Finite Group Databasebeta

← #25087415

Subgroups — #25087415

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147622C211yesmaximal, characteristic, complemented
2#19146946C211yesmaximal, characteristic
3#19146514C211yesmaximal, characteristic
4#19134227C211yesmaximal, characteristic, complemented
5#19134103C211yesmaximal, characteristic, complemented
6#19134025C211yesmaximal, characteristic, complemented
7#19133967C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133878C211yesmaximal, characteristic
10#19133872C211yesmaximal, characteristic, complemented
11#19133809C211yesmaximal, characteristic, complemented
12#19133766C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic, complemented
15C43×#3381C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583553C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583291—21no—
21#14583278C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583243—21no—
25#14583227—21no—
26#14583217—21no—
27#14583186C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583139—21no—
31#14583130—21no—
32#14583121—21no—
33#14583109C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583106—21no—
36#14583101C2211yescharacteristic
37#14583058—21no—
38#14583030C2211yescharacteristic
39#14583004—21no—
40C4×#10621884C2211yescharacteristic
41C8×D172C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43C2×#13063256—21no—
44#14582892—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#499—21no—
59C43×#498C2211yescharacteristic
60C43×#479—21no—
61C43×#478—21no—
62C43×#477C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621884—21no—
73C2×#10621884D411yescharacteristic
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063320—41no—
79#13063313—21no—
80#13063309—41no—
81#13063305—21no—
82#13063301—21no—
83#13063299—21no—
84C4×Dic86—21no—
85C4×D172C2311yescharacteristic
86#13063283—21no—
87C2×C4⋊Dic43—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—41no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—21no—
107#13063246—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111(C2×D43)⋊C8—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×SD16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#125×C43—21no—
120#125×C43—21no—
121#125×C43—41no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—41no—
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153#10621900—42no—
154#10621900—81no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159SD16×C43—22no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
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×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183#10621885—42no—
184#10621885—81no—
185#10621885—81no—
186#10621885—81no—
187#10621884—22no—
188#10621884—81no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—41no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C8×D43—81no—
209C23×C43—21no—
210C22×D43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—81no—
218D4×C43—21no—
219D4×C43#13712yes—
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—161no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C22⋊D43—82no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—82no—
238D172—21no—
239D172—21no—
240C4×D43—41no—
241C4×D43—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19853—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43D4211yescharacteristic
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278#3398—431no—
279#3381D4311yescharacteristic, complemented
280#3335—431no—
281#3302—431no—
282#1716—431no—
283#1692—431no—
284#1680—431no—
285#1671—431no—
286#1669—431no—
287#1654—431no—
288#1653—431no—
289#1644—431no—
290#1638—431no—
291#1582—431no—
292SD16⋊C8—431no—
293C2×C43—42no—
294C2×C43#326611yescharacteristic
295C2×C43#328411yescharacteristic
296C2×C43#328911yescharacteristic
297D43—81no—
298#557C2×D4311yescharacteristic
299#556—431no—
300#554C2×D4311yescharacteristic
301#547—431no—
302#499—21no—
303#498—431no—
304#498—431no—
305#498C2×D4311yescharacteristic
306#497—861no—
307#494—431no—
308#487—431no—
309#487—431no—
310#485—861no—
311#483—861no—
312#481—861no—
313#479—21no—
314#478—21no—
315#477C2×D4311yescharacteristic
316#476—431no—
317#475—431no—
318#474—431no—
319#474C2×D4311yescharacteristic
320#467—861no—
321#465—861no—
322#464—861no—
323#462—431no—
324#462—431no—
325#462—861no—
326#461—431no—
327#452—861no—
328#446—431no—
329C8×Q8C2×D4311yescharacteristic
330#441—861no—
331C4×SD16—21no—
332C4×SD16—431no—
333C4×SD16C2×D4311yescharacteristic
334C8×D4—431no—
335C8×D4—431no—
336C2×#106—861no—
337#416—861no—
338#335—431no—
339#334—431no—
340#333—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346D4⋊C8—431no—
347D4⋊C8—431no—
348#322—431no—
349C43#1985311yescharacteristic, complemented, Sylow
350C2×#41—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—431no—
356C2×SD16—861no—
357C2×SD16C22⋊D4311yescharacteristic
358C22×C8—861no—
359C22×C8—861no—
360C4⋊Q8—21no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#126—1721no—
366#125—21no—
367#125—21no—
368#125—41no—
369#124—861no—
370#123—1721no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—861no—
374C22⋊Q8—861no—
375#121—861no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4—431no—
383C4×D4C22×D4311yescharacteristic
384#117—861no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—861no—
387#107—21no—
388#107—21no—
389#107—861no—
390#106—21no—
391#106—21no—
392#106—431no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397#106—1721no—
398#106C22⋊D4311yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—431no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—1721no—
414#103C22⋊D4311yescharacteristic
415#102—21no—
416#102—431no—
417#102—861no—
418#102—861no—
419#102C22⋊D4311yescharacteristic
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—861no—
423C4×C8—21no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8C22×D4311yescharacteristic
427#41—3441no—
428#41—1722no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8D4×D4311yescharacteristic
434C2×Q8C2×C22⋊D4311yescharacteristic
435C2×D4—431no—
436C2×D4—1721no—
437C2×D4C2×C22⋊D4311yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4—861no—
441C22×C4—1721no—
442Q16—3441no—
443Q16—3441no—
444Q16—3441no—
445Q16—1722no—
446SD16—22no—
447SD16—862no—
448SD16—3441no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—3441no—
457C2×C8—1722no—
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4D4×D4311yescharacteristic
479C4⋊C4C2×C22⋊D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—1721no—
491C42C23×D4311yescharacteristic
492C23—21no—
493C23—861no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505D4—21no—
506D4—861no—
507D4—861no—
508D4—3442no—
509D4#1306335612yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—861no—
521C2×C4—3442no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4#1306337011yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—432no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—1721no—
542C22—1721no—
543C22—1721no—
544C22D4×C22⋊D4311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4#135×D4311yescharacteristic
557C4C2×#1306335611yescharacteristic
558C4#1458370611yescharacteristic
559C4#1458370711yescharacteristic
560C2—42no—
561C2—3441no—
562C2#1914610611yescharacteristic
563C2#1914631911yescharacteristic
564C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3381C2
socleC22×C43D42
prime radical#14583553C22
hypercenter#3381D43
hypocenterC43#19853
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3381

Complements

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

NH ≅ G/Ntype
1. #19147622C2semidirect
4. #19134227C2semidirect
5. #19134103C2semidirect
6. #19134025C2semidirect
7. #19133967C2semidirect
8. #19133958C2semidirect
10. #19133872C2semidirect
11. #19133809C2semidirect
12. #19133766C2semidirect
13. #19133432C2semidirect
14. #19133405C2semidirect
15. C43×#3381C2semidirect
279. #3381D43semidirect
349. C43#19853semidirect

Maximal subgroups

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

subgroupindex
#191476222
#191469462
#191465142
#191342272
#191341032
#191340252
#191339672
#191339582
#191338782
#191338722
#191338092
#191337662
#191334322
#191334052
C43×#33812
#1985343