Finite Group Databasebeta

← #25087997

Subgroups — #25087997

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147516C211yesmaximal, characteristic, complemented
2#19147235C211yesmaximal, characteristic, complemented
3#19146237C211yesmaximal, characteristic
4#19134191C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134087C211yesmaximal, characteristic, complemented
7#19134022C211yesmaximal, characteristic, complemented
8#19134018C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic
10#19133871C211yesmaximal, characteristic, complemented
11#19133858C211yesmaximal, characteristic, complemented
12#19133856C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621883C211yesmaximal, characteristic, complemented
15C43×#3298C211yesmaximal, characteristic
16C2×#13063355—21no—
17#14583627C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19#14583305—21no—
20#14583302C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583295C2211yescharacteristic
23#14583278C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583248—21no—
26#14583199—21no—
27#14583191—21no—
28#14583184C2211yescharacteristic
29#14583183—21no—
30#14583181C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583155—21no—
33#14583106C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583102—21no—
37#14583061—21no—
38#14583054—21no—
39#14583030C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14582999—21no—
42#14582990—21no—
43C4×#10621883C2211yescharacteristic
44#14582977C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56D4×Q8×C43C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#483—21no—
60C43×#475C2211yescharacteristic
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#448—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C22×Dic86—21no—
68#13063355—44no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883D411yescharacteristic
75C2×#10621877—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063323—21no—
80#13063317—21no—
81#13063315—41no—
82#13063304—21no—
83#13063302—41no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86#13063290—21no—
87D4×Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—41no—
94#13063256—41no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063250—21no—
102#13063250—21no—
103#13063249—21no—
104#13063249—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248D411yescharacteristic
109#13063246—21no—
110#13063246D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112#13063236—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C2×#41×C43—21no—
117C22×Q8×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—41no—
128#121×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—42no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×Dic43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—42no—
164C2×Dic86—41no—
165C2×Dic86—81no—
166C2×Dic86C2×D411yescharacteristic
167SD16×C43—41no—
168SD16×C43—81no—
169C2×C8×C43—21no—
170C2×C8×C43—81no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C42×C43—21no—
188C42×C43C2411yescharacteristic
189C22⋊Dic43—41no—
190#10621885—42no—
191#10621885—42no—
192#10621885—81no—
193#10621883—42no—
194#10621883—42no—
195#10621883SD1614yescomplemented
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206C4×Dic43—21no—
207C4×Dic43—41no—
208#10621877—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C23×C43—21no—
216C23×C43—21no—
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222Q8×C43—41no—
223Q8×C43—82no—
224D4×C43—21no—
225D4×C43—21no—
226D4×C43—21no—
227D4×C43—82no—
228D4×C43C2×SD1612yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43—82no—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—82no—
249Dic86—21no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—82no—
255Dic86C2×SD1612yes—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C43⋊C8—22no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264C43⋊C8C2×SD1612yes—
265#19894—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43D4211yescharacteristic
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43C22×SD1611yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57711yescharacteristic
283C4×C43#57711yescharacteristic
284Dic43—22no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288#3386—431no—
289#3359—431no—
290#3298D4311yescharacteristic
291#3276—431no—
292#1707—431no—
293#1693—431no—
294#1690—431no—
295#1680—431no—
296#1679—431no—
297#1654—431no—
298#1653—431no—
299#1651—431no—
300#1651—431no—
301#1590—431no—
302C8×SD16—431no—
303C2×C43—42no—
304C2×C43—81no—
305C2×C43#327511yescharacteristic
306C2×C43D4×SD1611yescharacteristic
307C2×C43#329311yescharacteristic
308C2×#137—861no—
309#557—431no—
310D4×Q8—431no—
311D4×Q8C2×D4311yescharacteristic
312#547C2×D4311yescharacteristic
313#501—861no—
314#500—431no—
315#498—431no—
316#498—431no—
317#494—431no—
318#487—431no—
319#487—861no—
320#487C2×D4311yescharacteristic
321#483—21no—
322#478—861no—
323#477—861no—
324#475—431no—
325#475—431no—
326#475—861no—
327#475C2×D4311yescharacteristic
328#474—431no—
329#470—861no—
330#465—21no—
331#462—431no—
332#461—431no—
333#461—431no—
334#461—861no—
335#461C2×D4311yescharacteristic
336#452—861no—
337#451—861no—
338#448—21no—
339#446—431no—
340C8×Q8—431no—
341#440—861no—
342C4×SD16—431no—
343C4×SD16—861no—
344C4×SD16C2×D4311yescharacteristic
345#436—431no—
346C8×D4C2×D4311yescharacteristic
347C2×#103—21no—
348#334—431no—
349#334—431no—
350#332—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354Q8⋊C8—431no—
355Q8⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358C82—431no—
359C43#1989411yescharacteristic, complemented, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362C22×Q8—861no—
363#137—1724no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—21no—
368C2×SD16—431no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×SD16C22⋊D4311yescharacteristic
372C2×M16—861no—
373C22×C8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—861no—
378C4⋊Q8—861no—
379C4⋊Q8C22×D4311yescharacteristic
380C4⋊Q8C22×D4311yescharacteristic
381#125—861no—
382#125—1721no—
383#123—41no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387C22⋊Q8—861no—
388C22⋊Q8—1721no—
389#121—21no—
390C4×Q8—431no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×Q8C22×D4311yescharacteristic
394C4×D4—21no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397C4×D4C22×D4311yescharacteristic
398C2×C4⋊C4—21no—
399#107—861no—
400#107—861no—
401#107—861no—
402#106—21no—
403#106—431no—
404#106—861no—
405#106—861no—
406#106—1721no—
407#106—1721no—
408#106C22⋊D4311yescharacteristic
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—431no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#103—861no—
427#103C22⋊D4311yescharacteristic
428#102—431no—
429#102—861no—
430#102C22⋊D4311yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—861no—
433#97—861no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—3441no—
449C2×Q8—1721no—
450C2×Q8—1722no—
451C2×Q8C2×C22⋊D4311yescharacteristic
452C2×D4—41no—
453C2×D4D4×D4311yescharacteristic
454C2×D4C2×C22⋊D4311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—1721no—
460Q16—3441no—
461Q16—1722no—
462Q16—1722no—
463SD16—41no—
464SD16—81no—
465SD16—434no—
466SD16—1722no—
467SD16—1722no—
468M16—1722no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8C2×C22⋊D4311yescharacteristic
478C2×C8C2×C22⋊D4311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—431no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C4⋊C4D4×D4311yescharacteristic
497C4⋊C4C2×C22⋊D4311yescharacteristic
498C4⋊C4C2×C22⋊D4311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—1721no—
504C42—21no—
505C42—861no—
506C42—1721no—
507C42C23×D4311yescharacteristic
508C23—21no—
509C23—21no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
517Q8—432no—
518Q8—861no—
519Q8—3442no—
520Q8—1721no—
521Q8—1721no—
522Q8—1721no—
523Q8—1721no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—82no—
528D4SD16×D4312yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—3442no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×C22⋊D4311yescharacteristic
548C2×C4#1306337011yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—432no—
553C8—862no—
554C8—861no—
555C8—1721no—
556C8—1721no—
557C8—1721no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22D4×C22⋊D4311yescharacteristic
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—862no—
573C4—3441no—
574C4—3441no—
575C4—1721no—
576C4C2×SD16×D4311yescharacteristic
577C4#1458369711yescharacteristic
578C4#1458370511yescharacteristic
579C4#1458371011yescharacteristic
580C2—42no—
581C2—81no—
582C2#1914622211yescharacteristic
583C2SD16×C22⋊D4311yescharacteristic
584C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3298C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3298D43
hypocenterC43#19894
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3298

Complements

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

NH ≅ G/Ntype
1. #19147516C2semidirect
2. #19147235C2semidirect
4. #19134191C2semidirect
5. #19134106C2semidirect
6. #19134087C2semidirect
7. #19134022C2semidirect
8. #19134018C2semidirect
10. #19133871C2semidirect
11. #19133858C2semidirect
12. #19133856C2semidirect
13. #19133486C2semidirect
14. C8×#10621883C2semidirect
195. #10621883SD16semidirect
359. C43#19894semidirect

Maximal subgroups

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

subgroupindex
#191475162
#191472352
#191462372
#191341912
#191341062
#191340872
#191340222
#191340182
#191338792
#191338712
#191338582
#191338562
#191334862
C8×#106218832
C43×#32982
#1989443