Finite Group Databasebeta

← #25088010

Subgroups — #25088010

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621884C211yesmaximal, characteristic, complemented
2#19146946C211yesmaximal, characteristic
3#19146242C211yesmaximal, characteristic
4#19134193C211yesmaximal, characteristic, complemented
5#19134115C211yesmaximal, characteristic, complemented
6#19134089C211yesmaximal, characteristic, complemented
7#19133979C211yesmaximal, characteristic, complemented
8#19133972C211yesmaximal, characteristic, complemented
9#19133816C211yesmaximal, characteristic, complemented
10#19133802C211yesmaximal, characteristic, complemented
11#19133758C211yesmaximal, characteristic, complemented
12#19133744C211yesmaximal, characteristic
13#19133485C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3385C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17Q8×D172C2211yescharacteristic
18#14583553C2211yescharacteristic
19#14583295—21no—
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583279C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583227—21no—
26#14583217—21no—
27#14583186—21no—
28#14583186C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583184—21no—
31#14583184C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583158—21no—
34#14583130—21no—
35#14583109C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583062—21no—
38#14583056—21no—
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621884—21no—
41C4×#10621884C2211yescharacteristic
42#14582978C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063256—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582646C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#474—21no—
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621884D411yescharacteristic
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063309—41no—
81#13063305—21no—
82#13063305—21no—
83#13063305—41no—
84#13063299—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C2×C4⋊Dic43—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256D411yescharacteristic
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063249—41no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—41no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43D411yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#97×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—41no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C2×C22⋊D43—41no—
154C22×Dic43—41no—
155Q8×D43—42no—
156Q8×D43—81no—
157#10621900—42no—
158#10621900—81no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—41no—
165SD16×C43SD1614yescomplemented
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—41no—
187C42×C43C2411yescharacteristic
188#10621885—42no—
189#10621884—22no—
190#10621883—42no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43—41no—
200C4⋊Dic43C2×D411yescharacteristic
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
208Dic172—42no—
209Dic172—81no—
210#10621872—42no—
211C23×C43—21no—
212C22×D43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—81no—
217Q8×C43—81no—
218Q8×C43—161no—
219Q8×C43C2×SD1612yes—
220D4×C43—21no—
221D4×C43C2×SD1612yes—
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—41no—
231C2×C4×C43—161no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C22⋊D43—82no—
236C2×Dic43—21no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—82no—
240D172—21no—
241D172—21no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—82no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43C2×SD1612yes—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13712yescomplemented
259#19895—431nomaximal, Sylow
260C22×C43—22no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43D4211yescharacteristic
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C22×SD1611yescharacteristic
276C4×C43C2×#13711yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3385D4311yescharacteristic, complemented
283Q8×SD16—431no—
284#3335—431no—
285#3276—431no—
286#1707—431no—
287#1695—431no—
288#1690—431no—
289#1672—431no—
290#1671—431no—
291#1645—431no—
292#1643—431no—
293#1637—431no—
294#1635—431no—
295#1590—431no—
296C8×SD16—431no—
297C2×C43—42no—
298C2×C43#327611yescharacteristic
299C2×C43D4×SD1611yescharacteristic
300C2×C43#329011yescharacteristic
301D43—81no—
302C2×#137—861no—
303Q82C2×D4311yescharacteristic
304#554C2×D4311yescharacteristic
305D4×Q8—431no—
306#547—431no—
307#501—21no—
308#500C2×D4311yescharacteristic
309#498—431no—
310#498—431no—
311#498—861no—
312#494—431no—
313#487—431no—
314#487—431no—
315#483—861no—
316#481—861no—
317#479—21no—
318#477C2×D4311yescharacteristic
319#476—431no—
320#476—431no—
321#476—861no—
322#476C2×D4311yescharacteristic
323#475—431no—
324#475—431no—
325#475—861no—
326#474—21no—
327#470—861no—
328#465—861no—
329#462—431no—
330#461—431no—
331#452—861no—
332#451—861no—
333#446C2×D4311yescharacteristic
334C8×Q8—431no—
335#440—21no—
336C4×SD16—431no—
337C4×SD16—861no—
338C4×SD16C2×D4311yescharacteristic
339#436—431no—
340C8×D4—431no—
341C2×#106—861no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#332—431no—
347#332—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352C82—431no—
353C43#1989511yescharacteristic, complemented, Sylow
354C2×#41—861no—
355C22×Q8—861no—
356#137—1724no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—431no—
361C2×SD16—861no—
362C2×SD16C22⋊D4311yescharacteristic
363C2×M16—861no—
364C22×C8—861no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8—41no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—861no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#125—21no—
374#123—1721no—
375C22⋊Q8—21no—
376C22⋊Q8—41no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379C22⋊Q8—1721no—
380#121—861no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C22×D4311yescharacteristic
384C4×Q8C22×D4311yescharacteristic
385C4×D4—21no—
386C4×D4—431no—
387C4×D4—861no—
388C4×D4C22×D4311yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—861no—
391#107—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—431no—
396#106—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106C22⋊D4311yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411#103—21no—
412#103—431no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—1721no—
418#103—1721no—
419#103C22⋊D4311yescharacteristic
420#102—21no—
421#102—431no—
422#102—861no—
423#102—861no—
424#102C22⋊D4311yescharacteristic
425C22⋊C8—861no—
426C22⋊C8—861no—
427#97—21no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—3441no—
433#41—1722no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—3441no—
440C2×Q8—1721no—
441C2×Q8—1722no—
442C2×Q8D4×D4311yescharacteristic
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—431no—
445C2×D4—1721no—
446C2×D4C2×C22⋊D4311yescharacteristic
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—861no—
450C22×C4—1721no—
451C22×C4—1721no—
452Q16—3441no—
453Q16—1722no—
454Q16—1722no—
455SD16—862no—
456SD16—1722no—
457SD16#1062188414yescomplemented
458M16—1722no—
459C2×C8—21no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—1722no—
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4D4×D4311yescharacteristic
487C4⋊C4C2×C22⋊D4311yescharacteristic
488C4⋊C4C2×C22⋊D4311yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—861no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42C23×D4311yescharacteristic
498C23—21no—
499C23—861no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—81no—
504Q8—81no—
505Q8—161no—
506Q8—3442no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8C2×#1062188412yes—
512D4—21no—
513D4—861no—
514D4—861no—
515D4—3442no—
516D4C2×#1062188412yes—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—861no—
528C2×C4—3442no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C22×C22⋊D4311yescharacteristic
536C2×C4#1306337011yescharacteristic
537C8—21no—
538C8—41no—
539C8—432no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C8C2×#1062188412yes—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—1721no—
550C22—1721no—
551C22—1721no—
552C22D4×C22⋊D4311yescharacteristic
553C4—22no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4C22×#1062188411yescharacteristic
565C4#137×D4311yescharacteristic
566C4#1458370711yescharacteristic
567C4#1458371511yescharacteristic
568C2—42no—
569C2—3441no—
570C2#1914623511yescharacteristic
571C2D4×#1062188411yescharacteristic
572C2#1914637711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3385C2
socleC22×C43D42
prime radical#14583553C22
hypercenter#3385D43
hypocenterC43#19895
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. Q8×#10621884C2semidirect
4. #19134193C2semidirect
5. #19134115C2semidirect
6. #19134089C2semidirect
7. #19133979C2semidirect
8. #19133972C2semidirect
9. #19133816C2semidirect
10. #19133802C2semidirect
11. #19133758C2semidirect
13. #19133485C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3385C2semidirect
165. SD16×C43SD16semidirect
258. C43⋊C8#137semidirect
282. #3385D43semidirect
353. C43#19895semidirect
457. SD16#10621884semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218842
#191469462
#191462422
#191341932
#191341152
#191340892
#191339792
#191339722
#191338162
#191338022
#191337582
#191337442
#191334852
SD16×C43⋊C82
C43×#33852
#1989543