Finite Group Databasebeta

← #26231943

Subgroups — #26231943

Order 12032.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689795C211yesmaximal, characteristic
2C2×#15689202C211yesmaximal, characteristic, complemented
3C2×#15689123C212yesmaximal, complemented
4C4⋊C4×D188C211yesmaximal, characteristic, complemented
5#20244315C211yesmaximal, characteristic, complemented
6#20244194C211yesmaximal, characteristic, complemented
7#20243825C212yesmaximal, complemented
8#20243704C212yesmaximal, complemented
9#20243393C211yesmaximal, characteristic, complemented
10#20243327C212yesmaximal, complemented
11C4×#103×C47C211yesmaximal, characteristic, complemented
12C22×#10625354C2212yes—
13C22×#10625324C2212yes—
14#15689795—24no—
15#15689795C418yescomplemented
16C2×#13094021—21no—
17C2×#13094021C2211yescharacteristic
18C2×#13093999—22no—
19C2×#13093999C2212yes—
20C2×C4×D188—21no—
21C2×C4×D188—21no—
22C2×C4×D188C2211yescharacteristic
23C2×C4⋊C4×D47C2212yes—
24#15689202—24no—
25C2×C4⋊(C47⋊C8)C2211yescharacteristic
26#15689123—28no—
27C2×#13093948C2212yes—
28C2×#13093946C2212yes—
29C2×#13093946C2212yes—
30C2×#13093944C2212yes—
31C2×#13093944C2212yes—
32C2×(C2×D47)⋊C8C2212yes—
33#15689021—21no—
34#15688997—22no—
35#15688993C2211yescharacteristic
36#15688980C2212yes—
37#15688885C2212yes—
38C2×C4×Q8×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×C4×C8×C47C2211yescharacteristic
42C4×C4⋊C4×C47C2211yescharacteristic
43C47×#340C2211yescharacteristic
44C47×#340C2211yescharacteristic
45C2×#10625354—24no—
46C2×#10625354—24no—
47C2×#10625354—24no—
48C2×#10625354—42no—
49C2×#10625354—42no—
50C2×#10625354C2×C418yescomplemented
51C22×D188—22no—
52C22×D188—21no—
53C22×D188—22no—
54C22×D188—21no—
55C22×D188D411yescharacteristic
56C22×D188C2312yes—
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47C2312yes—
60C2×#10625324—24no—
61C2×#10625324—24no—
62C2×#10625324—42no—
63C22×C47⋊C8C2312yes—
64#13094021—28no—
65#13094021—22no—
66#13094021C2×C414yescomplemented
67#13093999—24no—
68#13093999—216no—
69#13093999C2×C418yescomplemented
70C4×D188—28no—
71C4×D188—44no—
72C4×D188C2×C414yes—
73C4×D188D414yes—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47D411yescharacteristic
77C2×C4⋊Dic47C2312yes—
78C2×Dic47⋊C4—22no—
79C4⋊C4×D47—24no—
80C4⋊C4×D47—42no—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4D412yes—
84C4⋊(C47⋊C8)—22no—
85#13093948—24no—
86#13093946—24no—
87#13093946—42no—
88#13093944—24no—
89#13093944—42no—
90(C2×D47)⋊C8—24no—
91C47⋊#95—22no—
92C22×Q8×C47C2311yescharacteristic
93C22×C8×C47C2311yescharacteristic
94C22×C8×C47C2311yescharacteristic
95C4×Q8×C47—22no—
96C4×Q8×C47C2×C414yescomplemented
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47C2311yescharacteristic
101C2×C42×C47—21no—
102C2×C42×C47—21no—
103C2×C42×C47C2311yescharacteristic
104#103×C47—22no—
105#103×C47D414yescomplemented
106C4×C8×C47—22no—
107#95×C47—21no—
108C23×D47—22no—
109C23×D47C2×D412yes—
110C2×Q8×C47—21no—
111C2×Q8×C47—21no—
112C2×Q8×C47—21no—
113C2×Q8×C47C22×C412yes—
114C2×Q8×C47C2×D412yes—
115C2×Q8×C47#4112yes—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2411yescharacteristic
123C22×Dic47—22no—
124C22×Dic47C2×D412yes—
125#10625354—216no—
126#10625354—48no—
127#10625354—48no—
128#10625354—48no—
129C2×D188—22no—
130C2×D188—22no—
131C2×D188—22no—
132C2×D188—22no—
133C2×D188—22no—
134C2×D188—22no—
135C2×D188—28no—
136C2×D188—24no—
137C2×D188—22no—
138C2×D188—28no—
139C2×D188—24no—
140C2×D188—44no—
141C2×D188—44no—
142C2×D188—42no—
143C2×D188—42no—
144C2×D188—81no—
145C2×D188—81no—
146C2×D188—82no—
147C2×D188—82no—
148C2×D188C22⋊C414yes—
149C2×D188C22×C414yes—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—28no—
155C2×C4×D47—44no—
156C2×C4×D47—44no—
157C2×C4×D47—44no—
158C2×C4×D47—44no—
159C2×C4×D47—82no—
160C2×C4×D47C22×C414yes—
161C2×C4×D47C2×D414yes—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47C2×D412yes—
168C4⋊C4×C47—24no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47C22×C412yes—
174C4⋊C4×C47C2×D412yes—
175C42×C47—24no—
176C42×C47—42no—
177C42×C47C22×C412yes—
178C42×C47C2×D412yes—
179(C2×D47)⋊C4—28no—
180(C2×D47)⋊C4—44no—
181(C2×D47)⋊C4C22⋊C418yes—
182C4⋊Dic47—22no—
183C4⋊Dic47—22no—
184C4⋊Dic47—42no—
185C4⋊Dic47—81no—
186C4⋊Dic47C22⋊C414yes—
187Dic47⋊C4—44no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191#10625324—48no—
192C23×C47C22×D411yescharacteristic
193C22×D47—22no—
194C22×D47—22no—
195C22×D47—22no—
196C22×D47—22no—
197C22×D47—22no—
198C22×D47—22no—
199C22×D47—24no—
200C22×D47—42no—
201C22×D47—42no—
202C22×D47—42no—
203C22×D47—42no—
204C22×D47—42no—
205C22×D47—42no—
206C22×D47C2×C22⋊C414yes—
207Q8×C47—22no—
208Q8×C47—22no—
209Q8×C47—22no—
210Q8×C47C4×D414yescomplemented
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47C2×C22⋊C412yes—
226C2×C4×C47C2×C22⋊C412yes—
227C2×C4×C47AGL(1,ℤ/8)12yes—
228C2×C4×C47#13712yes—
229C2×C4×C47C23×C411yescharacteristic
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47H(5,𝔽2)11yescharacteristic
234C2×C4×C47H(5,𝔽2)11yescharacteristic
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47C2×C22⋊C414yes—
241D188—24no—
242D188—24no—
243D188—28no—
244D188—416no—
245D188—42no—
246D188—42no—
247D188—48no—
248D188—84no—
249D188—88no—
250C4×D47—24no—
251C4×D47—24no—
252C4×D47—24no—
253C4×D47—24no—
254C4×D47—416no—
255C4×D47—88no—
256C8×C47—22no—
257C8×C47—41no—
258C47⋊C8—42no—
259#22432—471nomaximal, Sylow
260C22×C47C22×C22⋊C411yescharacteristic
261C22×C47D4211yescharacteristic
262C22×C47#54611yescharacteristic
263C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C47C2×#13711yescharacteristic
265C22×C47#57611yescharacteristic
266C22×C47#57711yescharacteristic
267C2×D47—24no—
268C2×D47—24no—
269C2×D47—24no—
270C2×D47—42no—
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—44no—
275C2×D47—44no—
276C2×D47—44no—
277C2×D47—82no—
278C2×D47—82no—
279C2×D47—82no—
280C2×D47—82no—
281C4×C47—24no—
282C4×C47—22no—
283C4×C47—42no—
284C4×C47—42no—
285C4×C47—81no—
286C4×C47#41714yescomplemented
287C4×C47C2×C4×D411yescharacteristic
288C4×C47#51811yescharacteristic
289C4×C47D4211yescharacteristic
290C4×C47#54611yescharacteristic
291Dic47—24no—
292Dic47—82no—
293C2×#550—471no—
294C2×#436—471no—
295C2×#417—472no—
296D4×C4⋊C4—471no—
297#1982—471no—
298#1957—471no—
299#1895—472no—
300#1874—472no—
301#1803—471no—
302#1788—472no—
303C4×#103D4711yescharacteristic, complemented
304C2×C47D4×C22⋊C411yescharacteristic
305C2×C47C2×#41711yescharacteristic
306C2×C47#289711yescharacteristic
307C2×C47#327411yescharacteristic
308C2×C47#327811yescharacteristic
309C2×C47#333211yescharacteristic
310C2×C47#333311yescharacteristic
311D47—44no—
312D47—84no—
313C22×#41—472no—
314C22×M16—472no—
315#550—478no—
316#550—944no—
317C2×#127—471no—
318C2×#127—941no—
319C2×#121—472no—
320C2×#121—942no—
321C2×C4×Q8C2×D4711yescharacteristic
322C2×C4×D4—471no—
323C2×C4×D4—941no—
324C2×C4×D4—941no—
325C22×C4⋊C4—472no—
326#436—944no—
327C2×C4⋊C8—471no—
328#417—948no—
329C2×#103—472no—
330C2×#103C2×D4711yescharacteristic
331C2×#103C2×D4711yescharacteristic
332C2×#102—472no—
333C2×#102—472no—
334C2×#102—472no—
335C2×#102—472no—
336C2×C22⋊C8—472no—
337C2×C4×C8C2×D4711yescharacteristic
338#389—941no—
339#385—942no—
340#384—471no—
341#380—472no—
342C4×C4⋊C4C2×D4711yescharacteristic
343#340—472no—
344#340C2×D4711yescharacteristic
345#340C2×D4711yescharacteristic
346C47#2243211yescharacteristic, complemented, Sylow
347C2×#41—478no—
348C2×#41—944no—
349C2×#41—944no—
350C2×#41—944no—
351C2×#41—1882no—
352C2×#41—1882no—
353C22×Q8C22×D4711yescharacteristic
354C22×D4—471no—
355C22×D4—472no—
356C22×D4—942no—
357C22×D4—942no—
358C22×D4—941no—
359C22×D4—941no—
360C23×C4—472no—
361C23×C4—942no—
362C23×C4—942no—
363C2×M16—944no—
364C2×M16—944no—
365C2×M16—1882no—
366C22×C8—472no—
367C22×C8C22×D4711yescharacteristic
368C22×C8C22×D4711yescharacteristic
369#127—474no—
370#127—948no—
371#127—942no—
372#121—478no—
373#121—9416no—
374#121—944no—
375C4×Q8—22no—
376C4×Q8C4×D4714yescomplemented
377C4×D4—474no—
378C4×D4—474no—
379C4×D4—948no—
380C4×D4—1884no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—944no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—1882no—
389C2×C4⋊C4C22×D4711yescharacteristic
390C2×C4⋊C4C22×D4711yescharacteristic
391C2×C4⋊C4C22×D4711yescharacteristic
392C2×C22⋊C4—472no—
393C2×C22⋊C4—942no—
394C2×C22⋊C4—942no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C22×D4711yescharacteristic
398C4⋊C8—942no—
399#103—22no—
400#103—944no—
401#103D18814yescomplemented
402#102—944no—
403#102—944no—
404#102—1882no—
405#102—1882no—
406C22⋊C8—944no—
407C4×C8—22no—
408#95—21no—
409#95—942no—
410C24—472no—
411C24—942no—
412#41—9416no—
413#41—1888no—
414#41—1888no—
415#41—1888no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C2×C4×D4712yes—
420C2×Q8C2×D18812yes—
421C2×Q8#1062535012yes—
422C2×D4—474no—
423C2×D4—474no—
424C2×D4—948no—
425C2×D4—948no—
426C2×D4—944no—
427C2×D4—944no—
428C2×D4—942no—
429C2×D4—942no—
430C2×D4—942no—
431C2×D4—942no—
432C2×D4—942no—
433C2×D4—942no—
434C2×D4—942no—
435C2×D4—3761no—
436C2×D4—3761no—
437C2×D4—3762no—
438C2×D4—3762no—
439C2×D4—1884no—
440C2×D4—1884no—
441C2×D4—1882no—
442C2×D4—1882no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—472no—
448C22×C4—474no—
449C22×C4—474no—
450C22×C4—948no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—3762no—
457C22×C4—1884no—
458C22×C4—1884no—
459C22×C4—1884no—
460C22×C4—1884no—
461C22×C4D4×D4711yescharacteristic
462C22×C4D4×D4711yescharacteristic
463C22×C4C23×D4711yescharacteristic
464M16—1888no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—942no—
471C2×C8—942no—
472C2×C8—942no—
473C2×C8C2×D18812yes—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—474no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C4⋊C4—3761no—
483C4⋊C4—1884no—
484C4⋊C4—1882no—
485C4⋊C4C2×C4×D4712yes—
486C4⋊C4C2×D18812yes—
487C22⋊C4—478no—
488C22⋊C4—948no—
489C22⋊C4—1884no—
490C42—24no—
491C42—42no—
492C42C2×C4×D4712yes—
493C42D4×D4712yes—
494C23—474no—
495C23—942no—
496C23—942no—
497C23—942no—
498C23—942no—
499C23—942no—
500C23—942no—
501C23—944no—
502C23—1882no—
503C23—1882no—
504C23—1882no—
505C23—1882no—
506C23—1882no—
507C23—1882no—
508C23C2×D4×D4711yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8C4×D18814yescomplemented
513D4—944no—
514D4—944no—
515D4—948no—
516D4—3764no—
517D4—3768no—
518D4—18816no—
519D4—1882no—
520D4—1882no—
521D4—1888no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—474no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—944no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—944no—
543C2×C4—3768no—
544C2×C4—18816no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4C22⋊C4×D4712yes—
549C2×C4C22⋊C4×D4712yes—
550C2×C4#1309405112yes—
551C2×C4#1309405612yes—
552C2×C4C22×C4×D4711yescharacteristic
553C2×C4C2×D4×D4711yescharacteristic
554C2×C4C22×D18811yescharacteristic
555C2×C4C2×#1062535011yescharacteristic
556C2×C4#1309407011yescharacteristic
557C2×C4#1309407011yescharacteristic
558C8—22no—
559C8—41no—
560C8—1882no—
561C22—944no—
562C22—944no—
563C22—944no—
564C22—3762no—
565C22—3762no—
566C22—3762no—
567C22—3762no—
568C22—1884no—
569C22—1884no—
570C22—1884no—
571C22—1882no—
572C22—1882no—
573C22—1882no—
574C22—1882no—
575C22C2×C22⋊C4×D4711yescharacteristic
576C22D4×D18811yescharacteristic
577C22#1568976911yescharacteristic
578C22C2×#1309405111yescharacteristic
579C22C2×#1309405611yescharacteristic
580C22#1568992511yescharacteristic
581C22#1568993011yescharacteristic
582C4—22no—
583C4—24no—
584C4—42no—
585C4—42no—
586C4—81no—
587C4—944no—
588C4—3762no—
589C4#1568912314yescomplemented
590C4C2×C4×D18811yescharacteristic
591C4#1568959711yescharacteristic
592C4D4×D18811yescharacteristic
593C4#1568976911yescharacteristic
594C2—3764no—
595C2—1884no—
596C2C22⋊C4×D18811yescharacteristic
597C2C2×#1568912311yescharacteristic
598C2#2025191011yescharacteristic
599C2#2025500911yescharacteristic
600C2#2025505511yescharacteristic
601C2#2025571711yescharacteristic
602C2#2025572811yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×#103×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689795C2
cosocleC22×C4×C47C24
hypercenterC4×#103D47
hypocenterC47#22432
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×#15689202C2semidirect
3. C2×#15689123C2semidirect
4. C4⋊C4×D188C2semidirect
5. #20244315C2semidirect
6. #20244194C2semidirect
7. #20243825C2semidirect
8. #20243704C2semidirect
9. #20243393C2semidirect
10. #20243327C2semidirect
11. C4×#103×C47C2semidirect
15. #15689795C4semidirect
50. C2×#10625354C2×C4semidirect
66. #13094021C2×C4semidirect
69. #13093999C2×C4semidirect
96. C4×Q8×C47C2×C4semidirect
105. #103×C47D4semidirect
210. Q8×C47C4×D4semidirect
286. C4×C47#417semidirect
303. C4×#103D47semidirect
346. C47#22432semidirect
376. C4×Q8C4×D47semidirect
401. #103D188semidirect
512. Q8C4×D188semidirect
589. C4#15689123semidirect

Maximal subgroups

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

subgroupindex
C2×#156897952
C2×#156892022
C2×#156891232
C4⋊C4×D1882
#202443152
#202441942
#202438252
#202437042
#202433932
#202433272
C4×#103×C472
#2243247