C2×C8×C47—41no—
182C2×C8×C47—41no—
183C4⋊C4×C47—22no—
184C4⋊C4×C47—22no—
185C22⋊C4×C47—22no—
186C22⋊C4×C47C2×D414yes—
187C42×C47—22no—
188C42×C47—22no—
189C22⋊Dic47—22no—
190C22⋊Dic47—22no—
191C22⋊Dic47—22no—
192C22⋊Dic47—22no—
193C22⋊Dic47—22no—
194C22⋊Dic47—41no—
195C4⋊Dic47—28no—
196C4⋊Dic47—22no—
197C4⋊Dic47—22no—
198C4⋊Dic47—22no—
199C4⋊Dic47—22no—
200C4⋊Dic47—22no—
201C4⋊Dic47—41no—
202Dic47⋊C4—28no—
203Dic47⋊C4—28no—
204C4×Dic47—22no—
205C4×Dic47—22no—
206C4×Dic47—22no—
207C4×Dic47—41no—
208C4×Dic47C2×D414yes—
209C4×Dic47C2×D414yes—
210C23×C47—81no—
211C23×C47#12011yescharacteristic
212C23×C47#12011yescharacteristic
213C23×C47C22⋊Q811yescharacteristic
214C23×C47C22⋊Q811yescharacteristic
215C23×C47#12411yescharacteristic
216C23×C47#12411yescharacteristic
217C23×C47C22×D411yescharacteristic
218C22×D47—22no—
219C22×D47—41no—
220C22×D47—41no—
221C22×D47—82no—
222C2×C4×C47—24no—
223C2×C4×C47—82no—
224C2×C4×C47#12011yescharacteristic
225C2×C4×C47#12011yescharacteristic
226C2×C4×C47C22⋊Q811yescharacteristic
227C2×C4×C47C22⋊Q811yescharacteristic
228C2×C4×C47C22⋊Q811yescharacteristic
229C2×C4×C47C22⋊Q811yescharacteristic
230C2×C4×C47C22⋊Q811yescharacteristic
231C2×C4×C47C22⋊Q811yescharacteristic
232C2×C4×C47C22⋊Q811yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47#12411yescharacteristic
237C2×C4×C47#12411yescharacteristic
238C2×C4×C47#12411yescharacteristic
239C2×C4×C47#12411yescharacteristic
240C2×C4×C47#12411yescharacteristic
241C2×C4×C47#12411yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12411yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C22×Q811yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47C2×#4111yescharacteristic
252C22⋊D47—42no—
253C22⋊D47—42no—
254C22⋊D47—42no—
255C22⋊D47—42no—
256C2×Dic47—24no—
257C2×Dic47—24no—
258C2×Dic47—22no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—42no—
262C2×Dic47—82no—
263C2×Dic47—82no—
264C2×Dic47—82no—
265D188—22no—
266D188—22no—
267D188—41no—
268D188—41no—
269C4×D47—42no—
270C4×D47—42no—
271C4×D47—42no—
272C4×D47—42no—
273Dic94—22no—
274Dic94—22no—
275Dic94—41no—
276Dic94—41no—
277Dic94—88no—
278C8×C47—42no—
279C8×C47—42no—
280#23472—471nomaximal, Sylow
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47—41no—
285C22×C47—41no—
286C22×C47—41no—
287C22×C47—41no—
288C22×C47#39311yescharacteristic
289C22×C47#39311yescharacteristic
290C22×C47#39311yescharacteristic
291C22×C47#39311yescharacteristic
292C22×C47C2×#12011yescharacteristic
293C22×C47C2×C22⋊Q811yescharacteristic
294C22×C47C2×#12411yescharacteristic
295C2×D47—42no—
296C2×D47—82no—
297C2×D47—82no—
298C2×D47—82no—
299C4×C47—44no—
300C4×C47#39311yescharacteristic
301C4×C47#39311yescharacteristic
302C4×C47#39311yescharacteristic
303C4×C47#39311yescharacteristic
304C4×C47C2×C22⋊Q811yescharacteristic
305C4×C47C2×C22⋊Q811yescharacteristic
306C4×C47C2×#12411yescharacteristic
307C4×C47C2×#12411yescharacteristic
308Dic47—44no—
309Dic47—44no—
310Dic47—42no—
311Dic47—82no—
312#3458—471no—
313C2×#421—471no—
314C2×#421—471no—
315C2×#410—471no—
316#2031—478no—
317C2×#344D4711yescharacteristic, complemented
318#1733—471no—
319C2×H(3,ℤ/4)—471no—
320C2×C47—21no—
321C2×C47—21no—
322C2×C47—21no—
323C2×C47—21no—
324C2×C47—21no—
325C2×C47—21no—
326C2×C47—21no—
327C2×C47C2×#39311yescharacteristic
328D47—82no—
329C22×#41—471no—
330C22×M16C2×D4711yescharacteristic
331C22×M16C2×D4711yescharacteristic
332#544—942no—
333#544—942no—
334#544—942no—
335#543—942no—
336#533—474no—
337#533—942no—
338#533—942no—
339C2×#117—471no—
340C2×#117—471no—
341C2×#117—471no—
342C2×#117C2×D4711yescharacteristic
343#421—474no—
344#421—942no—
345#421—942no—
346#421—942no—
347C2×#104—474no—
348C2×#104—942no—
349#410—474no—
350#410—942no—
351C2×#99—942no—
352#344C2×D4714yescomplemented
353#339—474no—
354H(3,ℤ/4)—474no—
355C47#2347211yescharacteristic, complemented, Sylow
356C2×#41—472no—
357C2×#41—472no—
358C2×#41—941no—
359C2×#41—941no—
360C2×#41—941no—
361C2×#41—941no—
362C2×#41—941no—
363C2×#41—941no—
364C2×#41—941no—
365C2×#41—941no—
366C2×#41—941no—
367C2×#41—941no—
368C22×Q8—471no—
369C22×D4—471no—
370C22×D4—941no—
371C23×C4—941no—
372C23×C4C22×D4711yescharacteristic
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16C22×D4712yes—
384C2×M16C22×D4712yes—
385C22×C8—21no—
386C22×C8—21no—
387C4⋊Q8—944no—
388C4⋊Q8—944no—
389C4⋊Q8—944no—
390#125—944no—
391#125—944no—
392#125—944no—
393C22⋊Q8—948no—
394C22⋊Q8—948no—
395C22⋊Q8—948no—
396C4×Q8—948no—
397#117—21no—
398#117—21no—
399#117—472no—
400#117—472no—
401#117—472no—
402#117—472no—
403#117—472no—
404#117—941no—
405#117—941no—
406#117—941no—
407#117—941no—
408#117—941no—
409#117—941no—
410#117—941no—
411#117D18812yes—
412#117C22×D4712yes—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4—941no—
416C2×C4⋊C4—941no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—941no—
419C2×C22⋊C4—941no—
420C2×C22⋊C4D18812yes—
421C2×C42—21no—
422C2×C42—472no—
423C2×C42—472no—
424C2×C42—941no—
425#104—948no—
426#104—948no—
427#99—948no—
428C24—941no—
429C24C2×D18811yescharacteristic
430#41—942no—
431#41—942no—
432#41—942no—
433#41—942no—
434#41—942no—
435#41—942no—
436#41—942no—
437#41—942no—
438#41—1881no—
439#41—1881no—
440#41—1881no—
441#41—1881no—
442#41—1881no—
443#41—1881no—
444#41—1881no—
445#41—1881no—
446C2×Q8—472no—
447C2×Q8—948no—
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—22no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—941no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—1881no—
472C22×C4—1881no—
473C22×C4—1881no—
474C22×C4—1881no—
475C22×C4—1881no—
476C22×C4C2×D18811yescharacteristic
477C22×C4#1062535011yescharacteristic
478C22×C4#1062535011yescharacteristic
479C22×C4#1062535011yescharacteristic
480C22×C4#1062535011yescharacteristic
481C22×C4D4×D4711yescharacteristic
482C22×C4D4×D4711yescharacteristic
483C22×C4D4×D4711yescharacteristic
484C22×C4D4×D4711yescharacteristic
485C22×C4#1062535211yescharacteristic
486C22×C4#1062535211yescharacteristic
487C22×C4Q8×D4711yescharacteristic
488C22×C4Q8×D4711yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—22no—
491M16—22no—
492M16—22no—
493M16—22no—
494M16—41no—
495M16—41no—
496M16—41no—
497M16—41no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—948no—
507C4⋊C4—948no—
508C4⋊C4—948no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C4⋊C4—942no—
514C4⋊C4—1881no—
515C22⋊C4—22no—
516C22⋊C4—942no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4—1881no—
522C22⋊C4C2×D18814yes—
523C42—22no—
524C42—22no—
525C42—474no—
526C42—474no—
527C42—942no—
528C42—942no—
529C42—942no—
530C42—1881no—
531C23—81no—
532C23—942no—
533C23—3762no—
534C23—1881no—
535C23—1881no—
536C23#1309399411yescharacteristic
537C23#1309399411yescharacteristic
538C23#1309400411yescharacteristic
539C23#1309400411yescharacteristic
540C23#1309401211yescharacteristic
541C23#1309401211yescharacteristic
542C23C22×D18811yescharacteristic
543Q8—942no—
544Q8—942no—
545Q8—3768no—
546Q8—1881no—
547Q8—1881no—
548D4—942no—
549D4—942no—
550D4—1882no—
551D4—1882no—
552D4—1882no—
553D4—1882no—
554D4—1881no—
555D4—1881no—
556C2×C4—24no—
557C2×C4—82no—
558C2×C4—944no—
559C2×C4—944no—
560C2×C4—942no—
561C2×C4—3762no—
562C2×C4—3762no—
563C2×C4—3762no—
564C2×C4—1882no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4—1882no—
571C2×C4#1309399411yescharacteristic
572C2×C4#1309399411yescharacteristic
573C2×C4#1309400211yescharacteristic
574C2×C4#1309400211yescharacteristic
575C2×C4#1309400211yescharacteristic
576C2×C4#1309400211yescharacteristic
577C2×C4#1309400211yescharacteristic
578C2×C4#1309400211yescharacteristic
579C2×C4#1309400211yescharacteristic
580C2×C4#1309400211yescharacteristic
581C2×C4#1309400411yescharacteristic
582C2×C4#1309400411yescharacteristic
583C2×C4#1309401011yescharacteristic
584C2×C4#1309401011yescharacteristic
585C2×C4#1309401011yescharacteristic
586C2×C4#1309401011yescharacteristic
587C2×C4#1309401011yescharacteristic
588C2×C4#1309401011yescharacteristic
589C2×C4#1309401011yescharacteristic
590C2×C4#1309401011yescharacteristic
591C2×C4#1309401211yescharacteristic
592C2×C4#1309401211yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4C2×D4×D4711yescharacteristic
595C2×C4C2×Q8×D4711yescharacteristic
596C2×C4C2×#1062535211yescharacteristic
597C2×C4C2×#1062535011yescharacteristic
598C2×C4C2×#1062535011yescharacteristic
599C8—42no—
600C8—42no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—3762no—
609C22—3762no—
610C22—3762no—
611C22—1882no—
612C22#1568903611yescharacteristic
613C22#1568903611yescharacteristic
614C22#1568903611yescharacteristic
615C22#1568903611yescharacteristic
616C22C2×#1309399411yescharacteristic
617C22C2×#1309400411yescharacteristic
618C22C2×#1309401211yescharacteristic
619C4—44no—
620C4—3762no—
621C4—1884no—
622C4—1884no—
623C4—1882no—
624C4#1568903611yescharacteristic
625C4#1568903611yescharacteristic
626C4#1568903611yescharacteristic
627C4#1568903611yescharacteristic
628C4C2×#1309400211yescharacteristic
629C4C2×#1309400211yescharacteristic
630C4C2×#1309401011yescharacteristic
631C4C2×#1309401011yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—3762no—
640C2C2×#1568903611yescharacteristic
subgroupG/H
centerC4C2×#13094010
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#344C2
socleC2×C47C2×#393
prime radicalC22×#10625350C22
hypercenterC2×#344D47
hypocenterC47#23472
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. #20256793C2semidirect
5. #20244563C2semidirect
6. #20243099C2semidirect
7. C2×#15688880C2semidirect
8. C2×C47×#344C2semidirect
16. #15689676C22semidirect
29. #15688884C22semidirect
30. #15688880C22semidirect
34. C47×#344C22semidirect
45. C2×#10625350Q8semidirect
47. C22×Dic94Q8semidirect
48. C22×D188Q8semidirect
317. C2×#344D47semidirect
352. #344C2×D47semidirect
355. C47#23472semidirect

Maximal subgroups

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

subgroupindex
#202567932
C2×#156891392
C2×#156890962
#202445632
#202430992
C2×#156888802
C2×C47×#3442
#2347247