Finite Group Databasebeta

← #25086750

Subgroups — #25086750

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621885C211yesmaximal, characteristic, complemented
2SD16×Dic86C211yesmaximal, characteristic, complemented
3#19146261C211yesmaximal, characteristic
4#19134216C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19133977C211yesmaximal, characteristic, complemented
8#19133941C211yesmaximal, characteristic, complemented
9#19133816C211yesmaximal, characteristic, complemented
10#19133759C211yesmaximal, characteristic, complemented
11#19133722C211yesmaximal, characteristic
12#19133672C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3362C211yesmaximal, characteristic
16C2×#13063355—21no—
17Q8×Dic86C2211yescharacteristic
18D4×Dic86C2211yescharacteristic
19#14583302—21no—
20#14583302C2211yescharacteristic
21#14583297C2211yescharacteristic
22#14583296—21no—
23#14583271C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583194—21no—
27#14583194C2211yescharacteristic
28#14583191—21no—
29#14583191C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583187—21no—
32#14583184C2211yescharacteristic
33#14583182—21no—
34#14583143—21no—
35#14583109C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583061—21no—
38#14583037—21no—
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41C4×#10621885—21no—
42C4×#10621885C2211yescharacteristic
43SD16×Dic43—21no—
44#14582977C2211yescharacteristic
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#550C2211yescharacteristic
58C43×#486—21no—
59C43×#486C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#460—21no—
63C43×#460C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C22×Dic86—21no—
68#13063355—44no—
69C2×#10621885—21no—
70C2×#10621885D411yescharacteristic
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—41no—
75C2×#10621877—21no—
76#13063325—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063324—41no—
82#13063304—21no—
83#13063302—41no—
84Q8×Dic43—21no—
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87D4×Dic43—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258D411yescharacteristic
93#13063257—21no—
94#13063257—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—41no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—21no—
108#13063248D411yescharacteristic
109#13063246—21no—
110#13063246—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C8×Dic43—21no—
116C2×#41×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43D411yescharacteristic
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—41no—
122C4⋊Q8×C43C2311yescharacteristic
123#127×C43—21no—
124#127×C43C2311yescharacteristic
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×D4×C43—21no—
132C4×D4×C43C2311yescharacteristic
133#106×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145#41×C43—42no—
146#41×C43—81no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×Dic43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—42no—
163C2×Dic86—41no—
164C2×Dic86—41no—
165C2×Dic86—81no—
166C2×Dic86C2×D411yescharacteristic
167SD16×C43—22no—
168SD16×C43—42no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621885SD1614yescomplemented
190#10621883—42no—
191#10621883—42no—
192#10621883—81no—
193#10621883—82no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—41no—
205#10621877—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43—41no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—81no—
217Q8×C43—161no—
218Q8×C43C2×SD1612yes—
219Q8×C43#13712yescomplemented
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—82no—
227D4×C43—81no—
228D4×C43—161no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—82no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43H(5,𝔽2)11yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—82no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250Dic86—81no—
251Dic86—161no—
252Dic86C2×SD1612yes—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8C2×SD1612yes—
262#19809—431nomaximal, Sylow
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43D4211yescharacteristic
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—81no—
277C4×C43C22×SD1611yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Q8×Q16—431no—
286Q8×SD16—431no—
287#3362D4311yescharacteristic
288#3278—431no—
289#1714—431no—
290#1695—431no—
291#1678—431no—
292#1672—431no—
293#1666—431no—
294#1645—431no—
295#1637—431no—
296#1631—431no—
297#1623—431no—
298#1583—431no—
299#1579—431no—
300C2×C43—81no—
301C2×C43—161no—
302C2×C43#327011yescharacteristic
303C2×C43D4×SD1611yescharacteristic
304C2×C43#328811yescharacteristic
305C2×#137—861no—
306Q82—431no—
307Q82C2×D4311yescharacteristic
308#550C2×D4311yescharacteristic
309D4×Q8—431no—
310#500—431no—
311#500—861no—
312#498—431no—
313#498—861no—
314#492—431no—
315#492—431no—
316#487—431no—
317#486—21no—
318#486C2×D4311yescharacteristic
319#477—431no—
320#477—431no—
321#477—861no—
322#477—861no—
323#476—21no—
324#476—431no—
325#476—861no—
326#476C2×D4311yescharacteristic
327#475—431no—
328#475—861no—
329#468—861no—
330#462—431no—
331#460—21no—
332#460—431no—
333#460C2×D4311yescharacteristic
334#452—861no—
335#448—861no—
336C8×Q8—431no—
337C8×Q8—431no—
338C8×Q8C2×D4311yescharacteristic
339C4×Q16—431no—
340C4×Q16—861no—
341C4×SD16—21no—
342C4×SD16—861no—
343C4×SD16C2×D4311yescharacteristic
344#436—431no—
345#334—431no—
346#334—431no—
347#333—431no—
348#333—431no—
349#332—431no—
350#331—431no—
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8—431no—
354D4⋊C8—431no—
355#322—431no—
356C43#1980911yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C22×Q8—861no—
359#137—1724no—
360C2×Q16—431no—
361C2×Q16—861no—
362C2×SD16—21no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16—1721no—
367C2×SD16C22⋊D4311yescharacteristic
368C2×M16—861no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—41no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377C4⋊Q8—1721no—
378C4⋊Q8C22×D4311yescharacteristic
379#127—21no—
380#127C22×D4311yescharacteristic
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×Q8—861no—
390C4×Q8C22×D4311yescharacteristic
391C4×Q8C22×D4311yescharacteristic
392C4×D4—21no—
393C4×D4—861no—
394C4×D4C22×D4311yescharacteristic
395#107—431no—
396#107—861no—
397#107—861no—
398#107—861no—
399#107—861no—
400#106—21no—
401#106—861no—
402#106—861no—
403#106—861no—
404#106—861no—
405#106C22⋊D4311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8C22×D4311yescharacteristic
413#103—431no—
414#103—431no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—1721no—
420#103C22⋊D4311yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—861no—
426#102—861no—
427#102C22⋊D4311yescharacteristic
428C22⋊C8—861no—
429C4×C8—21no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—3441no—
443C2×Q8—1721no—
444C2×Q8—1721no—
445C2×Q8—1722no—
446C2×Q8D4×D4311yescharacteristic
447C2×Q8C2×C22⋊D4311yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C2×C22⋊D4311yescharacteristic
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—1721no—
457Q16—434no—
458Q16—1722no—
459SD16—22no—
460SD16—42no—
461SD16—3441no—
462SD16—3442no—
463SD16—1722no—
464SD16—1722no—
465M16—1722no—
466C2×C8—21no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—431no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—1721no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C4⋊C4D4×D4311yescharacteristic
491C4⋊C4C2×C22⋊D4311yescharacteristic
492C4⋊C4C2×C22⋊D4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—1721no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42—861no—
500C42—1721no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—81no—
507Q8—161no—
508Q8—432no—
509Q8—861no—
510Q8—3441no—
511Q8—3442no—
512Q8—1721no—
513Q8—1721no—
514Q8—6881no—
515Q8SD16×D4312yes—
516Q8#1306335512yescomplemented
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3442no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4#1306337011yescharacteristic
543C8—21no—
544C8—21no—
545C8—41no—
546C8—432no—
547C8—861no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D4×C22⋊D4311yescharacteristic
559C4—22no—
560C4—21no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—1721no—
570C4C2×SD16×D4311yescharacteristic
571C4C2×#1306335511yescharacteristic
572C4#1458370511yescharacteristic
573C4#1458371411yescharacteristic
574C2—81no—
575C2—161no—
576C2#1914616111yescharacteristic
577C2SD16×C22⋊D4311yescharacteristic
578C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3362C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3362D43
hypocenterC43#19809
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. Q8×#10621885C2semidirect
2. SD16×Dic86C2semidirect
4. #19134216C2semidirect
5. #19134116C2semidirect
6. #19134008C2semidirect
7. #19133977C2semidirect
8. #19133941C2semidirect
9. #19133816C2semidirect
10. #19133759C2semidirect
12. #19133672C2semidirect
13. #19133439C2semidirect
14. #19133412C2semidirect
189. #10621885SD16semidirect
219. Q8×C43#137semidirect
356. C43#19809semidirect
516. Q8#13063355semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218852
SD16×Dic862
#191462612
#191342162
#191341162
#191340082
#191339772
#191339412
#191338162
#191337592
#191337222
#191336722
#191334392
#191334122
C43×#33622
#1980943