Finite Group Databasebeta

← #26187183

Subgroups — #26187183

Order 12032.

618 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#20253410C211yesmaximal, characteristic
2#20252396C211yesmaximal, characteristic, complemented
3#20252391C211yesmaximal, characteristic, complemented
4#20242282C211yesmaximal, characteristic, complemented
5#20242280C211yesmaximal, characteristic, complemented
6#20242238C211yesmaximal, characteristic, complemented
7#20242225C211yesmaximal, characteristic, complemented
8#20242223C211yesmaximal, characteristic, complemented
9#20242217C211yesmaximal, characteristic, complemented
10#20242180C211yesmaximal, characteristic, complemented
11#20242165C211yesmaximal, characteristic, complemented
12#20241847C211yesmaximal, characteristic, complemented
13#20241767C211yesmaximal, characteristic, complemented
14C8×#10625324C211yesmaximal, characteristic, complemented
15C8×SD16×C47C211yesmaximal, characteristic, complemented
16#15689660C2211yescharacteristic
17C4×#10625352C2211yescharacteristic
18#15689462C411yescharacteristic
19#15689449C411yescharacteristic
20#15689433C411yescharacteristic
21#15689425C411yescharacteristic
22#15689348C411yescharacteristic
23#15689340C411yescharacteristic
24#15689282C411yescharacteristic
25#15689269C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689253C2211yescharacteristic
28#15689250C2211yescharacteristic
29C4×#10625337C2211yescharacteristic
30C4×#10625325C2211yescharacteristic
31C4×#10625334C2211yescharacteristic
32#15689202—21no—
33#15689202C2211yescharacteristic
34#15689194—21no—
35#15689193—21no—
36#15689191—21no—
37D4×C47⋊C8C2211yescharacteristic
38#15689188C2211yescharacteristic
39#15689183—21no—
40#15689179C2211yescharacteristic
41#15689177—21no—
42#15689175C2211yescharacteristic
43#15689174C2211yescharacteristic
44#15689077—21no—
45C4×#10625324C2211yescharacteristic
46C2×#13093934—21no—
47C4×C8×D47C2211yescharacteristic
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688874C2211yescharacteristic
51#15688855C2211yescharacteristic
52Q8⋊(C47⋊C8)C2211yescharacteristic
53#15688853C2211yescharacteristic
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C8×Q8×C47C2211yescharacteristic
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C82×C47C2211yescharacteristic
67C2×#10625352C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625325C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×#10625324D411yescharacteristic
73C2×#10625324D411yescharacteristic
74C22×C47⋊C8—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77#13094019—21no—
78#13094015C2×C411yescharacteristic
79#13094013C2×C411yescharacteristic
80#13094009—21no—
81#13094000C2×C411yescharacteristic
82#13093999C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84#13093989C2×C411yescharacteristic
85C4×D188—21no—
86C4×D188C2311yescharacteristic
87D4×Dic47C2×C411yescharacteristic
88C4×C22⋊D47—21no—
89(C22⋊D47)⋊C4—21no—
90#13093982C2×C411yescharacteristic
91#13093981—21no—
92#13093980—21no—
93C2×C4×Dic47—21no—
94C42×D47C2311yescharacteristic
95#13093957C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093956C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8C2×C411yescharacteristic
104Dic47⋊C8C2×C411yescharacteristic
105#13093949C2×C411yescharacteristic
106#13093948C2×C411yescharacteristic
107#13093947C2×C411yescharacteristic
108#13093946C2×C411yescharacteristic
109#13093945C2×C411yescharacteristic
110#13093944C2×C411yescharacteristic
111C22⋊(C47⋊C8)—21no—
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8C2×C411yescharacteristic
117(C2×D47)⋊C8C2×C411yescharacteristic
118#13093935—21no—
119#13093934—21no—
120#13093934—21no—
121#13093934—21no—
122#13093934D411yescharacteristic
123#13093934D411yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C8×Dic47—21no—
128C8×Dic47—21no—
129C2×SD16×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C4×Q8×C47C2311yescharacteristic
132C4×D4×C47C2311yescharacteristic
133#106×C47C2×C411yescharacteristic
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139C22⋊C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×D4×C47C22×C411yescharacteristic
146C22×C4×C47—21no—
147C2×C22⋊D47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150#10625352—22no—
151#10625352—41no—
152C2×D188—21no—
153C2×D188C22×C411yescharacteristic
154C2×C4×D47—21no—
155C2×C4×D47C22×C411yescharacteristic
156C2×C4×D47C2×D411yescharacteristic
157C2×C4×D47#4111yescharacteristic
158C2×Dic94C22×C411yescharacteristic
159SD16×C47—22no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—42no—
164C2×C8×C47C22×C411yescharacteristic
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C4⋊C4×C47—21no—
169C4⋊C4×C47C22×C411yescharacteristic
170C4⋊C4×C47C22×C411yescharacteristic
171C22⋊C4×C47—21no—
172C42×C47—21no—
173C42×C47C2411yescharacteristic
174C22⋊Dic47—21no—
175#10625337—41no—
176#10625334—22no—
177(C2×D47)⋊C4—21no—
178(C2×D47)⋊C4—21no—
179(C2×D47)⋊C4—21no—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47C22×C411yescharacteristic
185C4⋊Dic47C22×C411yescharacteristic
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188Dic47⋊C4—21no—
189Dic47⋊C4—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47C22×C411yescharacteristic
194C4×Dic47C2×D411yescharacteristic
195C4×Dic47#4111yescharacteristic
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—42no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204#10625325—41no—
205#10625324—22no—
206#10625324—22no—
207#10625324—42no—
208C8×D47—42no—
209C8×D47—42no—
210C23×C47—21no—
211C22×D47—21no—
212C22×D47C4×D411yescharacteristic
213Q8×C47—21no—
214Q8×C47—21no—
215D4×C47—21no—
216D4×C47#13112yes—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47C23×C411yescharacteristic
223C2×C4×C47C22×D411yescharacteristic
224C2×C4×C47C2×#4111yescharacteristic
225C22⋊D47—42no—
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—42no—
230C2×Dic47—81no—
231C2×Dic47C4×D411yescharacteristic
232C2×Dic47C4×D411yescharacteristic
233C2×Dic47C4×D411yescharacteristic
234D188—21no—
235D188—21no—
236D188—81no—
237C4×D47—21no—
238C4×D47—21no—
239C4×D47—21no—
240C4×D47—21no—
241C4×D47—41no—
242C4×D47—41no—
243C4×D47—41no—
244Dic94—21no—
245Dic94—21no—
246C8×C47—22no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—41no—
251C8×C47—41no—
252C8×C47#13512yes—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259C47⋊C8#13512yes—
260#17996—471nomaximal, Sylow
261C22×C47—22no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47C2×C4×D411yescharacteristic
265C2×D47—21no—
266C2×D47—21no—
267C2×D47—21no—
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C4×C47—21no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47C2×#13111yescharacteristic
276C4×C47#56811yescharacteristic
277C4×C47C2×#13511yescharacteristic
278C4×C47C2×#13511yescharacteristic
279Dic47—21no—
280Dic47—21no—
281Dic47—21no—
282Dic47—41no—
283Dic47—41no—
284Dic47—41no—
285#3102—471no—
286#2970—471no—
287#2969—471no—
288#1591—471no—
289#1590—471no—
290#1584—471no—
291#1582—471no—
292#1582—471no—
293#1581—471no—
294C8×SD16D4711yescharacteristic, complemented
295C8×D8—471no—
296#1572—471no—
297#1494—471no—
298#1476—471no—
299C8×M16—471no—
300C2×C47—42no—
301C2×C47#293311yescharacteristic
302C2×C47C4×#13511yescharacteristic
303C2×C47#295611yescharacteristic
304D47—41no—
305D47—81no—
306#529—471no—
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—
317#446—471no—
318#446—471no—
319C8×Q8C2×D4711yescharacteristic
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16C2×D4711yescharacteristic
323C4×D8—471no—
324#436—471no—
325#436—941no—
326#435—941no—
327#435—941no—
328#435—941no—
329C8×D4—471no—
330C8×D4—471no—
331C8×D4C2×D4711yescharacteristic
332#433—941no—
333#432—471no—
334#432—941no—
335#431—471no—
336#431—471no—
337#405—941no—
338C4×M16—471no—
339C2×#97—941no—
340C2×C4×C8—471no—
341#335—471no—
342#335—471no—
343#334—471no—
344#334C2×D4711yescharacteristic
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8C2×D4711yescharacteristic
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352D4⋊C8C2×D4711yescharacteristic
353#322—471no—
354#322—471no—
355C82—471no—
356C82C2×D4711yescharacteristic
357C47#1799611yescharacteristic, complemented, Sylow
358C2×#41—471no—
359C2×Q16—471no—
360C2×SD16—471no—
361C2×SD16C4×D4711yescharacteristic
362C2×D8—471no—
363C2×M16—471no—
364C2×M16—471no—
365C2×M16—941no—
366C22×C8—21no—
367C22×C8—941no—
368C22×C8—941no—
369C22×C8—941no—
370#126—941no—
371#125—471no—
372#124—471no—
373#123—941no—
374C22⋊Q8—471no—
375#121—471no—
376C4×Q8—471no—
377C4×Q8—471no—
378C4×Q8C22×D4711yescharacteristic
379C4×D4—471no—
380C4×D4—471no—
381C4×D4—941no—
382C4×D4—941no—
383C4×D4—941no—
384C4×D4C22×D4711yescharacteristic
385#117—471no—
386#117—941no—
387#117—941no—
388C2×C42—471no—
389C2×C42—941no—
390#107—471no—
391#107—471no—
392#106—471no—
393#106C4×D4711yescharacteristic
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⋊C8C22×D4711yescharacteristic
403C4⋊C8C22×D4711yescharacteristic
404#103—471no—
405#103—471no—
406#103—471no—
407#103C4×D4711yescharacteristic
408#102—471no—
409#102—471no—
410#102—471no—
411#102C4×D4711yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—471no—
414C22⋊C8—471no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—471no—
421#97—471no—
422#97—941no—
423#97—941no—
424#97—941no—
425#97—941no—
426C4×C8—21no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—941no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—942no—
436#41—1881no—
437C2×Q8—471no—
438C2×Q8C2×C4×D4711yescharacteristic
439C2×D4—471no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4C2×C4×D4711yescharacteristic
443C22×C4—21no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—471no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450Q16—1881no—
451SD16—22no—
452SD16—1881no—
453D8—942no—
454M16—942no—
455M16—942no—
456M16—1882no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—471no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—941no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—1882no—
469C2×C8—1882no—
470C2×C8—1882no—
471C2×C8C2×C4×D4711yescharacteristic
472C2×C8C2×C4×D4711yescharacteristic
473C2×C8D4×D4711yescharacteristic
474C2×C8D4×D4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—471no—
477C4⋊C4—471no—
478C4⋊C4—941no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4C2×C4×D4711yescharacteristic
484C4⋊C4C2×C4×D4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—941no—
487C22⋊C4—941no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—471no—
495C42—471no—
496C42—471no—
497C42—941no—
498C42—941no—
499C42—941no—
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—471no—
503C23—941no—
504Q8—21no—
505Q8—21no—
506Q8—941no—
507Q8—941no—
508D4—21no—
509D4—941no—
510D4—941no—
511D4—3761no—
512D4—1882no—
513D4#1309403012yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—471no—
520C2×C4—471no—
521C2×C4—471no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—3761no—
530C2×C4—1881no—
531C2×C4—1882no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C2×D4×D4711yescharacteristic
536C2×C4#41×D4711yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—472no—
544C8—941no—
545C8—941no—
546C8—941no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C8#1309404512yes—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—941no—
555C22—941no—
556C22—941no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22C4×D4×D4711yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—941no—
566C4—941no—
567C4—941no—
568C4—1881no—
569C4—1881no—
570C4—1881no—
571C4C2×#1309403011yescharacteristic
572C4#1568988811yescharacteristic
573C4#135×D4711yescharacteristic
574C4C2×#1309404511yescharacteristic
575C2—42no—
576C2—3761no—
577C2—1881no—
578C2#2025210811yescharacteristic
579C2C4×#1309404511yescharacteristic
580C2#2025229311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC8×SD16×C47C2
socleC22×C47C2×C4×D4
prime radical#15689269C4
cosocleC42×C47C24
hypercenterC8×SD16D47
hypocenterC47#17996
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #20252396C2semidirect
3. #20252391C2semidirect
4. #20242282C2semidirect
5. #20242280C2semidirect
6. #20242238C2semidirect
7. #20242225C2semidirect
8. #20242223C2semidirect
9. #20242217C2semidirect
10. #20242180C2semidirect
11. #20242165C2semidirect
12. #20241847C2semidirect
13. #20241767C2semidirect
14. C8×#10625324C2semidirect
15. C8×SD16×C47C2semidirect
294. C8×SD16D47semidirect
357. C47#17996semidirect

Maximal subgroups

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

subgroupindex
#202534102
#202523962
#202523912
#202422822
#202422802
#202422382
#202422252
#202422232
#202422172
#202421802
#202421652
#202418472
#202417672
C8×#106253242
C8×SD16×C472
#1799647