Finite Group Databasebeta

← #26187467

Subgroups — #26187467

Order 12032.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253464C211yesmaximal, characteristic
2#20252475C211yesmaximal, characteristic, complemented
3#20242283C211yesmaximal, characteristic, complemented
4#20242276C211yesmaximal, characteristic, complemented
5#20242264C211yesmaximal, characteristic, complemented
6#20242259C211yesmaximal, characteristic, complemented
7#20242257C211yesmaximal, characteristic, complemented
8#20242245C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242171C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic
13C2×#15688853C211yesmaximal, characteristic, complemented
14#20241672C211yesmaximal, characteristic, complemented
15C47×#2994C211yesmaximal, characteristic
16C2×C4×Dic94C2211yescharacteristic
17#15689451C411yescharacteristic
18#15689434C411yescharacteristic
19#15689427C411yescharacteristic
20#15689427C411yescharacteristic
21#15689342C411yescharacteristic
22#15689342C411yescharacteristic
23#15689278C411yescharacteristic
24#15689261C411yescharacteristic
25#15689253C2211yescharacteristic
26#15689253C2211yescharacteristic
27#15689252—21no—
28#15689252—21no—
29C8×Dic94C2211yescharacteristic
30C8×Dic94C2211yescharacteristic
31C4×#10625337C2211yescharacteristic
32C4×#10625337C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689180C2211yescharacteristic
36#15689177—21no—
37#15689176C2211yescharacteristic
38#15689173—21no—
39C2×C4×C47⋊C8C2211yescharacteristic
40#15688875C2211yescharacteristic
41#15688875C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48#15688853C2211yescharacteristic
49#15688853C2211yescharacteristic
50D4⋊(C47⋊C8)C2211yescharacteristic
51D4⋊(C47⋊C8)C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54C8×C47⋊C8C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C47×#529C2211yescharacteristic
57C47×#446C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C47×#436C2211yescharacteristic
60C47×#435—21no—
61C8×D4×C47—21no—
62C8×D4×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#431C2211yescharacteristic
65C47×#424—21no—
66C2×C4⋊C8×C47C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C22×C47⋊C8—21no—
73C4×Dic94—21no—
74C4×Dic94—21no—
75C4×Dic94C2×C411yescharacteristic
76C4×Dic94C2×C411yescharacteristic
77C4×Dic94C2311yescharacteristic
78C4×Dic94C2311yescharacteristic
79C2×C4⋊Dic47C2×C411yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×C4×Dic47—21no—
82#13093957C2×C411yescharacteristic
83#13093957C2×C411yescharacteristic
84#13093955C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86C4⋊(C47⋊C8)C2×C411yescharacteristic
87C4⋊(C47⋊C8)C2×C411yescharacteristic
88C4⋊(C47⋊C8)C2311yescharacteristic
89C4⋊(C47⋊C8)C2311yescharacteristic
90Dic47⋊C8—21no—
91Dic47⋊C8—21no—
92Dic47⋊C8—21no—
93Dic47⋊C8—21no—
94#13093948C2×C411yescharacteristic
95#13093948C2×C411yescharacteristic
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093947C2×C411yescharacteristic
99#13093947C2×C411yescharacteristic
100#13093945C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102C22⋊(C47⋊C8)—21no—
103C22⋊(C47⋊C8)C2×C411yescharacteristic
104C22⋊(C47⋊C8)C2×C411yescharacteristic
105#13093935—21no—
106#13093934—21no—
107#13093934—21no—
108C4×C47⋊C8—21no—
109C4×C47⋊C8C2311yescharacteristic
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C8×Dic47—21no—
114C8×Dic47—21no—
115C2×M16×C47—21no—
116C22×C8×C47—21no—
117C22×C8×C47—21no—
118#126×C47—21no—
119#125×C47C2×C411yescharacteristic
120#124×C47C2×C411yescharacteristic
121#123×C47—21no—
122C22⋊Q8×C47C2×C411yescharacteristic
123#121×C47C2×C411yescharacteristic
124C4×Q8×C47C2311yescharacteristic
125C4×D4×C47—21no—
126C4×D4×C47C2311yescharacteristic
127#117×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47—21no—
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47D411yescharacteristic
133C4⋊C8×C47D411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47D411yescharacteristic
139C22⋊C8×C47D411yescharacteristic
140#97×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47—21no—
146C2×D4×C47C22×C411yescharacteristic
147C22×C4×C47—21no—
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C22×Dic47—21no—
152C22×Dic47—21no—
153C2×Dic94—22no—
154C2×Dic94—21no—
155C2×Dic94—41no—
156C2×Dic94C22×C411yescharacteristic
157C2×Dic94C22×C411yescharacteristic
158M16×C47—81no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—81no—
162C2×C8×C47—81no—
163C2×C8×C47C2×D411yescharacteristic
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47C22×C411yescharacteristic
172C4⋊C4×C47C22×C411yescharacteristic
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C22⋊C4×C47—21no—
178C42×C47—21no—
179C42×C47C22×C411yescharacteristic
180C42×C47C2×D411yescharacteristic
181C42×C47#4111yescharacteristic
182C42×C47C2411yescharacteristic
183#10625337—22no—
184#10625337—41no—
185#10625335—22no—
186#10625335—41no—
187C4⋊Dic47—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47—21no—
197C4×Dic47—21no—
198C2×C47⋊C8—24no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C23×C47—21no—
208C23×C47C4×D411yescharacteristic
209Q8×C47—21no—
210Q8×C47—21no—
211D4×C47—21no—
212D4×C47—21no—
213D4×C47—42no—
214C2×C4×C47—22no—
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×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—42no—
235C2×Dic47—42no—
236Dic94—21no—
237Dic94—21no—
238Dic94—21no—
239Dic94—42no—
240Dic94#13112yes—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—21no—
244C8×C47—21no—
245C8×C47—41no—
246C8×C47—41no—
247C47⋊C8—22no—
248C47⋊C8—22no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#18017—471nomaximal, Sylow
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47—41no—
261C22×C47#44312yes—
262C22×C47C2×C4×D411yescharacteristic
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47C2×#13111yescharacteristic
271C4×C47#56811yescharacteristic
272C4×C47#57711yescharacteristic
273C4×C47#57811yescharacteristic
274Dic47—22no—
275Dic47—41no—
276Dic47—41no—
277Dic47—41no—
278#3108—471no—
279#2994D4711yescharacteristic
280#2984—471no—
281#1591—471no—
282#1590—471no—
283#1588—471no—
284#1587—471no—
285#1587—471no—
286#1585—471no—
287C8×Q16—471no—
288C8×SD16—471no—
289#1573—471no—
290#1494—471no—
291C2×Q8⋊C8—471no—
292#1450—471no—
293C2×C47—22no—
294C2×C47—81no—
295C2×C47#293311yescharacteristic
296C2×C47#294711yescharacteristic
297C2×C47C2×#44311yescharacteristic
298#529C2×D4711yescharacteristic
299C2×C4×Q8—471no—
300#483—471no—
301#480—471no—
302#479—471no—
303#479—471no—
304#464—471no—
305#464—471no—
306#451—471no—
307#448—471no—
308#446—471no—
309#446—471no—
310#446—941no—
311#446—941no—
312#446C2×D4711yescharacteristic
313C8×Q8—471no—
314C8×Q8—471no—
315C8×Q8C2×D4711yescharacteristic
316C4×Q16—471no—
317C4×Q16—471no—
318C4×SD16—471no—
319C4×SD16—471no—
320#436C2×D4711yescharacteristic
321#435—21no—
322C8×D4—21no—
323C8×D4C2×D4711yescharacteristic
324#433—21no—
325#432—471no—
326#432—941no—
327#431—471no—
328#431—941no—
329#431C2×D4711yescharacteristic
330#424—21no—
331C2×C4⋊C8C2×D4711yescharacteristic
332C2×C4×C8—471no—
333#335—471no—
334#335—471no—
335#334—471no—
336#334—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341Q8⋊C8—471no—
342Q8⋊C8—471no—
343D4⋊C8—471no—
344D4⋊C8—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C82—471no—
349C47#1801711yescharacteristic, complemented, Sylow
350C22×Q8—471no—
351C2×Q16—471no—
352C2×Q16—471no—
353C2×SD16—471no—
354C2×SD16—471no—
355C2×M16—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—941no—
359#126—21no—
360#125C4×D4711yescharacteristic
361#124C4×D4711yescharacteristic
362#123—21no—
363C22⋊Q8C4×D4711yescharacteristic
364#121C4×D4711yescharacteristic
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—471no—
368C4×Q8—471no—
369C4×Q8—941no—
370C4×Q8—941no—
371C4×Q8C22×D4711yescharacteristic
372C4×D4—21no—
373C4×D4C22×D4711yescharacteristic
374#117—21no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—941no—
377C2×C42—941no—
378C2×C42C22×D4711yescharacteristic
379#107—471no—
380#107—471no—
381#106—471no—
382#106—471no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—471no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8C22⋊D4711yescharacteristic
395C4⋊C8C22⋊D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397C4⋊C8C22×D4711yescharacteristic
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#103—471no—
404#102—471no—
405#102—471no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8C22⋊D4711yescharacteristic
412C22⋊C8C22⋊D4711yescharacteristic
413#97—21no—
414#97—941no—
415#97—941no—
416#97—941no—
417C4×C8—21no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—471no—
421C4×C8—471no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8—941no—
425C4×C8C22×D4711yescharacteristic
426C4×C8C22×D4711yescharacteristic
427C2×Q8—471no—
428C2×Q8—471no—
429C2×Q8—942no—
430C2×Q8—941no—
431C2×Q8—1881no—
432C2×Q8C2×C4×D4711yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D4711yescharacteristic
435C22×C4—21no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4#1062535011yescharacteristic
440C22×C4C2×C22⋊D4711yescharacteristic
441Q16—942no—
442Q16—1881no—
443SD16—942no—
444SD16—1881no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—81no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—944no—
455C2×C8—941no—
456C2×C8—941no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8C2×C22⋊D4711yescharacteristic
460C2×C8C2×C22⋊D4711yescharacteristic
461C2×C8C2×C22⋊D4711yescharacteristic
462C2×C8C2×C22⋊D4711yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—471no—
468C4⋊C4—471no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4—941no—
473C4⋊C4—941no—
474C4⋊C4C2×C4×D4711yescharacteristic
475C4⋊C4C2×C4×D4711yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—941no—
483C42—941no—
484C42—941no—
485C42—941no—
486C42C2×C4×D4711yescharacteristic
487C42#1062535011yescharacteristic
488C42C2×C22⋊D4711yescharacteristic
489C42C23×D4711yescharacteristic
490C23—21no—
491C23C4×C22⋊D4711yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—472no—
495Q8—941no—
496Q8—941no—
497Q8—941no—
498Q8—1882no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
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—941no—
513C2×C4—941no—
514C2×C4—941no—
515C2×C4—941no—
516C2×C4—1882no—
517C2×C4—1882no—
518C2×C4C4×C22⋊D4711yescharacteristic
519C2×C4C4×C22⋊D4711yescharacteristic
520C2×C4C4×C22⋊D4711yescharacteristic
521C2×C4C22×C4×D4711yescharacteristic
522C2×C4C22×C22⋊D4711yescharacteristic
523C2×C4C2×#1062535011yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—942no—
531C8—942no—
532C8—941no—
533C8—941no—
534C8—941no—
535C8—941no—
536C8—1881no—
537C8—1881no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1568923812yes—
544C22C2×C4×C22⋊D4711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—942no—
553C4—1881no—
554C4—1881no—
555C4—1881no—
556C4#131×D4711yescharacteristic
557C4#1568988811yescharacteristic
558C4#1568993411yescharacteristic
559C4#1568993811yescharacteristic
560C2—22no—
561C2—81no—
562C2#2025211011yescharacteristic
563C2#2025222711yescharacteristic
564C2C2×#1568923811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2994C2
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
cosocleC42×C47C24
hypercenter#2994D47
hypocenterC47#18017
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #20252475C2semidirect
3. #20242283C2semidirect
4. #20242276C2semidirect
5. #20242264C2semidirect
6. #20242259C2semidirect
7. #20242257C2semidirect
8. #20242245C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625335C2semidirect
11. #20242171C2semidirect
13. C2×#15688853C2semidirect
14. #20241672C2semidirect
349. C47#18017semidirect

Maximal subgroups

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

subgroupindex
#202534642
#202524752
#202422832
#202422762
#202422642
#202422592
#202422572
#202422452
C8×#106253372
C8×#106253352
#202421712
#202418482
C2×#156888532
#202416722
C47×#29942
#1801747