Finite Group Databasebeta

← #26187648

Subgroups — #26187648

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#20253415C211yesmaximal, characteristic
2#20252478C211yesmaximal, characteristic, complemented
3#20252455C211yesmaximal, characteristic
4#20242287C211yesmaximal, characteristic, complemented
5#20242281C211yesmaximal, characteristic, complemented
6#20242269C211yesmaximal, characteristic, complemented
7#20242242C211yesmaximal, characteristic, complemented
8#20242234C211yesmaximal, characteristic, complemented
9#20242221C211yesmaximal, characteristic, complemented
10#20242197C211yesmaximal, characteristic, complemented
11#20242191C211yesmaximal, characteristic, complemented
12#20242169C211yesmaximal, characteristic, complemented
13#20241784C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1496C211yesmaximal, characteristic
16C2×C4×Dic94C2211yescharacteristic
17#15689439C411yescharacteristic
18#15689439C411yescharacteristic
19#15689405C411yescharacteristic
20#15689405C411yescharacteristic
21#15689320C411yescharacteristic
22#15689320C411yescharacteristic
23#15689261C411yescharacteristic
24#15689261C411yescharacteristic
25#15689251—21no—
26#15689251—21no—
27#15689250C2211yescharacteristic
28#15689250C2211yescharacteristic
29#15689247C2211yescharacteristic
30#15689247C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625335C2211yescharacteristic
33C4×#10625335C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689201—21no—
36#15689201C2211yescharacteristic
37#15689201C2211yescharacteristic
38D4×C47⋊C8—21no—
39D4×C47⋊C8C2211yescharacteristic
40D4×C47⋊C8C2211yescharacteristic
41#15689177—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689173—21no—
46#15689090—21no—
47#15689090—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688855C2211yescharacteristic
55#15688855C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#532C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C22×Dic94C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625335C2×C411yescharacteristic
72C2×#10625329—21no—
73C2×#10625329—21no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C4×Dic94—21no—
77C4×Dic94—21no—
78C4×Dic94C2×C411yescharacteristic
79C4×Dic94C2×C411yescharacteristic
80C4×Dic94C2311yescharacteristic
81C4×Dic94C2311yescharacteristic
82C2×C4⋊Dic47C2×C411yescharacteristic
83C2×Dic47⋊C4—21no—
84C2×C4×Dic47—21no—
85#13093955C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
89C4⋊(C47⋊C8)C2×C411yescharacteristic
90C4⋊(C47⋊C8)C2×C411yescharacteristic
91C4⋊(C47⋊C8)D411yescharacteristic
92C4⋊(C47⋊C8)D411yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94C4⋊(C47⋊C8)C2311yescharacteristic
95Dic47⋊C8—21no—
96Dic47⋊C8—21no—
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093947C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093947C2×C411yescharacteristic
102#13093947C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093945C2×C411yescharacteristic
106#13093945C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113C22⋊(C47⋊C8)C2×C411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115C22⋊(C47⋊C8)D411yescharacteristic
116#13093934—21no—
117#13093934—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C2×#41×C47—21no—
126C4⋊Q8×C47C2×C411yescharacteristic
127#127×C47C2×C411yescharacteristic
128#124×C47—21no—
129#121×C47—21no—
130#121×C47C2×C411yescharacteristic
131#121×C47C2×C411yescharacteristic
132C4×D4×C47—21no—
133C4×D4×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—81no—
145#41×C47—81no—
146C2×Q8×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47C22×C411yescharacteristic
152C2×D4×C47C22×C411yescharacteristic
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47#4111yescharacteristic
158C22×Dic47—21no—
159C22×Dic47—21no—
160C2×Dic94—22no—
161C2×Dic94—21no—
162C2×Dic94—41no—
163C2×Dic94C22×C411yescharacteristic
164C2×Dic94C22×C411yescharacteristic
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47C22×C411yescharacteristic
171C4⋊C4×C47C22×C411yescharacteristic
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C42×C47C22×C411yescharacteristic
177C42×C47C2×D411yescharacteristic
178C42×C47#4111yescharacteristic
179C42×C47C2411yescharacteristic
180#10625335—22no—
181#10625335—22no—
182#10625335—41no—
183#10625335—41no—
184C4⋊Dic47—21no—
185C4⋊Dic47C22×C411yescharacteristic
186C4⋊Dic47C22×C411yescharacteristic
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C4×Dic47—21no—
195#10625329—81no—
196#10625329—81no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—81no—
200C2×C47⋊C8—81no—
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C23×C47—21no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212Q8×C47—81no—
213D4×C47—21no—
214D4×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—42no—
218D4×C47—81no—
219D4×C47—81no—
220D4×C47—81no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C23×C411yescharacteristic
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
241C2×Dic47—21no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244Dic94—21no—
245Dic94—21no—
246Dic94—21no—
247Dic94—42no—
248Dic94#13112yes—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47—41no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263#18030—471nomaximal, Sylow
264C22×C47—21no—
265C22×C47—21no—
266C22×C47—21no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C2×C4×D411yescharacteristic
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—41no—
279C4×C47—41no—
280C4×C47C2×#13111yescharacteristic
281C4×C47#56811yescharacteristic
282C4×C47#57711yescharacteristic
283C4×C47#57711yescharacteristic
284Dic47—22no—
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#1496D4711yescharacteristic
301#1479—471no—
302#1454—471no—
303C2×C47—41no—
304C2×C47—81no—
305C2×C47—81no—
306C2×C47#293311yescharacteristic
307C2×C47#294911yescharacteristic
308C2×C47#295511yescharacteristic
309#532C2×D4711yescharacteristic
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—941no—
336#432C2×D4711yescharacteristic
337#431—471no—
338#431—471no—
339#431—471no—
340#431—941no—
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⋊C8C2×D4711yescharacteristic
353D4⋊C8C2×D4711yescharacteristic
354D4⋊C8C2×D4711yescharacteristic
355D4⋊C8C2×D4711yescharacteristic
356#322—471no—
357#322—471no—
358#322—471no—
359C82—471no—
360C47#1803011yescharacteristic, complemented, Sylow
361C2×#41—21no—
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⋊Q8C4×D4711yescharacteristic
372#127C4×D4711yescharacteristic
373#124—21no—
374#121—21no—
375#121C4×D4711yescharacteristic
376#121C4×D4711yescharacteristic
377C4×Q8—471no—
378C4×Q8—471no—
379C4×Q8—471no—
380C4×Q8—471no—
381C4×Q8—941no—
382C4×Q8—941no—
383C4×D4—21no—
384C4×D4C22×D4711yescharacteristic
385C4×D4C22×D4711yescharacteristic
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—471no—
400C4⋊C8—471no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8C22×D4711yescharacteristic
406C4⋊C8C22×D4711yescharacteristic
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—21no—
417C22⋊C8—471no—
418C22⋊C8—471no—
419C22⋊C8—471no—
420C22⋊C8—471no—
421C22⋊C8—941no—
422C22⋊C8—941no—
423C22⋊C8—941no—
424C22⋊C8—941no—
425C22⋊C8—941no—
426#97—21no—
427#97—941no—
428#97—941no—
429C4×C8—471no—
430C4×C8—471no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—941no—
434C4×C8—941no—
435C4×C8—941no—
436C4×C8C22×D4711yescharacteristic
437C4×C8C22×D4711yescharacteristic
438#41—81no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—471no—
442C2×Q8—471no—
443C2×Q8—942no—
444C2×Q8—941no—
445C2×Q8—1881no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4711yescharacteristic
451C2×D4C2×C4×D4711yescharacteristic
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4D4×D4711yescharacteristic
458C22×C4#1062535211yescharacteristic
459SD16—942no—
460SD16—942no—
461SD16—1881no—
462SD16—1881no—
463M16—3761no—
464M16—3761no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—471no—
470C2×C8—471no—
471C2×C8—471no—
472C2×C8—471no—
473C2×C8—471no—
474C2×C8—471no—
475C2×C8—471no—
476C2×C8—471no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—3761no—
480C2×C8—3761no—
481C4⋊C4—21no—
482C4⋊C4—471no—
483C4⋊C4—471no—
484C4⋊C4—941no—
485C4⋊C4—941no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4C2×C4×D4711yescharacteristic
490C4⋊C4C2×C4×D4711yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C42—941no—
496C42—941no—
497C42—941no—
498C42—941no—
499C42C2×C4×D4711yescharacteristic
500C42D4×D4711yescharacteristic
501C42#1062535211yescharacteristic
502C42C23×D4711yescharacteristic
503C23—21no—
504C23—21no—
505C23(C22⋊D47)⋊C411yescharacteristic
506Q8—81no—
507Q8—472no—
508Q8—941no—
509Q8—941no—
510Q8—941no—
511Q8—1882no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4(C22⋊D47)⋊C411yescharacteristic
538C2×C4(C22⋊D47)⋊C411yescharacteristic
539C2×C4(C22⋊D47)⋊C411yescharacteristic
540C2×C4C22×C4×D4711yescharacteristic
541C2×C4C2×D4×D4711yescharacteristic
542C2×C4C2×#1062535211yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—941no—
548C8—941no—
549C8—941no—
550C8—941no—
551C8—941no—
552C8—941no—
553C8—941no—
554C8—941no—
555C8—1881no—
556C8—1881no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×(C22⋊D47)⋊C411yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—942no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4#131×D4711yescharacteristic
578C4#1568988811yescharacteristic
579C4#1568993311yescharacteristic
580C4#1568993311yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#2025211811yescharacteristic
585C2#2025225011yescharacteristic
586C2#2025228711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1496C2
socleC22×C47C2×C4×D4
prime radicalC47×#532C22
cosocleC42×C47C24
hypercenter#1496D47
hypocenterC47#18030
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #20252478C2semidirect
4. #20242287C2semidirect
5. #20242281C2semidirect
6. #20242269C2semidirect
7. #20242242C2semidirect
8. #20242234C2semidirect
9. #20242221C2semidirect
10. #20242197C2semidirect
11. #20242191C2semidirect
12. #20242169C2semidirect
13. #20241784C2semidirect
14. #20241688C2semidirect
360. C47#18030semidirect

Maximal subgroups

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

subgroupindex
#202534152
#202524782
#202524552
#202422872
#202422812
#202422692
#202422422
#202422342
#202422212
#202421972
#202421912
#202421692
#202417842
#202416882
C47×#14962
#1803047