Finite Group Databasebeta

← #25081886

Subgroups — #25081886

Order 11008.

740 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
1#19145509C211yesmaximal, characteristic
2#19144062C211yesmaximal, characteristic, complemented
3#460×D43C211yesmaximal, characteristic, complemented
4#19143674C211yesmaximal, characteristic, complemented
5#19134040C211yesmaximal, characteristic, complemented
6#19134039C211yesmaximal, characteristic, complemented
7#19134038C211yesmaximal, characteristic, complemented
8#19134037C211yesmaximal, characteristic, complemented
9#19133954C211yesmaximal, characteristic, complemented
10#19133953C211yesmaximal, characteristic, complemented
11#19133952C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133261C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1668C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17C2×SD16×D43—21no—
18#14583447C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×Q8×D43C2211yescharacteristic
21#14583275C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583120—21no—
25#14583119—21no—
26#14583110C2211yescharacteristic, complemented
27#14583109C2211yescharacteristic, complemented
28#14583100C2211yescharacteristic
29#14583099C2211yescharacteristic
30#14583098—21no—
31#14583097—21no—
32#14583096C2211yescharacteristic
33#14583096C2211yescharacteristic, complemented
34#14583092—21no—
35#14583092—21no—
36#14583031—21no—
37#14583031—21no—
38Q8×C43⋊C8C2211yescharacteristic, complemented
39C8×Dic86—21no—
40C8×Dic86C2211yescharacteristic, complemented
41#14583023—21no—
42#14583023C2211yescharacteristic, complemented
43#14582951—21no—
44#14582951C2211yescharacteristic
45#14582950—21no—
46#14582950C2211yescharacteristic
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#102×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#493C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#460C2211yescharacteristic, complemented
63C8×Q8×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×Q8×D43D411yescharacteristic
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43—21no—
72#13063354—44no—
73C2×Dic172—21no—
74C2×#10621885—21no—
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621884—21no—
79SD16×D43—44no—
80C2×#10621882—21no—
81C2×#10621882—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84#13063325C2311yescharacteristic
85#13063322C2311yescharacteristic
86#13063321—21no—
87#13063321—21no—
88#13063321—21no—
89#13063312—21no—
90#13063296—21no—
91#13063296—21no—
92Q8×Dic43D411yescharacteristic
93C4×Dic86—21no—
94C4×Dic86C2311yescharacteristic
95#13063290—21no—
96#13063290D411yescharacteristic
97D4×Dic43—21no—
98D4×Dic43—21no—
99C4⋊C4×D43—21no—
100C4⋊C4×D43D411yescharacteristic
101C42×D43—21no—
102C42×D43C2311yescharacteristic
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C2×SD16×C43—21no—
132C2×SD16×C43—21no—
133C2×D8×C43—21no—
134C2×D8×C43—21no—
135#127×C43C2311yescharacteristic
136#127×C43C2311yescharacteristic
137C4×Q8×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144C4×C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C22×Dic43—41no—
159Q8×D43—22no—
160Q8×D43D814yescomplemented
161#10621900—42no—
162#10621900—42no—
163D4×D43—42no—
164D4×D43—42no—
165D4×D43—81no—
166D4×D43—81no—
167D4×D43—82no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43#4111yescharacteristic
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86C2×D411yescharacteristic
179SD16×C43—42no—
180SD16×C43—42no—
181D8×C43—81no—
182D8×C43—81no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43C2×D411yescharacteristic
190C42×C43—21no—
191C42×C43C2411yescharacteristic
192C22⋊Dic43—41no—
193C22⋊Dic43—41no—
194#10621885—42no—
195#10621884—42no—
196#10621883—42no—
197#10621883—42no—
198#10621882—81no—
199#10621882—81no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43#4111yescharacteristic
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×D411yescharacteristic
217C2×C43⋊C8C2×D411yescharacteristic
218Dic172—42no—
219#10621873—42no—
220#10621872—42no—
221C8×D43—42no—
222C23×C43—41no—
223C23×C43—41no—
224C22×D43—41no—
225C22×D43—82no—
226C22×D43—82no—
227C22×D43—82no—
228C22×D43#12111yescharacteristic
229Q8×C43—21no—
230Q8×C43C2×D812yes—
231D4×C43—41no—
232D4×C43—41no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—81no—
240D4×C43—81no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C22⋊D43—82no—
247C22⋊D43—82no—
248C22⋊D43—82no—
249C22⋊D43—82no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—41no—
253C2×Dic43—82no—
254C2×Dic43#12111yescharacteristic
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257D172—41no—
258D172—41no—
259D172—41no—
260D172—41no—
261D172—81no—
262C4×D43—24no—
263C4×D43—21no—
264C4×D43—21no—
265C4×D43—41no—
266C4×D43—81no—
267C4×D43C2×D812yes—
268C4×D43#13512yes—
269Dic86—21no—
270Dic86—24no—
271Dic86—41no—
272Dic86—41no—
273Dic86C2×D812yes—
274C8×C43—21no—
275C8×C43—21no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43—41no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#19398—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43C2×#12111yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—164no—
298C2×D43#46612yes—
299C4×C43—22no—
300C4×C43—21no—
301C4×C43—41no—
302C4×C43C22×D811yescharacteristic
303C4×C43C2×#13511yescharacteristic
304C4×C43#57711yescharacteristic
305C4×C43#57711yescharacteristic
306Dic43—21no—
307Dic43—22no—
308Dic43—21no—
309Dic43—41no—
310Dic43—81no—
311Dic43#46612yes—
312#3205—431no—
313#3037—431no—
314C2×#460—431no—
315#2982—431no—
316#1682—431no—
317#1682—431no—
318#1682—431no—
319#1682—431no—
320#1668—431no—
321#1668—431no—
322#1668—431no—
323#1668D4311yescharacteristic, complemented
324#1571—431no—
325#1545—431no—
326#1540—431no—
327C2×C43—161no—
328C2×C43—161no—
329C2×C43#304311yescharacteristic
330C2×C43C2×#46611yescharacteristic
331C2×C43#306811yescharacteristic
332D43—22no—
333D43—161no—
334C2×#137—861no—
335C22×SD16—861no—
336#532—431no—
337C2×#127—431no—
338C2×C4×Q8—431no—
339#493—431no—
340#493C2×D4311yescharacteristic
341#486—431no—
342#486—431no—
343#464—861no—
344#464—861no—
345#462—431no—
346#462—431no—
347#460—431no—
348#460—431no—
349#460—431no—
350#460—431no—
351#460—861no—
352#460—861no—
353#460C2×D4311yescharacteristic
354#460C2×D4311yescharacteristic, complemented
355#459—861no—
356#459—861no—
357#447—861no—
358#447—861no—
359C8×Q8—431no—
360C8×Q8—431no—
361C8×Q8—431no—
362C8×Q8—861no—
363C8×Q8—861no—
364C8×Q8C2×D4311yescharacteristic, complemented
365#431—431no—
366#431—431no—
367#431—861no—
368#431—861no—
369#423—431no—
370C2×C4⋊C8—431no—
371#417—861no—
372C2×#102—861no—
373#335—431no—
374#335—431no—
375#335—431no—
376#335C2×D4311yescharacteristic, complemented
377#332—431no—
378#332—431no—
379#331—431no—
380#331—431no—
381#331—431no—
382#331—431no—
383#331C2×D4311yescharacteristic
384#331C2×D4311yescharacteristic, complemented
385C43#1939811yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C22×Q8—431no—
388C22×D4—861no—
389C22×D4—861no—
390C22×D4—861no—
391#137—1724no—
392C2×Q16—861no—
393C2×Q16—861no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—1724no—
401C2×D8—21no—
402C2×D8—21no—
403C2×D8—861no—
404C2×D8—861no—
405C2×M16—861no—
406C22×C8—861no—
407C4⋊Q8—431no—
408#127—431no—
409#127—861no—
410#127—861no—
411#127—861no—
412#127C22×D4311yescharacteristic
413#127C22×D4311yescharacteristic
414#124—861no—
415#121—861no—
416#121—861no—
417C4×Q8—431no—
418C4×Q8—431no—
419C4×Q8—431no—
420C4×Q8—861no—
421C4×Q8—861no—
422C4×Q8C22×D4311yescharacteristic
423C4×D4—861no—
424C4×D4—861no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C42—431no—
428C2×C42—861no—
429C4⋊C8—21no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—431no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438C4⋊C8—861no—
439C4⋊C8—861no—
440C4⋊C8C22×D4311yescharacteristic
441C4⋊C8C22×D4311yescharacteristic
442C4⋊C8C22×D4311yescharacteristic
443#103—861no—
444#103—861no—
445#102—21no—
446#102—21no—
447#102—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455C22⋊C8—431no—
456C22⋊C8—431no—
457C22⋊C8—861no—
458C4×C8—21no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8—861no—
462C4×C8—861no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—1721no—
466#41—1722no—
467#41—1722no—
468C2×Q8—434no—
469C2×Q8—431no—
470C2×Q8—861no—
471C2×Q8—862no—
472C2×Q8—861no—
473C2×Q8D4×D4311yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—3441no—
484C2×D4—3441no—
485C2×D4—3442no—
486C2×D4—1722no—
487C2×D4—1722no—
488C2×D4—1721no—
489C2×D4—1721no—
490C2×D4—1721no—
491C2×D4—1721no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—1721no—
498Q16—1722no—
499Q16—1722no—
500SD16—42no—
501SD16—42no—
502SD16—1722no—
503SD16—1722no—
504SD16—1722no—
505SD16—1722no—
506D8—81no—
507D8—81no—
508D8—3441no—
509D8—3441no—
510M16—1722no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—431no—
515C2×C8—431no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—1722no—
520C2×C8D4×D4311yescharacteristic
521C2×C8D4×D4311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—431no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4D4×D4311yescharacteristic
531C22⋊C4—1721no—
532C22⋊C4—1721no—
533C42—21no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42C23×D4311yescharacteristic
541C23—41no—
542C23—41no—
543C23—431no—
544C23—3442no—
545C23—3442no—
546C23—3442no—
547C23—1721no—
548Q8—21no—
549Q8—432no—
550Q8—864no—
551Q8—861no—
552Q8—1721no—
553Q8—1721no—
554Q8D8×D4312yes—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—81no—
565D4—3441no—
566D4—3442no—
567D4—3442no—
568D4—3442no—
569D4—3442no—
570D4—1721no—
571D4—1721no—
572D4—1721no—
573D4—1721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—431no—
577C2×C4—432no—
578C2×C4—432no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—864no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—3441no—
587C2×C4—3442no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—41no—
597C8—41no—
598C8—861no—
599C8—861no—
600C8—1721no—
601C8—1721no—
602C8—1721no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—432no—
610C22—861no—
611C22—861no—
612C22—3441no—
613C22—3441no—
614C22—3441no—
615C22—6884no—
616C22#121×D4311yescharacteristic
617C4—21no—
618C4—22no—
619C4—41no—
620C4—432no—
621C4—861no—
622C4—861no—
623C4—862no—
624C4—3441no—
625C4—1721no—
626C4C2×D8×D4311yescharacteristic
627C4#135×D4311yescharacteristic
628C4#1458370511yescharacteristic
629C4#1458370911yescharacteristic
630C2—161no—
631C2—161no—
632C2—862no—
633C2—6881no—
634C2#1914411111yescharacteristic
635C2#466×D4311yescharacteristic
636C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1668C2
socleC22×C43C2×#121
prime radical#19145509C2
hypercenter#1668D43
hypocenterC43#19398
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1668

Complements

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

NH ≅ G/Ntype
2. #19144062C2semidirect
3. #460×D43C2semidirect
4. #19143674C2semidirect
5. #19134040C2semidirect
6. #19134039C2semidirect
7. #19134038C2semidirect
8. #19134037C2semidirect
9. #19133954C2semidirect
10. #19133953C2semidirect
11. #19133952C2semidirect
12. #19133368C2semidirect
13. #19133261C2semidirect
14. #19133241C2semidirect
15. C43×#1668C2semidirect
26. #14583110C22semidirect
27. #14583109C22semidirect
33. #14583096C22semidirect
38. Q8×C43⋊C8C22semidirect
40. C8×Dic86C22semidirect
42. #14583023C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582644C22semidirect
57. #14582643C22semidirect
62. C43×#460C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#335C22semidirect
66. C43×#331C22semidirect
160. Q8×D43D8semidirect
323. #1668D43semidirect
354. #460C2×D43semidirect
364. C8×Q8C2×D43semidirect
376. #335C2×D43semidirect
384. #331C2×D43semidirect
385. C43#19398semidirect

Maximal subgroups

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

subgroupindex
#191455092
#191440622
#460×D432
#191436742
#191340402
#191340392
#191340382
#191340372
#191339542
#191339532
#191339522
#191333682
#191332612
#191332412
C43×#16682
#1939843