Finite Group Databasebeta

← #26275387

Subgroups — #26275387

Order 12032.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248616C211yesmaximal, characteristic, complemented
2#20246337C211yesmaximal, characteristic
3#20244914C211yesmaximal, characteristic
4#20244911C211yesmaximal, characteristic
5#20244774C211yesmaximal, characteristic
6#20244760C211yesmaximal, characteristic
7#20244155C211yesmaximal, characteristic, complemented
8#20244146C211yesmaximal, characteristic, complemented
9#20244145C211yesmaximal, characteristic, complemented
10#20244111C211yesmaximal, characteristic, complemented
11#20243979C211yesmaximal, characteristic, complemented
12#20243972C211yesmaximal, characteristic, complemented
13#20243556C211yesmaximal, characteristic, complemented
14#20243398C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×#13093983—21no—
17C2×#13093958C2211yescharacteristic
18C2×#13093958C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093956C2211yescharacteristic
22C2×#13093956C2211yescharacteristic
23C2×C4⋊(C47⋊C8)C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28#15689065—21no—
29#15689057—21no—
30#15689026C2211yescharacteristic
31#15689026C2211yescharacteristic
32#15689019C2211yescharacteristic
33#15689019C2211yescharacteristic
34#15689016—21no—
35#15689016—21no—
36#15689007—21no—
37#15689007—21no—
38#15688993C2211yescharacteristic
39#15688992C2211yescharacteristic
40#15688989C2211yescharacteristic
41#15688988C2211yescharacteristic
42#15688983—21no—
43C4⋊C4×Dic47C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45C4×C4⋊Dic47C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×#102×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×#97×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C22×C47⋊C8C2311yescharacteristic
60C22×C47⋊C8C2311yescharacteristic
61#13093983—44no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47D411yescharacteristic
65C2×C4⋊Dic47D411yescharacteristic
66C2×C4⋊Dic47C2311yescharacteristic
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×Dic47⋊C4—21no—
71C2×Dic47⋊C4—21no—
72C2×Dic47⋊C4—21no—
73C2×Dic47⋊C4—21no—
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80C2×C4×Dic47C2311yescharacteristic
81C2×C4×Dic47C2311yescharacteristic
82#13093958—22no—
83#13093958—41no—
84#13093957—41no—
85#13093957—41no—
86#13093956—22no—
87#13093956—41no—
88C4⋊(C47⋊C8)—22no—
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91#13093945—41no—
92#13093945—41no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95D411yescharacteristic
102C47⋊#95D411yescharacteristic
103C22×D4×C47C2311yescharacteristic
104C23×C4×C47—21no—
105C22×C8×C47C2311yescharacteristic
106C22×C8×C47C2311yescharacteristic
107C4×D4×C47—22no—
108C4×D4×C47Q814yes—
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C42×C47—21no—
114C2×C42×C47C2311yescharacteristic
115#102×C47—22no—
116#102×C47—22no—
117#97×C47—22no—
118#95×C47—21no—
119C24×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47C2×Q812yes—
126C22×C4×C47—21no—
127C22×C4×C47—24no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—42no—
131C22×C4×C47—42no—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2411yescharacteristic
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47C2×D411yescharacteristic
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C22×Dic47C2×D411yescharacteristic
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47#4112yes—
148C2×C8×C47#4112yes—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47C2×Q812yes—
155C22⋊C4×C47—24no—
156C42×C47—81no—
157C42×C47C2×Q812yes—
158C42×C47#4112yes—
159C22⋊Dic47—42no—
160C22⋊Dic47—42no—
161C22⋊Dic47—81no—
162C22⋊Dic47—81no—
163C4⋊Dic47—22no—
164C4⋊Dic47—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—41no—
173C4⋊Dic47—42no—
174C4⋊Dic47—81no—
175Dic47⋊C4—42no—
176Dic47⋊C4—42no—
177Dic47⋊C4—81no—
178Dic47⋊C4—81no—
179C4×Dic47—21no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—42no—
184C4×Dic47—42no—
185C2×C47⋊C8—21no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C23×C47—22no—
192C23×C47—41no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47C22×D411yescharacteristic
199D4×C47—22no—
200D4×C47—22no—
201D4×C47—41no—
202D4×C47—41no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—22no—
208C2×C4×C47—48no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47C22⋊Q812yes—
218C2×C4×C47C22⋊Q812yes—
219C2×C4×C47C22×Q811yescharacteristic
220C2×C4×C47C2×#4111yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C47H(5,𝔽2)11yescharacteristic
224C2×C4×C472−1+411yescharacteristic
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47AGL(1,ℤ/8)12yes—
249C8×C47—22no—
250C8×C47—22no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253#26098—471nomaximal, Sylow
254C22×C47—42no—
255C22×C47—42no—
256C22×C47—42no—
257C22×C47—81no—
258C22×C47—81no—
259C22×C47—81no—
260C22×C47—81no—
261C22×C47C2×C22⋊Q811yescharacteristic
262C22×C47#54711yescharacteristic
263C22×C47#55011yescharacteristic
264C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C47#57511yescharacteristic
266C22×C47#57611yescharacteristic
267C22×C47#57811yescharacteristic
268C4×C47—22no—
269C4×C47—22no—
270C4×C47—42no—
271C4×C47—81no—
272C4×C47—81no—
273C4×C47#53311yescharacteristic
274C4×C47#54411yescharacteristic
275C4×C47#55211yescharacteristic
276C4×C47#55311yescharacteristic
277Dic47—22no—
278Dic47—41no—
279Dic47—41no—
280Dic47—41no—
281Dic47—81no—
282Dic47—81no—
283Dic47—81no—
284Dic47—81no—
285#2570—471no—
286#2354—471no—
287#2093—471no—
288#2092—471no—
289#2067—471no—
290#2065—471no—
291#1949—471no—
292#1947—471no—
293#1947—471no—
294#1940—471no—
295#1921—471no—
296#1920—471no—
297#1847—471no—
298#1804—471no—
299#1762D4711yescharacteristic
300C2×C47—82no—
301C2×C47#244111yescharacteristic
302C2×C47#307711yescharacteristic
303C2×C47#308311yescharacteristic
304C2×C47#334311yescharacteristic
305C2×C47#334711yescharacteristic
306C2×C47#339911yescharacteristic
307C2×C47#340211yescharacteristic
308C2×C4×D4C2×D4711yescharacteristic
309C2×#117—941no—
310C2×#107—471no—
311C2×#107—471no—
312C2×#107—471no—
313C2×#107—471no—
314C2×#106—471no—
315C2×#106—471no—
316C2×C4⋊C8—471no—
317C2×C4⋊C8—471no—
318C2×C4⋊C8—471no—
319C2×#102—471no—
320C2×#102—471no—
321C2×#102C2×D4711yescharacteristic
322C2×#102C2×D4711yescharacteristic
323C2×#97C2×D4711yescharacteristic
324#400—941no—
325#398—941no—
326#390—471no—
327#390—471no—
328#389—471no—
329#389—471no—
330#388—941no—
331#388—941no—
332#387—941no—
333#387—941no—
334#384—471no—
335#384—471no—
336#382—471no—
337#382—471no—
338#380—941no—
339C4×C4⋊C4—471no—
340C4×C4⋊C4—471no—
341C4×C4⋊C4—471no—
342C4×C4⋊C4C2×D4711yescharacteristic
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340C2×D4711yescharacteristic
348#340C2×D4711yescharacteristic
349#336—471no—
350#336—471no—
351C47#2609811yescharacteristic, complemented, Sylow
352C22×D4C22×D4711yescharacteristic
353C23×C4—21no—
354C22×C8—471no—
355C22×C8—471no—
356C22×C8C22×D4711yescharacteristic
357C22×C8C22×D4711yescharacteristic
358C4×D4—22no—
359C4×D4Dic9414yes—
360#117—1884no—
361C2×C4⋊C4—471no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—471no—
364C2×C4⋊C4—471no—
365C2×C4⋊C4—471no—
366C2×C4⋊C4—471no—
367C2×C4⋊C4—941no—
368C2×C4⋊C4—941no—
369C2×C4⋊C4—941no—
370C2×C4⋊C4—941no—
371C2×C4⋊C4—941no—
372C2×C4⋊C4—941no—
373C2×C4⋊C4C22×D4711yescharacteristic
374C2×C4⋊C4C22×D4711yescharacteristic
375C2×C4⋊C4C22×D4711yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—941no—
378C2×C22⋊C4—941no—
379C2×C22⋊C4—941no—
380C2×C22⋊C4—941no—
381C2×C42—21no—
382C2×C42—471no—
383C2×C42—471no—
384C2×C42—941no—
385C2×C42—941no—
386C2×C42C22×D4711yescharacteristic
387#107—942no—
388#107—1881no—
389#107—1881no—
390#107—1881no—
391#106—942no—
392#106—1881no—
393C4⋊C8—942no—
394C4⋊C8—942no—
395C4⋊C8—942no—
396#102—22no—
397#102—22no—
398#102—1881no—
399#102—1881no—
400#97—22no—
401#95—21no—
402#95—471no—
403#95—471no—
404#95—941no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412C24—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×Dic9412yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—471no—
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—471no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—941no—
432C22×C4—941no—
433C22×C4D4×D4711yescharacteristic
434C22×C4D4×D4711yescharacteristic
435C22×C4C23×D4711yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8#1062535012yes—
447C2×C8#1062535012yes—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—942no—
454C4⋊C4—941no—
455C4⋊C4—941no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—3761no—
463C4⋊C4—3761no—
464C4⋊C4—3761no—
465C4⋊C4—1881no—
466C4⋊C4—1882no—
467C4⋊C4—1882no—
468C4⋊C4—1882no—
469C4⋊C4C2×Dic9412yes—
470C22⋊C4—24no—
471C22⋊C4—3761no—
472C22⋊C4—3761no—
473C22⋊C4—1882no—
474C22⋊C4—1882no—
475C42—81no—
476C42—941no—
477C42—941no—
478C42—941no—
479C42—941no—
480C42—1882no—
481C42—1882no—
482C42C2×Dic9412yes—
483C42#1062535212yes—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×D4×D4711yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—48no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—472no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—941no—
521C2×C4—941no—
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—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4#1309400112yes—
535C2×C4#1309400112yes—
536C2×C4C22×Dic9411yescharacteristic
537C2×C4C2×#1062535211yescharacteristic
538C2×C4C2×#1062535011yescharacteristic
539C2×C4C2×#1062535011yescharacteristic
540C2×C4#1309407011yescharacteristic
541C2×C4#1309407111yescharacteristic
542C8—22no—
543C8—22no—
544C8—1881no—
545C8—1881no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#1309400111yescharacteristic
554C22#1568977811yescharacteristic
555C22#1568979411yescharacteristic
556C22AGL(1,ℤ/8)×D4711yescharacteristic
557C22#1568991911yescharacteristic
558C22#1568992711yescharacteristic
559C22#1568993911yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—81no—
564C4—81no—
565C4—942no—
566C4—3761no—
567C4—3761no—
568C4—3761no—
569C4—3761no—
570C4—1881no—
571C4—1881no—
572C4—1881no—
573C4#1568968011yescharacteristic
574C4#1568975111yescharacteristic
575C4#1568981311yescharacteristic
576C4#1568981911yescharacteristic
577C2—82no—
578C2#2024710111yescharacteristic
579C2#2025318211yescharacteristic
580C2#2025324311yescharacteristic
581C2#2025583311yescharacteristic
582C2#2025589311yescharacteristic
583C2#2025643111yescharacteristic
584C2#2025646811yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#1762C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenter#1762D47
hypocenterC47#26098
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
1. #20248616C2semidirect
7. #20244155C2semidirect
8. #20244146C2semidirect
9. #20244145C2semidirect
10. #20244111C2semidirect
11. #20243979C2semidirect
12. #20243972C2semidirect
13. #20243556C2semidirect
351. C47#26098semidirect

Maximal subgroups

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

subgroupindex
#202486162
#202463372
#202449142
#202449112
#202447742
#202447602
#202441552
#202441462
#202441452
#202441112
#202439792
#202439722
#202435562
#202433982
C47×#17622
#2609847