Finite Group Databasebeta

← #25086462

Subgroups — #25086462

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147470C211yesmaximal, characteristic, complemented
2#19147375C211yesmaximal, characteristic, complemented
3#19146416C211yesmaximal, characteristic
4#19146413C211yesmaximal, characteristic
5#19134258C211yesmaximal, characteristic, complemented
6#19134138C211yesmaximal, characteristic, complemented
7#19134048C211yesmaximal, characteristic, complemented
8#19134013C211yesmaximal, characteristic, complemented
9#19133973C211yesmaximal, characteristic, complemented
10#19133777C211yesmaximal, characteristic
11#19133726C211yesmaximal, characteristic, complemented
12#19133693C211yesmaximal, characteristic, complemented
13#19133428C211yesmaximal, characteristic, complemented
14#19133410C211yesmaximal, characteristic, complemented
15C43×#1632C211yesmaximal, characteristic, complemented
16#14583627C2211yescharacteristic, complemented
17#14583610C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583298—21no—
20#14583295C2211yescharacteristic, complemented
21#14583266—21no—
22#14583251C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic
24#14583247C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583219—21no—
27#14583217—21no—
28#14583205—21no—
29#14583203—21no—
30#14583199—21no—
31#14583191C2211yescharacteristic, complemented
32#14583186C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583130—21no—
35#14583129—21no—
36#14583105C2211yescharacteristic
37#14583103—21no—
38#14583100C2211yescharacteristic
39#14583099C2211yescharacteristic
40#14583051—21no—
41#14583049—21no—
42#14583026C2211yescharacteristic, complemented
43Q8×C43⋊C8C2211yescharacteristic, complemented
44#14582998—21no—
45C4×#10621884C2211yescharacteristic
46C4×#10621883—21no—
47C4×#10621883C2211yescharacteristic
48D4×C43⋊C8C2211yescharacteristic
49#14582964C2211yescharacteristic
50C2×#13063245—21no—
51#102×D43—21no—
52#14582651C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582642C2211yescharacteristic
57#14582631C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic, complemented
60C43×#554C2211yescharacteristic
61C43×#494C2211yescharacteristic, complemented
62C43×#477C2211yescharacteristic, complemented
63C43×#476C2211yescharacteristic
64C43×#333C2211yescharacteristic, complemented
65C43×Q8⋊C8C2211yescharacteristic, complemented
66C43×D4⋊C8C2211yescharacteristic
67C22×D172—21no—
68C2×D4×D43—21no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621883D411yescharacteristic
72C2×#10621884—21no—
73C2×#10621884D411yescharacteristic
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063323—21no—
78#13063322C2311yescharacteristic
79#13063317—21no—
80#13063316—21no—
81#13063315—41no—
82#13063305—21no—
83#13063301—41no—
84#13063300—21no—
85#13063299—21no—
86#13063295—41no—
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90C4×D172C2311yescharacteristic
91#13063287—21no—
92C4⋊C4×D43—21no—
93#13063258—21no—
94#13063258—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256D411yescharacteristic
99#13063256D411yescharacteristic
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104#13063250—21no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248D411yescharacteristic
110#13063247—21no—
111#13063247—41no—
112#13063246—21no—
113#13063246D411yescharacteristic
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120#13063245D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C2×Q16×C43—41no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#107×C43—21no—
138#106×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C23×D43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—41no—
151C2×C22⋊D43—41no—
152D4×D43—42no—
153D4×D43—81no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—41no—
158C2×D172—42no—
159C2×D172—81no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165Q16×C43—82no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43C2411yescharacteristic
182#10621884—22no—
183#10621884—81no—
184#10621883—22no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621873—42no—
208#10621873—81no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43—41no—
213C22×D43—82no—
214C22×D43—82no—
215C22×D43—161no—
216Q8×C43—21no—
217Q8×C43—21no—
218Q8×C43—81no—
219Q8×C43—81no—
220D4×C43—21no—
221D4×C43#13712yes—
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—21no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238D172—21no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244D172—82no—
245D172#13512yes—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—161no—
249Dic86—21no—
250Dic86—21no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—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—
262#19790—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43D4211yescharacteristic
267C2×D43—22no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C2×D43—164no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13711yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287Dic43—81no—
288#3381—431no—
289#3372—431no—
290#3295—431no—
291#3295—431no—
292#1720—431no—
293#1698—431no—
294#1683—431no—
295#1678—431no—
296#1671—431no—
297#1639—431no—
298#1632—431no—
299#1632D4311yescharacteristic, complemented
300#1626—431no—
301#1582—431no—
302SD16⋊C8—431no—
303C2×C43—42no—
304C2×C43#326611yescharacteristic
305C2×C43#328211yescharacteristic
306C2×C43#328811yescharacteristic
307D43—42no—
308D43—161no—
309#557—431no—
310#554—431no—
311#554C2×D4311yescharacteristic
312D42—431no—
313#499—861no—
314#498—431no—
315#494C2×D4311yescharacteristic, complemented
316#491—861no—
317#487—431no—
318#486—431no—
319#486—431no—
320#486—431no—
321#481—861no—
322#481—861no—
323#479—861no—
324#479—861no—
325#478—861no—
326#477—431no—
327#477C2×D4311yescharacteristic, complemented
328#476—431no—
329#476C2×D4311yescharacteristic
330#474—431no—
331#465—861no—
332#465—861no—
333#461—431no—
334#461—861no—
335#460—431no—
336#460—431no—
337#450—861no—
338#450—861no—
339#446—431no—
340C8×Q8—431no—
341#440—861no—
342C4×SD16—431no—
343C4×SD16—431no—
344C4×SD16—861no—
345C8×D4—431no—
346C8×D4—431no—
347C2×#102—861no—
348C2×#102—861no—
349#335—431no—
350#334—431no—
351#333—431no—
352#333C2×D4311yescharacteristic, complemented
353#332—431no—
354#331—431no—
355Q8⋊C8—431no—
356Q8⋊C8C2×D4311yescharacteristic, complemented
357D4⋊C8—431no—
358D4⋊C8C2×D4311yescharacteristic
359#322—431no—
360C43#1979011yescharacteristic, complemented, Sylow
361C22×D4—861no—
362C22×D4—861no—
363C2×Q16—41no—
364C2×SD16—431no—
365C2×SD16—431no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—861no—
373C4⋊Q8C22×D4311yescharacteristic
374C4⋊Q8C22×D4311yescharacteristic
375#127—431no—
376#125—21no—
377#125—861no—
378#125—861no—
379#125—1721no—
380C22⋊Q8—21no—
381C22⋊Q8—41no—
382C22⋊Q8—861no—
383C22⋊Q8—1721no—
384#121—861no—
385#121—861no—
386#120—1721no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×D4—21no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395C2×C4⋊C4—21no—
396C2×C4⋊C4—861no—
397#107—21no—
398#107—861no—
399#107—861no—
400#106—21no—
401#106—431no—
402#106—431no—
403#106—861no—
404#106—861no—
405#106—861no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412#103—21no—
413#103—431no—
414#103—431no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—431no—
421#102—431no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—1721no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C24—1721no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8D4×D4311yescharacteristic
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—3441no—
449C2×D4—3441no—
450C2×D4—1721no—
451C2×D4—1722no—
452C2×D4—1721no—
453C2×D4—1722no—
454C2×D4D4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—861no—
458C22×C4—1721no—
459Q16—82no—
460SD16—862no—
461SD16—862no—
462SD16—3441no—
463SD16—3441no—
464SD16—1722no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—431no—
484C4⋊C4—431no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C4⋊C4—1721no—
492C4⋊C4—1721no—
493C4⋊C4D4×D4311yescharacteristic
494C4⋊C4D4×D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—861no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C42—21no—
501C42—861no—
502C42—1721no—
503C42C23×D4311yescharacteristic
504C23—21no—
505C23—861no—
506C23—3442no—
507C23—3442no—
508C23—1721no—
509C23—6881no—
510Q8—21no—
511Q8—21no—
512Q8—81no—
513Q8—81no—
514Q8—861no—
515Q8—861no—
516Q8—1721no—
517Q8—1721no—
518D4—21no—
519D4—432no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—3442no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4#1306335712yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—161no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—6881no—
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C2×D4×D4311yescharacteristic
546C2×C4#1306337011yescharacteristic
547C8—41no—
548C8—41no—
549C8—41no—
550C8—861no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—1721no—
555C8—1721no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—862no—
560C22—3441no—
561C22—3441no—
562C22—3441no—
563C22—1721no—
564C22—1721no—
565C22—6884no—
566C22#1458353111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—3441no—
574C4—1721no—
575C4—1721no—
576C4—1721no—
577C4#135×D4311yescharacteristic
578C4C2×#1306335711yescharacteristic
579C4#1458370811yescharacteristic
580C4#1458370811yescharacteristic
581C2—42no—
582C2—1722no—
583C2—6881no—
584C2#1914609811yescharacteristic
585C2#1914630011yescharacteristic
586C2#1914635611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1632C2
socleC22×C43D42
prime radicalD4×D172C22
hypercenter#1632D43
hypocenterC43#19790
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1632

Complements

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

NH ≅ G/Ntype
1. #19147470C2semidirect
2. #19147375C2semidirect
5. #19134258C2semidirect
6. #19134138C2semidirect
7. #19134048C2semidirect
8. #19134013C2semidirect
9. #19133973C2semidirect
11. #19133726C2semidirect
12. #19133693C2semidirect
13. #19133428C2semidirect
14. #19133410C2semidirect
15. C43×#1632C2semidirect
16. #14583627C22semidirect
20. #14583295C22semidirect
22. #14583251C22semidirect
31. #14583191C22semidirect
42. #14583026C22semidirect
43. Q8×C43⋊C8C22semidirect
52. #14582651C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582644C22semidirect
57. #14582631C22semidirect
59. #14582621C22semidirect
61. C43×#494C22semidirect
62. C43×#477C22semidirect
64. C43×#333C22semidirect
65. C43×Q8⋊C8C22semidirect
299. #1632D43semidirect
315. #494C2×D43semidirect
327. #477C2×D43semidirect
352. #333C2×D43semidirect
356. Q8⋊C8C2×D43semidirect
360. C43#19790semidirect

Maximal subgroups

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

subgroupindex
#191474702
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