Finite Group Databasebeta

← #25086711

Subgroups — #25086711

Order 11008.

676 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147460C211yesmaximal, characteristic, complemented
2#19146953C211yesmaximal, characteristic, complemented
3#19146420C211yesmaximal, characteristic, complemented
4#19146196C211yesmaximal, characteristic
5#19134217C211yesmaximal, characteristic, complemented
6#19134119C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133944C211yesmaximal, characteristic, complemented
10#19133804C211yesmaximal, characteristic, complemented
11#19133748C211yesmaximal, characteristic, complemented
12#19133713C211yesmaximal, characteristic, complemented
13#19133669C211yesmaximal, characteristic, complemented
14#19133440C211yesmaximal, characteristic, complemented
15C43×#1580C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583606C2211yescharacteristic
18#14583606C2211yescharacteristic, complemented
19#14583553C2211yescharacteristic
20D4×D172C2211yescharacteristic
21#14583304C2211yescharacteristic, complemented
22#14583300—21no—
23#14583297C2211yescharacteristic, complemented
24#14583272C2211yescharacteristic
25#14583272C2211yescharacteristic
26#14583250C2211yescharacteristic, complemented
27#14583246C2211yescharacteristic
28#14583230—21no—
29#14583218—21no—
30#14583218—21no—
31#14583197—21no—
32#14583197—21no—
33#14583190C2211yescharacteristic
34#14583190C2211yescharacteristic
35#14583189C2211yescharacteristic
36#14583189C2211yescharacteristic, complemented
37#14583185C2211yescharacteristic, complemented
38#14583146—21no—
39#14583128—21no—
40#14583128—21no—
41#14583104C2211yescharacteristic
42#14583100C2211yescharacteristic
43#14583094C2211yescharacteristic
44#14583052—21no—
45#14583051—21no—
46#14583045—21no—
47C8×Dic86C2211yescharacteristic, complemented
48C4×#10621873C2211yescharacteristic
49D8×Dic43—21no—
50#14582978C2211yescharacteristic
51C2×#13063257—21no—
52C2×#13063247—21no—
53#14582650C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582642C2211yescharacteristic
58#14582631C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic, complemented
63C43×#334C2211yescharacteristic, complemented
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic, complemented
66C43×#322C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063349—44no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—41no—
75C2×#10621873D411yescharacteristic
76C2×#10621883—21no—
77C2×#10621882—21no—
78C2×#10621872—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063322C2311yescharacteristic
83#13063316—21no—
84#13063316—21no—
85#13063309—41no—
86#13063305—21no—
87#13063304—21no—
88#13063304—21no—
89#13063302—41no—
90#13063302—41no—
91#13063300—21no—
92#13063299—21no—
93#13063299—21no—
94#13063295—41no—
95C4×Dic86C2311yescharacteristic
96C4×D172C2311yescharacteristic
97D4×Dic43—21no—
98D4×Dic43—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257D411yescharacteristic
110#13063256—21no—
111#13063256—21no—
112C4⋊(C43⋊C8)C2311yescharacteristic
113C4⋊(C43⋊C8)C2311yescharacteristic
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063250—41no—
117#13063250D411yescharacteristic
118#13063248—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247D411yescharacteristic
125#13063246—21no—
126#13063246—21no—
127#13063245—21no—
128(C2×D43)⋊C8—21no—
129C8×Dic43—21no—
130C2×D8×C43D411yescharacteristic
131C22×C8×C43—21no—
132C22×C8×C43—21no—
133C4×D4×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#107×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#102×C43D411yescharacteristic
139#102×C43D411yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×D4×C43C2×D411yescharacteristic
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152C22×Dic43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155#10621900—42no—
156#10621900—81no—
157D4×D43—42no—
158D4×D43—81no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—41no—
163C2×D172—42no—
164C2×D172—81no—
165C2×D172C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C2×D411yescharacteristic
171D8×C43SD1614yescomplemented
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—42no—
176C2×C8×C43—81no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188#10621883—42no—
189#10621882—42no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203C4⋊Dic43C2×D411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210#10621873—41no—
211#10621873—42no—
212#10621873—81no—
213#10621873—81no—
214#10621873—82no—
215#10621872—42no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43C2×SD1612yes—
226D4×C43C2×SD1612yes—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C22⋊D43—82no—
237C22⋊D43—82no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—82no—
245C2×Dic43—161no—
246C2×Dic43—161no—
247D172—21no—
248D172—21no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—41no—
253D172—81no—
254D172—82no—
255C4×D43—41no—
256C4×D43—41no—
257Dic86—21no—
258Dic86—21no—
259Dic86—41no—
260Dic86—41no—
261Dic86—81no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C8×C43C2×SD1612yes—
270C43⋊C8—41no—
271C43⋊C8—41no—
272#19806—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—22no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43D4211yescharacteristic
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—164no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43C22×SD1611yescharacteristic
291C4×C43#57511yescharacteristic
292C4×C43#57711yescharacteristic
293C4×C43#57711yescharacteristic
294Dic43—41no—
295Dic43—41no—
296Dic43—41no—
297Dic43—81no—
298Dic43—81no—
299Dic43—81no—
300#3380—431no—
301#3335—431no—
302#3295—431no—
303#3272—431no—
304#1714—431no—
305#1695—431no—
306#1677—431no—
307#1671—431no—
308#1666—431no—
309#1643—431no—
310#1635—431no—
311#1629—431no—
312#1622—431no—
313#1583—431no—
314#1580D4311yescharacteristic, complemented
315C2×C43—42no—
316C2×C43—42no—
317C2×C43#326711yescharacteristic
318C2×C43D4×SD1611yescharacteristic
319C2×C43#328811yescharacteristic
320D43—81no—
321D43—161no—
322C2×AGL(1,ℤ/8)—861no—
323#554—431no—
324#554—431no—
325#547—431no—
326D42—431no—
327#500—431no—
328#499—861no—
329#498—431no—
330#492—431no—
331#492—431no—
332#487—431no—
333#486—431no—
334#483—861no—
335#481—861no—
336#481—861no—
337#478—861no—
338#478—861no—
339#476—431no—
340#476—431no—
341#476—431no—
342#476—431no—
343#475—431no—
344#468—861no—
345#465—861no—
346#465—861no—
347#461—431no—
348#460—431no—
349#459—431no—
350#450—861no—
351#450—861no—
352#449—861no—
353C8×Q8—431no—
354C4×SD16—431no—
355C4×D8—861no—
356C4×D8C2×D4311yescharacteristic
357#436—431no—
358C8×D4C2×D4311yescharacteristic
359C8×D4C2×D4311yescharacteristic, complemented
360C2×#106—861no—
361C2×#102—861no—
362#334—431no—
363#334C2×D4311yescharacteristic, complemented
364#333—431no—
365#333—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8C2×D4311yescharacteristic
371D4⋊C8C2×D4311yescharacteristic, complemented
372#322C2×D4311yescharacteristic, complemented
373C43#1980611yescharacteristic, complemented, Sylow
374C2×#41—861no—
375C22×D4—861no—
376C22×D4—861no—
377AGL(1,ℤ/8)—1724no—
378C2×SD16—431no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×SD16—861no—
383C2×SD16—1721no—
384C2×D8—861no—
385C2×D8D17211yescharacteristic
386C2×M16—861no—
387C22×C8—21no—
388C22×C8—21no—
389C4⋊Q8—431no—
390C4⋊Q8—431no—
391C4⋊Q8—431no—
392#127—431no—
393#125—861no—
394#125—861no—
395#123—1721no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—1721no—
400C22⋊Q8—1721no—
401#121—861no—
402#121—861no—
403#121—861no—
404#120—1721no—
405C4×Q8—431no—
406C4×D4—431no—
407C4×D4—861no—
408C4×D4—861no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414#107—861no—
415#107—861no—
416#107D17211yescharacteristic
417#106—431no—
418#106—861no—
419#106—861no—
420#106—861no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—861no—
428C4⋊C8C22×D4311yescharacteristic
429C4⋊C8C22×D4311yescharacteristic
430#103—431no—
431#103—861no—
432#103—861no—
433#103—1721no—
434#102—431no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102D17211yescharacteristic
444#102D17211yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—861no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C4×C8C22×D4311yescharacteristic
452C24—1721no—
453#41—3441no—
454#41—1722no—
455C2×Q8—431no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×D4—431no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—3441no—
464C2×D4—3441no—
465C2×D4—1721no—
466C2×D4—1722no—
467C2×D4—1721no—
468C2×D4—1721no—
469C2×D4—1722no—
470C2×D4C2×D17211yescharacteristic
471C2×D4C2×D17211yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—861no—
475C22×C4—1721no—
476C22×C4—1721no—
477C22×C4—1721no—
478SD16—3441no—
479SD16—3442no—
480SD16—3441no—
481SD16—1721no—
482SD16—1722no—
483SD16—1722no—
484D8—1722no—
485D8#1062187314yescomplemented
486M16—1722no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—42no—
491C2×C8—81no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8C2×D17211yescharacteristic
495C2×C8C2×D17211yescharacteristic
496C2×C8D4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C4⋊C4C2×D17211yescharacteristic
513C4⋊C4C2×D17211yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—861no—
517C22⋊C4—1721no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—861no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—861no—
526C23—3442no—
527C23—3442no—
528C23—1721no—
529C23—6881no—
530Q8—861no—
531Q8—861no—
532Q8—3441no—
533Q8—3441no—
534Q8—1721no—
535Q8—1721no—
536D4—21no—
537D4—21no—
538D4—861no—
539D4—861no—
540D4—3441no—
541D4—3442no—
542D4—3442no—
543D4—3442no—
544D4—1721no—
545D4—1721no—
546D4—1721no—
547D4—1721no—
548D4C2×#1062187312yes—
549D4C2×#1062187312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—3442no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—6881no—
566C2×C4—6881no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×D17211yescharacteristic
569C2×C4#1306337111yescharacteristic
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—1721no—
577C8—1721no—
578C8C2×#1062187312yes—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—3441no—
586C22—3441no—
587C22—3441no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—6884no—
592C22D4×D17211yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—3441no—
597C4—3441no—
598C4—3441no—
599C4—1721no—
600C4—1721no—
601C4—1721no—
602C4C22×#1062187311yescharacteristic
603C4#1458369511yescharacteristic
604C4#1458370911yescharacteristic
605C4#1458371111yescharacteristic
606C2—42no—
607C2—42no—
608C2—3441no—
609C2—6881no—
610C2#1914612211yescharacteristic
611C2D4×#1062187311yescharacteristic
612C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1580C2
socleC22×C43D42
prime radical#19146196C2
hypercenter#1580D43
hypocenterC43#19806
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1580

Complements

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

NH ≅ G/Ntype
1. #19147460C2semidirect
2. #19146953C2semidirect
3. #19146420C2semidirect
5. #19134217C2semidirect
6. #19134119C2semidirect
7. #19134004C2semidirect
8. #19133970C2semidirect
9. #19133944C2semidirect
10. #19133804C2semidirect
11. #19133748C2semidirect
12. #19133713C2semidirect
13. #19133669C2semidirect
14. #19133440C2semidirect
15. C43×#1580C2semidirect
18. #14583606C22semidirect
21. #14583304C22semidirect
23. #14583297C22semidirect
26. #14583250C22semidirect
36. #14583189C22semidirect
37. #14583185C22semidirect
47. C8×Dic86C22semidirect
53. #14582650C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582644C22semidirect
58. #14582631C22semidirect
62. C8×D4×C43C22semidirect
63. C43×#334C22semidirect
65. C43×D4⋊C8C22semidirect
66. C43×#322C22semidirect
171. D8×C43SD16semidirect
314. #1580D43semidirect
359. C8×D4C2×D43semidirect
363. #334C2×D43semidirect
371. D4⋊C8C2×D43semidirect
372. #322C2×D43semidirect
373. C43#19806semidirect
485. D8#10621873semidirect

Maximal subgroups

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

subgroupindex
#191474602
#191469532
#191464202
#191461962
#191342172
#191341192
#191340042
#191339702
#191339442
#191338042
#191337482
#191337132
#191336692
#191334402
C43×#15802
#1980643