Finite Group Databasebeta

← #25087895

Subgroups — #25087895

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147226C211yesmaximal, characteristic, complemented
2#19146408C211yesmaximal, characteristic, complemented
3#19146242C211yesmaximal, characteristic, complemented
4#19134200C211yesmaximal, characteristic, complemented
5#19134084C211yesmaximal, characteristic, complemented
6#19134071C211yesmaximal, characteristic, complemented
7#19134037C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19133788C211yesmaximal, characteristic, complemented
10#19133774C211yesmaximal, characteristic, complemented
11#19133696C211yesmaximal, characteristic, complemented
12#19133682C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14SD16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3274C211yesmaximal, characteristic, complemented
16C2×#13063354—21no—
17Q8×D172C2211yescharacteristic, complemented
18#14583553C2211yescharacteristic
19#14583279C2211yescharacteristic, complemented
20#14583245—21no—
21#14583245C2211yescharacteristic
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583210—21no—
26#14583179—21no—
27#14583179C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583158—21no—
30#14583133—21no—
31#14583109C2211yescharacteristic, complemented
32#14583104C2211yescharacteristic
33#14583091—21no—
34#14583091C2211yescharacteristic
35#14583091C2211yescharacteristic, complemented
36#14583062—21no—
37#14583056—21no—
38#14583033—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621882—21no—
41C4×#10621882C2211yescharacteristic
42#14582978C2211yescharacteristic, complemented
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063246—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582646C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic
50#14582643C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#550C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#493C2211yescharacteristic
60C43×#469—21no—
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C43×#447—21no—
65C4×SD16×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69#13063354—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621885—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882D411yescharacteristic
77C2×#10621872—21no—
78C22×C43⋊C8—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063309—41no—
83#13063305—21no—
84#13063305—21no—
85#13063305—41no—
86#13063299—21no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C2×C4⋊Dic43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258D411yescharacteristic
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063246—41no—
109#13063246D411yescharacteristic
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119AGL(1,ℤ/8)×C43—44no—
120C2×SD16×C43—21no—
121C2×SD16×C43D411yescharacteristic
122C2×D8×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43—21no—
125C2×M16×C43—21no—
126#127×C43—21no—
127#127×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—41no—
133#120×C43—41no—
134C4×Q8×C43C2311yescharacteristic
135C4×D4×C43—21no—
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138#106×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43D411yescharacteristic
141#102×C43—21no—
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147#41×C43—42no—
148#41×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43C2×D411yescharacteristic
165C2×D4×C43C2×D411yescharacteristic
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C2×C22⋊D43—41no—
170C22×Dic43—41no—
171Q8×D43—42no—
172Q8×D43—81no—
173#10621900—42no—
174#10621900—81no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×C4×D43—41no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—41no—
181SD16×C43—42no—
182SD16×C43D814yescomplemented
183D8×C43—42no—
184D8×C43—42no—
185D8×C43—81no—
186M16×C43—42no—
187C2×C8×C43—21no—
188C2×C8×C43C2×D411yescharacteristic
189C2×C8×C43C2×D411yescharacteristic
190C4⋊C4×C43—21no—
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—41no—
197C22⋊C4×C43—41no—
198C42×C43—21no—
199C42×C43C2411yescharacteristic
200#10621885—42no—
201#10621883—42no—
202#10621882—41no—
203#10621882—42no—
204#10621882—81no—
205(C2×D43)⋊C4—21no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—41no—
213C4⋊Dic43—41no—
214C4⋊Dic43C2×D411yescharacteristic
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—81no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222Dic172—42no—
223Dic172—81no—
224#10621872—42no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—82no—
230C23×C43—82no—
231C23×C43—161no—
232C22×D43—21no—
233Q8×C43—21no—
234Q8×C43C2×D812yes—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—21no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—82no—
247D4×C43—81no—
248D4×C43—81no—
249D4×C43—82no—
250D4×C43—82no—
251D4×C43—161no—
252D4×C43C2×D812yes—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—82no—
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C22⋊D43—82no—
266C2×Dic43—21no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—82no—
270D172—21no—
271D172—21no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—82no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86—82no—
280C8×C43—21no—
281C8×C43—41no—
282C8×C43C2×D812yes—
283C43⋊C8—21no—
284C43⋊C8—21no—
285C43⋊C8—41no—
286C43⋊C8—41no—
287C43⋊C8—41no—
288C43⋊C8—41no—
289#19886—431nomaximal, Sylow
290C22×C43—22no—
291C22×C43—41no—
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—41no—
296C22×C43—81no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—164no—
303C22×C43D4211yescharacteristic
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C4×C43—22no—
308C4×C43—21no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43C22×D811yescharacteristic
313C4×C43#57511yescharacteristic
314C4×C43#57611yescharacteristic
315C4×C43#57711yescharacteristic
316Dic43—41no—
317Dic43—81no—
318Dic43—81no—
319#3358—431no—
320#3294—431no—
321#3276—431no—
322#3274D4311yescharacteristic, complemented
323#1709—431no—
324#1689—431no—
325#1687—431no—
326#1682—431no—
327#1681—431no—
328#1641—431no—
329#1639—431no—
330#1627—431no—
331#1625—431no—
332#1589—431no—
333C8×SD16—431no—
334C2×C43—42no—
335C2×C43—81no—
336C2×C43—161no—
337C2×C43—161no—
338C2×C43#327511yescharacteristic
339C2×C43D4×D811yescharacteristic
340C2×C43#329011yescharacteristic
341D43—81no—
342C2×#137—861no—
343C2×AGL(1,ℤ/8)—21no—
344#550C2×D4311yescharacteristic
345D4×Q8—431no—
346#547—431no—
347D42C2×D4311yescharacteristic
348#494—431no—
349#493C2×D4311yescharacteristic
350#486—431no—
351#486—431no—
352#486—431no—
353#486—431no—
354#486—861no—
355#480—861no—
356#474—431no—
357#474—431no—
358#474—861no—
359#470—861no—
360#469—21no—
361#466—861no—
362#462—431no—
363#461—431no—
364#460C2×D4311yescharacteristic
365#459—431no—
366#459—431no—
367#459—861no—
368#459C2×D4311yescharacteristic
369#452—861no—
370#451—861no—
371#449—21no—
372#447—21no—
373#447—861no—
374C8×Q8—431no—
375C4×SD16C2×D4311yescharacteristic
376C4×D8—431no—
377C4×D8—861no—
378#436—431no—
379#436C2×D4311yescharacteristic
380C8×D4—431no—
381C2×#102—861no—
382#335—431no—
383#334—431no—
384#332—431no—
385#332—431no—
386#331—431no—
387#331—431no—
388Q8⋊C8—431no—
389D4⋊C8—431no—
390D4⋊C8—431no—
391D4⋊C8—431no—
392C82—431no—
393C43#1988611yescharacteristic, complemented, Sylow
394C2×#41—21no—
395C2×#41—861no—
396C22×Q8—861no—
397C22×D4—21no—
398C22×D4—21no—
399#137—1724no—
400AGL(1,ℤ/8)—44no—
401C2×Q16—861no—
402C2×Q16—861no—
403C2×Q16—861no—
404C2×SD16—21no—
405C2×SD16—861no—
406C2×SD16C22⋊D4311yescharacteristic
407C2×D8—21no—
408C2×D8—21no—
409C2×D8—21no—
410C2×D8—431no—
411C2×D8—861no—
412C2×D8—861no—
413C2×M16—21no—
414C2×M16—861no—
415C22×C8—861no—
416C4⋊Q8—431no—
417C4⋊Q8—431no—
418C4⋊Q8—861no—
419#127—21no—
420#127C22×D4311yescharacteristic
421#127C22×D4311yescharacteristic
422#123—1721no—
423C22⋊Q8—861no—
424C22⋊Q8—861no—
425C22⋊Q8—1721no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—41no—
430#121—861no—
431#120—41no—
432C4×Q8C22×D4311yescharacteristic
433C4×D4—21no—
434C4×D4—431no—
435C4×D4—861no—
436C4×D4C22×D4311yescharacteristic
437C4×D4C22×D4311yescharacteristic
438C2×C4⋊C4—861no—
439#107—431no—
440#107—861no—
441#107—861no—
442#106C22⋊D4311yescharacteristic
443C4⋊C8—431no—
444C4⋊C8—431no—
445C4⋊C8—431no—
446C4⋊C8—861no—
447C4⋊C8C22×D4311yescharacteristic
448#103—861no—
449#103—861no—
450#103C22⋊D4311yescharacteristic
451#102—21no—
452#102—21no—
453#102—431no—
454#102—431no—
455#102—861no—
456#102—861no—
457#102—861no—
458#102—861no—
459#102—861no—
460#102—861no—
461#102—861no—
462#102—861no—
463#102—1721no—
464#102—1721no—
465#102C22⋊D4311yescharacteristic
466C22⋊C8—21no—
467C22⋊C8—861no—
468C22⋊C8—861no—
469C4×C8—431no—
470C4×C8—431no—
471C4×C8—861no—
472C4×C8C22×D4311yescharacteristic
473C24—41no—
474#41—42no—
475#41—81no—
476#41—3441no—
477#41—1722no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—3441no—
481C2×Q8—1721no—
482C2×Q8—1722no—
483C2×Q8C2×C22⋊D4311yescharacteristic
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4—431no—
499C2×D4—1721no—
500C2×D4D4×D4311yescharacteristic
501C2×D4C2×C22⋊D4311yescharacteristic
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—861no—
506C22×C4—1721no—
507C22×C4—1721no—
508Q16—3441no—
509Q16—1722no—
510Q16—1722no—
511SD16—42no—
512SD16—1722no—
513SD16#1062188214yescomplemented
514D8—42no—
515D8—42no—
516D8—81no—
517D8—3441no—
518D8—1721no—
519D8—1722no—
520M16—42no—
521M16—1722no—
522C2×C8—21no—
523C2×C8—431no—
524C2×C8—431no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—3441no—
530C2×C8C2×C22⋊D4311yescharacteristic
531C2×C8C2×C22⋊D4311yescharacteristic
532C4⋊C4—21no—
533C4⋊C4—431no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1721no—
539C4⋊C4—1721no—
540C4⋊C4D4×D4311yescharacteristic
541C4⋊C4C2×C22⋊D4311yescharacteristic
542C4⋊C4C2×C22⋊D4311yescharacteristic
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—861no—
548C22⋊C4—1721no—
549C22⋊C4—1721no—
550C42—21no—
551C42C23×D4311yescharacteristic
552C23—21no—
553C23—21no—
554C23—41no—
555C23—41no—
556C23—82no—
557C23—82no—
558C23—161no—
559C23—861no—
560Q8—21no—
561Q8—3442no—
562Q8—1721no—
563Q8—1721no—
564Q8—1721no—
565Q8—1721no—
566Q8C2×#1062188212yes—
567D4—21no—
568D4—21no—
569D4—21no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—82no—
579D4—81no—
580D4—81no—
581D4—82no—
582D4—82no—
583D4—161no—
584D4—861no—
585D4—861no—
586D4—3442no—
587D4C2×#1062188212yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—82no—
597C2×C4—861no—
598C2×C4—3442no—
599C2×C4—3442no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4C22×C22⋊D4311yescharacteristic
606C2×C4#1306337011yescharacteristic
607C8—21no—
608C8—41no—
609C8—861no—
610C8—861no—
611C8—1721no—
612C8—1721no—
613C8—1721no—
614C8—1721no—
615C8C2×#1062188212yes—
616C22—22no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—164no—
629C22—1721no—
630C22—1721no—
631C22—1721no—
632C22D4×C22⋊D4311yescharacteristic
633C4—22no—
634C4—21no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—3441no—
639C4—3441no—
640C4—1721no—
641C4C22×#1062188211yescharacteristic
642C4#1458369511yescharacteristic
643C4#1458370211yescharacteristic
644C4#1458370911yescharacteristic
645C2—42no—
646C2—81no—
647C2—161no—
648C2—161no—
649C2—3441no—
650C2#1914622611yescharacteristic
651C2D4×#1062188211yescharacteristic
652C2#1914637711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3274C2
socleC22×C43D42
hypercenter#3274D43
hypocenterC43#19886
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3274

Complements

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

NH ≅ G/Ntype
1. #19147226C2semidirect
2. #19146408C2semidirect
3. #19146242C2semidirect
4. #19134200C2semidirect
5. #19134084C2semidirect
6. #19134071C2semidirect
7. #19134037C2semidirect
8. #19134030C2semidirect
9. #19133788C2semidirect
10. #19133774C2semidirect
11. #19133696C2semidirect
12. #19133682C2semidirect
13. #19133478C2semidirect
14. SD16×C43⋊C8C2semidirect
15. C43×#3274C2semidirect
17. Q8×D172C22semidirect
19. #14583279C22semidirect
23. #14583245C22semidirect
24. #14583245C22semidirect
31. #14583109C22semidirect
35. #14583091C22semidirect
39. Q8×C43⋊C8C22semidirect
42. #14582978C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582646C22semidirect
48. #14582646C22semidirect
50. #14582643C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
182. SD16×C43D8semidirect
322. #3274D43semidirect
393. C43#19886semidirect
513. SD16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191472262
#191464082
#191462422
#191342002
#191340842
#191340712
#191340372
#191340302
#191337882
#191337742
#191336962
#191336822
#191334782
SD16×C43⋊C82
C43×#32742
#1988643