Finite Group Databasebeta

← #25086193

Subgroups — #25086193

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146410C211yesmaximal, characteristic, complemented
2#19146402C211yesmaximal, characteristic, complemented
3#19146313C211yesmaximal, characteristic, complemented
4#19134252C211yesmaximal, characteristic, complemented
5#19134156C211yesmaximal, characteristic, complemented
6#19134034C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic, complemented
10#19133877C211yesmaximal, characteristic, complemented
11#19133773C211yesmaximal, characteristic, complemented
12#19133684C211yesmaximal, characteristic, complemented
13#19133422C211yesmaximal, characteristic, complemented
14#19133419C211yesmaximal, characteristic, complemented
15C43×#3330C211yesmaximal, characteristic, complemented
16C2×#13063345—21no—
17#14583554C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583295C2211yescharacteristic, complemented
20#14583278C2211yescharacteristic, complemented
21#14583247C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583214—21no—
25#14583212—21no—
26#14583179C2211yescharacteristic
27#14583176C2211yescharacteristic
28#14583138—21no—
29#14583134—21no—
30#14583133—21no—
31#14583104C2211yescharacteristic, complemented
32#14583101C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583061—21no—
36#14583059—21no—
37#14583032—21no—
38#14583031—21no—
39C4×#10621882C2211yescharacteristic
40C8×D172C2211yescharacteristic
41D4×C43⋊C8C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063245—21no—
44#102×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582645C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic, complemented
56C43×#547C2211yescharacteristic
57C43×#547C2211yescharacteristic, complemented
58C43×#487C2211yescharacteristic, complemented
59C43×#484—21no—
60C43×#474C2211yescharacteristic
61C43×#468—21no—
62C43×#461C2211yescharacteristic, complemented
63C43×#449—21no—
64C4×D8×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic, complemented
66C43×#417—21no—
67C2×#10621898—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063345—44no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621884—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882D411yescharacteristic
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063307—41no—
84#13063304—21no—
85#13063300—21no—
86#13063299—21no—
87#13063296—21no—
88#13063295—41no—
89C4×D172C2311yescharacteristic
90C4⋊C4×D43—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258D411yescharacteristic
94#13063256—41no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98#13063249—21no—
99#13063248—21no—
100#13063247—21no—
101#13063247—21no—
102#13063246—21no—
103#13063246D411yescharacteristic
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C2×#41×C43—21no—
118C2×SD16×C43—21no—
119C2×D8×C43D411yescharacteristic
120C2×M16×C43—21no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#123×C43—41no—
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146#41×C43—42no—
147#41×C43—42no—
148#41×C43—81no—
149#41×C43—81no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C2×C22⋊D43—41no—
163C2×C22⋊D43—41no—
164D4×D43—42no—
165D4×D43—81no—
166#10621898—42no—
167#10621898—81no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—41no—
172C2×D172—42no—
173C2×D172—81no—
174C2×D172C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×C4×D43—41no—
177C2×Dic86—21no—
178SD16×C43—81no—
179D8×C43—22no—
180M16×C43—81no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—41no—
189C4⋊C4×C43—41no—
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43C2411yescharacteristic
199C22⋊Dic43—41no—
200#10621885—42no—
201#10621885—81no—
202#10621884—42no—
203#10621883—42no—
204#10621882—22no—
205#10621882—81no—
206#10621882—81no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—41no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—41no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—42no—
218C2×C43⋊C8—81no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C8×D43—81no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C22×D43—21no—
226C22×D43—41no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43—161no—
230Q8×C43—41no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—82no—
240D4×C43—82no—
241D4×C43#13512yescomplemented
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—82no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C22⋊D43—82no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262D172—21no—
263D172—41no—
264D172—41no—
265D172—41no—
266D172—41no—
267D172—81no—
268D172—82no—
269D172AGL(1,ℤ/8)12yes—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—82no—
273Dic86—41no—
274Dic86—41no—
275C8×C43—21no—
276C8×C43—21no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19772—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43D4211yescharacteristic
295C2×D43—22no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—81no—
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—164no—
302C4×C43—21no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C2×#13511yescharacteristic
309C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C43#57611yescharacteristic
311C4×C43#57611yescharacteristic
312Dic43—41no—
313Dic43—81no—
314#3330D4311yescharacteristic, complemented
315#3294—431no—
316#3294—431no—
317#3283—431no—
318#1720—431no—
319#1701—431no—
320#1681—431no—
321#1679—431no—
322#1669—431no—
323#1654—431no—
324#1654—431no—
325#1639—431no—
326#1625—431no—
327#1581—431no—
328#1580—431no—
329C2×C43—42no—
330C2×C43—81no—
331C2×C43—81no—
332C2×C43#326411yescharacteristic
333C2×C43#328011yescharacteristic
334C2×C43#328911yescharacteristic
335D43—42no—
336D43—161no—
337C2×#135—861no—
338#547—431no—
339#547C2×D4311yescharacteristic
340#547C2×D4311yescharacteristic, complemented
341D42—431no—
342#498—431no—
343#494—431no—
344#487C2×D4311yescharacteristic, complemented
345#486—431no—
346#486—431no—
347#486—431no—
348#484—21no—
349#480—861no—
350#480—861no—
351#474—431no—
352#474—431no—
353#474C2×D4311yescharacteristic
354#468—21no—
355#467—861no—
356#466—861no—
357#466—861no—
358#461—431no—
359#461—431no—
360#461C2×D4311yescharacteristic, complemented
361#459—431no—
362#459—431no—
363#452—861no—
364#452—861no—
365#449—21no—
366#447—861no—
367#447—861no—
368C4×D8—431no—
369C4×D8C2×D4311yescharacteristic
370#436C2×D4311yescharacteristic, complemented
371C8×D4—431no—
372C8×D4—431no—
373C8×D4—431no—
374#417—21no—
375C2×#102—861no—
376C2×#102—861no—
377#335—431no—
378#334—431no—
379#332—431no—
380#332—431no—
381#332—431no—
382#331—431no—
383D4⋊C8—431no—
384D4⋊C8—431no—
385D4⋊C8—431no—
386D4⋊C8—431no—
387#322—431no—
388C43#1977211yescharacteristic, complemented, Sylow
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—861no—
392C22×D4—861no—
393C22×D4—861no—
394#135—1724no—
395C2×Q16—861no—
396C2×Q16—861no—
397C2×SD16—21no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×D8—431no—
401C2×D8—861no—
402C2×D8—861no—
403C2×D8C22⋊D4311yescharacteristic
404C2×M16—21no—
405C22×C8—861no—
406C22×C8—861no—
407C22×C8—861no—
408C4⋊Q8—431no—
409C4⋊Q8C22×D4311yescharacteristic
410C4⋊Q8C22×D4311yescharacteristic
411#127—431no—
412#123—41no—
413#123—41no—
414#123—1721no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—861no—
418#121—21no—
419#121—21no—
420#121—861no—
421#121—861no—
422#121—861no—
423#120—1721no—
424C4×D4—431no—
425C4×D4C22×D4311yescharacteristic
426C4×D4C22×D4311yescharacteristic
427C4×D4C22×D4311yescharacteristic
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—861no—
431#107—21no—
432#107—431no—
433#107—861no—
434#107—861no—
435#107C22⋊D4311yescharacteristic
436#106—1721no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8C22×D4311yescharacteristic
441#103—21no—
442#103—21no—
443#103—21no—
444#103—861no—
445#103—861no—
446#102—21no—
447#102—431no—
448#102—431no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#102—1721no—
458#102C22⋊D4311yescharacteristic
459#102C22⋊D4311yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463C22⋊C8—861no—
464C4×C8—431no—
465C4×C8—431no—
466C4×C8C22×D4311yescharacteristic
467C24—1721no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—3441no—
473#41—1722no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—861no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—431no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—1721no—
486C2×D4—1722no—
487C2×D4—1721no—
488C2×D4—1721no—
489C2×D4—1722no—
490C2×D4D4×D4311yescharacteristic
491C2×D4C2×C22⋊D4311yescharacteristic
492C2×D4C2×C22⋊D4311yescharacteristic
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—861no—
499C22×C4—1721no—
500Q16—3441no—
501Q16—1722no—
502SD16—81no—
503SD16—1722no—
504SD16—1722no—
505D8—22no—
506D8—862no—
507D8—3441no—
508D8—3441no—
509M16—81no—
510C2×C8—21no—
511C2×C8—431no—
512C2×C8—431no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—3441no—
518C2×C8—3441no—
519C2×C8—1722no—
520C2×C8C2×C22⋊D4311yescharacteristic
521C2×C8C2×C22⋊D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—1721no—
532C4⋊C4D4×D4311yescharacteristic
533C4⋊C4C2×C22⋊D4311yescharacteristic
534C4⋊C4C2×C22⋊D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—861no—
541C22⋊C4—1721no—
542C22⋊C4—1721no—
543C42C23×D4311yescharacteristic
544C23—21no—
545C23—21no—
546C23—21no—
547C23—861no—
548C23—3442no—
549C23—3442no—
550C23—1721no—
551C23—6881no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—1721no—
557Q8—1721no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—21no—
563D4—82no—
564D4—82no—
565D4—432no—
566D4—861no—
567D4—3441no—
568D4—3442no—
569D4—3442no—
570D4—3442no—
571D4—1721no—
572D4—1721no—
573D4—1721no—
574D4—1721no—
575D4#1306334512yescomplemented
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—861no—
590C2×C4—3442no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C2×D4×D4311yescharacteristic
595C2×C4C22×C22⋊D4311yescharacteristic
596C2×C4#1306337011yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—861no—
601C8—861no—
602C8—1721no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—862no—
616C22—3441no—
617C22—3441no—
618C22—3441no—
619C22—1721no—
620C22—1721no—
621C22—6884no—
622C22D4×C22⋊D4311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—81no—
629C4—3441no—
630C4—1721no—
631C4C2×#1306334511yescharacteristic
632C4AGL(1,ℤ/8)×D4311yescharacteristic
633C4#1458370211yescharacteristic
634C4#1458370311yescharacteristic
635C2—42no—
636C2—81no—
637C2—81no—
638C2—1722no—
639C2—6881no—
640C2#1914606911yescharacteristic
641C2#1914627611yescharacteristic
642C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3330C2
socleC22×C43D42
hypercenter#3330D43
hypocenterC43#19772
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #19146410C2semidirect
2. #19146402C2semidirect
3. #19146313C2semidirect
4. #19134252C2semidirect
5. #19134156C2semidirect
6. #19134034C2semidirect
7. #19134015C2semidirect
8. #19133958C2semidirect
9. #19133879C2semidirect
10. #19133877C2semidirect
11. #19133773C2semidirect
12. #19133684C2semidirect
13. #19133422C2semidirect
14. #19133419C2semidirect
15. C43×#3330C2semidirect
19. #14583295C22semidirect
20. #14583278C22semidirect
31. #14583104C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582645C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582620C22semidirect
57. C43×#547C22semidirect
58. C43×#487C22semidirect
62. C43×#461C22semidirect
65. C43×#436C22semidirect
241. D4×C43#135semidirect
314. #3330D43semidirect
340. #547C2×D43semidirect
344. #487C2×D43semidirect
360. #461C2×D43semidirect
370. #436C2×D43semidirect
388. C43#19772semidirect
575. D4#13063345semidirect

Maximal subgroups

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

subgroupindex
#191464102
#191464022
#191463132
#191342522
#191341562
#191340342
#191340152
#191339582
#191338792
#191338772
#191337732
#191336842
#191334222
#191334192
C43×#33302
#1977243