Finite Group Databasebeta

← #26187678

Subgroups — #26187678

Order 12032.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253423C211yesmaximal, characteristic
2#20252490C211yesmaximal, characteristic
3#20252478C211yesmaximal, characteristic
4#20242294C211yesmaximal, characteristic, complemented
5#20242282C211yesmaximal, characteristic, complemented
6#20242262C211yesmaximal, characteristic, complemented
7#20242256C211yesmaximal, characteristic, complemented
8#20242241C211yesmaximal, characteristic, complemented
9#20242235C211yesmaximal, characteristic, complemented
10#20242204C211yesmaximal, characteristic, complemented
11#20242192C211yesmaximal, characteristic, complemented
12#20242169C211yesmaximal, characteristic
13#20241784C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic
15C47×#1497C211yesmaximal, characteristic
16C2×C4×Dic94C2211yescharacteristic
17#15689456C411yescharacteristic
18#15689456C411yescharacteristic
19#15689415C411yescharacteristic
20#15689415C411yescharacteristic
21#15689330C411yescharacteristic
22#15689330C411yescharacteristic
23#15689278C411yescharacteristic
24#15689278C411yescharacteristic
25#15689254—21no—
26#15689254C2211yescharacteristic
27#15689254C2211yescharacteristic
28#15689251—21no—
29#15689251—21no—
30#15689250C2211yescharacteristic
31#15689250C2211yescharacteristic
32Q8×C47⋊C8—21no—
33Q8×C47⋊C8C2211yescharacteristic
34Q8×C47⋊C8C2211yescharacteristic
35#15689247C2211yescharacteristic
36#15689247C2211yescharacteristic
37C4×#10625337C2211yescharacteristic
38C4×#10625337C2211yescharacteristic
39C4×#10625337C2211yescharacteristic
40C4×#10625337C2211yescharacteristic
41#15689184—21no—
42#15689184—21no—
43#15689177—21no—
44#15689176C2211yescharacteristic
45#15689176C2211yescharacteristic
46#15689176C2211yescharacteristic
47#15689173—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#533C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625337C2×C411yescharacteristic
71C2×#10625337C2×C411yescharacteristic
72C4×Dic94—21no—
73C4×Dic94—21no—
74C4×Dic94C2×C411yescharacteristic
75C4×Dic94C2×C411yescharacteristic
76C4×Dic94C2311yescharacteristic
77C4×Dic94C2311yescharacteristic
78C2×C4⋊Dic47C2×C411yescharacteristic
79C2×Dic47⋊C4—21no—
80C2×C4×Dic47—21no—
81#13093957C2×C411yescharacteristic
82#13093957C2×C411yescharacteristic
83#13093957C2×C411yescharacteristic
84#13093957C2×C411yescharacteristic
85C4⋊(C47⋊C8)—21no—
86C4⋊(C47⋊C8)—21no—
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)C2×C411yescharacteristic
90C4⋊(C47⋊C8)C2×C411yescharacteristic
91C4⋊(C47⋊C8)D411yescharacteristic
92C4⋊(C47⋊C8)D411yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94C4⋊(C47⋊C8)C2311yescharacteristic
95Dic47⋊C8—21no—
96Dic47⋊C8—21no—
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093947C2×C411yescharacteristic
106#13093947C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)C2×C411yescharacteristic
109C22⋊(C47⋊C8)C2×C411yescharacteristic
110C22⋊(C47⋊C8)D411yescharacteristic
111C22⋊(C47⋊C8)D411yescharacteristic
112#13093935—21no—
113#13093935—21no—
114#13093934—21no—
115#13093934—21no—
116C4×C47⋊C8—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C4⋊Q8×C47C2×C411yescharacteristic
126C4⋊Q8×C47C2×C411yescharacteristic
127#125×C47—21no—
128C22⋊Q8×C47—21no—
129C22⋊Q8×C47C2×C411yescharacteristic
130C22⋊Q8×C47C2×C411yescharacteristic
131C4×Q8×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×Q8×C47C2311yescharacteristic
134#117×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C22×Dic47—21no—
151C22×Dic47—21no—
152C2×Dic94—22no—
153C2×Dic94—21no—
154C2×Dic94—41no—
155C2×Dic94C22×C411yescharacteristic
156C2×Dic94C22×C411yescharacteristic
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C411yescharacteristic
169C4⋊C4×C47C22×C411yescharacteristic
170C22⋊C4×C47—21no—
171C22⋊C4×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47C22×C411yescharacteristic
175C42×C47C2×D411yescharacteristic
176C42×C47#4111yescharacteristic
177C42×C47C2411yescharacteristic
178#10625337—22no—
179#10625337—22no—
180#10625337—41no—
181#10625337—41no—
182C4⋊Dic47—21no—
183C4⋊Dic47C22×C411yescharacteristic
184C4⋊Dic47C22×C411yescharacteristic
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8C22×C411yescharacteristic
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C23×C47C4×D411yescharacteristic
204Q8×C47—21no—
205Q8×C47—21no—
206Q8×C47—21no—
207Q8×C47—21no—
208Q8×C47—42no—
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—41no—
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47C23×C411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C2×Dic47—21no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230Dic94—21no—
231Dic94—21no—
232Dic94—21no—
233Dic94—42no—
234Dic94#13112yes—
235C8×C47—41no—
236C8×C47—41no—
237C8×C47—41no—
238C8×C47—41no—
239C47⋊C8—21no—
240C47⋊C8—21no—
241C47⋊C8—21no—
242C47⋊C8—21no—
243C47⋊C8—21no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249#18032—471nomaximal, Sylow
250C22×C47—21no—
251C22×C47—21no—
252C22×C47—21no—
253C22×C47C2×C4×D411yescharacteristic
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47—41no—
262C4×C47C2×#13111yescharacteristic
263C4×C47#56811yescharacteristic
264C4×C47#57811yescharacteristic
265C4×C47#57811yescharacteristic
266Dic47—22no—
267Dic47—41no—
268Dic47—41no—
269Dic47—41no—
270#3104—471no—
271#2986—471no—
272#2984—471no—
273#1593—471no—
274#1591—471no—
275#1587—471no—
276#1587—471no—
277#1584—471no—
278#1584—471no—
279#1579—471no—
280C8×Q16—471no—
281#1572—471no—
282#1497D4711yescharacteristic
283#1479—471no—
284#1454—471no—
285C2×C47—41no—
286C2×C47#293311yescharacteristic
287C2×C47#295011yescharacteristic
288C2×C47#295511yescharacteristic
289#533C2×D4711yescharacteristic
290C2×C4×Q8—471no—
291#484—471no—
292#484—471no—
293#477—471no—
294#477—471no—
295#462—471no—
296#462—471no—
297#451—471no—
298#451—471no—
299#446—471no—
300#446—471no—
301#446—471no—
302#446—471no—
303#446—941no—
304#446—941no—
305#446—941no—
306C8×Q8—471no—
307C8×Q8—471no—
308C8×Q8—471no—
309C8×Q8—471no—
310C8×Q8—941no—
311C4×Q16—471no—
312C4×Q16—471no—
313C4×Q16—471no—
314C4×Q16—471no—
315#433—941no—
316#433—941no—
317#432—941no—
318#432C2×D4711yescharacteristic
319#431—471no—
320#431—471no—
321#431—471no—
322#431—941no—
323#431C2×D4711yescharacteristic
324#335—471no—
325#335—471no—
326#334—471no—
327#334—471no—
328Q8⋊C8—471no—
329Q8⋊C8—471no—
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8C2×D4711yescharacteristic
333Q8⋊C8C2×D4711yescharacteristic
334Q8⋊C8C2×D4711yescharacteristic
335Q8⋊C8C2×D4711yescharacteristic
336#322—471no—
337#322—471no—
338#322—471no—
339C82—471no—
340C47#1803211yescharacteristic, complemented, Sylow
341C22×Q8—471no—
342C2×Q16—471no—
343C2×Q16—471no—
344C2×Q16—471no—
345C2×Q16—471no—
346C4⋊Q8C4×D4711yescharacteristic
347C4⋊Q8C4×D4711yescharacteristic
348#125—21no—
349C22⋊Q8—21no—
350C22⋊Q8C4×D4711yescharacteristic
351C22⋊Q8C4×D4711yescharacteristic
352C4×Q8—21no—
353C4×Q8—471no—
354C4×Q8—471no—
355C4×Q8—471no—
356C4×Q8—471no—
357C4×Q8—941no—
358C4×Q8—941no—
359C4×Q8C22×D4711yescharacteristic
360C4×Q8C22×D4711yescharacteristic
361#117—21no—
362C2×C4⋊C4—471no—
363C2×C4⋊C4—941no—
364C2×C42—941no—
365C2×C42C22×D4711yescharacteristic
366#107—471no—
367#107—471no—
368#107—471no—
369#107—471no—
370C4⋊C8—21no—
371C4⋊C8—471no—
372C4⋊C8—471no—
373C4⋊C8—471no—
374C4⋊C8—471no—
375C4⋊C8—471no—
376C4⋊C8—471no—
377C4⋊C8—941no—
378C4⋊C8—941no—
379C4⋊C8—941no—
380C4⋊C8—941no—
381C4⋊C8—941no—
382C4⋊C8—941no—
383C4⋊C8—941no—
384C4⋊C8—941no—
385C4⋊C8C22×D4711yescharacteristic
386C4⋊C8C22×D4711yescharacteristic
387#103—471no—
388#103—471no—
389#103—471no—
390#103—471no—
391#103—471no—
392#103—471no—
393#103—471no—
394#103—471no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397C22⋊C8—471no—
398C22⋊C8—471no—
399C22⋊C8—471no—
400C22⋊C8—471no—
401C22⋊C8—941no—
402#97—21no—
403#97—941no—
404#97—941no—
405#97—941no—
406#97—941no—
407C4×C8—471no—
408C4×C8—471no—
409C4×C8—471no—
410C4×C8—471no—
411C4×C8—941no—
412C4×C8—941no—
413C4×C8—941no—
414C4×C8—941no—
415C4×C8—941no—
416C4×C8C22×D4711yescharacteristic
417C4×C8C22×D4711yescharacteristic
418C2×Q8—21no—
419C2×Q8—471no—
420C2×Q8—471no—
421C2×Q8—942no—
422C2×Q8—941no—
423C2×Q8—1881no—
424C2×Q8C2×C4×D4711yescharacteristic
425C2×Q8C2×C4×D4711yescharacteristic
426C22×C4—941no—
427C22×C4—941no—
428C22×C4C2×C4×D4711yescharacteristic
429C22×C4D4×D4711yescharacteristic
430C22×C4#1062535211yescharacteristic
431Q16—942no—
432Q16—942no—
433Q16—1881no—
434Q16—1881no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—471no—
440C2×C8—471no—
441C2×C8—471no—
442C2×C8—471no—
443C2×C8—471no—
444C2×C8—471no—
445C2×C8—471no—
446C2×C8—471no—
447C2×C8—941no—
448C2×C8—941no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—471no—
457C4⋊C4—471no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4C2×C4×D4711yescharacteristic
464C4⋊C4C2×C4×D4711yescharacteristic
465C22⋊C4—21no—
466C22⋊C4—21no—
467C42—21no—
468C42—21no—
469C42—941no—
470C42—941no—
471C42—941no—
472C42—941no—
473C42C2×C4×D4711yescharacteristic
474C42D4×D4711yescharacteristic
475C42#1062535211yescharacteristic
476C42C23×D4711yescharacteristic
477C23(C22⋊D47)⋊C411yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—472no—
484Q8—941no—
485Q8—941no—
486Q8—941no—
487Q8—1882no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—941no—
498C2×C4—941no—
499C2×C4—941no—
500C2×C4—941no—
501C2×C4—1882no—
502C2×C4—1882no—
503C2×C4(C22⋊D47)⋊C411yescharacteristic
504C2×C4(C22⋊D47)⋊C411yescharacteristic
505C2×C4(C22⋊D47)⋊C411yescharacteristic
506C2×C4C22×C4×D4711yescharacteristic
507C2×C4C2×D4×D4711yescharacteristic
508C2×C4C2×#1062535211yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—941no—
514C8—941no—
515C8—941no—
516C8—941no—
517C8—941no—
518C8—941no—
519C8—941no—
520C8—941no—
521C8—1881no—
522C8—1881no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×(C22⋊D47)⋊C411yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—942no—
536C4—1881no—
537C4—1881no—
538C4—1881no—
539C4#131×D4711yescharacteristic
540C4#1568988811yescharacteristic
541C4#1568993911yescharacteristic
542C4#1568993911yescharacteristic
543C2—41no—
544C2#2025211811yescharacteristic
545C2#2025225211yescharacteristic
546C2#2025228711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1497C2
socleC22×C47C2×C4×D4
prime radicalC23×C47C4×D4
cosocleC42×C47C24
hypercenter#1497D47
hypocenterC47#18032
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #20242294C2semidirect
5. #20242282C2semidirect
6. #20242262C2semidirect
7. #20242256C2semidirect
8. #20242241C2semidirect
9. #20242235C2semidirect
10. #20242204C2semidirect
11. #20242192C2semidirect
340. C47#18032semidirect

Maximal subgroups

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

subgroupindex
#202534232
#202524902
#202524782
#202422942
#202422822
#202422622
#202422562
#202422412
#202422352
#202422042
#202421922
#202421692
#202417842
#202416882
C47×#14972
#1803247