Finite Group Databasebeta

← #25086660

Subgroups — #25086660

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
1Q8×#10621882C211yesmaximal, characteristic, complemented
2#19146462C211yesmaximal, characteristic, complemented
3#19146191C211yesmaximal, characteristic
4#19134215C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134018C211yesmaximal, characteristic, complemented
7#19133941C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133877C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133774C211yesmaximal, characteristic, complemented
12#19133696C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17Q8×D172C2211yescharacteristic, complemented
18#14583554C2211yescharacteristic
19#14583302—21no—
20#14583302C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583271C2211yescharacteristic
23#14583250C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic
25#14583231—21no—
26#14583184C2211yescharacteristic, complemented
27#14583179—21no—
28#14583179C2211yescharacteristic
29#14583176—21no—
30#14583176C2211yescharacteristic, complemented
31#14583143—21no—
32#14583127—21no—
33#14583104C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583050—21no—
37#14583042—21no—
38#14583036—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621882—21no—
41C4×#10621882C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic, complemented
44#103×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55#14582621C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×Q8×D43—21no—
69#13063351—44no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621877—21no—
77C2×C8×D43—21no—
78#13063325—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063307—41no—
82#13063305—21no—
83#13063305—41no—
84#13063304—21no—
85#13063296—21no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88C4⋊C4×D43—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258D411yescharacteristic
94#13063256—21no—
95#13063256—41no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063250—21no—
101#13063250—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—44no—
124C2×SD16×C43D411yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C2×C22⋊D43—41no—
167Q8×D43—42no—
168Q8×D43—81no—
169#10621898—42no—
170#10621898—81no—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—41no—
178SD16×C43—22no—
179SD16×C43—42no—
180SD16×C43—42no—
181SD16×C43—42no—
182SD16×C43—81no—
183C2×C8×C43—21no—
184C2×C8×C43—42no—
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43C2×D411yescharacteristic
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43C2411yescharacteristic
200C22⋊Dic43—41no—
201#10621883—42no—
202#10621883—42no—
203#10621883—81no—
204#10621883—81no—
205#10621882—42no—
206#10621882SD1614yescomplemented
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—41no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—41no—
214C4⋊Dic43C2×D411yescharacteristic
215Dic43⋊C4—41no—
216#10621877—42no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C2×D411yescharacteristic
222C2×C43⋊C8C2×D411yescharacteristic
223C8×D43—81no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—41no—
227C23×C43—82no—
228C23×C43—82no—
229C23×C43—161no—
230C22×D43—21no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234Q8×C43—82no—
235Q8×C43AGL(1,ℤ/8)12yescomplemented
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—81no—
244D4×C43—82no—
245D4×C43—82no—
246D4×C43C2×SD1612yes—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—82no—
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C22⋊D43—82no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264D172—21no—
265D172C2×SD1612yescomplemented
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—82no—
269C4×D43—82no—
270Dic86—41no—
271Dic86—41no—
272Dic86—41no—
273Dic86—41no—
274Dic86—82no—
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×SD1612yescomplemented
284#19803—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—164no—
295C22×C43D4211yescharacteristic
296C2×D43—22no—
297C2×D43—41no—
298C2×D43—41no—
299C4×C43—22no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43C22×SD1611yescharacteristic
306C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C43#57611yescharacteristic
308C4×C43#57711yescharacteristic
309Dic43—41no—
310Dic43—81no—
311Dic43—81no—
312Q8×D8—431no—
313#3298—431no—
314D4×SD16D4311yescharacteristic, complemented
315#3272—431no—
316#1714—431no—
317#1693—431no—
318#1679—431no—
319#1666—431no—
320#1665—431no—
321#1654—431no—
322#1651—431no—
323#1639—431no—
324#1627—431no—
325#1583—431no—
326#1580—431no—
327C2×C43—42no—
328C2×C43—81no—
329C2×C43—161no—
330C2×C43#326411yescharacteristic
331C2×C43D4×SD1611yescharacteristic
332C2×C43#328911yescharacteristic
333D43—42no—
334C2×AGL(1,ℤ/8)—861no—
335C22×SD16—21no—
336D4×Q8—431no—
337D4×Q8C2×D4311yescharacteristic
338#547—431no—
339D42C2×D4311yescharacteristic
340#500—431no—
341#500—861no—
342#498—431no—
343#492—431no—
344#492C2×D4311yescharacteristic
345#487—431no—
346#486—431no—
347#483—861no—
348#475—431no—
349#474—431no—
350#474—431no—
351#474—861no—
352#474—861no—
353#468—861no—
354#465—21no—
355#465—861no—
356#461—431no—
357#461—431no—
358#461C2×D4311yescharacteristic
359#460C2×D4311yescharacteristic
360#459—431no—
361#450—21no—
362#450—861no—
363#449—861no—
364#448—21no—
365#448—861no—
366C8×Q8—431no—
367C4×SD16C2×D4311yescharacteristic
368C4×D8—431no—
369C4×D8—861no—
370#436—431no—
371C8×D4—431no—
372C8×D4C2×D4311yescharacteristic
373C2×#103—861no—
374#334—431no—
375#334—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#1980311yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C22×Q8—21no—
388C22×Q8—861no—
389C22×D4—21no—
390C22×D4—21no—
391AGL(1,ℤ/8)—1724no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—44no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16C22⋊D4311yescharacteristic
402C2×D8—431no—
403C2×D8—861no—
404C2×M16—861no—
405C22×C8—21no—
406C22×C8—861no—
407C4⋊Q8—21no—
408C4⋊Q8—431no—
409C4⋊Q8—431no—
410C4⋊Q8—861no—
411C4⋊Q8C22×D4311yescharacteristic
412#127C22×D4311yescharacteristic
413#123—1721no—
414C22⋊Q8—21no—
415C22⋊Q8—41no—
416C22⋊Q8—861no—
417C22⋊Q8—861no—
418C22⋊Q8—1721no—
419#121—21no—
420#121—21no—
421#121—861no—
422#120—41no—
423C4×Q8C22×D4311yescharacteristic
424C4×D4—21no—
425C4×D4—431no—
426C4×D4—861no—
427C4×D4C22×D4311yescharacteristic
428C4×D4C22×D4311yescharacteristic
429C2×C4⋊C4—861no—
430#107—431no—
431#107—861no—
432#107—861no—
433#107—861no—
434#107—861no—
435#106—861no—
436#106—1721no—
437#106C22⋊D4311yescharacteristic
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—861no—
442C4⋊C8C22×D4311yescharacteristic
443#103—21no—
444#103—861no—
445#103—861no—
446#103—861no—
447#103—861no—
448#103—861no—
449#103C22⋊D4311yescharacteristic
450#102—21no—
451#102—431no—
452#102—431no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—1721no—
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—3441no—
467#41—1722no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—3441no—
475C2×Q8—1721no—
476C2×Q8—1722no—
477C2×Q8C2×C22⋊D4311yescharacteristic
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—431no—
488C2×D4—1721no—
489C2×D4D4×D4311yescharacteristic
490C2×D4C2×C22⋊D4311yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—861no—
495C22×C4—1721no—
496C22×C4—1721no—
497SD16—22no—
498SD16—42no—
499SD16—42no—
500SD16—42no—
501SD16—81no—
502SD16—3441no—
503SD16—3441no—
504SD16—1722no—
505SD16—1722no—
506D8—434no—
507D8—1722no—
508M16—1722no—
509C2×C8—21no—
510C2×C8—42no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—3441no—
518C2×C8C2×C22⋊D4311yescharacteristic
519C2×C8C2×C22⋊D4311yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—431no—
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—41no—
537C22⋊C4—41no—
538C22⋊C4—861no—
539C22⋊C4—1721no—
540C22⋊C4—1721no—
541C42—21no—
542C42C23×D4311yescharacteristic
543C23—21no—
544C23—21no—
545C23—41no—
546C23—82no—
547C23—82no—
548C23—161no—
549C23—861no—
550Q8—21no—
551Q8—41no—
552Q8—41no—
553Q8—82no—
554Q8—3442no—
555Q8—1721no—
556Q8—1721no—
557Q8—1721no—
558Q8—1721no—
559Q8#1306335112yescomplemented
560D4—21no—
561D4—21no—
562D4—21no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—432no—
571D4—861no—
572D4—3442no—
573D4SD16×D4312yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—82no—
584C2×C4—861no—
585C2×C4—3442no—
586C2×C4—3442no—
587C2×C4—1721no—
588C2×C4—1721no—
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—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—164no—
613C22—862no—
614C22—1721no—
615C22—1721no—
616C22D4×C22⋊D4311yescharacteristic
617C4—22no—
618C4—21no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—3441no—
624C4—3441no—
625C4—1721no—
626C4C2×SD16×D4311yescharacteristic
627C4C2×#1306335111yescharacteristic
628C4#1458370211yescharacteristic
629C4#1458370511yescharacteristic
630C2—42no—
631C2—81no—
632C2—161no—
633C2—1722no—
634C2#1914607111yescharacteristic
635C2SD16×C22⋊D4311yescharacteristic
636C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146191C2
hypercenterD4×SD16D43
hypocenterC43#19803
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×#10621882C2semidirect
2. #19146462C2semidirect
4. #19134215C2semidirect
5. #19134106C2semidirect
6. #19134018C2semidirect
7. #19133941C2semidirect
8. #19133933C2semidirect
9. #19133877C2semidirect
10. #19133858C2semidirect
11. #19133774C2semidirect
12. #19133696C2semidirect
13. #19133439C2semidirect
14. #19133417C2semidirect
15. D4×SD16×C43C2semidirect
17. Q8×D172C22semidirect
20. #14583302C22semidirect
21. #14583295C22semidirect
23. #14583250C22semidirect
26. #14583184C22semidirect
30. #14583176C22semidirect
39. Q8×C43⋊C8C22semidirect
43. C8×D172C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. #14582621C22semidirect
206. #10621882SD16semidirect
235. Q8×C43AGL(1,ℤ/8)semidirect
265. D172C2×SD16semidirect
283. C43⋊C8C2×SD16semidirect
314. D4×SD16D43semidirect
385. C43#19803semidirect
559. Q8#13063351semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191464622
#191461912
#191342152
#191341062
#191340182
#191339412
#191339332
#191338772
#191338582
#191337742
#191336962
#191334392
#191334172
D4×SD16×C432
#1980343