Finite Group Databasebeta

← #26186389

Subgroups — #26186389

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253453C211yesmaximal, characteristic
2#20252497C211yesmaximal, characteristic
3#20252483C211yesmaximal, characteristic, complemented
4#20242262C211yesmaximal, characteristic, complemented
5#20242248C211yesmaximal, characteristic, complemented
6#20242241C211yesmaximal, characteristic, complemented
7#20242227C211yesmaximal, characteristic, complemented
8#20242204C211yesmaximal, characteristic, complemented
9#20242203C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242185C211yesmaximal, characteristic, complemented
12#20242171C211yesmaximal, characteristic, complemented
13#20241823C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1481C211yesmaximal, characteristic, complemented
16C4×#10625350C2211yescharacteristic
17#15689461C411yescharacteristic
18#15689461C411yescharacteristic
19#15689405C411yescharacteristic
20#15689400C411yescharacteristic
21#15689330C411yescharacteristic
22#15689325C411yescharacteristic
23#15689283C411yescharacteristic
24#15689283C411yescharacteristic
25#15689254—21no—
26#15689254—21no—
27#15689254C2211yescharacteristic
28#15689254C2211yescharacteristic
29Q8×C47⋊C8C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31#15689247C2211yescharacteristic
32#15689247C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625336C2211yescharacteristic
36C4×#10625336C2211yescharacteristic
37#15689188C2211yescharacteristic
38#15689188C2211yescharacteristic
39C8×C22⋊D47—21no—
40C8×C22⋊D47—21no—
41#15689184—21no—
42#15689184—21no—
43#15689180C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689176C2211yescharacteristic
46#15689175—21no—
47C4⋊C8×D47—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688855C2211yescharacteristic
53#15688855C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#533C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C2×C4⋊C8×C47C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625336C2×C411yescharacteristic
72C2×C8×D47—21no—
73C2×C8×D47—21no—
74C4×Dic94C2×C411yescharacteristic
75C4×Dic94C2311yescharacteristic
76C4×D188C2×C411yescharacteristic
77C4×D188C2311yescharacteristic
78C4×C22⋊D47—21no—
79C4×C22⋊D47—21no—
80#13093983C2×C411yescharacteristic
81#13093981—21no—
82C42×D47—21no—
83#13093957C2×C411yescharacteristic
84#13093957C2×C411yescharacteristic
85#13093955C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87C4⋊(C47⋊C8)—21no—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)—21no—
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2×C411yescharacteristic
93C4⋊(C47⋊C8)D411yescharacteristic
94C4⋊(C47⋊C8)D411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093948C2×C411yescharacteristic
100#13093948C2×C411yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093947C2×C411yescharacteristic
104#13093947C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)C2×C411yescharacteristic
109C22⋊(C47⋊C8)C2×C411yescharacteristic
110C22⋊(C47⋊C8)D411yescharacteristic
111C22⋊(C47⋊C8)D411yescharacteristic
112(C2×D47)⋊C8—21no—
113(C2×D47)⋊C8—21no—
114#13093935—21no—
115#13093935—21no—
116#13093935—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8C2311yescharacteristic
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C22×C8×C47—21no—
126C4⋊Q8×C47C2×C411yescharacteristic
127C4⋊Q8×C47C2×C411yescharacteristic
128#125×C47—21no—
129C22⋊Q8×C47—21no—
130C22⋊Q8×C47C2×C411yescharacteristic
131C22⋊Q8×C47C2×C411yescharacteristic
132C4×Q8×C47—21no—
133C4×Q8×C47C2311yescharacteristic
134C4×Q8×C47C2311yescharacteristic
135#117×C47—21no—
136C2×C42×C47C2311yescharacteristic
137C4⋊C8×C47—21no—
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141C22⋊C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C411yescharacteristic
146C2×Q8×C47C22×C411yescharacteristic
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C2×C22⋊D47—21no—
151#10625350—22no—
152#10625350—22no—
153C2×D188C22×C411yescharacteristic
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×Dic94C22×C411yescharacteristic
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—81no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47C22×C411yescharacteristic
171C4⋊C4×C47C22×C411yescharacteristic
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47C22×C411yescharacteristic
177C42×C47C2×D411yescharacteristic
178C42×C47#4111yescharacteristic
179C42×C47C2411yescharacteristic
180C22⋊Dic47—21no—
181#10625337—22no—
182#10625337—22no—
183#10625336—22no—
184#10625336—22no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C2×D411yescharacteristic
201C2×C47⋊C8C2×D411yescharacteristic
202C2×C47⋊C8C2×D411yescharacteristic
203C2×C47⋊C8C2×D411yescharacteristic
204C8×D47—81no—
205C8×D47—81no—
206C23×C47C4×D411yescharacteristic
207C22×D47—21no—
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212Q8×C47—81no—
213C2×C4×C47—21no—
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×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C23×C411yescharacteristic
226C2×C4×C47C22×D411yescharacteristic
227C2×C4×C47C2×#4111yescharacteristic
228C22⋊D47—24no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232D188—21no—
233D188#13112yes—
234C4×D47—24no—
235C4×D47—41no—
236C4×D47—41no—
237C4×D47—81no—
238Dic94—21no—
239Dic94#13112yes—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C8×C47—41no—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—21no—
247C47⋊C8—21no—
248C47⋊C8—21no—
249C47⋊C8—21no—
250C47⋊C8—21no—
251C47⋊C8—21no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254#17921—471nomaximal, Sylow
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47C2×C4×D411yescharacteristic
259C2×D47—22no—
260C2×D47—41no—
261C2×D47—41no—
262C4×C47—21no—
263C4×C47—21no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47C2×#13111yescharacteristic
271C4×C47C2×#13111yescharacteristic
272C4×C47#57711yescharacteristic
273C4×C47#57811yescharacteristic
274Dic47—22no—
275Dic47—41no—
276Dic47—41no—
277#3107—471no—
278#2988—471no—
279#2985—471no—
280#1587—471no—
281#1585—471no—
282#1584—471no—
283#1582—471no—
284#1579—471no—
285SD16⋊C8—471no—
286C8×Q16—471no—
287C8×SD16—471no—
288#1573—471no—
289#1488—471no—
290#1481D4711yescharacteristic, complemented
291#1454—471no—
292C2×C47—41no—
293C2×C47#292911yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295711yescharacteristic
296D47—42no—
297#533C2×D4711yescharacteristic
298C4×#41—471no—
299#485—471no—
300#485—471no—
301#475—471no—
302#474—471no—
303#462—471no—
304#461—471no—
305#452—471no—
306#452—471no—
307#446—471no—
308#446—471no—
309#446—941no—
310#446—941no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—471no—
314C8×Q8—471no—
315C4×Q16—471no—
316C4×Q16—471no—
317C4×SD16—471no—
318C4×SD16—471no—
319C8×D4—471no—
320C8×D4—471no—
321C8×D4—941no—
322C8×D4—941no—
323#433—941no—
324#433—941no—
325#432—471no—
326#431—471no—
327#431—471no—
328#431—941no—
329#431C2×D4711yescharacteristic
330C2×C4⋊C8—941no—
331C2×C4⋊C8C2×D4711yescharacteristic
332#335—471no—
333#335—471no—
334#334—471no—
335#334—471no—
336Q8⋊C8—471no—
337Q8⋊C8—471no—
338Q8⋊C8C2×D4711yescharacteristic
339Q8⋊C8C2×D4711yescharacteristic
340Q8⋊C8C2×D4711yescharacteristic
341Q8⋊C8C2×D4711yescharacteristic
342D4⋊C8—471no—
343D4⋊C8—471no—
344#322—471no—
345#322—471no—
346#322—471no—
347C82—471no—
348C47#1792111yescharacteristic, complemented, Sylow
349C2×#41—471no—
350C2×Q16—471no—
351C2×Q16—471no—
352C2×SD16—471no—
353C2×SD16—471no—
354C22×C8—21no—
355C22×C8—941no—
356C22×C8—941no—
357C4⋊Q8C4×D4711yescharacteristic
358C4⋊Q8C4×D4711yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C4×D4711yescharacteristic
362C22⋊Q8C4×D4711yescharacteristic
363C4×Q8—21no—
364C4×Q8—471no—
365C4×Q8—471no—
366C4×Q8C22×D4711yescharacteristic
367C4×Q8C22×D4711yescharacteristic
368C4×D4—471no—
369C4×D4—471no—
370C4×D4—941no—
371C4×D4—941no—
372#117—21no—
373#117—471no—
374#117—941no—
375C2×C42—941no—
376C2×C42C22×D4711yescharacteristic
377#107—471no—
378#107—471no—
379#106—471no—
380#106—471no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—471no—
384C4⋊C8—471no—
385C4⋊C8—471no—
386C4⋊C8—471no—
387C4⋊C8—471no—
388C4⋊C8—471no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8—941no—
392C4⋊C8—941no—
393C4⋊C8—941no—
394C4⋊C8—941no—
395C4⋊C8C22×D4711yescharacteristic
396C4⋊C8C22×D4711yescharacteristic
397#103—471no—
398#103—471no—
399#103—471no—
400#103—471no—
401#103—471no—
402#103—471no—
403#102—471no—
404#102—471no—
405C22⋊C8—21no—
406C22⋊C8—471no—
407C22⋊C8—471no—
408C22⋊C8—471no—
409C22⋊C8—471no—
410C22⋊C8—941no—
411C22⋊C8—941no—
412C22⋊C8—941no—
413#97—941no—
414#97—941no—
415#97—941no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—471no—
419C4×C8—471no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426#41—942no—
427#41—942no—
428C2×Q8—21no—
429C2×Q8—471no—
430C2×Q8C2×C4×D4711yescharacteristic
431C2×Q8C2×C4×D4711yescharacteristic
432C2×D4—471no—
433C2×D4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4D4×D4711yescharacteristic
439C22×C4#1062535211yescharacteristic
440Q16—942no—
441Q16—942no—
442SD16—942no—
443SD16—942no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—471no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—941no—
458C2×C8—941no—
459C2×C8—3761no—
460C2×C8—3761no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—471no—
469C4⋊C4—471no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4C2×C4×D4711yescharacteristic
473C4⋊C4C2×C4×D4711yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C42—21no—
480C42—21no—
481C42—941no—
482C42—941no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42D4×D4711yescharacteristic
486C42#1062535211yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23(C22⋊D47)⋊C411yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—472no—
496Q8—941no—
497D4—472no—
498D4—944no—
499D4—941no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—944no—
510C2×C4—941no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—3761no—
514C2×C4—1881no—
515C2×C4—1881no—
516C2×C4(C22⋊D47)⋊C411yescharacteristic
517C2×C4(C22⋊D47)⋊C411yescharacteristic
518C2×C4(C22⋊D47)⋊C411yescharacteristic
519C2×C4C22×C4×D4711yescharacteristic
520C2×C4C2×D4×D4711yescharacteristic
521C2×C4C2×#1062535211yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—941no—
527C8—941no—
528C8—941no—
529C8—941no—
530C8—941no—
531C8—941no—
532C8—941no—
533C8—941no—
534C8—1881no—
535C8—1881no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—942no—
540C22—1881no—
541C22—1881no—
542C22C2×(C22⋊D47)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—942no—
552C4—1881no—
553C4—1881no—
554C4#131×D4711yescharacteristic
555C4#131×D4711yescharacteristic
556C4#1568992911yescharacteristic
557C4#1568993611yescharacteristic
558C2—41no—
559C2—1882no—
560C2#2025208511yescharacteristic
561C2#2025222511yescharacteristic
562C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1481C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C2×C4
cosocleC42×C47C24
hypercenter#1481D47
hypocenterC47#17921
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #20252483C2semidirect
4. #20242262C2semidirect
5. #20242248C2semidirect
6. #20242241C2semidirect
7. #20242227C2semidirect
8. #20242204C2semidirect
9. #20242203C2semidirect
10. #20242192C2semidirect
11. #20242185C2semidirect
12. #20242171C2semidirect
14. #20241688C2semidirect
15. C47×#1481C2semidirect
290. #1481D47semidirect
348. C47#17921semidirect

Maximal subgroups

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

subgroupindex
#202534532
#202524972
#202524832
#202422622
#202422482
#202422412
#202422272
#202422042
#202422032
#202421922
#202421852
#202421712
#202418232
#202416882
C47×#14812
#1792147