Finite Group Databasebeta

← #26186347

Subgroups — #26186347

Order 12032.

596 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#20253468C211yesmaximal, characteristic
2#20252533C211yesmaximal, characteristic
3#20252469C211yesmaximal, characteristic, complemented
4#20242263C211yesmaximal, characteristic, complemented
5#20242256C211yesmaximal, characteristic, complemented
6#20242235C211yesmaximal, characteristic, complemented
7#20242228C211yesmaximal, characteristic, complemented
8#20242204C211yesmaximal, characteristic, complemented
9#20242203C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#20242185C211yesmaximal, characteristic, complemented
12#20242179C211yesmaximal, characteristic, complemented
13#20241797C211yesmaximal, characteristic
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1487C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689453C411yescharacteristic
18#15689436C411yescharacteristic
19#15689430C411yescharacteristic
20#15689430C411yescharacteristic
21#15689345C411yescharacteristic
22#15689345C411yescharacteristic
23#15689279C411yescharacteristic
24#15689262C411yescharacteristic
25#15689250C2211yescharacteristic
26Q8×C47⋊C8—21no—
27Q8×C47⋊C8—21no—
28Q8×C47⋊C8C2211yescharacteristic
29Q8×C47⋊C8C2211yescharacteristic
30Q8×C47⋊C8C2211yescharacteristic
31Q8×C47⋊C8C2211yescharacteristic
32#15689247C2211yescharacteristic
33C4×#10625337C2211yescharacteristic
34C4×#10625337C2211yescharacteristic
35C4×#10625336C2211yescharacteristic
36C4×#10625336C2211yescharacteristic
37#15689200C2211yescharacteristic
38#15689199—21no—
39#15689192—21no—
40#15689188C2211yescharacteristic
41#15689183—21no—
42#15689176—21no—
43#15689176—21no—
44#15689176C2211yescharacteristic
45#15689176C2211yescharacteristic
46#15689176C2211yescharacteristic
47#15689148—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
60C2×C4×Q8×C47C2211yescharacteristic
61C47×#431C2211yescharacteristic
62C47×#423C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×Q8⋊C8C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625336C2×C411yescharacteristic
71C2×#10625324—21no—
72C2×C8×D47—21no—
73#13094018—21no—
74#13094016C2×C411yescharacteristic
75#13094012C2×C411yescharacteristic
76#13094007—21no—
77#13094003C2×C411yescharacteristic
78#13093998C2×C411yescharacteristic
79C4×Dic94C2311yescharacteristic
80C4×D188C2311yescharacteristic
81C4×C22⋊D47—21no—
82#13093981—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#13093934—21no—
115C4×C47⋊C8—21no—
116C4×C47⋊C8—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C4×C47⋊C8—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C22×Q8×C47C2×C411yescharacteristic
126C2×M16×C47—21no—
127C4×Q8×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47C2×C411yescharacteristic
130C4×Q8×C47C2×C411yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132C4×Q8×C47C2311yescharacteristic
133C2×C4⋊C4×C47—21no—
134C2×C4⋊C4×C47C2×C411yescharacteristic
135C2×C42×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—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—21no—
147C2×Q8×C47C22×C411yescharacteristic
148C2×Q8×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C2×C22⋊D47—21no—
155C2×D188C22×C411yescharacteristic
156C2×C4×D47—21no—
157C2×Dic94C22×C411yescharacteristic
158M16×C47—81no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47C22×C411yescharacteristic
169C4⋊C4×C47C22×C411yescharacteristic
170C42×C47—21no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47C22×C411yescharacteristic
175C42×C47C2×D411yescharacteristic
176C42×C47#4111yescharacteristic
177C42×C47C2411yescharacteristic
178C22⋊Dic47—21no—
179#10625337—22no—
180#10625337—22no—
181#10625336—22no—
182#10625336—22no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186(C2×D47)⋊C4—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—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
204#10625324—81no—
205C8×D47—81no—
206C23×C47C4×D411yescharacteristic
207C22×D47—21no—
208Q8×C47—24no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47#13112yes—
212Q8×C47#13112yes—
213C2×C4×C47—24no—
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—21no—
222C2×C4×C47—41no—
223C2×C4×C47—81no—
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C23×C411yescharacteristic
228C2×C4×C47C22×D411yescharacteristic
229C2×C4×C47C2×#4111yescharacteristic
230C22⋊D47—81no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234D188—21no—
235D188—21no—
236C4×D47—41no—
237C4×D47—41no—
238Dic94—21no—
239Dic94—21no—
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#17919—471nomaximal, Sylow
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47C2×C4×D411yescharacteristic
259C2×D47—41no—
260C2×D47—41no—
261C2×D47—41no—
262C4×C47—22no—
263C4×C47—22no—
264C4×C47—21no—
265C4×C47—21no—
266C4×C47—21no—
267C4×C47—21no—
268C4×C47—41no—
269C4×C47—41no—
270C4×C47C2×#13111yescharacteristic
271C4×C47C2×#13111yescharacteristic
272C4×C47#57711yescharacteristic
273C4×C47#57811yescharacteristic
274Dic47—41no—
275Dic47—41no—
276Dic47—41no—
277#3108—471no—
278#2993—471no—
279#2982—471no—
280#1588—471no—
281#1587—471no—
282#1584—471no—
283#1583—471no—
284#1579—471no—
285SD16⋊C8—471no—
286C8×Q16—471no—
287C8×SD16—471no—
288#1574—471no—
289#1487D4711yescharacteristic, complemented
290#1482—471no—
291#1454—471no—
292C2×C47—41no—
293C2×C47#292911yescharacteristic
294C2×C47#294711yescharacteristic
295C2×C47#295711yescharacteristic
296D47—81no—
297#529—471no—
298C2×C4×Q8C2×D4711yescharacteristic
299#483—471no—
300#480—471no—
301#479—471no—
302#479—471no—
303#464—471no—
304#464—471no—
305#451—471no—
306#448—471no—
307#446—471no—
308C8×Q8—471no—
309C8×Q8—471no—
310C8×Q8—471no—
311C8×Q8—471no—
312C8×Q8—471no—
313C8×Q8—941no—
314C8×Q8—941no—
315C4×Q16—471no—
316C4×Q16—471no—
317C4×SD16—471no—
318C4×SD16—471no—
319#436—471no—
320#436—941no—
321#435—941no—
322C8×D4—471no—
323#433—941no—
324#431—471no—
325#431—471no—
326#431—471no—
327#431—941no—
328#431—941no—
329#431C2×D4711yescharacteristic
330#424—941no—
331#423C2×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#1791911yescharacteristic, complemented, Sylow
349C22×Q8C4×D4711yescharacteristic
350C2×Q16—471no—
351C2×Q16—471no—
352C2×SD16—471no—
353C2×SD16—471no—
354C2×M16—21no—
355C2×M16—941no—
356C22×C8—941no—
357#126—941no—
358#125—471no—
359#124—471no—
360#123—941no—
361C22⋊Q8—471no—
362#121—471no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—471no—
366C4×Q8C4×D4711yescharacteristic
367C4×Q8C4×D4711yescharacteristic
368C4×Q8C22×D4711yescharacteristic
369C4×Q8C22×D4711yescharacteristic
370C4×D4—471no—
371C4×D4—941no—
372#117—941no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C4×D4711yescharacteristic
375C2×C42—21no—
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—
414C4×C8—471no—
415C4×C8—471no—
416C4×C8—471no—
417C4×C8—471no—
418C4×C8—941no—
419C4×C8—941no—
420C4×C8—941no—
421C4×C8—941no—
422C4×C8—941no—
423C4×C8—941no—
424C4×C8C22×D4711yescharacteristic
425C4×C8C22×D4711yescharacteristic
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—471no—
430C2×Q8C2×C4×D4711yescharacteristic
431C2×Q8C2×C4×D4711yescharacteristic
432C2×D4—471no—
433C2×D4—941no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—941no—
437C22×C4C2×C4×D4711yescharacteristic
438C22×C4D4×D4711yescharacteristic
439C22×C4#1062535211yescharacteristic
440Q16—942no—
441Q16—942no—
442SD16—942no—
443SD16—942no—
444M16—81no—
445M16—3761no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—471no—
451C2×C8—471no—
452C2×C8—471no—
453C2×C8—471no—
454C2×C8—471no—
455C2×C8—471no—
456C2×C8—471no—
457C2×C8—471no—
458C2×C8—941no—
459C2×C8—941no—
460C2×C8—3761no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—471no—
467C4⋊C4—471no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4—941no—
472C4⋊C4C2×C4×D4711yescharacteristic
473C4⋊C4C2×C4×D4711yescharacteristic
474C22⋊C4—941no—
475C22⋊C4—941no—
476C22⋊C4—941no—
477C22⋊C4—941no—
478C22⋊C4—941no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—941no—
484C42C2×C4×D4711yescharacteristic
485C42D4×D4711yescharacteristic
486C42#1062535211yescharacteristic
487C42C23×D4711yescharacteristic
488C23—941no—
489C23(C22⋊D47)⋊C411yescharacteristic
490Q8—24no—
491Q8—21no—
492Q8—21no—
493Q8—941no—
494Q8—941no—
495Q8#1309403212yes—
496Q8#1309403212yes—
497D4—941no—
498D4—941no—
499D4—3761no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4—941no—
512C2×C4—941no—
513C2×C4—941no—
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—1881no—
540C22—1881no—
541C22—1881no—
542C22C2×(C22⋊D47)⋊C411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—1881no—
552C4—1881no—
553C4—1881no—
554C4C2×#1309403211yescharacteristic
555C4C2×#1309403211yescharacteristic
556C4#1568992911yescharacteristic
557C4#1568993611yescharacteristic
558C2—41no—
559C2—3761no—
560C2#2025207811yescharacteristic
561C2#2025222511yescharacteristic
562C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1487C2
socleC22×C47C2×C4×D4
prime radical#13093998C2×C4
cosocleC42×C47C24
hypercenter#1487D47
hypocenterC47#17919
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
3. #20252469C2semidirect
4. #20242263C2semidirect
5. #20242256C2semidirect
6. #20242235C2semidirect
7. #20242228C2semidirect
8. #20242204C2semidirect
9. #20242203C2semidirect
10. #20242192C2semidirect
11. #20242185C2semidirect
12. #20242179C2semidirect
14. #20241688C2semidirect
15. C47×#1487C2semidirect
289. #1487D47semidirect
348. C47#17919semidirect

Maximal subgroups

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

subgroupindex
#202534682
#202525332
#202524692
#202422632
#202422562
#202422352
#202422282
#202422042
#202422032
#202421922
#202421852
#202421792
#202417972
#202416882
C47×#14872
#1791947