Finite Group Databasebeta

← #26215873

Subgroups — #26215873

Order 12032.

1438 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094030C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic, complemented
3C2×#107×D47C211yesmaximal, characteristic, complemented
4#20245977C212yesmaximal
5#20243420C212yesmaximal, complemented
6#20243419C212yesmaximal, complemented
7#20243417C211yesmaximal, characteristic, complemented
8#20243414C211yesmaximal, characteristic, complemented
9#20243414C211yesmaximal, characteristic, complemented
10#20243106C212yesmaximal, complemented
11C47×#1808C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C2×#13094030—24no—
14C2×#13094030—24no—
15C2×#13094030C418yescomplemented
16C22×#10625329C2211yescharacteristic
17C22×#10625324C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20C22×C8×D47C2211yescharacteristic
21C2×#13093982C2212yes—
22C2×C4⋊C4×D47C2212yes—
23#15689160—24no—
24C2×#13093958C2211yescharacteristic
25C2×#13093958C2211yescharacteristic
26C2×#13093957C2212yes—
27#107×D47—24no—
28C2×#13093955C2212yes—
29#15689027—22no—
30#15689023—22no—
31#15689001—22no—
32#15688999—22no—
33#15688983C2212yes—
34#15688980C2212yes—
35#15688980C2212yes—
36#15688886C2212yes—
37#15688885C2212yes—
38#15688885C2212yes—
39C23×C8×C47C2211yescharacteristic
40C2×#107×C47C2211yescharacteristic
41C2×#107×C47C2211yescharacteristic
42C47×#380C2212yes—
43C47×#340C2212yes—
44C2×#10625350—22no—
45C2×#10625350—22no—
46C2×#10625350—22no—
47C2×#10625350—22no—
48C2×#10625350C2×C414yes—
49C2×#10625350Q814yes—
50C22×Dic94D411yescharacteristic
51C22×D188D411yescharacteristic
52C22×C22⋊D47D411yescharacteristic
53C22×C22⋊D47D411yescharacteristic
54C22×C4×D47—22no—
55C22×C4×D47C2311yescharacteristic
56C22×C4×D47C2311yescharacteristic
57#13094030—232no—
58C2×#10625329—22no—
59C2×#10625329—22no—
60C2×#10625329C2×C414yescomplemented
61C2×#10625324—22no—
62C2×#10625324—22no—
63C2×#10625324—22no—
64C2×#10625324—22no—
65C2×#10625324C2×C414yes—
66C2×#10625324C2×C414yescomplemented
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C2×C8×D47—22no—
70C2×C8×D47—22no—
71C2×C8×D47C2×C414yes—
72C2×C8×D47C2×C414yescomplemented
73C2×C8×D47D414yes—
74C2×C8×D47D414yes—
75#13093982—24no—
76#13093982—24no—
77C2×C4⋊Dic47C2312yes—
78C2×C4⋊Dic47C2312yes—
79C2×Dic47⋊C4—22no—
80C4⋊C4×D47—24no—
81C4⋊C4×D47—24no—
82C2×C22⋊Dic47—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×C4×Dic47—22no—
87#13093958—22no—
88#13093958—22no—
89#13093957—24no—
90#13093955—24no—
91C47⋊#95—22no—
92C47⋊#95—22no—
93C47⋊#95—22no—
94C23×C4×C47C2311yescharacteristic
95C22×C8×C47—22no—
96C22×C8×C47—22no—
97C22×C8×C47C2×C414yescomplemented
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2312yes—
101C2×C4⋊C4×C47C2312yes—
102C2×C22⋊C4×C47—22no—
103#107×C47—22no—
104#107×C47—22no—
105#95×C47—22no—
106C24×C47C2×D411yescharacteristic
107C23×D47C2×D411yescharacteristic
108C23×D47C2×D411yescharacteristic
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47C22×C412yes—
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×Q812yes—
118C22×C4×C47C2411yescharacteristic
119C2×C22⋊D47—22no—
120C2×C22⋊D47—22no—
121C2×C22⋊D47—22no—
122C2×C22⋊D47—22no—
123C2×C22⋊D47C4⋊C414yes—
124C2×C22⋊D47C4⋊C414yes—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47C2×D411yescharacteristic
128C22×Dic47C2×D411yescharacteristic
129#10625350—28no—
130#10625350—28no—
131#10625350—28no—
132#10625350—28no—
133C2×D188—22no—
134C2×D188—22no—
135C2×D188C4⋊C414yes—
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—44no—
141C2×C4×D47—82no—
142C2×C4×D47—82no—
143C2×C4×D47C22×C412yes—
144C2×C4×D47C22×C412yes—
145C2×C4×D47C2×D412yes—
146C2×C4×D47C2×D412yes—
147C2×C4×D47C2×Q812yes—
148C2×C4×D47C2×Q812yes—
149C2×C4×D47#4112yes—
150C2×C4×D47#4112yes—
151C2×Dic94—22no—
152C2×Dic94—22no—
153C2×Dic94C4⋊C414yes—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—28no—
157C2×C8×C47C22×C412yes—
158C2×C8×C47C22×C412yes—
159C2×C8×C47C2×D412yes—
160C2×C8×C47C2×D412yes—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C22⋊C4×C47—82no—
166C22⋊Dic47—82no—
167(C2×D47)⋊C4—44no—
168(C2×D47)⋊C4—82no—
169(C2×D47)⋊C4—82no—
170C4⋊Dic47—22no—
171C4⋊Dic47—22no—
172C4⋊Dic47—22no—
173C4⋊Dic47—22no—
174Dic47⋊C4—44no—
175C4×Dic47—44no—
176#10625329—28no—
177C2×C47⋊C8—21no—
178C2×C47⋊C8—21no—
179C2×C47⋊C8C22×C412yes—
180C2×C47⋊C8C22×C412yes—
181C2×C47⋊C8C2×D412yes—
182C2×C47⋊C8C2×D412yes—
183#10625324—28no—
184#10625324—28no—
185C8×D47—28no—
186C8×D47C22⋊C4116yescomplemented
187C23×C47—21no—
188C23×C47—21no—
189C23×C47—21no—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47C2×C4⋊C412yes—
194C23×C47C22×D411yescharacteristic
195C22×D47—21no—
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47—21no—
201C22×D47—21no—
202C22×D47—21no—
203C22×D47—21no—
204C22×D47—21no—
205C22×D47C2×C4⋊C412yes—
206C22×D47C2×C4⋊C412yes—
207C22×D47#12112yes—
208C22×D47#12112yes—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47C2×C4⋊C412yes—
222C2×C4×C47C23×C411yescharacteristic
223C2×C4×C47C22×D411yescharacteristic
224C2×C4×C47C22×D411yescharacteristic
225C2×C4×C47C22×Q811yescharacteristic
226C2×C4×C47C2×#4111yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C22⋊D47—28no—
229C22⋊D47—28no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47C2×C4⋊C412yes—
239C2×Dic47C2×C4⋊C412yes—
240C2×Dic47#12112yes—
241C2×Dic47#12112yes—
242D188—28no—
243C4×D47—22no—
244C4×D47—22no—
245C4×D47—22no—
246C4×D47—22no—
247C4×D47—88no—
248C4×D47C2×C22⋊C414yes—
249C4×D47#11714yes—
250C4×D47C22⋊Q814yes—
251C4×D47C22⋊Q814yes—
252Dic94—28no—
253C8×C47—22no—
254C8×C47C2×C22⋊C414yes—
255C47⋊C8—22no—
256C47⋊C8C2×C22⋊C414yes—
257#20663—471nomaximal, Sylow
258C22×C47—22no—
259C22×C47—22no—
260C22×C47—22no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47C22×C4⋊C411yescharacteristic
266C22×C47C2×#12111yescharacteristic
267C22×C47C2×#12111yescharacteristic
268C22×C47#57611yescharacteristic
269C22×C47#57611yescharacteristic
270C22×C47#57811yescharacteristic
271C22×C47#57811yescharacteristic
272C2×D47—22no—
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—22no—
276C2×D47—22no—
277C2×D47—22no—
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—41no—
284C2×D47—41no—
285C2×D47#38014yes—
286C4×C47—22no—
287C4×C47—82no—
288C4×C47—82no—
289C4×C47C22×C22⋊C411yescharacteristic
290C4×C47C2×#11711yescharacteristic
291C4×C47C2×C22⋊Q811yescharacteristic
292C4×C47C2×C22⋊Q811yescharacteristic
293Dic47—22no—
294Dic47—82no—
295Dic47—82no—
296Dic47#38014yes—
297C22×#131—471no—
298C2×#427—471no—
299C22×#107—471no—
300#2311—472no—
301#1809—472no—
302#1809—472no—
303#1808—471no—
304#1808—471no—
305#1808—471no—
306#1808D4711yescharacteristic, complemented
307#1736—472no—
308C2×C47—42no—
309C2×C47C2×#38011yescharacteristic
310C2×C47#291311yescharacteristic
311C2×C47#291311yescharacteristic
312C2×C47#305811yescharacteristic
313C2×C47#305911yescharacteristic
314C2×C47#306111yescharacteristic
315C2×C47#306111yescharacteristic
316D47—24no—
317D47—42no—
318C22×#41—471no—
319C2×#131—478no—
320C2×#131—944no—
321C2×#131—944no—
322C22×M16—471no—
323C22×M16—471no—
324C22×M16—471no—
325C23×C8—471no—
326C23×C8—471no—
327C23×C8C2×D4711yescharacteristic
328C2×#117—472no—
329C22×C4⋊C4—472no—
330#427—944no—
331C2×#107—471no—
332C2×#107—471no—
333C2×#107—472no—
334C2×#107—944no—
335C2×#107C2×D4711yescharacteristic
336C2×#107C2×D4711yescharacteristic
337C2×#106—472no—
338#391—942no—
339#390—942no—
340#386—942no—
341#386—942no—
342#380—472no—
343#380—472no—
344#380—472no—
345#380C2×D4712yes—
346#340—472no—
347#340—472no—
348#340—472no—
349#340C2×D4712yes—
350C47#2066311yescharacteristic, complemented, Sylow
351C2×#41—474no—
352C2×#41—474no—
353C2×#41—942no—
354C2×#41—942no—
355C2×#41—942no—
356C2×#41—942no—
357C22×Q8—471no—
358C22×D4—471no—
359C22×D4—471no—
360C22×D4—471no—
361C23×C4—471no—
362C23×C4—471no—
363C23×C4—942no—
364C23×C4C22×D4711yescharacteristic
365#131—9432no—
366C2×M16—474no—
367C2×M16—474no—
368C2×M16—474no—
369C2×M16—942no—
370C2×M16—942no—
371C2×M16—942no—
372C2×M16—942no—
373C2×M16—942no—
374C2×M16—942no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—471no—
378C22×C8—474no—
379C22×C8—474no—
380C22×C8—474no—
381C22×C8—471no—
382C22×C8—474no—
383C22×C8—942no—
384C22×C8—942no—
385C22×C8C4×D4714yescomplemented
386C22×C8C22×D4711yescharacteristic
387C22×C8C22×D4711yescharacteristic
388#117—944no—
389#117—944no—
390C2×C4⋊C4—472no—
391C2×C4⋊C4—472no—
392C2×C4⋊C4—944no—
393C2×C4⋊C4—944no—
394C2×C4⋊C4—942no—
395C2×C4⋊C4C22×D4712yes—
396C2×C4⋊C4C22×D4712yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—942no—
399C2×C22⋊C4—942no—
400C2×C22⋊C4—942no—
401C2×C22⋊C4—942no—
402C2×C42—942no—
403#107—22no—
404#107—22no—
405#107—944no—
406#107—942no—
407#107—942no—
408#106—944no—
409#95—22no—
410#95—942no—
411#95—942no—
412#95—942no—
413C24—471no—
414C24—471no—
415C24D4×D4711yescharacteristic
416#41—948no—
417#41—948no—
418#41—948no—
419#41—948no—
420C2×Q8—474no—
421C2×Q8—942no—
422C2×Q8—942no—
423C2×D4—474no—
424C2×D4—474no—
425C2×D4—474no—
426C2×D4—942no—
427C2×D4—942no—
428C2×D4—942no—
429C2×D4—942no—
430C2×D4—942no—
431C2×D4—942no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—471no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—472no—
443C22×C4—472no—
444C22×C4—472no—
445C22×C4—471no—
446C22×C4—472no—
447C22×C4—472no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—3762no—
455C22×C4—3762no—
456C22×C4—1884no—
457C22×C4C2×C4×D4712yes—
458C22×C4D4×D4711yescharacteristic
459C22×C4Q8×D4712yes—
460C22×C4C23×D4711yescharacteristic
461M16—948no—
462M16—948no—
463M16—948no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—28no—
467C2×C8—472no—
468C2×C8—472no—
469C2×C8—472no—
470C2×C8—4716no—
471C2×C8—472no—
472C2×C8—941no—
473C2×C8—941no—
474C2×C8—948no—
475C2×C8C2×C4×D4712yes—
476C2×C8C2×C4×D4712yes—
477C2×C8D4×D4712yes—
478C2×C8D4×D4712yes—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—942no—
484C4⋊C4—942no—
485C4⋊C4—942no—
486C4⋊C4—942no—
487C4⋊C4—1884no—
488C22⋊C4—82no—
489C22⋊C4—3762no—
490C22⋊C4—3762no—
491C22⋊C4—3762no—
492C22⋊C4—1884no—
493C42—1884no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—472no—
501C23—472no—
502C23—472no—
503C23—472no—
504C23—941no—
505C23—941no—
506C23—941no—
507C23—941no—
508C23—941no—
509C23—941no—
510C23—941no—
511C23—941no—
512C23—941no—
513C23—941no—
514C23C4⋊C4×D4712yes—
515C23C2×D4×D4711yescharacteristic
516Q8—948no—
517D4—948no—
518D4—948no—
519D4—948no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—472no—
533C2×C4—472no—
534C2×C4—472no—
535C2×C4—474no—
536C2×C4—474no—
537C2×C4—474no—
538C2×C4—474no—
539C2×C4—472no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—3768no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4C4⋊C4×D4712yes—
554C2×C4C22×C4×D4711yescharacteristic
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4C2×D4×D4711yescharacteristic
557C2×C4C2×Q8×D4711yescharacteristic
558C2×C4#41×D4711yescharacteristic
559C2×C4#41×D4711yescharacteristic
560C8—22no—
561C8—474no—
562C8—942no—
563C8C22⋊C4×D4714yes—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—474no—
572C22—942no—
573C22—942no—
574C22—942no—
575C22—942no—
576C22—942no—
577C22—942no—
578C22—942no—
579C22—942no—
580C22—942no—
581C22—1881no—
582C22—1881no—
583C22—1881no—
584C22—1881no—
585C22C2×C4⋊C4×D4711yescharacteristic
586C22#121×D4711yescharacteristic
587C22#121×D4711yescharacteristic
588C22#1568992411yescharacteristic
589C22#1568992511yescharacteristic
590C22#1568993611yescharacteristic
591C22#1568993711yescharacteristic
592C4—22no—
593C4—82no—
594C4—82no—
595C4—474no—
596C4—942no—
597C4—3762no—
598C4—3762no—
599C4C2×C22⋊C4×D4711yescharacteristic
600C4#117×D4711yescharacteristic
601C4C22⋊Q8×D4711yescharacteristic
602C4C22⋊Q8×D4711yescharacteristic
603C2—42no—
604C2—944no—
605C2—1882no—
606C2#380×D4711yescharacteristic
607C2#2025198411yescharacteristic
608C2#2025198511yescharacteristic
609C2#2025303111yescharacteristic
610C2#2025303811yescharacteristic
611C2#2025305311yescharacteristic
612C2#2025305911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1808C2
socleC23×C47C22×D4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenter#1808D47
hypocenterC47#20663
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#15689160C2semidirect
3. C2×#107×D47C2semidirect
5. #20243420C2semidirect
6. #20243419C2semidirect
7. #20243417C2semidirect
8. #20243414C2semidirect
9. #20243414C2semidirect
10. #20243106C2semidirect
11. C47×#1808C2semidirect
15. C2×#13094030C4semidirect
60. C2×#10625329C2×C4semidirect
66. C2×#10625324C2×C4semidirect
72. C2×C8×D47C2×C4semidirect
97. C22×C8×C47C2×C4semidirect
186. C8×D47C22⋊C4semidirect
306. #1808D47semidirect
350. C47#20663semidirect
385. C22×C8C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×#130940302
C2×#156891602
C2×#107×D472
#202459772
#202434202
#202434192
#202434172
#202434142
#202431062
C47×#18082
#2066347