Finite Group Databasebeta

← #25082001

Subgroups — #25082001

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145537C211yesmaximal, characteristic, complemented
2#19144384C211yesmaximal, characteristic, complemented
3#19144070C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic, complemented
5#19134014C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19133944C211yesmaximal, characteristic, complemented
9#19133942C211yesmaximal, characteristic, complemented
10#19133936C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133364C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1677C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583454C2211yescharacteristic
18#127×D43C2211yescharacteristic
19C4×#10621900C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583271C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583209—21no—
24#14583201—21no—
25#14583191C2211yescharacteristic, complemented
26#14583185C2211yescharacteristic, complemented
27#14583179C2211yescharacteristic, complemented
28#14583100C2211yescharacteristic
29#14583098—21no—
30#14583098—21no—
31#14583098—21no—
32#14583096C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583092—21no—
35#14583051—21no—
36#14583051—21no—
37C8×Dic86C2211yescharacteristic, complemented
38#14583023C2211yescharacteristic, complemented
39D4×C43⋊C8C2211yescharacteristic, complemented
40C8×C22⋊D43—21no—
41(C22⋊D43)⋊C8—21no—
42#14582950C2211yescharacteristic
43#14582949—21no—
44#14582934—21no—
45#14582921C2211yescharacteristic
46C2×Dic43⋊C8—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582902—21no—
50#14582892—21no—
51#14582650C2211yescharacteristic, complemented
52#14582649C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, complemented
54#14582648C2211yescharacteristic, complemented
55#14582646C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#476C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#334C2211yescharacteristic, complemented
65C43×#333C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71#13063349—44no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621883—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621882—21no—
79C2×#10621872—21no—
80C22×C43⋊C8—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83#13063325C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063321—21no—
86#13063321—21no—
87#13063321—21no—
88#13063316—21no—
89#13063305—21no—
90#13063301—21no—
91Q8×Dic43—21no—
92C4×Dic86C2311yescharacteristic
93#13063290—21no—
94#13063290D411yescharacteristic
95D4×Dic43D411yescharacteristic
96C4×C22⋊D43—21no—
97(C22⋊D43)⋊C4—21no—
98#13063283—21no—
99#13063283D411yescharacteristic
100#13063281—21no—
101C2×C4×Dic43—21no—
102C42×D43C2311yescharacteristic
103#13063258—21no—
104#13063258—21no—
105#13063257—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116#13063250—21no—
117#13063248—21no—
118#13063247—21no—
119#13063246—21no—
120#13063246—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×D8×C43—21no—
131C22×C8×C43—21no—
132C4⋊Q8×C43C2311yescharacteristic
133#127×C43C2311yescharacteristic
134C4×D4×C43C2311yescharacteristic
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146C2×Q8×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621900—22no—
159#10621900SD1614yescomplemented
160D4×D43—42no—
161D4×D43—42no—
162D4×D43—81no—
163D4×D43—81no—
164D4×D43—82no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43#4111yescharacteristic
171C2×Dic86—21no—
172C2×Dic86C2×D411yescharacteristic
173D8×C43—42no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—81no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186#10621883—42no—
187#10621883—81no—
188#10621883—81no—
189#10621882—42no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—41no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212#10621873—42no—
213#10621873—81no—
214#10621873—81no—
215#10621872—42no—
216C8×D43—42no—
217C8×D43—81no—
218C23×C43—21no—
219C23×C43—41no—
220C22×D43—41no—
221C22×D43—82no—
222C22×D43—82no—
223C22×D43—82no—
224C22×D43#12111yescharacteristic
225Q8×C43—81no—
226D4×C43—21no—
227D4×C43—41no—
228D4×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—81no—
232D4×C43C2×SD1612yes—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—24no—
241C22⋊D43—82no—
242C22⋊D43—82no—
243C22⋊D43—82no—
244C2×Dic43—21no—
245C2×Dic43—24no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—81no—
249C2×Dic43#12111yescharacteristic
250C2×Dic43#12111yescharacteristic
251C2×Dic43#12111yescharacteristic
252D172—41no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—81no—
257C4×D43—21no—
258C4×D43—21no—
259C4×D43—41no—
260C4×D43C2×SD1612yes—
261C4×D43#13512yes—
262Dic86—21no—
263Dic86—41no—
264Dic86—41no—
265Dic86C2×SD1612yes—
266C8×C43—21no—
267C8×C43—21no—
268C8×C43—41no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—21no—
272C43⋊C8—21no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#19409—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43C2×#12111yescharacteristic
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—164no—
290C2×D43#46512yes—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43C22×SD1611yescharacteristic
295C4×C43C2×#13511yescharacteristic
296C4×C43#57611yescharacteristic
297C4×C43#57711yescharacteristic
298Dic43—21no—
299Dic43—22no—
300Dic43—21no—
301Dic43—41no—
302Dic43—81no—
303Dic43#46512yes—
304#3208—431no—
305#3076—431no—
306#3038—431no—
307#2988—431no—
308#1678—431no—
309#1678—431no—
310#1677—431no—
311#1677D4311yescharacteristic, complemented
312#1666—431no—
313#1666—431no—
314#1665—431no—
315#1665—431no—
316#1570—431no—
317#1550—431no—
318C2×#331—431no—
319C2×C43—42no—
320C2×C43—161no—
321C2×C43#304511yescharacteristic
322C2×C43C2×#46511yescharacteristic
323C2×C43#306811yescharacteristic
324D43—22no—
325D43—161no—
326C2×AGL(1,ℤ/8)—861no—
327#533—431no—
328C2×#127—431no—
329C4×#41—431no—
330#492—431no—
331#492—431no—
332#486—431no—
333#486C2×D4311yescharacteristic
334#479—861no—
335#478—861no—
336#477—431no—
337#476C2×D4311yescharacteristic, complemented
338#475—431no—
339#474—431no—
340#460—431no—
341#460—431no—
342#460—861no—
343#460—861no—
344#460—861no—
345#459—431no—
346#459—861no—
347#459C2×D4311yescharacteristic
348#450—861no—
349#450—861no—
350C8×Q8—431no—
351C8×Q8—431no—
352C8×D4—431no—
353C8×D4—861no—
354C8×D4—861no—
355C8×D4C2×D4311yescharacteristic, complemented
356#431—431no—
357#431—861no—
358#427—861no—
359#423—431no—
360C2×C4⋊C8—431no—
361C2×C4⋊C8—431no—
362C2×C4⋊C8—861no—
363#418—861no—
364#416—861no—
365#334—431no—
366#334—431no—
367#334—431no—
368#334C2×D4311yescharacteristic, complemented
369#333—431no—
370#333C2×D4311yescharacteristic, complemented
371#332—431no—
372#332—431no—
373#331—431no—
374#331—431no—
375#331—431no—
376#331C2×D4311yescharacteristic
377C43#1940911yescharacteristic, complemented, Sylow
378C2×#41—431no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—861no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16—861no—
389C2×D8—21no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—21no—
393C22×C8—861no—
394C22×C8—861no—
395C22×C8—861no—
396C4⋊Q8—431no—
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#127—861no—
400#127—861no—
401#127—861no—
402#127C22×D4311yescharacteristic
403#125—861no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406C4×Q8—431no—
407C4×Q8—431no—
408C4×Q8—861no—
409C4×Q8—861no—
410C4×D4—431no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4C22×D4311yescharacteristic
414#117—431no—
415#117—861no—
416#117—861no—
417C2×C42—431no—
418C2×C42—861no—
419#107—861no—
420#107—861no—
421#106—21no—
422#106—861no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8C22×D4311yescharacteristic
434C4⋊C8C22×D4311yescharacteristic
435C4⋊C8C22×D4311yescharacteristic
436#103—861no—
437#103—861no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448C22⋊C8—21no—
449C22⋊C8—431no—
450C22⋊C8—431no—
451C22⋊C8—861no—
452C4×C8—431no—
453C4×C8—861no—
454C4×C8—861no—
455C4×C8C22×D4311yescharacteristic
456C24—1721no—
457#41—434no—
458#41—862no—
459C2×Q8—21no—
460C2×Q8—431no—
461C2×Q8—861no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—3441no—
470C2×D4—3441no—
471C2×D4—3442no—
472C2×D4—1722no—
473C2×D4—1722no—
474C2×D4—1721no—
475C2×D4—1721no—
476C2×D4—1721no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—861no—
483C22×C4—861no—
484SD16—3441no—
485SD16—3441no—
486SD16—3441no—
487SD16—3441no—
488SD16—1722no—
489SD16—1722no—
490D8—42no—
491D8—1722no—
492M16—1722no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—81no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8—3441no—
504C2×C8—1722no—
505C2×C8D4×D4311yescharacteristic
506C2×C8D4×D4311yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—431no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1721no—
515C4⋊C4—1721no—
516C4⋊C4D4×D4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—1721no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—861no—
525C42—861no—
526C42—861no—
527C42—1721no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—41no—
531C23—431no—
532C23—3442no—
533C23—3442no—
534C23—3442no—
535C23—1721no—
536Q8—81no—
537Q8—432no—
538Q8—861no—
539Q8—1721no—
540Q8—1721no—
541D4—21no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—864no—
548D4—3441no—
549D4—3442no—
550D4—3442no—
551D4—3442no—
552D4—1721no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4SD16×D4312yes—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—431no—
562C2×C4—432no—
563C2×C4—432no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—864no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3441no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—861no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—432no—
594C22—861no—
595C22—861no—
596C22—3441no—
597C22—3441no—
598C22—3441no—
599C22—6884no—
600C22#121×D4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—81no—
604C4—432no—
605C4—861no—
606C4—861no—
607C4—862no—
608C4—3441no—
609C4—1721no—
610C4C2×SD16×D4311yescharacteristic
611C4#135×D4311yescharacteristic
612C4#1458370311yescharacteristic
613C4#1458370611yescharacteristic
614C2—42no—
615C2—161no—
616C2—862no—
617C2—6881no—
618C2#1914413511yescharacteristic
619C2#465×D4311yescharacteristic
620C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1677C2
socleC22×C43C2×#121
prime radical#19144070C2
hypercenter#1677D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1677

Complements

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

NH ≅ G/Ntype
1. #19145537C2semidirect
2. #19144384C2semidirect
4. #19143702C2semidirect
5. #19134014C2semidirect
6. #19134008C2semidirect
7. #19134006C2semidirect
8. #19133944C2semidirect
9. #19133942C2semidirect
10. #19133936C2semidirect
11. #19133934C2semidirect
12. #19133364C2semidirect
13. #19133282C2semidirect
14. #331×D43C2semidirect
15. C43×#1677C2semidirect
25. #14583191C22semidirect
26. #14583185C22semidirect
27. #14583179C22semidirect
37. C8×Dic86C22semidirect
38. #14583023C22semidirect
39. D4×C43⋊C8C22semidirect
51. #14582650C22semidirect
52. #14582649C22semidirect
53. #14582649C22semidirect
54. #14582648C22semidirect
55. #14582646C22semidirect
56. #14582644C22semidirect
61. C43×#476C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#334C22semidirect
65. C43×#333C22semidirect
159. #10621900SD16semidirect
311. #1677D43semidirect
337. #476C2×D43semidirect
355. C8×D4C2×D43semidirect
368. #334C2×D43semidirect
370. #333C2×D43semidirect
377. C43#19409semidirect

Maximal subgroups

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

subgroupindex
#191455372
#191443842
#191440702
#191437022
#191340142
#191340082
#191340062
#191339442
#191339422
#191339362
#191339342
#191333642
#191332822
#331×D432
C43×#16772
#1940943