Finite Group Databasebeta

← #25087937

Subgroups — #25087937

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147490C211yesmaximal, characteristic, complemented
2#19146954C211yesmaximal, characteristic, complemented
3#19146191C211yesmaximal, characteristic
4#19134181C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134065C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133933C211yesmaximal, characteristic, complemented
9#19133877C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133711C211yesmaximal, characteristic, complemented
12#19133666C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15D4×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063351—21no—
17#14583609C2211yescharacteristic, complemented
18#14583554C2211yescharacteristic
19#14583305—21no—
20#14583297C2211yescharacteristic, complemented
21#14583295C2211yescharacteristic, complemented
22#14583295C2211yescharacteristic, complemented
23#14583271C2211yescharacteristic
24#14583271C2211yescharacteristic
25#14583228—21no—
26#14583216—21no—
27#14583199—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583186—21no—
31#14583184C2211yescharacteristic, complemented
32#14583176C2211yescharacteristic, complemented
33#14583143—21no—
34#14583125—21no—
35#14583104C2211yescharacteristic
36#14583091C2211yescharacteristic
37#14583050—21no—
38#14583042—21no—
39#14583030C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621882C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic, complemented
44#106×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582644C2211yescharacteristic, complemented
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C22×SD16×C43—21no—
57D4×Q8×C43C2211yescharacteristic
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#465—21no—
61C43×#461C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C43×#450—21no—
64C43×#448—21no—
65C4×SD16×C43C2211yescharacteristic
66C8×D4×C43C2211yescharacteristic
67C2×#10621898—21no—
68#13063351—44no—
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—41no—
73C2×#10621882—21no—
74C2×#10621882D411yescharacteristic
75C2×#10621877—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063317—21no—
80#13063307—41no—
81#13063304—21no—
82#13063303—41no—
83#13063301—21no—
84#13063296—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C4⋊C4×D43—21no—
88C4⋊C4×D43—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—41no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103#13063249—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C22×Q8×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119C2×SD16×C43—21no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—44no—
124C2×SD16×C43D411yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—41no—
131#121×C43—21no—
132#121×C43—21no—
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×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43—21no—
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—41no—
166C2×C22⋊D43—41no—
167#10621898—42no—
168#10621898—81no—
169C2×D172C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—41no—
172C2×C4×D43—41no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175SD16×C43—22no—
176SD16×C43—42no—
177SD16×C43—42no—
178SD16×C43—42no—
179SD16×C43—81no—
180C2×C8×C43—21no—
181C2×C8×C43—42no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—41no—
194C22⋊C4×C43—41no—
195C42×C43—21no—
196C42×C43C2411yescharacteristic
197C22⋊Dic43—41no—
198#10621883—42no—
199#10621883—42no—
200#10621883—81no—
201#10621883—82no—
202#10621882—42no—
203#10621882SD1614yescomplemented
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—41no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43C2×D411yescharacteristic
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214#10621877—42no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C2×D411yescharacteristic
220C2×C43⋊C8C2×D411yescharacteristic
221C8×D43—42no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—82no—
226C23×C43—82no—
227C23×C43—161no—
228C22×D43—21no—
229Q8×C43—21no—
230Q8×C43—21no—
231Q8×C43—41no—
232Q8×C43—41no—
233Q8×C43—82no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—21no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—81no—
242D4×C43—82no—
243D4×C43—82no—
244D4×C43C2×SD1612yes—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—82no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C22⋊D43—82no—
259C2×Dic43—21no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262D172—21no—
263D172C2×SD1612yescomplemented
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—82no—
267C4×D43—161no—
268Dic86—41no—
269Dic86—41no—
270Dic86—81no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43AGL(1,ℤ/8)12yescomplemented
274C43⋊C8—22no—
275C43⋊C8—21no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8C2×SD1612yescomplemented
280#19890—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—164no—
291C22×C43D4211yescharacteristic
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C4×C43—21no—
296C4×C43—41no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—81no—
301C4×C43C22×SD1611yescharacteristic
302C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C43#57711yescharacteristic
304C4×C43#57711yescharacteristic
305Dic43—41no—
306Dic43—81no—
307Dic43—81no—
308#3384—431no—
309#3335—431no—
310D4×SD16D4311yescharacteristic, complemented
311#3272—431no—
312#1705—431no—
313#1691—431no—
314#1686—431no—
315#1671—431no—
316#1665—431no—
317#1654—431no—
318#1651—431no—
319#1629—431no—
320#1622—431no—
321#1590—431no—
322C8×D8—431no—
323C2×C43—42no—
324C2×C43—81no—
325C2×C43—161no—
326C2×C43#327211yescharacteristic
327C2×C43D4×SD1611yescharacteristic
328C2×C43#329111yescharacteristic
329D43—42no—
330C2×AGL(1,ℤ/8)—861no—
331C22×SD16—21no—
332#554—431no—
333D4×Q8C2×D4311yescharacteristic
334#547—431no—
335D42C2×D4311yescharacteristic
336#501—861no—
337#498—431no—
338#498—431no—
339#498—431no—
340#492—431no—
341#492—431no—
342#492C2×D4311yescharacteristic
343#483—861no—
344#481—861no—
345#478—861no—
346#476—431no—
347#476—431no—
348#476—861no—
349#475—431no—
350#474—431no—
351#468—861no—
352#465—21no—
353#465—861no—
354#461—431no—
355#461C2×D4311yescharacteristic
356#460C2×D4311yescharacteristic
357#459—431no—
358#450—21no—
359#450—861no—
360#449—861no—
361#448—21no—
362#446—431no—
363#442—861no—
364C4×SD16C2×D4311yescharacteristic
365C4×D8—431no—
366#436—431no—
367C8×D4—431no—
368C8×D4C2×D4311yescharacteristic
369C2×#106—861no—
370#335—431no—
371#334—431no—
372#333—431no—
373#332—431no—
374#332—431no—
375#331—431no—
376Q8⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8—431no—
379D4⋊C8—431no—
380C82—431no—
381C43#1989011yescharacteristic, complemented, Sylow
382C2×#41—861no—
383C22×Q8—21no—
384C22×D4—21no—
385C22×D4—21no—
386AGL(1,ℤ/8)—1724no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—44no—
392C2×SD16—861no—
393C2×SD16—861no—
394C2×SD16—861no—
395C2×SD16—1721no—
396C2×SD16C22⋊D4311yescharacteristic
397C2×D8—431no—
398C2×D8—861no—
399C2×M16—861no—
400C22×C8—21no—
401C22×C8—861no—
402C4⋊Q8—21no—
403C4⋊Q8—431no—
404C4⋊Q8—431no—
405C4⋊Q8C22×D4311yescharacteristic
406#127C22×D4311yescharacteristic
407#125—861no—
408#123—1721no—
409C22⋊Q8—21no—
410C22⋊Q8—41no—
411C22⋊Q8—861no—
412C22⋊Q8—861no—
413C22⋊Q8—1721no—
414#121—21no—
415#121—21no—
416#121—861no—
417#120—41no—
418C4×Q8C22×D4311yescharacteristic
419C4×D4—21no—
420C4×D4—431no—
421C4×D4—861no—
422C4×D4C22×D4311yescharacteristic
423C4×D4C22×D4311yescharacteristic
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426#107—431no—
427#107—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435#106—1721no—
436#106C22⋊D4311yescharacteristic
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—861no—
441C4⋊C8C22×D4311yescharacteristic
442#103—21no—
443#103—861no—
444#103—861no—
445#103C22⋊D4311yescharacteristic
446#102—21no—
447#102—431no—
448#102—431no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102C22⋊D4311yescharacteristic
454C22⋊C8—21no—
455C22⋊C8—861no—
456C22⋊C8—861no—
457#97—861no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8C22×D4311yescharacteristic
461C24—41no—
462#41—3441no—
463#41—1722no—
464C2×Q8—21no—
465C2×Q8—41no—
466C2×Q8—42no—
467C2×Q8—81no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8C2×C22⋊D4311yescharacteristic
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—431no—
481C2×D4—1721no—
482C2×D4D4×D4311yescharacteristic
483C2×D4C2×C22⋊D4311yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—861no—
488C22×C4—1721no—
489C22×C4—1721no—
490SD16—22no—
491SD16—42no—
492SD16—42no—
493SD16—42no—
494SD16—81no—
495SD16—3441no—
496SD16—3442no—
497SD16—1722no—
498SD16—1722no—
499D8—434no—
500D8—1722no—
501M16—1722no—
502C2×C8—21no—
503C2×C8—42no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—1722no—
511C2×C8C2×C22⋊D4311yescharacteristic
512C2×C8C2×C22⋊D4311yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—431no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4D4×D4311yescharacteristic
526C4⋊C4C2×C22⋊D4311yescharacteristic
527C4⋊C4C2×C22⋊D4311yescharacteristic
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—861no—
533C22⋊C4—1721no—
534C22⋊C4—1721no—
535C42—21no—
536C42C23×D4311yescharacteristic
537C23—21no—
538C23—21no—
539C23—41no—
540C23—82no—
541C23—82no—
542C23—161no—
543C23—861no—
544Q8—21no—
545Q8—21no—
546Q8—41no—
547Q8—41no—
548Q8—82no—
549Q8—3441no—
550Q8—1721no—
551Q8—1721no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—432no—
563D4—861no—
564D4—3442no—
565D4SD16×D4312yes—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—861no—
577C2×C4—3442no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—6881no—
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4C22×C22⋊D4311yescharacteristic
585C2×C4#1306337011yescharacteristic
586C8—21no—
587C8—41no—
588C8—432no—
589C8—862no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C8#1306335112yescomplemented
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—164no—
605C22—862no—
606C22—1721no—
607C22—1721no—
608C22D4×C22⋊D4311yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—3441no—
616C4—3441no—
617C4—1721no—
618C4C2×SD16×D4311yescharacteristic
619C4C2×#1306335111yescharacteristic
620C4#1458370511yescharacteristic
621C4#1458371011yescharacteristic
622C2—42no—
623C2—81no—
624C2—161no—
625C2—1722no—
626C2#1914619111yescharacteristic
627C2SD16×C22⋊D4311yescharacteristic
628C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×SD16×C43C2
socleC22×C43D42
prime radical#19146191C2
hypercenterD4×SD16D43
hypocenterC43#19890
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #19147490C2semidirect
2. #19146954C2semidirect
4. #19134181C2semidirect
5. #19134092C2semidirect
6. #19134065C2semidirect
7. #19133970C2semidirect
8. #19133933C2semidirect
9. #19133877C2semidirect
10. #19133858C2semidirect
11. #19133711C2semidirect
12. #19133666C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. D4×SD16×C43C2semidirect
17. #14583609C22semidirect
20. #14583297C22semidirect
21. #14583295C22semidirect
22. #14583295C22semidirect
31. #14583184C22semidirect
32. #14583176C22semidirect
39. #14583030C22semidirect
43. C8×D172C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582644C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
203. #10621882SD16semidirect
263. D172C2×SD16semidirect
273. C8×C43AGL(1,ℤ/8)semidirect
279. C43⋊C8C2×SD16semidirect
310. D4×SD16D43semidirect
381. C43#19890semidirect
594. C8#13063351semidirect

Maximal subgroups

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

subgroupindex
#191474902
#191469542
#191461912
#191341812
#191340922
#191340652
#191339702
#191339332
#191338772
#191338582
#191337112
#191336662
#191334862
C8×#106218822
D4×SD16×C432
#1989043