Finite Group Databasebeta

← #26319479

Subgroups — #26319479

Order 12032.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246032C211yesmaximal, characteristic
2#20244889C211yesmaximal, characteristic, complemented
3#20244769C211yesmaximal, characteristic, complemented
4#20244759C211yesmaximal, characteristic
5#20244703C211yesmaximal, characteristic
6#20244245C211yesmaximal, characteristic
7#20244113C211yesmaximal, characteristic, complemented
8#20244084C211yesmaximal, characteristic
9#20244081C211yesmaximal, characteristic, complemented
10#20244019C211yesmaximal, characteristic, complemented
11#20243963C211yesmaximal, characteristic, complemented
12#20243725C211yesmaximal, characteristic
13#20243648C211yesmaximal, characteristic
14#20243245C211yesmaximal, characteristic, complemented
15C47×#2645C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C2×C4×D188C2211yescharacteristic
18C2×#13093955C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093948C2211yescharacteristic
24C2×#13093948C2211yescharacteristic
25C2×#13093948C2211yescharacteristic
26C2×#13093944C2211yescharacteristic
27C2×#13093944C2211yescharacteristic
28C2×#13093944C2211yescharacteristic
29C2×#13093935C2211yescharacteristic
30C2×C4×C47⋊C8C2211yescharacteristic
31#15689025C2211yescharacteristic
32#15689025C2211yescharacteristic
33#15689021C2211yescharacteristic
34#15689021C2211yescharacteristic
35#15689012—21no—
36#15689012—21no—
37#15688985—21no—
38#15688982—21no—
39C4×C4⋊Dic47C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C47×#401—21no—
49C47×#400—21no—
50C47×#400—21no—
51C47×#400—21no—
52C47×#391C2211yescharacteristic
53C47×#391C2211yescharacteristic
54C47×#391C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#389C2211yescharacteristic
58C47×#376C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C4×D47—21no—
61C2×#10625336—22no—
62C2×#10625336—22no—
63C2×#10625336—41no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C4×D188—22no—
69C4×D188—22no—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×(C2×D47)⋊C4—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×C4×Dic47—21no—
81#13093955—22no—
82#13093955—22no—
83#13093955—41no—
84C4⋊(C47⋊C8)—22no—
85C4⋊(C47⋊C8)—22no—
86#13093948—22no—
87#13093948—22no—
88#13093948—41no—
89#13093944—22no—
90#13093944—22no—
91#13093944—41no—
92#13093935—41no—
93C4×C47⋊C8—41no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C22×Q8×C47C2311yescharacteristic
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2311yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C42×C47C2311yescharacteristic
105C2×C42×C47C2311yescharacteristic
106C2×C42×C47C2311yescharacteristic
107#95×C47—21no—
108#95×C47—21no—
109#95×C47—21no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118#95×C47D411yescharacteristic
119#95×C47D411yescharacteristic
120C23×D47—21no—
121C2×Q8×C47—21no—
122C2×Q8×C47—21no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2411yescharacteristic
138C22×Dic47—21no—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188#4112yes—
147C2×C4×D47—24no—
148C2×C4×D47—81no—
149C2×C4×D47—81no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—81no—
157C4⋊C4×C47—81no—
158C4⋊C4×C47—81no—
159C42×C47—21no—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—21no—
164C42×C47—21no—
165#10625336—44no—
166(C2×D47)⋊C4—24no—
167(C2×D47)⋊C4—81no—
168(C2×D47)⋊C4—81no—
169(C2×D47)⋊C4—81no—
170(C2×D47)⋊C4—81no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47#4112yes—
177Dic47⋊C4—81no—
178Dic47⋊C4—81no—
179C4×Dic47—81no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8#4112yes—
191C2×C47⋊C8#4112yes—
192C23×C47C22×D411yescharacteristic
193C22×D47—22no—
194C22×D47—41no—
195C22×D47—41no—
196C22×D47—41no—
197C22×D47—41no—
198C22×D47—41no—
199C22×D47—41no—
200Q8×C47—41no—
201Q8×C47—41no—
202Q8×C47—41no—
203Q8×C47—41no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47H(5,𝔽2)11yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×Dic47—22no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249D188—22no—
250D188—22no—
251D188—41no—
252D188—41no—
253C4×D47—84no—
254C47⋊C8—22no—
255C47⋊C8—22no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258#29440—471nomaximal, Sylow
259C22×C47#52511yescharacteristic
260C22×C47#53211yescharacteristic
261C22×C47#53711yescharacteristic
262C22×C47#57711yescharacteristic
263C22×C47#57711yescharacteristic
264C22×C47#57711yescharacteristic
265C22×C47#57711yescharacteristic
266C2×D47—42no—
267C2×D47—42no—
268C2×D47—42no—
269C2×D47—81no—
270C2×D47—81no—
271C2×D47—81no—
272C2×D47—81no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—41no—
279C4×C47—81no—
280C4×C47—81no—
281C4×C47—81no—
282C4×C47—81no—
283C4×C47#55111yescharacteristic
284C4×C47#55211yescharacteristic
285C4×C47#55311yescharacteristic
286C4×C47#55611yescharacteristic
287Dic47—42no—
288Dic47—81no—
289Dic47—81no—
290#2645D4711yescharacteristic, complemented
291#2319—471no—
292#2088—471no—
293#2066—471no—
294#2065—471no—
295#2055—471no—
296#1968—471no—
297#1941—471no—
298#1936—471no—
299#1935—471no—
300#1927—471no—
301#1919—471no—
302#1877—471no—
303#1864—471no—
304#1768—471no—
305C2×C47#260111yescharacteristic
306C2×C47#312311yescharacteristic
307C2×C47#312511yescharacteristic
308C2×C47#317311yescharacteristic
309C2×C47#317411yescharacteristic
310C2×C47#326011yescharacteristic
311C2×C47#326311yescharacteristic
312D47—82no—
313C22×SD16—471no—
314C2×C4×D4—471no—
315C2×#106—471no—
316C2×#106—471no—
317C2×#106—471no—
318C2×C4⋊C8—471no—
319C2×C4⋊C8—471no—
320C2×#103—471no—
321C2×#103—471no—
322C2×#103—471no—
323C2×#102—471no—
324C2×#102—471no—
325C2×#102—471no—
326C2×#97—471no—
327C2×C4×C8—471no—
328#401—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#391C2×D4711yescharacteristic
333#391C2×D4711yescharacteristic
334#391C2×D4711yescharacteristic
335#390—471no—
336#390—471no—
337#389—471no—
338#389—471no—
339#389C2×D4711yescharacteristic
340#389C2×D4711yescharacteristic
341#389C2×D4711yescharacteristic
342#388—941no—
343#388—941no—
344#381—941no—
345#380—941no—
346C4×C4⋊C4—471no—
347#376C2×D4711yescharacteristic
348#340—471no—
349#340—471no—
350#340—471no—
351#340—471no—
352#340—471no—
353#340—471no—
354#336—471no—
355#336—471no—
356C47#2944011yescharacteristic, complemented, Sylow
357C22×Q8C22×D4711yescharacteristic
358C22×D4—471no—
359C23×C4—941no—
360C2×SD16—942no—
361C2×SD16—942no—
362C2×SD16—1881no—
363C22×C8—471no—
364C22×C8—471no—
365C22×C8—471no—
366C22×C8—471no—
367C4×D4—942no—
368C4×D4—942no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4C22×D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C22⋊C4—941no—
381C2×C22⋊C4—941no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C42—941no—
386C2×C42C22×D4711yescharacteristic
387C2×C42C22×D4711yescharacteristic
388C2×C42C22×D4711yescharacteristic
389#106—942no—
390#106—942no—
391#106—1881no—
392C4⋊C8—942no—
393C4⋊C8—942no—
394#103—942no—
395#103—942no—
396#103—1881no—
397#102—942no—
398#102—942no—
399#102—1881no—
400#97—1881no—
401C4×C8—1881no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—941no—
412#95—941no—
413#95—941no—
414#95C22⋊D4711yescharacteristic
415#95C22⋊D4711yescharacteristic
416#95C22⋊D4711yescharacteristic
417#95C22⋊D4711yescharacteristic
418C24—941no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—472no—
426C2×D4—941no—
427C2×D4—941no—
428C2×D4—941no—
429C2×D4—941no—
430C2×D4—941no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—944no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—3761no—
440C22×C4—3761no—
441C22×C4C2×C22⋊D4711yescharacteristic
442C22×C4C2×C22⋊D4711yescharacteristic
443C22×C4C2×C22⋊D4711yescharacteristic
444C22×C4C2×C22⋊D4711yescharacteristic
445C22×C4C2×C22⋊D4711yescharacteristic
446C22×C4C2×C22⋊D4711yescharacteristic
447C22×C4C23×D4711yescharacteristic
448SD16—1884no—
449C2×C8—472no—
450C2×C8—472no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—941no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—941no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—472no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4—941no—
475C4⋊C4—941no—
476C4⋊C4—3761no—
477C4⋊C4—3761no—
478C22⋊C4—944no—
479C22⋊C4—3761no—
480C22⋊C4—3761no—
481C22⋊C4—3761no—
482C22⋊C4—3761no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—3761no—
490C23—942no—
491C23—1881no—
492C23—1881no—
493C23—1881no—
494C23—1881no—
495C23—1881no—
496C23—1881no—
497C23C22×C22⋊D4711yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—942no—
503D4—942no—
504D4—1881no—
505D4—1881no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—942no—
537C2×C4—3764no—
538C2×C4—1881no—
539C2×C4—1881no—
540C2×C4—1881no—
541C2×C4—1881no—
542C2×C4—1881no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4#41×D4711yescharacteristic
547C2×C4#41×D4711yescharacteristic
548C2×C4#41×D4711yescharacteristic
549C2×C4#41×D4711yescharacteristic
550C2×C4#1309407011yescharacteristic
551C2×C4#1309407111yescharacteristic
552C8—942no—
553C8—942no—
554C8—1881no—
555C8—1881no—
556C22—3761no—
557C22—3761no—
558C22—3761no—
559C22—3761no—
560C22—1882no—
561C22—1882no—
562C22—1882no—
563C22#1568963011yescharacteristic
564C22#1568966911yescharacteristic
565C22#1568970111yescharacteristic
566C22#1568993111yescharacteristic
567C22#1568993111yescharacteristic
568C22#1568993111yescharacteristic
569C22#1568993411yescharacteristic
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—3761no—
581C4—3761no—
582C4—1882no—
583C4#1568979811yescharacteristic
584C4#1568980911yescharacteristic
585C4#1568982411yescharacteristic
586C4#1568984011yescharacteristic
587C2—3762no—
588C2#2024898711yescharacteristic
589C2#2025363511yescharacteristic
590C2#2025365911yescharacteristic
591C2#2025399911yescharacteristic
592C2#2025401711yescharacteristic
593C2#2025482911yescharacteristic
594C2#2025485311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2645C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2645D47
hypocenterC47#29440
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ #376 ◁ #2645

Complements

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

NH ≅ G/Ntype
2. #20244889C2semidirect
3. #20244769C2semidirect
7. #20244113C2semidirect
9. #20244081C2semidirect
10. #20244019C2semidirect
11. #20243963C2semidirect
14. #20243245C2semidirect
15. C47×#2645C2semidirect
290. #2645D47semidirect
356. C47#29440semidirect

Maximal subgroups

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

subgroupindex
#202460322
#202448892
#202447692
#202447592
#202447032
#202442452
#202441132
#202440842
#202440812
#202440192
#202439632
#202437252
#202436482
#202432452
C47×#26452
#2944047