Finite Group Databasebeta

← #25081744

Subgroups — #25081744

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145957C211yesmaximal, characteristic
2#19145619C211yesmaximal, characteristic, complemented
3#19144989C211yesmaximal, characteristic, complemented
4#19134163C211yesmaximal, characteristic, complemented
5#19134156C211yesmaximal, characteristic, complemented
6#19134149C211yesmaximal, characteristic, complemented
7#19134142C211yesmaximal, characteristic, complemented
8#19134039C211yesmaximal, characteristic, complemented
9#19134032C211yesmaximal, characteristic, complemented
10#19134025C211yesmaximal, characteristic, complemented
11#19134018C211yesmaximal, characteristic, complemented
12#19133362C211yesmaximal, characteristic, complemented
13#19133298C211yesmaximal, characteristic, complemented
14#19133266C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583294—21no—
19#14583269—21no—
20#14583259—21no—
21#14583259—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583196—21no—
27#14583184C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583150—21no—
30#14583147—21no—
31#14583111—21no—
32#14583109C2211yescharacteristic
33#14583109C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583099C2211yescharacteristic
37#14583094C2211yescharacteristic
38#14583054—21no—
39#14583037—21no—
40#14582956C2211yescharacteristic
41#14582923C2211yescharacteristic
42#14582901—21no—
43#14582901—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621877—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063313—21no—
84#13063299—21no—
85#13063299—21no—
86C4×D172—21no—
87C4×D172—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063258—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063247—21no—
107#13063247—21no—
108#13063247—21no—
109#13063247—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
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×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153#10621898—42no—
154#10621898—42no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163C2×Dic86—81no—
164C2×Dic86—81no—
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43#4111yescharacteristic
190C42×C43C2411yescharacteristic
191#10621885—81no—
192#10621885—81no—
193#10621884—81no—
194#10621883—81no—
195#10621883—81no—
196#10621882—81no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—41no—
206C4⋊Dic43—41no—
207#10621877—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C23×C43—21no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—82no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—81no—
246C4×D43—82no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19383—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43#57511yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#3251—431no—
290#3218—431no—
291#3141—431no—
292#2969D4311yescharacteristic, complemented
293#1702—431no—
294#1701—431no—
295#1700—431no—
296#1699—431no—
297#1682—431no—
298#1681—431no—
299#1680—431no—
300#1679—431no—
301#1569—431no—
302#1553—431no—
303#1546—431no—
304C2×C43—41no—
305C2×C43—81no—
306C2×C43#304011yescharacteristic
307C2×C43#306211yescharacteristic
308C2×C43#306911yescharacteristic
309D43—161no—
310#532—431no—
311C2×C4⋊Q8—431no—
312#529C2×D4311yescharacteristic
313#497—861no—
314#491—861no—
315#489—861no—
316#489—861no—
317#487—431no—
318#487—431no—
319#486—431no—
320#486—431no—
321#478—861no—
322#475—431no—
323#474—431no—
324#469—861no—
325#468—861no—
326#463—861no—
327#462—431no—
328#462—431no—
329#461—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333#451—861no—
334#448—861no—
335#446C2×D4311yescharacteristic
336C8×Q8C2×D4311yescharacteristic
337#436—21no—
338#436C2×D4311yescharacteristic
339#435—21no—
340C8×D4C2×D4311yescharacteristic
341#433—21no—
342#432—431no—
343#431C2×D4311yescharacteristic
344#423—431no—
345#417—861no—
346#417—861no—
347#405—21no—
348C4×M16C2×D4311yescharacteristic
349#335—431no—
350#335—431no—
351#334—431no—
352#334—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#331—431no—
360#331—431no—
361C43#1938311yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C22×Q8—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—861no—
370C2×M16—21no—
371C2×M16—861no—
372C2×M16C22⋊D4311yescharacteristic
373C2×M16C22⋊D4311yescharacteristic
374C22×C8—21no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381#127—431no—
382#126—21no—
383#125D17211yescharacteristic
384#124—861no—
385#124D17211yescharacteristic
386#123—21no—
387C22⋊Q8D17211yescharacteristic
388#121—861no—
389#121—861no—
390#121D17211yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396#117—21no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—861no—
431#97—21no—
432#97—861no—
433#97C22⋊D4311yescharacteristic
434#97C22⋊D4311yescharacteristic
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—1722no—
440#41—1722no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—3441no—
445C2×Q8—3441no—
446C2×Q8—1721no—
447C2×Q8C2×D17211yescharacteristic
448C2×D4—21no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—1721no—
453C2×D4C2×D17211yescharacteristic
454C22×C4—21no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4C2×D17211yescharacteristic
458C22×C4#1062189811yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460Q16—3441no—
461Q16—3441no—
462SD16—3441no—
463SD16—3441no—
464SD16—3441no—
465D8—3441no—
466M16—41no—
467M16—41no—
468M16—42no—
469M16—3441no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C2×C8C2×C22⋊D4311yescharacteristic
480C2×C8C2×C22⋊D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4C2×D17211yescharacteristic
494C4⋊C4C2×D17211yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—21no—
503C42C2×D17211yescharacteristic
504C42#1062189811yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—1721no—
509C23#1306329911yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—3442no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519D4—21no—
520D4—21no—
521D4—81no—
522D4—3441no—
523D4—3442no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—3442no—
539C2×C4—3442no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306329911yescharacteristic
544C2×C4#1306329911yescharacteristic
545C2×C4#1306329911yescharacteristic
546C2×C4C22×C22⋊D4311yescharacteristic
547C2×C4C22×D17211yescharacteristic
548C2×C4C2×#1062189811yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—3441no—
566C22—3441no—
567C22—3441no—
568C22C2×#1306329911yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—3441no—
577C4—3441no—
578C4—3441no—
579C4#1458369711yescharacteristic
580C4#1458369711yescharacteristic
581C4#1458370411yescharacteristic
582C4#1458371111yescharacteristic
583C2—41no—
584C2—81no—
585C2—6881no—
586C2#1914408911yescharacteristic
587C2#1914427511yescharacteristic
588C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
prime radical#19145957C2
hypercenter#2969D43
hypocenterC43#19383
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #19145619C2semidirect
3. #19144989C2semidirect
4. #19134163C2semidirect
5. #19134156C2semidirect
6. #19134149C2semidirect
7. #19134142C2semidirect
8. #19134039C2semidirect
9. #19134032C2semidirect
10. #19134025C2semidirect
11. #19134018C2semidirect
12. #19133362C2semidirect
13. #19133298C2semidirect
14. #19133266C2semidirect
15. C43×#2969C2semidirect
292. #2969D43semidirect
361. C43#19383semidirect

Maximal subgroups

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

subgroupindex
#191459572
#191456192
#191449892
#191341632
#191341562
#191341492
#191341422
#191340392
#191340322
#191340252
#191340182
#191333622
#191332982
#191332662
C43×#29692
#1938343