Finite Group Databasebeta

← #25085970

Subgroups — #25085970

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D8×Dic86C211yesmaximal, characteristic, complemented
2D4×#10621883C211yesmaximal, characteristic, complemented
3#19146237C211yesmaximal, characteristic, complemented
4#19134268C211yesmaximal, characteristic, complemented
5#19134058C211yesmaximal, characteristic, complemented
6#19134036C211yesmaximal, characteristic, complemented
7#19133984C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133843C211yesmaximal, characteristic, complemented
10#19133830C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133697C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3294C211yesmaximal, characteristic
16C2×#13063355—21no—
17C22×#10621883—21no—
18D4×Dic86C2211yescharacteristic
19D4×Dic86C2211yescharacteristic, complemented
20#14583304C2211yescharacteristic, complemented
21#14583303—21no—
22#14583302C2211yescharacteristic, complemented
23#14583278C2211yescharacteristic, complemented
24#14583271C2211yescharacteristic
25#14583245C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583179C2211yescharacteristic, complemented
28#14583177—21no—
29#14583177—21no—
30#14583155—21no—
31#14583126—21no—
32#14583106C2211yescharacteristic, complemented
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583096C2211yescharacteristic
36#14583061—21no—
37#14583054—21no—
38#14583050—21no—
39#14583037—21no—
40C8×Dic86C2211yescharacteristic, complemented
41C4×#10621883C2211yescharacteristic
42D8×Dic43—21no—
43#14582977C2211yescharacteristic, complemented
44D4×C43⋊C8C2211yescharacteristic
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582644C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51#14582629C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57D42×C43C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#480—21no—
60C43×#474C2211yescharacteristic
61C43×#466—21no—
62C43×#459C2211yescharacteristic
63C43×#447—21no—
64C4×D8×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#102×C43—21no—
67C22×Dic86—21no—
68C22×Dic86—21no—
69#13063355—44no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621883—44no—
79C2×#10621883D411yescharacteristic
80C2×#10621877—21no—
81C22×C43⋊C8—21no—
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063324—21no—
85#13063324—21no—
86#13063304—21no—
87#13063304—21no—
88#13063302—41no—
89#13063302—41no—
90C4×Dic86C2311yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93#13063259—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—41no—
98#13063256D411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246—21no—
110#13063246—41no—
111#13063246D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C8×Dic43—21no—
117C2×#41×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120C2×D8×C43—21no—
121C2×D8×C43D411yescharacteristic
122C22×C8×C43—21no—
123C4⋊Q8×C43C2311yescharacteristic
124#127×C43C2311yescharacteristic
125#123×C43—41no—
126C22⋊Q8×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#120×C43—41no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134C2×C4⋊C4×C43—21no—
135#107×C43—21no—
136#107×C43D411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C2×D411yescharacteristic
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86—41no—
174C2×Dic86—41no—
175C2×Dic86—81no—
176C2×Dic86—81no—
177C2×Dic86C2×D411yescharacteristic
178D8×C43—22no—
179D8×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43—81no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43C2411yescharacteristic
196C22⋊Dic43—41no—
197C22⋊Dic43—41no—
198#10621885—42no—
199#10621885—42no—
200#10621885—81no—
201#10621883—42no—
202#10621883—42no—
203#10621883—42no—
204#10621883—42no—
205#10621883—81no—
206#10621883D814yescomplemented
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—21no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215C4×Dic43—21no—
216#10621877—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—42no—
222C2×C43⋊C8C2×D411yescharacteristic
223C2×C43⋊C8C2×D411yescharacteristic
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—41no—
228C23×C43—82no—
229C23×C43—82no—
230C23×C43—161no—
231Q8×C43—41no—
232Q8×C43—41no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43—82no—
245D4×C43C2×D812yes—
246D4×C43#13712yescomplemented
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—82no—
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—82no—
266C2×Dic43—82no—
267Dic86—21no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272Dic86—82no—
273Dic86—82no—
274Dic86C2×D812yes—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8C2×D812yes—
284#19757—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43—164no—
298C22×C43D4211yescharacteristic
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43C22×D811yescharacteristic
305C4×C43C2×#13711yescharacteristic
306C4×C43#57611yescharacteristic
307C4×C43#57711yescharacteristic
308Dic43—22no—
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Q8×D8—431no—
313#3294D4311yescharacteristic
314D4×SD16—431no—
315#3276—431no—
316#1722—431no—
317#1685—431no—
318#1682—431no—
319#1673—431no—
320#1669—431no—
321#1649—431no—
322#1647—431no—
323#1639—431no—
324#1627—431no—
325#1581—431no—
326SD16⋊C8—431no—
327C2×C43—42no—
328C2×C43—42no—
329C2×C43—81no—
330C2×C43—161no—
331C2×C43#326611yescharacteristic
332C2×C43D4×D811yescharacteristic
333C2×C43#328911yescharacteristic
334C2×#137—861no—
335C22×SD16—861no—
336D4×Q8—431no—
337D4×Q8—431no—
338#547C2×D4311yescharacteristic
339D42C2×D4311yescharacteristic
340#500—431no—
341#500—431no—
342#500—861no—
343#494—431no—
344#492—431no—
345#486—431no—
346#486C2×D4311yescharacteristic
347#480—21no—
348#474—431no—
349#474—431no—
350#474—861no—
351#474—861no—
352#474C2×D4311yescharacteristic
353#470—861no—
354#466—21no—
355#465—861no—
356#462—431no—
357#461—431no—
358#461—431no—
359#460—431no—
360#459C2×D4311yescharacteristic
361#452—861no—
362#451—861no—
363#450—861no—
364#448—861no—
365#447—21no—
366C8×Q8—431no—
367C4×SD16—431no—
368C4×D8—861no—
369C4×D8C2×D4311yescharacteristic
370#436—431no—
371C8×D4—431no—
372C8×D4C2×D4311yescharacteristic
373C2×#102—21no—
374#335—431no—
375#335—431no—
376#332—431no—
377#332—431no—
378#332—431no—
379#331—431no—
380Q8⋊C8—431no—
381D4⋊C8—431no—
382D4⋊C8—431no—
383D4⋊C8—431no—
384#322—431no—
385C43#1975711yescharacteristic, complemented, Sylow
386C2×#41—21no—
387C22×Q8—861no—
388C22×Q8—861no—
389C22×D4—21no—
390C22×D4—21no—
391#137—1724no—
392C2×Q16—861no—
393C2×Q16—861no—
394C2×Q16—861no—
395C2×SD16—431no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—1724no—
402C2×D8—21no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—861no—
405C22×C8—21no—
406C22×C8—861no—
407C4⋊Q8—431no—
408C4⋊Q8—431no—
409C4⋊Q8—861no—
410C4⋊Q8—861no—
411C4⋊Q8C22×D4311yescharacteristic
412#127C22×D4311yescharacteristic
413#123—41no—
414C22⋊Q8—21no—
415C22⋊Q8—861no—
416C22⋊Q8—861no—
417C22⋊Q8—1721no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—21no—
421#121—21no—
422#120—41no—
423C4×Q8—431no—
424C4×D4—861no—
425C4×D4—861no—
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428C4×D4C22×D4311yescharacteristic
429C2×C4⋊C4—21no—
430#107—21no—
431#107—861no—
432#107—861no—
433#107—861no—
434#107—861no—
435#107—1721no—
436#107C22⋊D4311yescharacteristic
437#106—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443#103—431no—
444#103—861no—
445#103—861no—
446#103—861no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—431no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—1721no—
456#102C22⋊D4311yescharacteristic
457#102C22⋊D4311yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C4×C8—431no—
462C4×C8—431no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—41no—
466#41—42no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—431no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—3441no—
473C2×Q8—3441no—
474C2×Q8—1721no—
475C2×Q8—1721no—
476C2×Q8—1722no—
477C2×Q8—1722no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—41no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4D4×D4311yescharacteristic
489C2×D4C2×C22⋊D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—1721no—
496C22×C4—1721no—
497Q16—3441no—
498Q16—1722no—
499Q16—1722no—
500SD16—434no—
501SD16—3441no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—22no—
507D8—81no—
508M16—1722no—
509C2×C8—21no—
510C2×C8—81no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—1722no—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—1721no—
530C4⋊C4—1721no—
531C4⋊C4D4×D4311yescharacteristic
532C4⋊C4C2×C22⋊D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—861no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—82no—
548C23—82no—
549C23—161no—
550Q8—41no—
551Q8—41no—
552Q8—432no—
553Q8—861no—
554Q8—3442no—
555Q8—3442no—
556Q8—1721no—
557Q8—1721no—
558Q8—1721no—
559Q8—1721no—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—21no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4D8×D4312yes—
573D4#1306335512yescomplemented
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3442no—
588C2×C4—3442no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4C22×C22⋊D4311yescharacteristic
593C2×C4#1306337011yescharacteristic
594C8—21no—
595C8—21no—
596C8—41no—
597C8—432no—
598C8—861no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—164no—
616C22D4×C22⋊D4311yescharacteristic
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—862no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4C2×D8×D4311yescharacteristic
627C4C2×#1306335511yescharacteristic
628C4#1458370011yescharacteristic
629C4#1458371011yescharacteristic
630C2—42no—
631C2—42no—
632C2—81no—
633C2—161no—
634C2#1914610111yescharacteristic
635C2D8×C22⋊D4311yescharacteristic
636C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3294C2
socleC22×C43D42
hypercenter#3294D43
hypocenterC43#19757
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. D8×Dic86C2semidirect
2. D4×#10621883C2semidirect
3. #19146237C2semidirect
4. #19134268C2semidirect
5. #19134058C2semidirect
6. #19134036C2semidirect
7. #19133984C2semidirect
8. #19133958C2semidirect
9. #19133843C2semidirect
10. #19133830C2semidirect
11. #19133774C2semidirect
12. #19133697C2semidirect
13. #19133425C2semidirect
14. #19133407C2semidirect
19. D4×Dic86C22semidirect
20. #14583304C22semidirect
22. #14583302C22semidirect
23. #14583278C22semidirect
27. #14583179C22semidirect
32. #14583106C22semidirect
40. C8×Dic86C22semidirect
43. #14582977C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582645C22semidirect
48. #14582644C22semidirect
49. #14582644C22semidirect
51. #14582629C22semidirect
54. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
206. #10621883D8semidirect
246. D4×C43#137semidirect
385. C43#19757semidirect
573. D4#13063355semidirect

Maximal subgroups

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

subgroupindex
D8×Dic862
D4×#106218832
#191462372
#191342682
#191340582
#191340362
#191339842
#191339582
#191338432
#191338302
#191337742
#191336972
#191334252
#191334072
C43×#32942
#1975743