Finite Group Databasebeta

← #26186463

Subgroups — #26186463

Order 12032.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253400C211yesmaximal, characteristic
2#20252537C211yesmaximal, characteristic, complemented
3#20252497C211yesmaximal, characteristic, complemented
4#20242262C211yesmaximal, characteristic, complemented
5#20242255C211yesmaximal, characteristic, complemented
6#20242234C211yesmaximal, characteristic, complemented
7#20242227C211yesmaximal, characteristic, complemented
8#20242209C211yesmaximal, characteristic, complemented
9#20242204C211yesmaximal, characteristic, complemented
10#20242191C211yesmaximal, characteristic, complemented
11#20242185C211yesmaximal, characteristic, complemented
12#20242158C211yesmaximal, characteristic, complemented
13#20241828C211yesmaximal, characteristic, complemented
14#20241685C211yesmaximal, characteristic, complemented
15C47×#1483C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689461C411yescharacteristic
18#15689444C411yescharacteristic
19#15689427C411yescharacteristic
20#15689420C411yescharacteristic
21#15689342C411yescharacteristic
22#15689335C411yescharacteristic
23#15689283C411yescharacteristic
24#15689266C411yescharacteristic
25#15689254C2211yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic
27#15689247C2211yescharacteristic
28#15689247C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625336C2211yescharacteristic
31C4×#10625335C2211yescharacteristic
32C4×#10625334C2211yescharacteristic
33#15689201—21no—
34#15689201C2211yescharacteristic
35#15689195—21no—
36D4×C47⋊C8C2211yescharacteristic
37#15689188C2211yescharacteristic
38#15689188C2211yescharacteristic
39C8×C22⋊D47—21no—
40C8×C22⋊D47—21no—
41#15689184—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689175—21no—
45#15689150—21no—
46#15689147C2211yescharacteristic
47C4⋊C8×D47—21no—
48#15688873C2211yescharacteristic
49#15688873C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#529C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C4×M16×C47C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625335C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625329—21no—
73C2×#10625329—21no—
74C22×C47⋊C8—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C4×Dic94C2×C411yescharacteristic
78C4×Dic94C2311yescharacteristic
79C4×D188C2×C411yescharacteristic
80C4×D188C2311yescharacteristic
81C4×C22⋊D47—21no—
82C4×C22⋊D47—21no—
83#13093983C2×C411yescharacteristic
84#13093981—21no—
85C42×D47—21no—
86#13093957C2×C411yescharacteristic
87#13093957C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)—21no—
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)C2×C411yescharacteristic
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)D411yescharacteristic
96C4⋊(C47⋊C8)D411yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99Dic47⋊C8—21no—
100Dic47⋊C8—21no—
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093945C2×C411yescharacteristic
106#13093945C2×C411yescharacteristic
107#13093944C2×C411yescharacteristic
108#13093944C2×C411yescharacteristic
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113C22⋊(C47⋊C8)D411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117#13093935—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C2×M16×C47—21no—
126C22×C8×C47—21no—
127#126×C47—21no—
128#125×C47C2×C411yescharacteristic
129#124×C47C2×C411yescharacteristic
130#123×C47—21no—
131C22⋊Q8×C47C2×C411yescharacteristic
132#121×C47C2×C411yescharacteristic
133C4×Q8×C47C2311yescharacteristic
134C4×D4×C47—21no—
135C4×D4×C47C2311yescharacteristic
136#117×C47—21no—
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141#97×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×C22⋊D47—21no—
152#10625350—22no—
153#10625350—22no—
154C2×D188C22×C411yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×Dic94C22×C411yescharacteristic
159M16×C47—42no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—81no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C22⋊C4×C47—21no—
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C42×C47—21no—
177C42×C47C22×C411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C42×C47#4111yescharacteristic
180C42×C47C2411yescharacteristic
181C22⋊Dic47—21no—
182#10625337—22no—
183#10625336—22no—
184#10625335—22no—
185#10625334—22no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188C4⋊Dic47C22×C411yescharacteristic
189C4⋊Dic47C22×C411yescharacteristic
190Dic47⋊C4—21no—
191Dic47⋊C4—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⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C8×D47—81no—
209C8×D47—81no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212C22×D47—21no—
213Q8×C47—21no—
214Q8×C47—21no—
215D4×C47—21no—
216D4×C47—21no—
217D4×C47—81no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C4×D411yescharacteristic
229C2×C4×C47C4×D411yescharacteristic
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C23×C411yescharacteristic
232C2×C4×C47C22×D411yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C22⋊D47—24no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—21no—
238D188—21no—
239D188#13112yes—
240C4×D47—24no—
241C4×D47—41no—
242C4×D47—41no—
243C4×D47—81no—
244Dic94—21no—
245Dic94#13112yes—
246C8×C47—22no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—21no—
258C47⋊C8—41no—
259C47⋊C8—41no—
260#17927—471nomaximal, Sylow
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47C2×C4×D411yescharacteristic
268C2×D47—22no—
269C2×D47—41no—
270C2×D47—41no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47C2×#13111yescharacteristic
279C4×C47C2×#13111yescharacteristic
280C4×C47#57711yescharacteristic
281C4×C47#57711yescharacteristic
282Dic47—22no—
283Dic47—41no—
284Dic47—41no—
285#3102—471no—
286#2993—471no—
287#2988—471no—
288#1587—471no—
289#1586—471no—
290#1583—471no—
291#1582—471no—
292#1580—471no—
293#1579—471no—
294C8×SD16—471no—
295C8×SD16—471no—
296#1570—471no—
297#1489—471no—
298#1483D4711yescharacteristic, complemented
299#1453—471no—
300C2×C47—41no—
301C2×C47—81no—
302C2×C47#292911yescharacteristic
303C2×C47#295211yescharacteristic
304C2×C47#295611yescharacteristic
305D47—42no—
306#529C2×D4711yescharacteristic
307C4×#41—471no—
308#485—471no—
309#482—471no—
310#479—471no—
311#478—471no—
312#464—471no—
313#463—471no—
314#452—471no—
315#449—471no—
316#446—471no—
317C8×Q8—471no—
318C8×Q8—471no—
319C8×Q8—471no—
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×D8—471no—
324#436—471no—
325#436—941no—
326#435—941no—
327C8×D4—471no—
328C8×D4—471no—
329C8×D4—471no—
330C8×D4—941no—
331C8×D4—941no—
332#433—941no—
333#431—471no—
334#431—471no—
335#431—941no—
336#424—941no—
337#423—471no—
338C2×C4⋊C8—941no—
339C2×C4⋊C8C2×D4711yescharacteristic
340C4×M16C2×D4711yescharacteristic
341#334—471no—
342#334—471no—
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8C2×D4711yescharacteristic
348Q8⋊C8C2×D4711yescharacteristic
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8C2×D4711yescharacteristic
352D4⋊C8C2×D4711yescharacteristic
353#322—471no—
354#322—471no—
355#322—471no—
356C82—471no—
357C47#1792711yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C2×Q16—471no—
360C2×SD16—471no—
361C2×SD16—471no—
362C2×D8—471no—
363C2×M16—21no—
364C2×M16—941no—
365C2×M16—941no—
366C22×C8—21no—
367C22×C8—941no—
368C22×C8—941no—
369C22×C8—941no—
370#126—21no—
371#125C4×D4711yescharacteristic
372#124C4×D4711yescharacteristic
373#123—21no—
374C22⋊Q8C4×D4711yescharacteristic
375#121C4×D4711yescharacteristic
376C4×Q8—471no—
377C4×Q8—471no—
378C4×Q8C22×D4711yescharacteristic
379C4×D4—21no—
380C4×D4—471no—
381C4×D4—471no—
382C4×D4—941no—
383C4×D4—941no—
384C4×D4C22×D4711yescharacteristic
385#117—21no—
386#117—471no—
387#117—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390#107—471no—
391#107—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⋊C8—941no—
406C4⋊C8C22×D4711yescharacteristic
407C4⋊C8C22×D4711yescharacteristic
408#103—471no—
409#103—471no—
410#103—471no—
411#103—471no—
412#102—471no—
413#102—471no—
414#102—471no—
415#102—471no—
416C22⋊C8—471no—
417C22⋊C8—471no—
418C22⋊C8—471no—
419C22⋊C8—471no—
420C22⋊C8—941no—
421C22⋊C8—941no—
422C22⋊C8—941no—
423C22⋊C8—941no—
424#97—21no—
425#97—941no—
426C4×C8—471no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—942no—
436#41—942no—
437C2×Q8—471no—
438C2×Q8C2×C4×D4711yescharacteristic
439C2×D4—21no—
440C2×D4—471no—
441C2×D4—941no—
442C2×D4C2×C4×D4711yescharacteristic
443C22×C4—21no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4D4×D4711yescharacteristic
449C22×C4#1062535211yescharacteristic
450Q16—942no—
451SD16—942no—
452SD16—942no—
453D8—942no—
454M16—42no—
455M16—3761no—
456M16—3761no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—471no—
467C2×C8—471no—
468C2×C8—471no—
469C2×C8—471no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—3761no—
473C2×C8—3761no—
474C2×C8—3761no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—471no—
480C4⋊C4—471no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4C2×C4×D4711yescharacteristic
484C4⋊C4C2×C4×D4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—941no—
495C42—941no—
496C42—941no—
497C42C2×C4×D4711yescharacteristic
498C42D4×D4711yescharacteristic
499C42#1062535211yescharacteristic
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—941no—
503C23(C22⋊D47)⋊C411yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—472no—
507Q8—941no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—472no—
512D4—944no—
513D4—941no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—944no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—3761no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4(C22⋊D47)⋊C411yescharacteristic
532C2×C4(C22⋊D47)⋊C411yescharacteristic
533C2×C4(C22⋊D47)⋊C411yescharacteristic
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4C2×#1062535211yescharacteristic
537C8—22no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—941no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—941no—
546C8—941no—
547C8—941no—
548C8—941no—
549C8—1881no—
550C8—1881no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—942no—
558C22—1881no—
559C22—1881no—
560C22C2×(C22⋊D47)⋊C411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—942no—
569C4—1881no—
570C4—1881no—
571C4#131×D4711yescharacteristic
572C4#131×D4711yescharacteristic
573C4#1568993211yescharacteristic
574C4#1568993311yescharacteristic
575C2—41no—
576C2—81no—
577C2—1882no—
578C2#2025208511yescharacteristic
579C2#2025226711yescharacteristic
580C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1483C2
socleC22×C47C2×C4×D4
prime radical#15689266C4
cosocleC42×C47C24
hypercenter#1483D47
hypocenterC47#17927
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #20252537C2semidirect
3. #20252497C2semidirect
4. #20242262C2semidirect
5. #20242255C2semidirect
6. #20242234C2semidirect
7. #20242227C2semidirect
8. #20242209C2semidirect
9. #20242204C2semidirect
10. #20242191C2semidirect
11. #20242185C2semidirect
12. #20242158C2semidirect
13. #20241828C2semidirect
14. #20241685C2semidirect
15. C47×#1483C2semidirect
298. #1483D47semidirect
357. C47#17927semidirect

Maximal subgroups

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

subgroupindex
#202534002
#202525372
#202524972
#202422622
#202422552
#202422342
#202422272
#202422092
#202422042
#202421912
#202421852
#202421582
#202418282
#202416852
C47×#14832
#1792747