Finite Group Databasebeta

← #25081710

Subgroups — #25081710

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145968C211yesmaximal, characteristic
2#19144975C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic
4#19134175C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134147C211yesmaximal, characteristic, complemented
7#19134140C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19134023C211yesmaximal, characteristic, complemented
11#19134016C211yesmaximal, characteristic, complemented
12#19133363C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133280C211yesmaximal, characteristic, complemented
15C43×#3239C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583267—21no—
18#14583267—21no—
19#14583249C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583203—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583155—21no—
27#14583143—21no—
28#14583118—21no—
29#14583109C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582971—21no—
36D4×C43⋊C8C2211yescharacteristic
37#14582960—21no—
38#14582952C2211yescharacteristic
39#14582923C2211yescharacteristic
40#14582908—21no—
41#14582908—21no—
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#501—21no—
59C43×#489—21no—
60C43×#484—21no—
61C43×#481—21no—
62C43×#475C2211yescharacteristic
63C43×#475C2211yescharacteristic
64C43×#474C2211yescharacteristic
65C43×#474C2211yescharacteristic
66C43×#432C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877D411yescharacteristic
72C2×#10621877D411yescharacteristic
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284—21no—
82#13063258—21no—
83#13063256—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91#13063249—21no—
92#13063249—21no—
93#13063249—21no—
94#13063249—21no—
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C22×Q8×C43—21no—
114C4⋊Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—42no—
147C2×Q8×C43—42no—
148C2×Q8×C43—41no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—81no—
185#10621883—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—41no—
193#10621877—41no—
194#10621877—41no—
195#10621877—42no—
196#10621877—81no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—82no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—81no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—82no—
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×Dic43—41no—
238C2×Dic43—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—81no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43C2×#12111yescharacteristic
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43#57511yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—81no—
274Dic43—81no—
275#3252—431no—
276#3239D4311yescharacteristic
277#3139—431no—
278#2969—431no—
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699—431no—
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569—431no—
288#1554—431no—
289#1549—431no—
290C2×C43—41no—
291C2×C43—81no—
292C2×C43#304011yescharacteristic
293C2×C43#306311yescharacteristic
294C2×C43#306911yescharacteristic
295#533—431no—
296C2×C4⋊Q8C2×D4311yescharacteristic
297#529C2×D4311yescharacteristic
298#501—21no—
299#491—861no—
300#491—861no—
301#489—21no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#484—21no—
307#481—21no—
308#479—861no—
309#477—431no—
310#476—431no—
311#475C2×D4311yescharacteristic
312#475C2×D4311yescharacteristic
313#474C2×D4311yescharacteristic
314#474C2×D4311yescharacteristic
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461—431no—
320#446—431no—
321C8×Q8—431no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432C2×D4311yescharacteristic
328#431—431no—
329#423—431no—
330#419—861no—
331#419—861no—
332#405—861no—
333C4×M16—431no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—21no—
348C2×Q16—861no—
349C2×SD16—861no—
350C2×M16—431no—
351C2×M16—431no—
352C2×M16—861no—
353C2×M16—861no—
354C22×C8—861no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362#126—21no—
363#125—861no—
364#125C22⋊D4311yescharacteristic
365#124C22⋊D4311yescharacteristic
366#123—21no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C22⋊Q8C22⋊D4311yescharacteristic
370#121C22⋊D4311yescharacteristic
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—861no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C42C22×D4311yescharacteristic
381#107—21no—
382#107—21no—
383#107—861no—
384#106—21no—
385#106—21no—
386#106—861no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#102—21no—
410#102—21no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—21no—
417#97—431no—
418#97—431no—
419#97—861no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—41no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8C2×C22⋊D4311yescharacteristic
432C2×D4—21no—
433C2×D4C2×C22⋊D4311yescharacteristic
434C22×C4—21no—
435C22×C4—41no—
436C22×C4D4×D4311yescharacteristic
437C22×C4#1062190011yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—3441no—
440SD16—3441no—
441M16—3441no—
442M16—1721no—
443M16—1721no—
444M16—1722no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4C2×C22⋊D4311yescharacteristic
473C4⋊C4C2×C22⋊D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1721no—
480C42—21no—
481C42—1721no—
482C42D4×D4311yescharacteristic
483C42#1062190011yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—21no—
487C23#1306329711yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—82no—
495Q8—3441no—
496Q8—1721no—
497Q8—1721no—
498D4—21no—
499D4—21no—
500D4—81no—
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—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—82no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329711yescharacteristic
517C2×C4#1306329711yescharacteristic
518C2×C4#1306329711yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C8—41no—
523C8—41no—
524C8—861no—
525C8—861no—
526C8—861no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#1306329711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—3441no—
549C4—3441no—
550C4#1458369511yescharacteristic
551C4#1458369511yescharacteristic
552C4#1458370711yescharacteristic
553C4#1458371411yescharacteristic
554C2—41no—
555C2—81no—
556C2#1914408711yescharacteristic
557C2#1914428211yescharacteristic
558C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3239C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3239D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
2. #19144975C2semidirect
4. #19134175C2semidirect
5. #19134168C2semidirect
6. #19134147C2semidirect
7. #19134140C2semidirect
8. #19134051C2semidirect
9. #19134044C2semidirect
10. #19134023C2semidirect
11. #19134016C2semidirect
12. #19133363C2semidirect
13. #19133306C2semidirect
14. #19133280C2semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459682
#191449752
#191436002
#191341752
#191341682
#191341472
#191341402
#191340512
#191340442
#191340232
#191340162
#191333632
#191333062
#191332802
C43×#32392
#1938143