Finite Group Databasebeta

← #26188018

Subgroups — #26188018

Order 12032.

718 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252422C211yesmaximal, characteristic, complemented
2C2×C4×#10625334C211yesmaximal, characteristic
3#20242300C212yesmaximal, complemented
4#20242217C212yesmaximal, complemented
5#20242215C212yesmaximal, complemented
6#20242210C212yesmaximal, complemented
7#20242149C211yesmaximal, characteristic, complemented
8#20241831C211yesmaximal, characteristic, complemented
9#20241830C211yesmaximal, characteristic, complemented
10#20241678C211yesmaximal, characteristic, complemented
11C47×#2974C211yesmaximal, characteristic, complemented
12C22×#10625334C411yescharacteristic
13C2×C4×D188C2211yescharacteristic
14C4×#10625334C411yescharacteristic
15C4×#10625334C411yescharacteristic
16C4×#10625334C411yescharacteristic
17C4×#10625334C411yescharacteristic
18C4×#10625334C2211yescharacteristic
19C4×#10625334C2211yescharacteristic
20C4×#10625334C2211yescharacteristic
21C4×#10625334C2211yescharacteristic
22#15689202C2212yescomplemented
23#15689193—22no—
24C8×D188C2212yescomplemented
25#15689180C2211yescharacteristic
26C2×#13093957C411yescharacteristic
27C2×#13093945C411yescharacteristic
28C2×#13093944C411yescharacteristic
29#15689085—21no—
30C22⋊C8×D47—21no—
31C4×#10625329C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33#15688875C2212yescomplemented
34#15688873C2212yescomplemented
35D4⋊(C47⋊C8)C2212yescomplemented
36D4⋊(C47⋊C8)C2212yescomplemented
37#15688850C2212yescomplemented
38#15688850C2212yescomplemented
39#15688845C2212yescomplemented
40#15688844C2212yescomplemented
41C2×C4×D4×C47C2211yescharacteristic
42C47×#436C2212yescomplemented
43C47×#435—22no—
44C8×D4×C47C2212yescomplemented
45C47×#432C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#407—21no—
48C2×C22⋊C8×C47—21no—
49C22×D188C2×C411yescharacteristic
50C22×C4×D47—21no—
51C2×#10625334—24no—
52C2×#10625334C2×C411yescharacteristic
53C2×#10625334C2×C411yescharacteristic
54C2×#10625334C2×C411yescharacteristic
55C2×#10625334C2×C411yescharacteristic
56C2×#10625329—21no—
57C2×#10625324—22no—
58C22×C47⋊C8C2×C411yescharacteristic
59C22×C47⋊C8C2×C411yescharacteristic
60C2×C8×D47—22no—
61C4×D188—21no—
62C4×D188—21no—
63C4×D188C2×C411yescharacteristic
64C4×D188C2×C411yescharacteristic
65C4×D188C2311yescharacteristic
66C4×D188C2311yescharacteristic
67C2×C4⋊Dic47C2×C411yescharacteristic
68C2×(C2×D47)⋊C4—21no—
69#13093957C2×C411yescharacteristic
70#13093957C2×C411yescharacteristic
71#13093957C2×C411yescharacteristic
72#13093957C2×C411yescharacteristic
73C4⋊(C47⋊C8)C2312yes—
74#13093945C2×C411yescharacteristic
75#13093945C2×C411yescharacteristic
76#13093945C2×C411yescharacteristic
77#13093945C2×C411yescharacteristic
78#13093944C2×C411yescharacteristic
79#13093944C2×C411yescharacteristic
80#13093944C2×C411yescharacteristic
81#13093944C2×C411yescharacteristic
82C22⋊(C47⋊C8)—21no—
83(C2×D47)⋊C8—22no—
84(C2×D47)⋊C8—22no—
85#13093935—21no—
86#13093935—21no—
87C4×C47⋊C8C2×C411yescharacteristic
88C4×C47⋊C8C2×C411yescharacteristic
89C4×C47⋊C8C2312yes—
90C4×C47⋊C8C2311yescharacteristic
91C4×C47⋊C8C2311yescharacteristic
92C22×D4×C47C2×C411yescharacteristic
93C23×C4×C47—21no—
94C2×M16×C47—22no—
95C22×C8×C47—22no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47C2×C411yescharacteristic
99C4×D4×C47C2×C411yescharacteristic
100C4×D4×C47C2311yescharacteristic
101C4×D4×C47C2311yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C22⋊C4×C47—21no—
104C2×C42×C47C2311yescharacteristic
105C4⋊C8×C47D412yes—
106C4⋊C8×C47C2312yes—
107C22⋊C8×C47—21no—
108C22⋊C8×C47—22no—
109C22⋊C8×C47—22no—
110C22⋊C8×C47D411yescharacteristic
111C22⋊C8×C47D411yescharacteristic
112#97×C47—21no—
113C4×C8×C47C2312yes—
114C24×C47—21no—
115C23×D47—21no—
116C2×D4×C47—22no—
117C2×D4×C47—21no—
118C2×D4×C47—41no—
119C2×D4×C47C22×C411yescharacteristic
120C2×D4×C47C22×C411yescharacteristic
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—82no—
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47#4111yescharacteristic
130C22×Dic47—21no—
131C2×D188—22no—
132C2×D188—21no—
133C2×D188—41no—
134C2×D188C22×C411yescharacteristic
135C2×D188C22×C411yescharacteristic
136C2×C4×D47—21no—
137C2×C4×D47—21no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—82no—
141M16×C47—82no—
142C2×C8×C47—22no—
143C2×C8×C47—82no—
144C2×C8×C47C2×D412yes—
145C2×C8×C47C2×D412yes—
146C4⋊C4×C47—21no—
147C4⋊C4×C47C22×C411yescharacteristic
148C4⋊C4×C47C22×C411yescharacteristic
149C22⋊C4×C47—21no—
150C22⋊C4×C47—21no—
151C22⋊C4×C47—21no—
152C22⋊C4×C47—21no—
153C42×C47C22×C411yescharacteristic
154C42×C47C2×D411yescharacteristic
155C42×C47#4111yescharacteristic
156C42×C47C2411yescharacteristic
157#10625334—22no—
158#10625334—22no—
159#10625334—22no—
160#10625334M1614yescomplemented
161(C2×D47)⋊C4—21no—
162(C2×D47)⋊C4—21no—
163(C2×D47)⋊C4—21no—
164(C2×D47)⋊C4—21no—
165C4⋊Dic47—21no—
166C4⋊Dic47C22×C411yescharacteristic
167C4⋊Dic47C22×C411yescharacteristic
168#10625329—42no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—41no—
173C2×C47⋊C8C22×C411yescharacteristic
174C2×C47⋊C8C22×C411yescharacteristic
175C2×C47⋊C8C22×C411yescharacteristic
176C2×C47⋊C8C22×C411yescharacteristic
177#10625324—82no—
178C8×D47—82no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—42no—
182C23×C47—42no—
183C23×C47—81no—
184C23×C47C4×D411yescharacteristic
185C22×D47—21no—
186C22×D47—21no—
187C22×D47—42no—
188C22×D47—42no—
189C22×D47—81no—
190D4×C47—21no—
191D4×C47—21no—
192D4×C47—21no—
193D4×C47—42no—
194D4×C47C2×M1612yes—
195C2×C4×C47—22no—
196C2×C4×C47—21no—
197C2×C4×C47—21no—
198C2×C4×C47—22no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—81no—
204C2×C4×C47—81no—
205C2×C4×C47—81no—
206C2×C4×C47C4×D411yescharacteristic
207C2×C4×C47C4×D411yescharacteristic
208C2×C4×C47C4×D411yescharacteristic
209C2×C4×C47C23×C411yescharacteristic
210C2×C4×C47C22×D411yescharacteristic
211C2×C4×C47C2×#4111yescharacteristic
212C2×Dic47—21no—
213C2×Dic47—21no—
214C2×Dic47—81no—
215D188—21no—
216D188—21no—
217D188—21no—
218D188—42no—
219D188C2×M1612yes—
220C4×D47—42no—
221C4×D47—42no—
222C4×D47—81no—
223C4×D47—81no—
224C8×C47—22no—
225C8×C47—22no—
226C8×C47—42no—
227C47⋊C8—21no—
228C47⋊C8—21no—
229C47⋊C8—21no—
230C47⋊C8—42no—
231C47⋊C8—42no—
232C47⋊C8C2×M1612yes—
233#18064—471nomaximal, Sylow
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—22no—
237C22×C47—41no—
238C22×C47—41no—
239C22×C47—41no—
240C22×C47—41no—
241C22×C47—41no—
242C22×C47—84no—
243C22×C47#44412yes—
244C22×C47C2×C4×D411yescharacteristic
245C2×D47—22no—
246C2×D47—41no—
247C2×D47—41no—
248C2×D47—41no—
249C2×D47—41no—
250C2×D47—41no—
251C2×D47—84no—
252C4×C47—21no—
253C4×C47—21no—
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—41no—
257C4×C47—41no—
258C4×C47C22×M1611yescharacteristic
259C4×C47#56811yescharacteristic
260C4×C47#57612yes—
261Dic47—41no—
262Dic47—41no—
263#2974—471no—
264#2974D4711yescharacteristic, complemented
265C2×C4×D8—471no—
266#1594—472no—
267#1581—472no—
268#1581—472no—
269#1580—472no—
270#1568—471no—
271#1490—471no—
272#1490—471no—
273#1451—471no—
274C2×C47—22no—
275C2×C47—42no—
276C2×C47—81no—
277C2×C47D4×M1611yescharacteristic
278C2×C47#294811yescharacteristic
279C2×C47C2×#44411yescharacteristic
280D47—42no—
281D47—81no—
282C22×D8—471no—
283C2×C4×D4—471no—
284C2×C4×D4C2×D4711yescharacteristic
285C4×D8—471no—
286C4×D8—471no—
287C4×D8—471no—
288C4×D8—471no—
289C4×D8—471no—
290C4×D8—471no—
291C4×D8—471no—
292C4×D8—471no—
293#436—472no—
294#436C2×D4712yescomplemented
295#435—22no—
296#435—942no—
297C8×D4—472no—
298C8×D4C2×D4712yescomplemented
299#432—471no—
300#432C2×D4711yescharacteristic
301#431C2×D4711yescharacteristic
302C2×#107—471no—
303C2×#102—471no—
304C2×#102—471no—
305#407—21no—
306#407—941no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—941no—
309C4×M16—471no—
310C2×C4×C8—471no—
311#335—472no—
312#334—472no—
313D4⋊C8—472no—
314D4⋊C8—472no—
315D4⋊C8—472no—
316D4⋊C8—472no—
317#322—472no—
318#322—472no—
319C47#1806411yescharacteristic, complemented, Sylow
320C22×D4—471no—
321C22×D4C4×D4711yescharacteristic
322C23×C4—21no—
323C23×C4—941no—
324C2×D8—471no—
325C2×D8—471no—
326C2×D8—471no—
327C2×D8—471no—
328C2×D8—944no—
329C2×M16—22no—
330C2×M16—941no—
331C2×M16—942no—
332C22×C8—22no—
333C22×C8—471no—
334C22×C8—471no—
335C22×C8—942no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—471no—
339C4×D4—471no—
340C4×D4—471no—
341C4×D4—471no—
342C4×D4—941no—
343C4×D4—941no—
344C4×D4C4×D4711yescharacteristic
345C4×D4C4×D4711yescharacteristic
346C4×D4C22×D4711yescharacteristic
347C4×D4C22×D4711yescharacteristic
348C2×C4⋊C4—471no—
349C2×C4⋊C4C4×D4711yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—941no—
352C2×C42C22×D4711yescharacteristic
353#107—471no—
354#107—471no—
355#107—471no—
356#107—471no—
357C4⋊C8—472no—
358C4⋊C8C22⋊D4712yes—
359C4⋊C8C22×D4712yes—
360#102—471no—
361#102—471no—
362#102—471no—
363#102—471no—
364#102—471no—
365#102—471no—
366#102—471no—
367#102—471no—
368C22⋊C8—21no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—941no—
372C22⋊C8—942no—
373C22⋊C8—942no—
374C22⋊C8C22⋊D4711yescharacteristic
375C22⋊C8C22⋊D4711yescharacteristic
376#97—21no—
377#97—941no—
378#97—941no—
379C4×C8—471no—
380C4×C8—471no—
381C4×C8—471no—
382C4×C8—471no—
383C4×C8—472no—
384C4×C8C22×D4712yes—
385C24—21no—
386C24—941no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—471no—
391C2×D4—471no—
392C2×D4—942no—
393C2×D4—941no—
394C2×D4—1881no—
395C2×D4C2×C4×D4711yescharacteristic
396C2×D4C2×C4×D4711yescharacteristic
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—82no—
403C22×C4—941no—
404C22×C4—941no—
405C22×C4—941no—
406C22×C4—941no—
407C22×C4—941no—
408C22×C4—3762no—
409C22×C4C2×C4×D4711yescharacteristic
410C22×C4#1062535011yescharacteristic
411C22×C4C2×C22⋊D4711yescharacteristic
412D8—474no—
413D8—942no—
414D8—942no—
415D8—942no—
416M16—82no—
417M16—3762no—
418M16—1882no—
419C2×C8—22no—
420C2×C8—82no—
421C2×C8—471no—
422C2×C8—471no—
423C2×C8—471no—
424C2×C8—471no—
425C2×C8—942no—
426C2×C8—942no—
427C2×C8—942no—
428C2×C8—3762no—
429C2×C8—1881no—
430C2×C8C2×C22⋊D4712yes—
431C2×C8C2×C22⋊D4712yes—
432C4⋊C4—21no—
433C4⋊C4—471no—
434C4⋊C4—471no—
435C4⋊C4—941no—
436C4⋊C4C2×C4×D4711yescharacteristic
437C4⋊C4C2×C4×D4711yescharacteristic
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—941no—
443C22⋊C4—941no—
444C22⋊C4—941no—
445C22⋊C4—941no—
446C42C2×C4×D4711yescharacteristic
447C42#1062535011yescharacteristic
448C42C2×C22⋊D4711yescharacteristic
449C42C23×D4711yescharacteristic
450C23—21no—
451C23—21no—
452C23—42no—
453C23—42no—
454C23—81no—
455C23—941no—
456C23—941no—
457C23—3761no—
458C23—1882no—
459C23—1882no—
460C23C4×C22⋊D4711yescharacteristic
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—472no—
466D4—941no—
467D4—941no—
468D4—941no—
469D4—1882no—
470D4M16×D4712yes—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—941no—
483C2×C4—941no—
484C2×C4—3761no—
485C2×C4—3761no—
486C2×C4—3761no—
487C2×C4—1882no—
488C2×C4—1882no—
489C2×C4C4×C22⋊D4711yescharacteristic
490C2×C4C4×C22⋊D4711yescharacteristic
491C2×C4C4×C22⋊D4711yescharacteristic
492C2×C4C22×C4×D4711yescharacteristic
493C2×C4C22×C22⋊D4711yescharacteristic
494C2×C4C2×#1062535011yescharacteristic
495C8—22no—
496C8—22no—
497C8—42no—
498C8—472no—
499C8—941no—
500C8—941no—
501C8—941no—
502C8—1882no—
503C8—1882no—
504C22—21no—
505C22—21no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—84no—
513C22—942no—
514C22—3764no—
515C22—1881no—
516C22—1881no—
517C22—1881no—
518C22—1881no—
519C22—1881no—
520C22#1568924312yes—
521C22C2×C4×C22⋊D4711yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—41no—
528C4—1881no—
529C4—1881no—
530C4C2×M16×D4711yescharacteristic
531C4#1568988911yescharacteristic
532C4#1568992612yes—
533C2—22no—
534C2—42no—
535C2—81no—
536C2—3761no—
537C2—1882no—
538C2M16×C22⋊D4711yescharacteristic
539C2#2025223811yescharacteristic
540C2C2×#1568924311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2974C2
socleC22×C47C2×C4×D4
prime radicalC22×#10625334C4
cosocleC42×C47C24
hypercenter#2974D47
hypocenterC47#18064
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
1. #20252422C2semidirect
3. #20242300C2semidirect
4. #20242217C2semidirect
5. #20242215C2semidirect
6. #20242210C2semidirect
7. #20242149C2semidirect
8. #20241831C2semidirect
9. #20241830C2semidirect
10. #20241678C2semidirect
11. C47×#2974C2semidirect
22. #15689202C22semidirect
24. C8×D188C22semidirect
33. #15688875C22semidirect
34. #15688873C22semidirect
35. D4⋊(C47⋊C8)C22semidirect
36. D4⋊(C47⋊C8)C22semidirect
37. #15688850C22semidirect
38. #15688850C22semidirect
39. #15688845C22semidirect
40. #15688844C22semidirect
42. C47×#436C22semidirect
44. C8×D4×C47C22semidirect
160. #10625334M16semidirect
264. #2974D47semidirect
294. #436C2×D47semidirect
298. C8×D4C2×D47semidirect
319. C47#18064semidirect

Maximal subgroups

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

subgroupindex
#202524222
C2×C4×#106253342
#202423002
#202422172
#202422152
#202422102
#202421492
#202418312
#202418302
#202416782
C47×#29742
#1806447