Finite Group Databasebeta

← #26186919

Subgroups — #26186919

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253995C211yesmaximal, characteristic
2#20252482C211yesmaximal, characteristic, complemented
3#20242295C211yesmaximal, characteristic, complemented
4#20242290C211yesmaximal, characteristic, complemented
5#20242283C211yesmaximal, characteristic, complemented
6#20242276C211yesmaximal, characteristic, complemented
7#20242205C211yesmaximal, characteristic, complemented
8#20242200C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242153C211yesmaximal, characteristic, complemented
12#20241848C211yesmaximal, characteristic
13#20241842C211yesmaximal, characteristic, complemented
14#20241669C211yesmaximal, characteristic, complemented
15C47×#2993C211yesmaximal, characteristic
16#15689680C2211yescharacteristic
17#15689533C411yescharacteristic
18#15689518C411yescharacteristic
19#15689493C411yescharacteristic
20#15689482C411yescharacteristic
21#15689379C411yescharacteristic
22#15689379C411yescharacteristic
23#15689367C411yescharacteristic
24#15689367C411yescharacteristic
25#15689253C2211yescharacteristic
26#15689253C2211yescharacteristic
27#15689252—21no—
28#15689252—21no—
29C8×Dic94C2211yescharacteristic
30C8×Dic94C2211yescharacteristic
31C4×#10625337C2211yescharacteristic
32C4×#10625337C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689181—21no—
36#15689181—21no—
37#15689180C2211yescharacteristic
38C4×#10625329C2211yescharacteristic
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×#436—21no—
60C47×#436C2211yescharacteristic
61C47×#435—21no—
62C8×D4×C47C2211yescharacteristic
63C47×#433—21no—
64C47×#431C2211yescharacteristic
65C47×#424—21no—
66C47×#423C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625329C2×C411yescharacteristic
72C2×#10625329C2×C411yescharacteristic
73C22×C47⋊C8—21no—
74#13094024C2×C411yescharacteristic
75#13094024C2×C411yescharacteristic
76#13094016—21no—
77#13094003—21no—
78#13094003C2×C411yescharacteristic
79#13094003C2×C411yescharacteristic
80C4×Dic94—21no—
81C4×Dic94C2311yescharacteristic
82C4×Dic94C2311yescharacteristic
83#13093983—21no—
84#13093957C2×C411yescharacteristic
85#13093957C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87#13093955C2×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—
103#13093935—21no—
104#13093935C2×C411yescharacteristic
105#13093935C2×C411yescharacteristic
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—
116C2×M16×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
151C2×Dic94—21no—
152C2×Dic94C22×C411yescharacteristic
153C2×Dic94C22×C411yescharacteristic
154M16×C47—81no—
155M16×C47—81no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—81no—
159C2×C8×C47C2×D411yescharacteristic
160C2×C8×C47C2×D411yescharacteristic
161C2×C8×C47C2×D411yescharacteristic
162C2×C8×C47C2×D411yescharacteristic
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47C22×C411yescharacteristic
168C4⋊C4×C47C22×C411yescharacteristic
169C22⋊C4×C47—21no—
170C22⋊C4×C47—21no—
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C42×C47—21no—
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180C22⋊Dic47—21no—
181#10625337—22no—
182#10625337—22no—
183#10625335—22no—
184#10625335—22no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
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—
196#10625329—22no—
197#10625329—22no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—42no—
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—81no—
214C2×C4×C47—21no—
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—41no—
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—
234Dic94—21no—
235Dic94—21no—
236Dic94—21no—
237Dic94—21no—
238Dic94—81no—
239C8×C47—21no—
240C8×C47—21no—
241C8×C47—21no—
242C8×C47—21no—
243C8×C47—41no—
244C8×C47—41no—
245C47⋊C8—22no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—41no—
249C47⋊C8—41no—
250C47⋊C8—41no—
251C47⋊C8#13112yes—
252C47⋊C8#13112yes—
253#17969—471nomaximal, Sylow
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47C2×C4×D411yescharacteristic
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—41no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47C2×#13111yescharacteristic
269C4×C47C2×#13111yescharacteristic
270C4×C47#57711yescharacteristic
271C4×C47#57811yescharacteristic
272Dic47—41no—
273Dic47—41no—
274Dic47—41no—
275Dic47—41no—
276#3172—471no—
277#2993D4711yescharacteristic
278#2985—471no—
279#1593—471no—
280#1592—471no—
281#1591—471no—
282#1590—471no—
283#1579—471no—
284SD16⋊C8—471no—
285C8×Q16—471no—
286C8×SD16—471no—
287#1569—471no—
288#1494—471no—
289#1493—471no—
290C8×M16—471no—
291C2×C47—41no—
292C2×C47—81no—
293C2×C47#293111yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295611yescharacteristic
296#533—471no—
297#529C2×D4711yescharacteristic
298#501—471no—
299#497—471no—
300#491—471no—
301#489—471no—
302#470—471no—
303#470—471no—
304#468—471no—
305#468—471no—
306#446—471no—
307#446—471no—
308#446—941no—
309#446—941no—
310#446C2×D4711yescharacteristic
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8C2×D4711yescharacteristic
314C4×Q16—471no—
315C4×Q16—471no—
316C4×SD16—471no—
317C4×SD16—471no—
318#436—21no—
319#436C2×D4711yescharacteristic
320#435—21no—
321C8×D4C2×D4711yescharacteristic
322#433—21no—
323#433—941no—
324#433—941no—
325#432—471no—
326#431C2×D4711yescharacteristic
327#424—21no—
328#423C2×D4711yescharacteristic
329C4×M16—471no—
330C2×C4×C8—471no—
331#335—471no—
332#335—471no—
333#334—471no—
334#334—471no—
335Q8⋊C8—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8—471no—
339Q8⋊C8—471no—
340Q8⋊C8—471no—
341D4⋊C8—471no—
342D4⋊C8—471no—
343#322—471no—
344#322—471no—
345C82—471no—
346C82—471no—
347C47#1796911yescharacteristic, complemented, Sylow
348C2×Q16—471no—
349C2×Q16—471no—
350C2×SD16—471no—
351C2×SD16—471no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—471no—
355C2×M16—471no—
356C22×C8—21no—
357C22×C8—941no—
358C4⋊Q8—471no—
359C4⋊Q8—471no—
360#126—21no—
361#125—941no—
362#125C4×D4711yescharacteristic
363#124C4×D4711yescharacteristic
364#123—21no—
365C22⋊Q8—471no—
366C22⋊Q8—471no—
367C22⋊Q8—941no—
368C22⋊Q8C4×D4711yescharacteristic
369#121C4×D4711yescharacteristic
370C4×Q8—471no—
371C4×Q8—471no—
372C4×Q8—941no—
373C4×Q8C22×D4711yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4711yescharacteristic
376#117—21no—
377#117—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—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8C22⋊D4711yescharacteristic
393C4⋊C8C22⋊D4711yescharacteristic
394C4⋊C8C22×D4711yescharacteristic
395C4⋊C8C22×D4711yescharacteristic
396#103—471no—
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#102—471no—
403#102—471no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—941no—
407C22⋊C8C22⋊D4711yescharacteristic
408C22⋊C8C22⋊D4711yescharacteristic
409#97—21no—
410#97—471no—
411#97—471no—
412#97—941no—
413#97—941no—
414#97—941no—
415C4×C8—21no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8C22×D4711yescharacteristic
424C4×C8C22×D4711yescharacteristic
425C2×Q8—471no—
426C2×Q8—471no—
427C2×Q8—941no—
428C2×Q8C2×C4×D4711yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D4711yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4#1062535011yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435Q16—942no—
436Q16—942no—
437SD16—942no—
438SD16—942no—
439M16—81no—
440M16—81no—
441M16—942no—
442M16—942no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—471no—
447C2×C8—471no—
448C2×C8—471no—
449C2×C8—471no—
450C2×C8—941no—
451C2×C8—941no—
452C2×C8—941no—
453C2×C8—941no—
454C2×C8—1882no—
455C2×C8C2×C22⋊D4711yescharacteristic
456C2×C8C2×C22⋊D4711yescharacteristic
457C2×C8C2×C22⋊D4711yescharacteristic
458C2×C8C2×C22⋊D4711yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—471no—
464C4⋊C4—471no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4C2×C4×D4711yescharacteristic
473C4⋊C4C2×C4×D4711yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—941no—
480C22⋊C4—941no—
481C42—21no—
482C42—941no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42#1062535011yescharacteristic
486C42C2×C22⋊D4711yescharacteristic
487C42C23×D4711yescharacteristic
488C23—21no—
489C23C4×C22⋊D4711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—941no—
493Q8—941no—
494Q8—941no—
495Q8—941no—
496Q8—3761no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
514C2×C4C4×C22⋊D4711yescharacteristic
515C2×C4C4×C22⋊D4711yescharacteristic
516C2×C4C4×C22⋊D4711yescharacteristic
517C2×C4C22×C4×D4711yescharacteristic
518C2×C4C22×C22⋊D4711yescharacteristic
519C2×C4C2×#1062535011yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—472no—
527C8—472no—
528C8—942no—
529C8—941no—
530C8—941no—
531C8—1881no—
532C8—1881no—
533C8—1881no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D4711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—1881no—
549C4—1881no—
550C4—1881no—
551C4—1881no—
552C4#131×D4711yescharacteristic
553C4#131×D4711yescharacteristic
554C4#1568993411yescharacteristic
555C4#1568993811yescharacteristic
556C2—41no—
557C2—81no—
558C2#2025209811yescharacteristic
559C2#2025222711yescharacteristic
560C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2993C2
socleC22×C47C2×C4×D4
prime radical#121×C47C2×C4
cosocleC42×C47C24
hypercenter#2993D47
hypocenterC47#17969
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #20252482C2semidirect
3. #20242295C2semidirect
4. #20242290C2semidirect
5. #20242283C2semidirect
6. #20242276C2semidirect
7. #20242205C2semidirect
8. #20242200C2semidirect
9. C8×#10625337C2semidirect
10. C8×#10625335C2semidirect
11. #20242153C2semidirect
13. #20241842C2semidirect
14. #20241669C2semidirect
347. C47#17969semidirect

Maximal subgroups

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

subgroupindex
#202539952
#202524822
#202422952
#202422902
#202422832
#202422762
#202422052
#202422002
C8×#106253372
C8×#106253352
#202421532
#202418482
#202418422
#202416692
C47×#29932
#1796947