Finite Group Databasebeta

← #25081748

Subgroups — #25081748

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#19144991C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134165C211yesmaximal, characteristic, complemented
5#19134158C211yesmaximal, characteristic, complemented
6#19134151C211yesmaximal, characteristic, complemented
7#19134144C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19134034C211yesmaximal, characteristic, complemented
10#19134027C211yesmaximal, characteristic, complemented
11#19134020C211yesmaximal, characteristic, complemented
12#19133363C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133267C211yesmaximal, characteristic, complemented
15C43×#3218C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583261—21no—
18#14583261—21no—
19#14583251C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583196—21no—
24#14583184C2211yescharacteristic
25#14583179C2211yescharacteristic
26#14583150—21no—
27#14583147—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582971—21no—
36D4×C43⋊C8C2211yescharacteristic
37#14582960—21no—
38#14582952C2211yescharacteristic
39#14582923C2211yescharacteristic
40#14582898—21no—
41#14582898—21no—
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#497—21no—
59C43×#491—21no—
60C43×#462C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#461C2211yescharacteristic
64C43×#451—21no—
65C43×#448—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C22×C43⋊C8—21no—
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063313—21no—
78#13063299—21no—
79#13063299—21no—
80C4×D172—21no—
81C4×D172—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#13063248—21no—
93#13063248—21no—
94#13063248—21no—
95#13063248—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—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—
114C2×Q16×C43—21no—
115C2×Q16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#126×C43—21no—
124#125×C43D411yescharacteristic
125#124×C43D411yescharacteristic
126#123×C43—21no—
127C22⋊Q8×C43D411yescharacteristic
128#121×C43D411yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—81no—
148C2×Q8×C43—81no—
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×C22⋊D43—41no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×C4×D43—41no—
164C2×Dic86—21no—
165Q16×C43—81no—
166Q16×C43—81no—
167SD16×C43—81no—
168SD16×C43—81no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C22⋊C4×C43—21no—
187C22⋊C4×C43—21no—
188C42×C43—21no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621884—81no—
194#10621882—81no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199#10621877—41no—
200#10621877—41no—
201#10621877—42no—
202#10621877—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—81no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C22⋊D43—82no—
245C2×Dic43—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—81no—
251C4×D43—82no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
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—81no—
283C4×C43—81no—
284C4×C43#57511yescharacteristic
285C4×C43#57511yescharacteristic
286C4×C43#57611yescharacteristic
287C4×C43#57711yescharacteristic
288Dic43—81no—
289#3251—431no—
290#3218D4311yescharacteristic, complemented
291#3141—431no—
292#2969—431no—
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⋊Q8C2×D4311yescharacteristic
312#529C2×D4311yescharacteristic
313#497—21no—
314#491—21no—
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#462C2×D4311yescharacteristic
328#462C2×D4311yescharacteristic
329#461C2×D4311yescharacteristic
330#461C2×D4311yescharacteristic
331#460—431no—
332#459—431no—
333#451—21no—
334#448—21no—
335#446—431no—
336C8×Q8—431no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#432C2×D4311yescharacteristic
343#431—431no—
344#423—431no—
345#417—861no—
346#417—861no—
347#405—861no—
348C4×M16—431no—
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—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—861no—
369C2×D8—861no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16—861no—
373C2×M16—861no—
374C22×C8—861no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—431no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#127—431no—
382#126—21no—
383#125C22⋊D4311yescharacteristic
384#124—861no—
385#124C22⋊D4311yescharacteristic
386#123—21no—
387C22⋊Q8C22⋊D4311yescharacteristic
388#121—861no—
389#121—861no—
390#121C22⋊D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4C22×D4311yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#106—861no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
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—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432#97—431no—
433#97—431no—
434#97—861no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—861no—
438C4×C8—861no—
439#41—1722no—
440#41—1722no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—81no—
445C2×Q8—81no—
446C2×Q8—861no—
447C2×Q8C2×C22⋊D4311yescharacteristic
448C2×D4—21no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—1721no—
453C2×D4C2×C22⋊D4311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—1721no—
457C22×C4D4×D4311yescharacteristic
458C22×C4#1062190011yescharacteristic
459C22×C4C2×C22⋊D4311yescharacteristic
460Q16—81no—
461Q16—81no—
462SD16—81no—
463SD16—81no—
464SD16—3441no—
465D8—3441no—
466M16—3441no—
467M16—1721no—
468M16—1721no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—431no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—1722no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4C2×C22⋊D4311yescharacteristic
494C4⋊C4C2×C22⋊D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—21no—
503C42D4×D4311yescharacteristic
504C42#1062190011yescharacteristic
505C42C2×C22⋊D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—21no—
508C23—1721no—
509C23#1306329711yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
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—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—3442no—
542C2×C4—1721no—
543C2×C4#1306329711yescharacteristic
544C2×C4#1306329711yescharacteristic
545C2×C4#1306329711yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C8—41no—
550C8—41no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—861no—
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×#1306329711yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—3441no—
579C4#1458369811yescharacteristic
580C4#1458369811yescharacteristic
581C4#1458370211yescharacteristic
582C4#1458371011yescharacteristic
583C2—41no—
584C2—81no—
585C2—6881no—
586C2#1914409111yescharacteristic
587C2#1914427111yescharacteristic
588C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3218C2
socleC22×C43C2×#121
prime radical#19145957C2
hypercenter#3218D43
hypocenterC43#19383
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. #19144991C2semidirect
3. #19143600C2semidirect
4. #19134165C2semidirect
5. #19134158C2semidirect
6. #19134151C2semidirect
7. #19134144C2semidirect
8. #19134041C2semidirect
9. #19134034C2semidirect
10. #19134027C2semidirect
11. #19134020C2semidirect
12. #19133363C2semidirect
13. #19133301C2semidirect
14. #19133267C2semidirect
15. C43×#3218C2semidirect
290. #3218D43semidirect
361. C43#19383semidirect

Maximal subgroups

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

subgroupindex
#191459572
#191449912
#191436002
#191341652
#191341582
#191341512
#191341442
#191340412
#191340342
#191340272
#191340202
#191333632
#191333012
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C43×#32182
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