Finite Group Databasebeta

← #26188052

Subgroups — #26188052

Order 12032.

586 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253971C211yesmaximal, characteristic
2#20252336C211yesmaximal, characteristic
3#20252330C211yesmaximal, characteristic
4#20242283C211yesmaximal, characteristic, complemented
5#20242282C211yesmaximal, characteristic, complemented
6#20242240C211yesmaximal, characteristic, complemented
7#20242239C211yesmaximal, characteristic, complemented
8#20242237C211yesmaximal, characteristic, complemented
9C8×#10625337C211yesmaximal, characteristic, complemented
10#20242192C211yesmaximal, characteristic, complemented
11#335×D47C211yesmaximal, characteristic
12#20241789C211yesmaximal, characteristic
13#20241789C211yesmaximal, characteristic
14#20241667C211yesmaximal, characteristic
15C47×#1584C211yesmaximal, characteristic, complemented
16#15689677C2211yescharacteristic
17#15689677C2211yescharacteristic
18#15689527C411yescharacteristic
19#15689501C411yescharacteristic
20#15689472C411yescharacteristic
21#15689472C411yescharacteristic
22#15689365C411yescharacteristic
23#15689363C411yescharacteristic
24#15689363C411yescharacteristic
25#15689361C411yescharacteristic
26#15689254C2211yescharacteristic
27#15689253—21no—
28#15689253C2211yescharacteristic
29#15689252—21no—
30#15689251—21no—
31#15689250—21no—
32#15689250C2211yescharacteristic
33Q8×C47⋊C8C2211yescharacteristic
34C8×Dic94C2211yescharacteristic
35#15689247C2211yescharacteristic
36C4×Dic188C2211yescharacteristic
37C4×#10625337C2211yescharacteristic
38C4×#10625337C2211yescharacteristic
39#15689174C2211yescharacteristic
40#15689148—21no—
41#15689148—21no—
42C4⋊C8×D47C2211yescharacteristic
43C4⋊C8×D47C2211yescharacteristic
44#15689080—21no—
45#15689077—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688855C2211yescharacteristic
52#15688855C2211yescharacteristic
53Q8⋊(C47⋊C8)C2211yescharacteristic
54Q8⋊(C47⋊C8)C2211yescharacteristic
55#15688853C2211yescharacteristic
56#15688853C2211yescharacteristic
57#15688845C2211yescharacteristic
58C8×C47⋊C8C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C47×#446C2211yescharacteristic
61C8×Q8×C47C2211yescharacteristic
62C4×Q16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×Q8⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic
67C2×Dic188C2×C411yescharacteristic
68C2×#10625337C2×C411yescharacteristic
69C2×#10625337C2×C411yescharacteristic
70C2×#10625324D411yescharacteristic
71C2×#10625324D411yescharacteristic
72C2×C8×D47—21no—
73C2×C8×D47—21no—
74C2×C8×D47C2×C411yescharacteristic
75C2×C8×D47C2×C411yescharacteristic
76#13094023C2×C411yescharacteristic
77#13094023C2×C411yescharacteristic
78#13094022C2×C411yescharacteristic
79#13094022C2×C411yescharacteristic
80#13094014—21no—
81#13094014—21no—
82#13094004C2×C411yescharacteristic
83#13094004C2×C411yescharacteristic
84#13094002—21no—
85#13094002—21no—
86#13094000C2×C411yescharacteristic
87#13094000C2×C411yescharacteristic
88C4×Dic94—21no—
89C4×Dic94—21no—
90C4×Dic94C2311yescharacteristic
91C4×Dic94C2311yescharacteristic
92#13093981—21no—
93#13093981—21no—
94C42×D47C2311yescharacteristic
95#13093958C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093957C2×C411yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8—21no—
109#13093949C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093948C2×C411yescharacteristic
112#13093948C2×C411yescharacteristic
113#13093947C2×C411yescharacteristic
114#13093947C2×C411yescharacteristic
115(C2×D47)⋊C8—21no—
116#13093935—21no—
117#13093934—21no—
118#13093934—21no—
119#13093934D411yescharacteristic
120#13093934D411yescharacteristic
121C4×C47⋊C8—21no—
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47—21no—
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47C2×C411yescharacteristic
129C2×Q16×C47C2×C411yescharacteristic
130C4×Q8×C47C2311yescharacteristic
131C4×Q8×C47C2311yescharacteristic
132#107×C47C2×C411yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47—21no—
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137#103×C47C2×C411yescharacteristic
138#103×C47C2×C411yescharacteristic
139#97×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C2×Q8×C47C22×C411yescharacteristic
145C2×Q8×C47C22×C411yescharacteristic
146C2×C4×D47C22×C411yescharacteristic
147C2×C4×D47C2×D411yescharacteristic
148C2×C4×D47#4111yescharacteristic
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94C22×C411yescharacteristic
152C2×Dic94C22×C411yescharacteristic
153Q16×C47—41no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47C22×C411yescharacteristic
158C2×C8×C47C22×C411yescharacteristic
159C2×C8×C47C2×D411yescharacteristic
160C2×C8×C47C2×D411yescharacteristic
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47C22×C411yescharacteristic
164C4⋊C4×C47C22×C411yescharacteristic
165C42×C47—21no—
166C42×C47—21no—
167C42×C47C2411yescharacteristic
168#10625337—22no—
169#10625337—22no—
170(C2×D47)⋊C4—21no—
171(C2×D47)⋊C4—21no—
172(C2×D47)⋊C4—21no—
173(C2×D47)⋊C4—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47C22×C411yescharacteristic
177C4⋊Dic47C22×C411yescharacteristic
178Dic47⋊C4—21no—
179Dic47⋊C4—21no—
180Dic47⋊C4—21no—
181Dic47⋊C4—21no—
182Dic47⋊C4—21no—
183Dic47⋊C4—21no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—21no—
187Dic47⋊C4—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47C22×C411yescharacteristic
191C4×Dic47C2×D411yescharacteristic
192C4×Dic47#4111yescharacteristic
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C2×D411yescharacteristic
199C2×C47⋊C8C2×D411yescharacteristic
200Dic188—41no—
201#10625324—22no—
202#10625324Q1614yescomplemented
203C8×D47—22no—
204C8×D47—41no—
205C8×D47—42no—
206C8×D47—42no—
207C22×D47C4×D411yescharacteristic
208Q8×C47—21no—
209Q8×C47—21no—
210Q8×C47—21no—
211Q8×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47C23×C411yescharacteristic
217C2×C4×C47C22×D411yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C2×Dic47—21no—
220C2×Dic47—21no—
221C2×Dic47—21no—
222C2×Dic47—21no—
223C2×Dic47C4×D411yescharacteristic
224C2×Dic47C4×D411yescharacteristic
225C2×Dic47C4×D411yescharacteristic
226C4×D47—21no—
227C4×D47—21no—
228C4×D47—41no—
229C4×D47C2×Q1612yes—
230C4×D47#13512yes—
231Dic94—21no—
232Dic94—21no—
233Dic94—21no—
234Dic94—21no—
235Dic94—81no—
236Dic94—81no—
237C8×C47—21no—
238C8×C47—21no—
239C8×C47—21no—
240C8×C47—41no—
241C8×C47—41no—
242C8×C47—41no—
243C8×C47C2×Q1612yes—
244C47⋊C8—21no—
245C47⋊C8—21no—
246C47⋊C8—41no—
247C47⋊C8—41no—
248C47⋊C8—41no—
249C47⋊C8#13112yes—
250C47⋊C8C2×Q1612yes—
251#18068—471nomaximal, Sylow
252C22×C47C2×C4×D411yescharacteristic
253C2×D47—21no—
254C2×D47—21no—
255C2×D47C4×Q1612yes—
256C4×C47—21no—
257C4×C47—41no—
258C4×C47—41no—
259C4×C47—41no—
260C4×C47—41no—
261C4×C47C2×#13111yescharacteristic
262C4×C47#56811yescharacteristic
263C4×C47C22×Q1611yescharacteristic
264C4×C47C2×#13511yescharacteristic
265Dic47—21no—
266Dic47—21no—
267Dic47—41no—
268Dic47—41no—
269Dic47—41no—
270Dic47—41no—
271Dic47C4×Q1612yes—
272#3170—471no—
273#2962—471no—
274#2962—471no—
275#1591—471no—
276#1591—471no—
277#1584—471no—
278#1584—471no—
279#1584—471no—
280#1584D4711yescharacteristic, complemented
281C8×Q16—471no—
282C8×Q16—471no—
283C2×#335—471no—
284#1481—471no—
285#1481—471no—
286C8×M16—471no—
287C2×C47#293511yescharacteristic
288C2×C47C2×C4×Q1611yescharacteristic
289C2×C47#295711yescharacteristic
290D47—22no—
291#533—471no—
292#533—471no—
293#500—471no—
294#494—471no—
295#487—471no—
296#487—471no—
297#467—471no—
298#467—471no—
299#467—471no—
300#467—471no—
301#446—471no—
302#446—471no—
303#446—471no—
304#446—941no—
305#446—941no—
306#446—941no—
307#446—941no—
308#446C2×D4711yescharacteristic
309C8×Q8—471no—
310C8×Q8—471no—
311C8×Q8—471no—
312C8×Q8C2×D4711yescharacteristic
313C4×Q16—471no—
314C4×Q16—471no—
315C4×Q16—471no—
316C4×Q16C2×D4711yescharacteristic
317#431—471no—
318#424—941no—
319#424—941no—
320C2×C4⋊C8—471no—
321C2×C4⋊C8—471no—
322#405—941no—
323#405—941no—
324C4×M16—471no—
325C2×C4×C8—471no—
326#335—471no—
327#335—471no—
328#335—471no—
329#335C2×D4711yescharacteristic
330Q8⋊C8—471no—
331Q8⋊C8—471no—
332Q8⋊C8—471no—
333Q8⋊C8—471no—
334Q8⋊C8—471no—
335Q8⋊C8—471no—
336Q8⋊C8C2×D4711yescharacteristic
337Q8⋊C8C2×D4711yescharacteristic
338#322—471no—
339#322C2×D4711yescharacteristic
340C82—471no—
341C82—471no—
342C47#1806811yescharacteristic, complemented, Sylow
343C2×Q16—471no—
344C2×Q16—471no—
345C2×Q16—471no—
346C2×Q16C4×D4711yescharacteristic
347C2×M16—471no—
348C2×M16—471no—
349C22×C8—471no—
350C22×C8—471no—
351C22×C8—941no—
352C22×C8—941no—
353C4⋊Q8—471no—
354C4⋊Q8—471no—
355C4⋊Q8—471no—
356C4⋊Q8—471no—
357#125—941no—
358#125—941no—
359C22⋊Q8—471no—
360C22⋊Q8—471no—
361C22⋊Q8—471no—
362C22⋊Q8—471no—
363C22⋊Q8—941no—
364C22⋊Q8—941no—
365C4×Q8—471no—
366C4×Q8—471no—
367C4×Q8—941no—
368C4×Q8—941no—
369C4×Q8C22×D4711yescharacteristic
370C4×Q8C22×D4711yescharacteristic
371#117—941no—
372#117—941no—
373C2×C42—471no—
374#107—471no—
375#107—471no—
376#107—471no—
377#107C4×D4711yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—471no—
381C4⋊C8—471no—
382C4⋊C8—941no—
383C4⋊C8—941no—
384C4⋊C8—941no—
385C4⋊C8—941no—
386C4⋊C8—941no—
387C4⋊C8—941no—
388C4⋊C8—941no—
389C4⋊C8—941no—
390C4⋊C8—941no—
391C4⋊C8C22×D4711yescharacteristic
392C4⋊C8C22×D4711yescharacteristic
393#103—471no—
394#103—471no—
395#103—471no—
396#103—471no—
397#103—471no—
398#103—471no—
399#103C4×D4711yescharacteristic
400#103C4×D4711yescharacteristic
401C22⋊C8—941no—
402#97—21no—
403#97—471no—
404#97—471no—
405#97—941no—
406#97—941no—
407#97—941no—
408C4×C8—21no—
409C4×C8—471no—
410C4×C8—471no—
411C4×C8—471no—
412C4×C8—471no—
413C4×C8—471no—
414C4×C8—941no—
415C4×C8—941no—
416C4×C8—941no—
417C4×C8C22×D4711yescharacteristic
418C4×C8C22×D4711yescharacteristic
419C4×C8C22×D4711yescharacteristic
420C2×Q8—471no—
421C2×Q8—471no—
422C2×Q8—941no—
423C2×Q8—941no—
424C2×Q8C2×C4×D4711yescharacteristic
425C2×Q8C2×C4×D4711yescharacteristic
426C22×C4—471no—
427C22×C4—471no—
428C22×C4—471no—
429Q16—41no—
430Q16—942no—
431Q16—942no—
432Q16—1881no—
433M16—474no—
434M16—942no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—471no—
439C2×C8—471no—
440C2×C8—471no—
441C2×C8—471no—
442C2×C8—942no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—1881no—
447C2×C8—1882no—
448C2×C8—1882no—
449C2×C8C2×C4×D4711yescharacteristic
450C2×C8C2×C4×D4711yescharacteristic
451C2×C8D4×D4711yescharacteristic
452C2×C8D4×D4711yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—471no—
456C4⋊C4—471no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—941no—
465C4⋊C4—941no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4C2×C4×D4711yescharacteristic
470C4⋊C4C2×C4×D4711yescharacteristic
471C22⋊C4—941no—
472C22⋊C4—941no—
473C22⋊C4—941no—
474C22⋊C4—941no—
475C42—21no—
476C42—21no—
477C42—471no—
478C42—471no—
479C42—471no—
480C42—941no—
481C42—941no—
482C42C23×D4711yescharacteristic
483C23—471no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—941no—
489Q8—941no—
490Q8—941no—
491Q8—941no—
492Q8—3761no—
493Q8—3761no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—471no—
499C2×C4—472no—
500C2×C4—472no—
501C2×C4—471no—
502C2×C4—471no—
503C2×C4—941no—
504C2×C4—941no—
505C2×C4—941no—
506C2×C4—941no—
507C2×C4—941no—
508C2×C4—941no—
509C2×C4—1881no—
510C2×C4C22×C4×D4711yescharacteristic
511C2×C4C2×D4×D4711yescharacteristic
512C2×C4#41×D4711yescharacteristic
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—472no—
520C8—472no—
521C8—941no—
522C8—941no—
523C8—1881no—
524C8—1881no—
525C8—1881no—
526C8Q16×D4712yes—
527C22—472no—
528C22—941no—
529C22—941no—
530C22C4×D4×D4711yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—472no—
537C4—941no—
538C4—941no—
539C4—1881no—
540C4—1881no—
541C4—1881no—
542C4—1881no—
543C4#131×D4711yescharacteristic
544C4#1568988911yescharacteristic
545C4C2×Q16×D4711yescharacteristic
546C4#135×D4711yescharacteristic
547C2—942no—
548C2#2025212911yescharacteristic
549C2C4×Q16×D4711yescharacteristic
550C2#2025230211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1584C2
socleC22×C47C2×C4×D4
prime radicalC22×D47C4×D4
cosocleC42×C47C24
hypercenter#1584D47
hypocenterC47#18068
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #20242283C2semidirect
5. #20242282C2semidirect
6. #20242240C2semidirect
7. #20242239C2semidirect
8. #20242237C2semidirect
9. C8×#10625337C2semidirect
10. #20242192C2semidirect
15. C47×#1584C2semidirect
202. #10625324Q16semidirect
280. #1584D47semidirect
342. C47#18068semidirect

Maximal subgroups

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

subgroupindex
#202539712
#202523362
#202523302
#202422832
#202422822
#202422402
#202422392
#202422372
C8×#106253372
#202421922
#335×D472
#202417892
#202416672
C47×#15842
#1806847