Finite Group Databasebeta

← #26187646

Subgroups — #26187646

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253420C211yesmaximal, characteristic
2#20252475C211yesmaximal, characteristic, complemented
3#20252454C211yesmaximal, characteristic
4#20242292C211yesmaximal, characteristic, complemented
5#20242280C211yesmaximal, characteristic, complemented
6#20242268C211yesmaximal, characteristic, complemented
7#20242247C211yesmaximal, characteristic, complemented
8#20242233C211yesmaximal, characteristic, complemented
9#20242226C211yesmaximal, characteristic, complemented
10#20242202C211yesmaximal, characteristic, complemented
11C8×#10625325C211yesmaximal, characteristic, complemented
12#20242168C211yesmaximal, characteristic, complemented
13#20241858C211yesmaximal, characteristic
14#20241784C211yesmaximal, characteristic, complemented
15C47×#1454C211yesmaximal, characteristic, complemented
16#15689673C2211yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18#15689442C411yescharacteristic
19#15689442C411yescharacteristic
20#15689409C411yescharacteristic
21#15689409C411yescharacteristic
22#15689324C411yescharacteristic
23#15689324C411yescharacteristic
24#15689264C411yescharacteristic
25#15689264C411yescharacteristic
26#15689253C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689252—21no—
29#15689252—21no—
30C8×Dic94C2211yescharacteristic
31C8×Dic94C2211yescharacteristic
32C4×#10625325C2211yescharacteristic
33C4×#10625325C2211yescharacteristic
34C4×#10625325C2211yescharacteristic
35C4×#10625325C2211yescharacteristic
36#15689202C2211yescharacteristic
37#15689202C2211yescharacteristic
38#15689200—21no—
39C8×D188C2211yescharacteristic
40C8×D188C2211yescharacteristic
41#15689188—21no—
42#15689180C2211yescharacteristic
43#15689177—21no—
44#15689176C2211yescharacteristic
45#15689173—21no—
46#15689088—21no—
47#15689088—21no—
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688874C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688852C2211yescharacteristic
57#15688852C2211yescharacteristic
58#15688852C2211yescharacteristic
59#15688852C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×#322C2211yescharacteristic
64C47×#322C2211yescharacteristic
65C47×#322C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625350—21no—
68C22×Dic94C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625325C2×C411yescharacteristic
71C2×#10625325C2×C411yescharacteristic
72C2×#10625325C2×C411yescharacteristic
73C2×#10625324—21no—
74C2×#10625324—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77#13094024C2×C411yescharacteristic
78#13094021C2×C411yescharacteristic
79#13094012—21no—
80#13093998—21no—
81#13093998C2×C411yescharacteristic
82#13093998C2×C411yescharacteristic
83C4×Dic94—21no—
84C4×Dic94—21no—
85C4×Dic94C2×C411yescharacteristic
86C4×Dic94C2×C411yescharacteristic
87C4×Dic94C2311yescharacteristic
88C4×Dic94C2311yescharacteristic
89C4×D188—21no—
90C4×D188C2311yescharacteristic
91C4×D188C2311yescharacteristic
92C2×C4⋊Dic47C2×C411yescharacteristic
93C2×Dic47⋊C4—21no—
94C2×C4×Dic47—21no—
95#13093956C2×C411yescharacteristic
96#13093956C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98#13093956C2×C411yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107#13093949C2×C411yescharacteristic
108#13093949C2×C411yescharacteristic
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093946C2×C411yescharacteristic
112#13093946C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093946C2×C411yescharacteristic
115C22⋊(C47⋊C8)—21no—
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121#13093935—21no—
122#13093934—21no—
123#13093934—21no—
124C4×C47⋊C8—21no—
125C8×Dic47—21no—
126C8×Dic47—21no—
127C2×C42×C47C2311yescharacteristic
128C4⋊C8×C47—21no—
129C4⋊C8×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47D411yescharacteristic
133C22⋊C8×C47—21no—
134C22⋊C8×C47C2×C411yescharacteristic
135C22⋊C8×C47C2×C411yescharacteristic
136C22⋊C8×C47D411yescharacteristic
137C22⋊C8×C47D411yescharacteristic
138C4×C8×C47C2311yescharacteristic
139C4×C8×C47C2311yescharacteristic
140C4×C8×C47C2311yescharacteristic
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C2×C22⋊D47—21no—
148C2×C22⋊D47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151#10625350—81no—
152#10625350—81no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188C22×C411yescharacteristic
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×Dic94—22no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94—41no—
163C2×Dic94C22×C411yescharacteristic
164C2×Dic94C22×C411yescharacteristic
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C2×C8×C47C2×D411yescharacteristic
175C42×C47C22×C411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47#4111yescharacteristic
178C42×C47C2411yescharacteristic
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195C4×Dic47—21no—
196C4×Dic47—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201#10625325—22no—
202#10625325—22no—
203#10625325—41no—
204#10625325—41no—
205#10625324—81no—
206#10625324—81no—
207C8×D47—81no—
208C8×D47—81no—
209C23×C47C4×D411yescharacteristic
210C22×D47—21no—
211C22×D47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—41no—
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C23×C411yescharacteristic
221C2×C4×C47C22×D411yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C22⋊D47—81no—
224C22⋊D47—81no—
225C2×Dic47—21no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—42no—
232C2×Dic47—42no—
233D188—21no—
234D188—21no—
235D188—21no—
236D188—21no—
237D188—42no—
238D188—81no—
239C4×D47—41no—
240C4×D47—41no—
241C4×D47—41no—
242C4×D47—41no—
243Dic94—21no—
244Dic94—21no—
245Dic94—21no—
246Dic94—42no—
247Dic94—81no—
248Dic94#13112yes—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—21no—
252C8×C47—21no—
253C8×C47—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263#18030—471nomaximal, Sylow
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—21no—
267C22×C47C2×C4×D411yescharacteristic
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C2×D47—41no—
272C2×D47—41no—
273C2×D47—41no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47C2×#13111yescharacteristic
279C4×C47#56811yescharacteristic
280C4×C47#57711yescharacteristic
281C4×C47#57711yescharacteristic
282Dic47—22no—
283Dic47—41no—
284Dic47—41no—
285Dic47—41no—
286Dic47—41no—
287Dic47—41no—
288#3103—471no—
289#2984—471no—
290#2979—471no—
291#1592—471no—
292#1590—471no—
293#1588—471no—
294#1585—471no—
295#1583—471no—
296#1582—471no—
297SD16⋊C8—471no—
298C8×SD16—471no—
299#1572—471no—
300#1496—471no—
301#1479—471no—
302#1454D4711yescharacteristic, complemented
303C2×C47—41no—
304C2×C47#293311yescharacteristic
305C2×C47#294911yescharacteristic
306C2×C47#295511yescharacteristic
307D47—81no—
308D47—81no—
309#532—471no—
310C2×C4×Q8—471no—
311#481—471no—
312#481—471no—
313#475—471no—
314#475—471no—
315#460—471no—
316#460—471no—
317#448—471no—
318#448—471no—
319#446—471no—
320#446—471no—
321#446—941no—
322#446—941no—
323C8×Q8—471no—
324C8×Q8—471no—
325C4×SD16—471no—
326C4×SD16—471no—
327C4×SD16—471no—
328C4×SD16—471no—
329#436—471no—
330#436—471no—
331#436—941no—
332C8×D4—471no—
333C8×D4—471no—
334C8×D4—941no—
335#432—471no—
336#432—941no—
337#431—471no—
338#431—941no—
339#431C2×D4711yescharacteristic
340#431C2×D4711yescharacteristic
341#431C2×D4711yescharacteristic
342#408—941no—
343#408—941no—
344#335—471no—
345#335—471no—
346#334—471no—
347#334—471no—
348Q8⋊C8—471no—
349Q8⋊C8—471no—
350Q8⋊C8—471no—
351Q8⋊C8—471no—
352D4⋊C8—471no—
353D4⋊C8—471no—
354D4⋊C8—471no—
355D4⋊C8—471no—
356#322C2×D4711yescharacteristic
357#322C2×D4711yescharacteristic
358#322C2×D4711yescharacteristic
359C82C2×D4711yescharacteristic
360C47#1803011yescharacteristic, complemented, Sylow
361C2×#41—941no—
362C22×Q8—471no—
363C2×SD16—471no—
364C2×SD16—471no—
365C2×SD16—471no—
366C2×SD16—471no—
367C2×M16—941no—
368C2×M16—941no—
369C22×C8—941no—
370C22×C8—941no—
371C4⋊Q8—471no—
372#127—471no—
373#124—941no—
374#121—471no—
375#121—471no—
376#121—941no—
377C4×Q8—471no—
378C4×Q8—471no—
379C4×Q8—471no—
380C4×Q8—471no—
381C4×Q8—941no—
382C4×Q8—941no—
383C4×D4—471no—
384C4×D4—471no—
385C4×D4—941no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390#106—471no—
391#106—471no—
392#106—471no—
393#106—471no—
394C4⋊C8—21no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8C4×D4711yescharacteristic
404C4⋊C8C4×D4711yescharacteristic
405C4⋊C8D18811yescharacteristic
406C4⋊C8D18811yescharacteristic
407#103—471no—
408#103—471no—
409#103—471no—
410#103—471no—
411#102—471no—
412#102—471no—
413#102—471no—
414#102—471no—
415C22⋊C8—21no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420C22⋊C8—941no—
421C22⋊C8—941no—
422C22⋊C8C4×D4711yescharacteristic
423C22⋊C8C4×D4711yescharacteristic
424C22⋊C8D18811yescharacteristic
425C22⋊C8D18811yescharacteristic
426#97—941no—
427#97—941no—
428#97—941no—
429C4×C8—941no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435C4×C8C22×D4711yescharacteristic
436C4×C8C22×D4711yescharacteristic
437C4×C8C22×D4711yescharacteristic
438#41—3761no—
439#41—3761no—
440C2×Q8—471no—
441C2×Q8—471no—
442C2×Q8—942no—
443C2×Q8—941no—
444C2×Q8—941no—
445C2×Q8—1881no—
446C2×D4—471no—
447C2×D4—471no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4#1062535011yescharacteristic
459SD16—942no—
460SD16—942no—
461SD16—1881no—
462SD16—1881no—
463M16—3761no—
464M16—3761no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—3761no—
472C2×C8—3761no—
473C2×C8C2×C4×D4711yescharacteristic
474C2×C8C2×C4×D4711yescharacteristic
475C2×C8C2×C4×D4711yescharacteristic
476C2×C8C2×C4×D4711yescharacteristic
477C2×C8C2×D18811yescharacteristic
478C2×C8C2×D18811yescharacteristic
479C2×C8C2×D18811yescharacteristic
480C2×C8C2×D18811yescharacteristic
481C4⋊C4—471no—
482C4⋊C4—471no—
483C4⋊C4—471no—
484C4⋊C4—471no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C22⋊C4—941no—
494C22⋊C4—941no—
495C42—941no—
496C42—941no—
497C42—941no—
498C42—941no—
499C42C2×C4×D4711yescharacteristic
500C42C2×D18811yescharacteristic
501C42#1062535011yescharacteristic
502C42C23×D4711yescharacteristic
503C23—941no—
504C23—941no—
505C23C4×D18811yescharacteristic
506Q8—472no—
507Q8—941no—
508Q8—941no—
509Q8—941no—
510Q8—3761no—
511Q8—1882no—
512D4—941no—
513D4—941no—
514D4—941no—
515D4—941no—
516D4—3761no—
517D4—3761no—
518D4—3761no—
519D4—1882no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4C4×D18811yescharacteristic
538C2×C4C4×D18811yescharacteristic
539C2×C4C4×D18811yescharacteristic
540C2×C4C22×C4×D4711yescharacteristic
541C2×C4C22×D18811yescharacteristic
542C2×C4C2×#1062535011yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—1881no—
554C8—1881no—
555C8—1881no—
556C8—1881no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—1881no—
561C22—1881no—
562C22—1881no—
563C22—1881no—
564C22—1881no—
565C22—1881no—
566C22C2×C4×D18811yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—942no—
572C4—1881no—
573C4—1881no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4#131×D4711yescharacteristic
578C4#1568988811yescharacteristic
579C4#1568993511yescharacteristic
580C4#1568993511yescharacteristic
581C2—41no—
582C2—3761no—
583C2—3761no—
584C2#2025211611yescharacteristic
585C2#2025224911yescharacteristic
586C2#2025229211yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1454C2
socleC22×C47C2×C4×D4
prime radical#15689673C22
cosocleC42×C47C24
hypercenter#1454D47
hypocenterC47#18030
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #20252475C2semidirect
4. #20242292C2semidirect
5. #20242280C2semidirect
6. #20242268C2semidirect
7. #20242247C2semidirect
8. #20242233C2semidirect
9. #20242226C2semidirect
10. #20242202C2semidirect
11. C8×#10625325C2semidirect
12. #20242168C2semidirect
14. #20241784C2semidirect
15. C47×#1454C2semidirect
302. #1454D47semidirect
360. C47#18030semidirect

Maximal subgroups

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

subgroupindex
#202534202
#202524752
#202524542
#202422922
#202422802
#202422682
#202422472
#202422332
#202422262
#202422022
C8×#106253252
#202421682
#202418582
#202417842
C47×#14542
#1803047