Finite Group Databasebeta

← #26188026

Subgroups — #26188026

Order 12032.

652 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252509C211yesmaximal, characteristic, complemented
2C4×#13094044C211yesmaximal, characteristic
3#20242295C212yesmaximal, complemented
4#20242224C212yesmaximal, complemented
5#20242222C212yesmaximal, complemented
6#20242210C212yesmaximal, complemented
7#20242143C211yesmaximal, characteristic, complemented
8#20241827C211yesmaximal, characteristic, complemented
9#20241825C211yesmaximal, characteristic, complemented
10#20241678C211yesmaximal, characteristic, complemented
11C47×#2990C211yesmaximal, characteristic, complemented
12C2×#13094044C411yescharacteristic
13C4×#10625350C2211yescharacteristic
14#15689253C2212yes—
15C4×#10625337C411yescharacteristic
16C4×#10625337C2211yescharacteristic
17C4×#10625336C411yescharacteristic
18C4×#10625336C2211yescharacteristic
19C4×#10625335C411yescharacteristic
20C4×#10625335C2211yescharacteristic
21C4×#10625334C411yescharacteristic
22C4×#10625334C2211yescharacteristic
23#15689197—22no—
24C8×D188C2212yes—
25#15689179—21no—
26#15689159C411yescharacteristic
27#15689147C2211yescharacteristic
28C4⋊C8×D47—21no—
29#15689119C411yescharacteristic
30#15689117C411yescharacteristic
31C4×#10625329C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15688873C2212yes—
34#15688873C2212yes—
35Q8⋊(C47⋊C8)C2212yes—
36#15688853C2212yes—
37D4⋊(C47⋊C8)C2212yes—
38#15688850C2212yes—
39#15688845C2212yes—
40#15688844C2212yes—
41C4×#41×C47C2211yescharacteristic
42C47×#446C2212yes—
43C47×#435—22no—
44C8×D4×C47C2212yes—
45C47×#432—21no—
46C47×#431C2211yescharacteristic
47C47×#423C2211yescharacteristic
48C2×C4⋊C8×C47—21no—
49C2×#10625350C2×C411yescharacteristic
50#13094044—24no—
51C2×#10625337C2×C411yescharacteristic
52C2×#10625335C2×C411yescharacteristic
53C2×#10625336C2×C411yescharacteristic
54C2×#10625334C2×C411yescharacteristic
55C2×#10625329—21no—
56C2×#10625329—21no—
57C22×C47⋊C8C2×C411yescharacteristic
58C22×C47⋊C8C2×C411yescharacteristic
59C2×C8×D47—22no—
60C4×Dic94C2×C411yescharacteristic
61C4×Dic94C2311yescharacteristic
62C4×D188C2×C411yescharacteristic
63C4×D188C2311yescharacteristic
64C4×C22⋊D47—21no—
65C4×C22⋊D47—21no—
66#13093983C2×C411yescharacteristic
67#13093981—21no—
68C42×D47—21no—
69#13093957C2×C411yescharacteristic
70#13093957C2×C411yescharacteristic
71#13093955C2×C411yescharacteristic
72#13093955C2×C411yescharacteristic
73C4⋊(C47⋊C8)—21no—
74C4⋊(C47⋊C8)C2312yes—
75Dic47⋊C8—22no—
76#13093948C2×C411yescharacteristic
77#13093948C2×C411yescharacteristic
78#13093947C2×C411yescharacteristic
79#13093947C2×C411yescharacteristic
80#13093945C2×C411yescharacteristic
81#13093945C2×C411yescharacteristic
82#13093944C2×C411yescharacteristic
83#13093944C2×C411yescharacteristic
84(C2×D47)⋊C8—22no—
85#13093935—21no—
86#13093934—22no—
87C4×C47⋊C8C2×C411yescharacteristic
88C4×C47⋊C8C2×C411yescharacteristic
89C4×C47⋊C8C2312yes—
90C4×C47⋊C8C2311yescharacteristic
91C4×C47⋊C8C2311yescharacteristic
92C2×#41×C47C2×C411yescharacteristic
93C2×M16×C47—21no—
94C22×C8×C47—22no—
95C4×Q8×C47C2×C411yescharacteristic
96C4×Q8×C47C2311yescharacteristic
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2×C411yescharacteristic
100C4×D4×C47C2311yescharacteristic
101#117×C47—21no—
102#117×C47C2×C411yescharacteristic
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105C4⋊C8×C47—22no—
106C4⋊C8×C47—21no—
107C4⋊C8×C47D411yescharacteristic
108C4⋊C8×C47D411yescharacteristic
109C4⋊C8×C47C2312yes—
110C22⋊C8×C47—22no—
111C22⋊C8×C47D412yes—
112#97×C47—22no—
113C4×C8×C47C2312yes—
114#41×C47—22no—
115#41×C47—41no—
116C2×Q8×C47C22×C411yescharacteristic
117C2×D4×C47—21no—
118C2×D4×C47C22×C411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C2×C22⋊D47—21no—
126#10625350—22no—
127#10625350—41no—
128C2×D188C22×C411yescharacteristic
129C2×C4×D47—21no—
130C2×C4×D47—21no—
131C2×C4×D47—21no—
132C2×Dic94C22×C411yescharacteristic
133M16×C47—81no—
134C2×C8×C47—22no—
135C2×C8×C47—82no—
136C2×C8×C47C2×D412yes—
137C2×C8×C47C2×D412yes—
138C4⋊C4×C47—21no—
139C4⋊C4×C47—21no—
140C4⋊C4×C47C22×C411yescharacteristic
141C4⋊C4×C47C22×C411yescharacteristic
142C22⋊C4×C47—21no—
143C22⋊C4×C47—21no—
144C22⋊C4×C47—21no—
145C42×C47—21no—
146C42×C47—21no—
147C42×C47—21no—
148C42×C47C22×C411yescharacteristic
149C42×C47C2×D411yescharacteristic
150C42×C47#4111yescharacteristic
151C42×C47C2411yescharacteristic
152C22⋊Dic47—21no—
153#10625337—22no—
154#10625336—22no—
155#10625335—22no—
156#10625334M1614yescomplemented
157(C2×D47)⋊C4—21no—
158(C2×D47)⋊C4—21no—
159C4⋊Dic47C22×C411yescharacteristic
160C4⋊Dic47C22×C411yescharacteristic
161Dic47⋊C4—21no—
162Dic47⋊C4—21no—
163C4×Dic47—21no—
164C4×Dic47—21no—
165C4×Dic47—21no—
166#10625329—42no—
167#10625329—81no—
168C2×C47⋊C8—22no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—41no—
172C2×C47⋊C8C22×C411yescharacteristic
173C2×C47⋊C8C22×C411yescharacteristic
174C2×C47⋊C8C22×C411yescharacteristic
175C2×C47⋊C8C22×C411yescharacteristic
176C8×D47—82no—
177C23×C47—21no—
178C23×C47C4×D411yescharacteristic
179C22×D47—21no—
180Q8×C47—21no—
181Q8×C47—21no—
182D4×C47—21no—
183D4×C47—42no—
184D4×C47C2×M1612yes—
185C2×C4×C47—21no—
186C2×C4×C47—21no—
187C2×C4×C47—21no—
188C2×C4×C47—21no—
189C2×C4×C47—22no—
190C2×C4×C47—21no—
191C2×C4×C47—21no—
192C2×C4×C47—21no—
193C2×C4×C47—42no—
194C2×C4×C47—41no—
195C2×C4×C47—41no—
196C2×C4×C47—42no—
197C2×C4×C47C4×D411yescharacteristic
198C2×C4×C47C4×D411yescharacteristic
199C2×C4×C47C4×D411yescharacteristic
200C2×C4×C47C23×C411yescharacteristic
201C2×C4×C47C22×D411yescharacteristic
202C2×C4×C47C2×#4111yescharacteristic
203C22⋊D47—42no—
204C2×Dic47—21no—
205C2×Dic47—21no—
206C2×Dic47—21no—
207D188—21no—
208D188C2×M1612yes—
209C4×D47—42no—
210C4×D47—41no—
211C4×D47—41no—
212C4×D47—42no—
213Dic94—21no—
214Dic94—21no—
215C8×C47—22no—
216C8×C47—22no—
217C8×C47—42no—
218C47⋊C8—21no—
219C47⋊C8—21no—
220C47⋊C8—21no—
221C47⋊C8—42no—
222C47⋊C8—42no—
223C47⋊C8C2×M1612yes—
224#18065—471nomaximal, Sylow
225C22×C47—21no—
226C22×C47—22no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—41no—
230C22×C47—41no—
231C22×C47C2×C4×D411yescharacteristic
232C2×D47—22no—
233C2×D47—41no—
234C2×D47—41no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—41no—
239C4×C47—41no—
240C4×C47—41no—
241C4×C47#44412yes—
242C4×C47C22×M1611yescharacteristic
243C4×C47#56811yescharacteristic
244C4×C47#57711yescharacteristic
245C4×C47#57711yescharacteristic
246Dic47—41no—
247Dic47—41no—
248Dic47—41no—
249#2990—471no—
250#2990D4711yescharacteristic, complemented
251C4×#135—471no—
252#1593—472no—
253#1582—472no—
254#1582—472no—
255#1580—472no—
256#1566—471no—
257#1489—471no—
258#1489—471no—
259#1451—471no—
260C2×C47—41no—
261C2×C47—42no—
262C2×C47D4×M1611yescharacteristic
263C2×C47#295211yescharacteristic
264C2×C47C2×#44411yescharacteristic
265D47—42no—
266C2×#135—471no—
267C4×#41—471no—
268C4×#41C2×D4711yescharacteristic
269#446—472no—
270#446C2×D4712yes—
271C4×Q16—471no—
272C4×Q16—471no—
273C4×SD16—471no—
274C4×SD16—471no—
275C4×SD16—471no—
276C4×SD16—471no—
277C4×D8—471no—
278C4×D8—471no—
279#435—22no—
280#435—942no—
281C8×D4—472no—
282C8×D4C2×D4712yes—
283#432—21no—
284#432—941no—
285#431C2×D4711yescharacteristic
286#427—471no—
287#423—471no—
288#423C2×D4711yescharacteristic
289C2×C4⋊C8—21no—
290C2×C4⋊C8—941no—
291#416—471no—
292#416—471no—
293C4×M16—471no—
294C2×C4×C8—471no—
295#334—472no—
296#334—472no—
297Q8⋊C8—472no—
298Q8⋊C8—472no—
299D4⋊C8—472no—
300D4⋊C8—472no—
301#322—472no—
302#322—472no—
303C47#1806511yescharacteristic, complemented, Sylow
304C2×#41—471no—
305C2×#41C4×D4711yescharacteristic
306#135—944no—
307C2×Q16—471no—
308C2×SD16—471no—
309C2×SD16—471no—
310C2×D8—471no—
311C2×M16—21no—
312C2×M16—941no—
313C2×M16—941no—
314C22×C8—22no—
315C22×C8—471no—
316C22×C8—471no—
317C22×C8—942no—
318C4×Q8—471no—
319C4×Q8—471no—
320C4×Q8C4×D4711yescharacteristic
321C4×Q8C22×D4711yescharacteristic
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—471no—
325C4×D4—471no—
326C4×D4—941no—
327C4×D4—941no—
328C4×D4C4×D4711yescharacteristic
329C4×D4C22×D4711yescharacteristic
330#117—21no—
331#117—471no—
332#117—941no—
333#117C4×D4711yescharacteristic
334C2×C42—21no—
335C2×C42—941no—
336C2×C42C22×D4711yescharacteristic
337#107—471no—
338#107—471no—
339#106—471no—
340#106—471no—
341C4⋊C8—22no—
342C4⋊C8—21no—
343C4⋊C8—472no—
344C4⋊C8—942no—
345C4⋊C8—941no—
346C4⋊C8C22⋊D4711yescharacteristic
347C4⋊C8C22⋊D4711yescharacteristic
348C4⋊C8C22×D4712yes—
349#103—471no—
350#103—471no—
351#103—471no—
352#103—471no—
353#102—471no—
354#102—471no—
355#102—471no—
356#102—471no—
357C22⋊C8—22no—
358C22⋊C8—942no—
359C22⋊C8C22⋊D4712yes—
360#97—22no—
361#97—942no—
362#97—941no—
363C4×C8—471no—
364C4×C8—471no—
365C4×C8—471no—
366C4×C8—471no—
367C4×C8—472no—
368C4×C8C22×D4712yes—
369#41—22no—
370#41—41no—
371#41—942no—
372#41—1881no—
373C2×Q8—471no—
374C2×Q8C2×C4×D4711yescharacteristic
375C2×D4—21no—
376C2×D4—471no—
377C2×D4—941no—
378C2×D4C2×C4×D4711yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—941no—
383C22×C4—941no—
384C22×C4—941no—
385C22×C4C2×C4×D4711yescharacteristic
386C22×C4#1062535011yescharacteristic
387C22×C4C2×C22⋊D4711yescharacteristic
388Q16—942no—
389SD16—942no—
390SD16—942no—
391D8—474no—
392M16—81no—
393M16—3761no—
394M16—1882no—
395C2×C8—22no—
396C2×C8—82no—
397C2×C8—471no—
398C2×C8—471no—
399C2×C8—471no—
400C2×C8—471no—
401C2×C8—942no—
402C2×C8—942no—
403C2×C8—942no—
404C2×C8—3762no—
405C2×C8—1881no—
406C2×C8C2×C22⋊D4712yes—
407C2×C8C2×C22⋊D4712yes—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—471no—
411C4⋊C4—471no—
412C4⋊C4—941no—
413C4⋊C4—941no—
414C4⋊C4C2×C4×D4711yescharacteristic
415C4⋊C4C2×C4×D4711yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—941no—
420C22⋊C4—941no—
421C22⋊C4—941no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—941no—
426C42—941no—
427C42—941no—
428C42C2×C4×D4711yescharacteristic
429C42#1062535011yescharacteristic
430C42C2×C22⋊D4711yescharacteristic
431C42C23×D4711yescharacteristic
432C23—21no—
433C23—941no—
434C23C4×C22⋊D4711yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—941no—
438Q8—941no—
439D4—21no—
440D4—42no—
441D4—472no—
442D4—941no—
443D4—1882no—
444D4M16×D4712yes—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—941no—
458C2×C4—941no—
459C2×C4—941no—
460C2×C4—1882no—
461C2×C4—1882no—
462C2×C4—1881no—
463C2×C4—1881no—
464C2×C4C4×C22⋊D4711yescharacteristic
465C2×C4C4×C22⋊D4711yescharacteristic
466C2×C4C4×C22⋊D4711yescharacteristic
467C2×C4C22×C4×D4711yescharacteristic
468C2×C4C22×C22⋊D4711yescharacteristic
469C2×C4C2×#1062535011yescharacteristic
470C8—22no—
471C8—22no—
472C8—42no—
473C8—472no—
474C8—941no—
475C8—941no—
476C8—941no—
477C8—1882no—
478C8—1882no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—942no—
486C22—1881no—
487C22—1881no—
488C22C2×C4×C22⋊D4711yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—1881no—
496C4—1881no—
497C4—1881no—
498C4#1568924312yes—
499C4C2×M16×D4711yescharacteristic
500C4#1568988911yescharacteristic
501C4#1568993111yescharacteristic
502C4#1568993411yescharacteristic
503C2—41no—
504C2—42no—
505C2—1882no—
506C2M16×C22⋊D4711yescharacteristic
507C2#2025226911yescharacteristic
508C2C2×#1568924311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2990C2
socleC22×C47C2×C4×D4
prime radicalC2×#13094044C4
cosocleC42×C47C24
hypercenter#2990D47
hypocenterC47#18065
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2990

Complements

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

NH ≅ G/Ntype
1. #20252509C2semidirect
3. #20242295C2semidirect
4. #20242224C2semidirect
5. #20242222C2semidirect
6. #20242210C2semidirect
7. #20242143C2semidirect
8. #20241827C2semidirect
9. #20241825C2semidirect
10. #20241678C2semidirect
11. C47×#2990C2semidirect
156. #10625334M16semidirect
250. #2990D47semidirect
303. C47#18065semidirect

Maximal subgroups

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

subgroupindex
#202525092
C4×#130940442
#202422952
#202422242
#202422222
#202422102
#202421432
#202418272
#202418252
#202416782
C47×#29902
#1806547