Finite Group Databasebeta

← #26318874

Subgroups — #26318874

Order 12032.

722 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245852C211yesmaximal, characteristic
2#20244870C211yesmaximal, characteristic, complemented
3#20244802C211yesmaximal, characteristic
4#20244723C211yesmaximal, characteristic, complemented
5#20244531C211yesmaximal, characteristic
6#20244015C211yesmaximal, characteristic
7#20244008C211yesmaximal, characteristic
8#20243980C211yesmaximal, characteristic, complemented
9#20243973C211yesmaximal, characteristic, complemented
10#20243970C211yesmaximal, characteristic, complemented
11#20243956C211yesmaximal, characteristic, complemented
12#20243648C211yesmaximal, characteristic
13#20243634C211yesmaximal, characteristic
14#20243531C211yesmaximal, characteristic, complemented
15C4×#125×C47C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17C2×#13093981—21no—
18C2×#13093957C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093955C2211yescharacteristic
21C2×#13093955C2211yescharacteristic
22C2×#13093944C2211yescharacteristic
23C2×#13093944C2211yescharacteristic
24C2×#13093944C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26#15689025C2211yescharacteristic
27#15689025C2211yescharacteristic
28#15689021C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15689014—21no—
31#15689014—21no—
32C4×C4⋊Dic47C2211yescharacteristic
33C4×(C2×D47)⋊C4—21no—
34#15688885C2211yescharacteristic
35#15688885C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×#125×C47C2211yescharacteristic
49C47×#389C2211yescharacteristic
50C47×#389C2211yescharacteristic
51C47×#387—21no—
52C47×#387—21no—
53C47×#382C2211yescharacteristic
54C4×C4⋊C4×C47—21no—
55C4×C4⋊C4×C47—21no—
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C43×C47C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C4×D47—21no—
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C4×D188—22no—
66C4×D188—22no—
67#13093981—44no—
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×(C2×D47)⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×(C2×D47)⋊C4—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×C4×Dic47—21no—
79#13093957—22no—
80#13093957—22no—
81#13093955—22no—
82#13093955—22no—
83#13093944—22no—
84#13093944—22no—
85#13093944—22no—
86#13093944—22no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90#125×C47—22no—
91#125×C47—22no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47C2311yescharacteristic
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102C2×C42×C47D411yescharacteristic
103C2×C42×C47D411yescharacteristic
104C2×C42×C47D411yescharacteristic
105C2×C42×C47D411yescharacteristic
106C2×C42×C47C2311yescharacteristic
107C2×C42×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109#95×C47—21no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115C23×D47—21no—
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×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2411yescharacteristic
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C2×D188—21no—
131C2×D188—21no—
132C2×D188—21no—
133C2×D188—21no—
134C2×D188—21no—
135C2×D188#4112yes—
136C2×C4×D47—24no—
137C2×C4×D47—42no—
138C2×C4×D47—42no—
139C4⋊C4×C47—24no—
140C4⋊C4×C47—24no—
141C4⋊C4×C47—21no—
142C4⋊C4×C47—21no—
143C4⋊C4×C47—21no—
144C4⋊C4×C47—21no—
145C4⋊C4×C47—21no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—42no—
148C4⋊C4×C47—42no—
149C4⋊C4×C47#4112yes—
150C4⋊C4×C47#4112yes—
151C42×C47—22no—
152C42×C47—22no—
153C42×C47—21no—
154C42×C47—21no—
155C42×C47—21no—
156C42×C47—21no—
157C42×C47—21no—
158C42×C47—21no—
159C42×C47—41no—
160C42×C47—41no—
161C42×C47—42no—
162C42×C47—42no—
163(C2×D47)⋊C4—24no—
164(C2×D47)⋊C4—42no—
165(C2×D47)⋊C4—42no—
166(C2×D47)⋊C4—42no—
167(C2×D47)⋊C4—42no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47#4112yes—
174Dic47⋊C4—42no—
175Dic47⋊C4—42no—
176C4×Dic47—42no—
177C2×C47⋊C8—21no—
178C2×C47⋊C8—21no—
179C2×C47⋊C8—21no—
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—
189C23×C47C22×D411yescharacteristic
190C22×D47—22no—
191C22×D47—41no—
192C22×D47—41no—
193C22×D47—41no—
194C22×D47—41no—
195C22×D47—41no—
196C22×D47—41no—
197C2×C4×C47—21no—
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
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—41no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
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×C47#13512yes—
226C2×C4×C47AGL(1,ℤ/8)12yes—
227C2×C4×C47C2×#4111yescharacteristic
228C2×C4×C47C2×#4111yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×C4×C47C2×#4111yescharacteristic
231C2×C4×C472−1+411yescharacteristic
232C2×C4×C472−1+411yescharacteristic
233C2×Dic47—22no—
234C2×Dic47—41no—
235C2×Dic47—41no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242D188—22no—
243D188—22no—
244D188—41no—
245D188—41no—
246C4×D47—48no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249C47⋊C8—41no—
250C47⋊C8—41no—
251#29397—471nomaximal, Sylow
252C22×C47#52511yescharacteristic
253C22×C47#52511yescharacteristic
254C22×C47#53611yescharacteristic
255C22×C47C2×#13511yescharacteristic
256C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C47#57511yescharacteristic
258C22×C47#57511yescharacteristic
259C2×D47—42no—
260C2×D47—42no—
261C2×D47—42no—
262C2×D47—81no—
263C2×D47—81no—
264C2×D47—81no—
265C2×D47—81no—
266C4×C47—22no—
267C4×C47—22no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47—42no—
271C4×C47—41no—
272C4×C47—42no—
273C4×C47—41no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47#55211yescharacteristic
277C4×C47#55211yescharacteristic
278C4×C47#55611yescharacteristic
279C4×C47#55611yescharacteristic
280Dic47—42no—
281Dic47—81no—
282Dic47—81no—
283C4×#125D4711yescharacteristic, complemented
284#2293—471no—
285#2085—471no—
286#2073—471no—
287#2059—471no—
288#2025—471no—
289#1926—471no—
290#1925—471no—
291#1921—471no—
292#1920—471no—
293#1920—471no—
294#1918—471no—
295#1864—471no—
296#1862—471no—
297#1839—471no—
298C2×C47#259911yescharacteristic
299C2×C47#310211yescharacteristic
300C2×C47#310611yescharacteristic
301C2×C47#311111yescharacteristic
302C2×C47#311411yescharacteristic
303C2×C47#323211yescharacteristic
304C2×C47#323511yescharacteristic
305D47—82no—
306C2×#125C2×D4711yescharacteristic
307C2×C4×D4—471no—
308C2×#117—941no—
309C2×#107—471no—
310C2×#107—471no—
311C2×#106—471no—
312C2×#106—471no—
313C2×#102—471no—
314C2×#102—471no—
315C2×#102—471no—
316C2×#102—471no—
317#390—471no—
318#390—471no—
319#389—471no—
320#389—471no—
321#389C2×D4711yescharacteristic
322#389C2×D4711yescharacteristic
323#388—941no—
324#388—941no—
325#387—21no—
326#387—21no—
327#382C2×D4711yescharacteristic
328C4×C4⋊C4—21no—
329C4×C4⋊C4—21no—
330C4×C4⋊C4—471no—
331C4×C4⋊C4C2×D4711yescharacteristic
332C4×C4⋊C4C2×D4711yescharacteristic
333C4×C22⋊C4—941no—
334C43C2×D4711yescharacteristic
335#340—471no—
336#340—471no—
337#340—471no—
338#340—471no—
339#340—471no—
340#340—471no—
341#340—471no—
342#340—471no—
343#336—471no—
344#336—471no—
345#336—471no—
346#336—471no—
347#336—471no—
348#336—471no—
349C47#2939711yescharacteristic, complemented, Sylow
350C22×D4—471no—
351C23×C4—941no—
352C22×C8—471no—
353C22×C8—471no—
354C22×C8—471no—
355C22×C8—471no—
356#125—22no—
357#125—22no—
358C4×D4—942no—
359C4×D4—942no—
360#117—1884no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—471no—
366C2×C4⋊C4—471no—
367C2×C4⋊C4—471no—
368C2×C4⋊C4—941no—
369C2×C4⋊C4—941no—
370C2×C4⋊C4C22×D4711yescharacteristic
371C2×C4⋊C4C22×D4711yescharacteristic
372C2×C4⋊C4C22×D4711yescharacteristic
373C2×C4⋊C4C22×D4711yescharacteristic
374C2×C22⋊C4—941no—
375C2×C22⋊C4—941no—
376C2×C22⋊C4—941no—
377C2×C22⋊C4—941no—
378C2×C22⋊C4—941no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—941no—
382C2×C42C22⋊D4711yescharacteristic
383C2×C42C22⋊D4711yescharacteristic
384C2×C42C22⋊D4711yescharacteristic
385C2×C42C22⋊D4711yescharacteristic
386C2×C42C22×D4711yescharacteristic
387C2×C42C22×D4711yescharacteristic
388C2×C42C22×D4711yescharacteristic
389#107—942no—
390#107—942no—
391#106—942no—
392#106—942no—
393#102—942no—
394#102—942no—
395#102—942no—
396#102—942no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—941no—
404#95—941no—
405#95—941no—
406C24—941no—
407C2×D4—472no—
408C2×D4—941no—
409C2×D4—941no—
410C2×D4—941no—
411C2×D4—941no—
412C2×D4—941no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—944no—
418C22×C4—941no—
419C22×C4—941no—
420C22×C4—941no—
421C22×C4—1882no—
422C22×C4—1882no—
423C22×C4C2×C22⋊D4711yescharacteristic
424C22×C4C2×C22⋊D4711yescharacteristic
425C22×C4C2×C22⋊D4711yescharacteristic
426C22×C4C2×C22⋊D4711yescharacteristic
427C22×C4C2×C22⋊D4711yescharacteristic
428C22×C4C2×C22⋊D4711yescharacteristic
429C22×C4C23×D4711yescharacteristic
430C2×C8—941no—
431C2×C8—941no—
432C2×C8—941no—
433C2×C8—941no—
434C2×C8—941no—
435C2×C8—941no—
436C2×C8—941no—
437C2×C8—941no—
438C2×C8—941no—
439C2×C8—941no—
440C2×C8—941no—
441C2×C8—941no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—472no—
453C4⋊C4—941no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—1882no—
459C4⋊C4—1882no—
460C4⋊C4#1062535012yes—
461C4⋊C4#1062535012yes—
462C22⋊C4—944no—
463C22⋊C4—1882no—
464C22⋊C4—1882no—
465C22⋊C4—1882no—
466C22⋊C4—1882no—
467C42—22no—
468C42—22no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—42no—
478C42—42no—
479C42—1882no—
480C23—942no—
481C23—1881no—
482C23—1881no—
483C23—1881no—
484C23—1881no—
485C23—1881no—
486C23—1881no—
487C23C22×C22⋊D4711yescharacteristic
488D4—942no—
489D4—942no—
490D4—1881no—
491D4—1881no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—942no—
521C2×C4—1888no—
522C2×C4—1881no—
523C2×C4—1881no—
524C2×C4—1881no—
525C2×C4—1881no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4#1309404412yes—
531C2×C4#1309404912yes—
532C2×C4#41×D4711yescharacteristic
533C2×C4#41×D4711yescharacteristic
534C2×C4C2×#1062535011yescharacteristic
535C2×C4C2×#1062535011yescharacteristic
536C2×C4#1309407211yescharacteristic
537C2×C4#1309407211yescharacteristic
538C8—1881no—
539C8—1881no—
540C8—1881no—
541C8—1881no—
542C22—3761no—
543C22—3761no—
544C22—3761no—
545C22—3761no—
546C22—1882no—
547C22—1882no—
548C22—1882no—
549C22#1568963011yescharacteristic
550C22#1568963411yescharacteristic
551C22#1568969711yescharacteristic
552C22C2×#1309404411yescharacteristic
553C22C2×#1309404911yescharacteristic
554C22#1568992111yescharacteristic
555C22#1568992111yescharacteristic
556C4—22no—
557C4—22no—
558C4—41no—
559C4—42no—
560C4—41no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—3761no—
567C4—3761no—
568C4—1882no—
569C4#1568981411yescharacteristic
570C4#1568981411yescharacteristic
571C4#1568984511yescharacteristic
572C4#1568984511yescharacteristic
573C2—3762no—
574C2#2024895911yescharacteristic
575C2#2025340011yescharacteristic
576C2#2025344811yescharacteristic
577C2#2025349711yescharacteristic
578C2#2025352211yescharacteristic
579C2#2025455611yescharacteristic
580C2#2025458611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#125×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC4×#125D47
hypocenterC47#29397
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
2. #20244870C2semidirect
4. #20244723C2semidirect
8. #20243980C2semidirect
9. #20243973C2semidirect
10. #20243970C2semidirect
11. #20243956C2semidirect
14. #20243531C2semidirect
15. C4×#125×C47C2semidirect
283. C4×#125D47semidirect
349. C47#29397semidirect

Maximal subgroups

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

subgroupindex
#202458522
#202448702
#202448022
#202447232
#202445312
#202440152
#202440082
#202439802
#202439732
#202439702
#202439562
#202436482
#202436342
#202435312
C4×#125×C472
#2939747