Finite Group Databasebeta

← #25080168

Subgroups — #25080168

Order 11008.

722 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#19145909C211yesmaximal, characteristic, complemented
2#19145535C211yesmaximal, characteristic, complemented
3#19145046C211yesmaximal, characteristic
4#19143537C211yesmaximal, characteristic, complemented
5#19134077C211yesmaximal, characteristic, complemented
6#19134076C211yesmaximal, characteristic, complemented
7#19134068C211yesmaximal, characteristic, complemented
8#19134065C211yesmaximal, characteristic, complemented
9#19133954C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133942C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133241C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1668C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×#13063349—21no—
18#14583453C2211yescharacteristic
19#14583447C2211yescharacteristic
20#127×D43C2211yescharacteristic
21#14583287—21no—
22#14583287—21no—
23#14583275C2211yescharacteristic
24#14583272C2211yescharacteristic
25#14583271C2211yescharacteristic
26#14583270—21no—
27#14583244—21no—
28#14583187—21no—
29#14583185C2211yescharacteristic, complemented
30#14583184C2211yescharacteristic, complemented
31#14583127—21no—
32#14583125—21no—
33#14583102—21no—
34#14583100C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583096C2211yescharacteristic, complemented
38#14583051—21no—
39#14583048—21no—
40#14583030C2211yescharacteristic, complemented
41#14583029—21no—
42#14583029C2211yescharacteristic, complemented
43#14583028—21no—
44#14583023C2211yescharacteristic, complemented
45#14582951C2211yescharacteristic
46#14582924—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582853—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic, complemented
52#14582650C2211yescharacteristic, complemented
53#14582649C2211yescharacteristic, 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×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71#13063349—44no—
72#13063349—44no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621883—21no—
80C2×#10621884—21no—
81C2×#10621882—21no—
82C2×#10621882—21no—
83C2×#10621872D411yescharacteristic
84C2×#10621872D411yescharacteristic
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063325C2311yescharacteristic
88#13063324D411yescharacteristic
89#13063323D411yescharacteristic
90#13063322C2311yescharacteristic
91#13063321—21no—
92#13063321—21no—
93#13063321—21no—
94#13063315—21no—
95#13063312—21no—
96#13063305D411yescharacteristic
97#13063303—21no—
98#13063301D411yescharacteristic
99#13063296—21no—
100#13063296—21no—
101C4×Dic86—21no—
102C4×Dic86C2311yescharacteristic
103D4×Dic43—21no—
104D4×Dic43—21no—
105#13063282—21no—
106C42×D43C2311yescharacteristic
107#13063257—21no—
108#13063256—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063250—21no—
118#13063249—21no—
119#13063247—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123(C2×D43)⋊C8—21no—
124#13063236—21no—
125#13063235—21no—
126#13063235D411yescharacteristic
127#13063235D411yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
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—
159#10621900—42no—
160#10621900—42no—
161D4×D43—42no—
162D4×D43—42no—
163D4×D43—81no—
164D4×D43—81no—
165D4×D43—82no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×C4×D43#4111yescharacteristic
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86C2×D411yescharacteristic
175SD16×C43—81no—
176SD16×C43—81no—
177D8×C43—42no—
178D8×C43—42no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2×D411yescharacteristic
186C42×C43—21no—
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189C22⋊Dic43—41no—
190#10621884—81no—
191#10621883—42no—
192#10621883—42no—
193#10621883—81no—
194#10621883—81no—
195#10621882—42no—
196#10621882—42no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—21no—
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208C4×Dic43—21no—
209C4×Dic43C2×D411yescharacteristic
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43#4111yescharacteristic
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D411yescharacteristic
216C2×C43⋊C8C2×D411yescharacteristic
217#10621873—42no—
218#10621873—42no—
219#10621873—81no—
220#10621872—22no—
221#10621872SD1614yescomplemented
222C8×D43—42no—
223C8×D43—81no—
224C23×C43—41no—
225C23×C43—41no—
226C22×D43—41no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43—82no—
230C22×D43#12111yescharacteristic
231Q8×C43—21no—
232Q8×C43—21no—
233D4×C43—41no—
234D4×C43—41no—
235D4×C43—41no—
236D4×C43—41no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—81no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—82no—
249C22⋊D43—82no—
250C22⋊D43—82no—
251C22⋊D43—82no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—82no—
256C2×Dic43#12111yescharacteristic
257C2×Dic43#12111yescharacteristic
258C2×Dic43#12111yescharacteristic
259D172—41no—
260D172—41no—
261D172—41no—
262D172—41no—
263D172—81no—
264C4×D43—21no—
265C4×D43—21no—
266C4×D43—41no—
267C4×D43C2×SD1612yes—
268C4×D43AGL(1,ℤ/8)12yes—
269Dic86—21no—
270Dic86—21no—
271Dic86—41no—
272Dic86—41no—
273Dic86—81no—
274C8×C43—21no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C8×C43C2×SD1612yes—
279C43⋊C8—21no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283C43⋊C8C2×SD1612yes—
284#19238—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#46012yes—
299C4×C43—21no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43C22×SD1611yescharacteristic
303C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C43#57611yescharacteristic
305C4×C43#57711yescharacteristic
306Dic43—21no—
307Dic43—21no—
308Dic43—41no—
309Dic43—41no—
310Dic43—81no—
311Dic43#46012yes—
312#3246—431no—
313#3208—431no—
314#3151—431no—
315#2962—431no—
316#1688—431no—
317#1688—431no—
318#1686—431no—
319#1686—431no—
320#1668—431no—
321#1668D4311yescharacteristic, complemented
322#1666—431no—
323#1666—431no—
324#1565—431no—
325#1540—431no—
326C2×#331—431no—
327C2×C43—161no—
328C2×C43—161no—
329C2×C43C2×#46011yescharacteristic
330C2×C43#306211yescharacteristic
331C2×C43#306811yescharacteristic
332D43—22no—
333D43—161no—
334C2×AGL(1,ℤ/8)—861no—
335C2×AGL(1,ℤ/8)—861no—
336#533—431no—
337#532—431no—
338C2×#127—431no—
339#496—861no—
340#496—861no—
341#493—431no—
342#493C2×D4311yescharacteristic
343#492—431no—
344#492—431no—
345#492—861no—
346#486—861no—
347#476—861no—
348#475—431no—
349#475—431no—
350#465—861no—
351#465—861no—
352#461—861no—
353#460—431no—
354#460—431no—
355#460—431no—
356#460—431no—
357#460C2×D4311yescharacteristic
358#460C2×D4311yescharacteristic, complemented
359#450—861no—
360#450—861no—
361#446—431no—
362#446—431no—
363#446—861no—
364#446—861no—
365C8×Q8—431no—
366C8×Q8C2×D4311yescharacteristic, complemented
367#431—431no—
368#424—861no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8—431no—
371#405—861no—
372C4×M16—431no—
373#335—431no—
374#335C2×D4311yescharacteristic, complemented
375#334—431no—
376#334—431no—
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#1923811yescharacteristic, complemented, Sylow
386C2×#41—861no—
387C22×D4—861no—
388C22×D4—861no—
389C22×D4—861no—
390AGL(1,ℤ/8)—1724no—
391AGL(1,ℤ/8)—1724no—
392C2×SD16—21no—
393C2×SD16—21no—
394C2×SD16—861no—
395C2×SD16—861no—
396C2×SD16—861no—
397C2×SD16—861no—
398C2×SD16—861no—
399C2×SD16—861no—
400C2×SD16—861no—
401C2×SD16—861no—
402C2×D8—21no—
403C2×D8—21no—
404C2×D8—861no—
405C2×D8—861no—
406C2×M16—431no—
407C2×M16—431no—
408C22×C8—861no—
409C22×C8—861no—
410C4⋊Q8—431no—
411C4⋊Q8—431no—
412C4⋊Q8—431no—
413#127—431no—
414#127—861no—
415#127—861no—
416#127—861no—
417#127C22×D4311yescharacteristic
418#127C22×D4311yescharacteristic
419#125—861no—
420#124—861no—
421C22⋊Q8—431no—
422C22⋊Q8—431no—
423C22⋊Q8—861no—
424#121—861no—
425#121—861no—
426C4×Q8—431no—
427C4×Q8—861no—
428C4×Q8C22×D4311yescharacteristic
429C4×D4—861no—
430C4×D4—861no—
431#117—861no—
432C2×C42—431no—
433#106—861no—
434#106—861no—
435C4⋊C8—21no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—861no—
440C4⋊C8—861no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443C4⋊C8—861no—
444C4⋊C8C22×D4311yescharacteristic
445C4⋊C8C22×D4311yescharacteristic
446C4⋊C8C22×D4311yescharacteristic
447#103—861no—
448#103—861no—
449#102—21no—
450#102—21no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455C22⋊C8—861no—
456#97—431no—
457#97—431no—
458#97—861no—
459#97—861no—
460C4×C8—21no—
461C4×C8—431no—
462C4×C8—861no—
463C4×C8—861no—
464C4×C8C22×D4311yescharacteristic
465C24—1721no—
466#41—1722no—
467#41—1722no—
468C2×Q8—431no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8D4×D4311yescharacteristic
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—3441no—
482C2×D4—3441no—
483C2×D4—3442no—
484C2×D4—1722no—
485C2×D4—1722no—
486C2×D4—1721no—
487C2×D4—1721no—
488C2×D4—1721no—
489C2×D4—1721no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—1721no—
494SD16—81no—
495SD16—81no—
496SD16—3441no—
497SD16—3441no—
498SD16—3441no—
499SD16—3441no—
500SD16—1722no—
501SD16—1722no—
502SD16—1722no—
503SD16—1722no—
504D8—42no—
505D8—42no—
506D8—1722no—
507D8—1722no—
508M16—434no—
509M16—862no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—3441no—
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⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4D4×D4311yescharacteristic
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—1721no—
536C22⋊C4—1721no—
537C42—21no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—861no—
542C42C23×D4311yescharacteristic
543C23—41no—
544C23—41no—
545C23—431no—
546C23—3442no—
547C23—3442no—
548C23—3442no—
549C23—1721no—
550Q8—21no—
551Q8—21no—
552Q8—861no—
553Q8—861no—
554Q8—3441no—
555Q8—1721no—
556Q8—1721no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—81no—
566D4—81no—
567D4—3441no—
568D4—3442no—
569D4—3442no—
570D4—3442no—
571D4—3442no—
572D4—1721no—
573D4—1721no—
574D4—1721no—
575D4—1721no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—431no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—431no—
582C2×C4—431no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3442no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×D4×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C8—21no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—432no—
598C8—861no—
599C8—1721no—
600C8—1721no—
601C8—1721no—
602C8SD16×D4312yes—
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—41no—
619C4—41no—
620C4—432no—
621C4—861no—
622C4—861no—
623C4—3441no—
624C4—1721no—
625C4—1721no—
626C4C2×SD16×D4311yescharacteristic
627C4AGL(1,ℤ/8)×D4311yescharacteristic
628C4#1458370011yescharacteristic
629C4#1458370611yescharacteristic
630C2—161no—
631C2—161no—
632C2—862no—
633C2—6881no—
634C2#460×D4311yescharacteristic
635C2#1914427411yescharacteristic
636C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1668C2
socleC22×C43C2×#121
prime radical#19145046C2
hypercenter#1668D43
hypocenterC43#19238
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #19145909C2semidirect
2. #19145535C2semidirect
4. #19143537C2semidirect
5. #19134077C2semidirect
6. #19134076C2semidirect
7. #19134068C2semidirect
8. #19134065C2semidirect
9. #19133954C2semidirect
10. #19133943C2semidirect
11. #19133942C2semidirect
12. #19133346C2semidirect
13. #19133241C2semidirect
14. #331×D43C2semidirect
15. C43×#1668C2semidirect
29. #14583185C22semidirect
30. #14583184C22semidirect
37. #14583096C22semidirect
40. #14583030C22semidirect
42. #14583029C22semidirect
44. #14583023C22semidirect
51. #14582651C22semidirect
52. #14582650C22semidirect
53. #14582649C22semidirect
54. #14582646C22semidirect
55. #14582644C22semidirect
57. #14582643C22semidirect
62. C43×#460C22semidirect
63. C8×Q8×C43C22semidirect
64. C43×#335C22semidirect
66. C43×#331C22semidirect
221. #10621872SD16semidirect
321. #1668D43semidirect
358. #460C2×D43semidirect
366. C8×Q8C2×D43semidirect
374. #335C2×D43semidirect
384. #331C2×D43semidirect
385. C43#19238semidirect

Maximal subgroups

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

subgroupindex
#191459092
#191455352
#191450462
#191435372
#191340772
#191340762
#191340682
#191340652
#191339542
#191339432
#191339422
#191333462
#191332412
#331×D432
C43×#16682
#1923843