Finite Group Databasebeta

← #25087957

Subgroups — #25087957

Order 11008.

686 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#19147490C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146195C211yesmaximal, characteristic
4#19134198C211yesmaximal, characteristic, complemented
5#19134092C211yesmaximal, characteristic, complemented
6#19134069C211yesmaximal, characteristic, complemented
7#19134015C211yesmaximal, characteristic, complemented
8#19134004C211yesmaximal, characteristic, complemented
9#19133801C211yesmaximal, characteristic, complemented
10#19133772C211yesmaximal, characteristic, complemented
11#19133746C211yesmaximal, characteristic, complemented
12#19133698C211yesmaximal, characteristic, complemented
13#19133486C211yesmaximal, characteristic, complemented
14C8×#10621882C211yesmaximal, characteristic, complemented
15C43×#3298C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17#14583609C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583305—21no—
20#14583295C2211yescharacteristic, complemented
21#14583273C2211yescharacteristic
22#14583251C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583219—21no—
26#14583199—21no—
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic, complemented
29#14583186—21no—
30#14583176C2211yescharacteristic
31#14583147—21no—
32#14583131—21no—
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583049—21no—
37#14583048—21no—
38#14583044—21no—
39#14583030C2211yescharacteristic, complemented
40#14583009—21no—
41C4×#10621882C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#102×D43—21no—
45#14582651C2211yescharacteristic, complemented
46#14582650C2211yescharacteristic, complemented
47#14582647C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic, complemented
56D4×Q8×C43C2211yescharacteristic, complemented
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic, complemented
59C43×#483—21no—
60C43×#475C2211yescharacteristic, complemented
61C43×#465—21no—
62C43×#461C2211yescharacteristic
63C43×#448—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C2×#103×C43—21no—
67C22×D172—21no—
68C2×D4×D43—21no—
69#13063350—44no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621882—21no—
75C2×#10621882D411yescharacteristic
76C2×#10621877—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063317—21no—
81#13063303—41no—
82#13063301—21no—
83#13063300—21no—
84#13063299—21no—
85#13063295—41no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88C4⋊C4×D43—21no—
89#13063258—21no—
90#13063258D411yescharacteristic
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063248—41no—
101#13063247—21no—
102#13063247—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246D411yescharacteristic
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113#13063236—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×Q8×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43D411yescharacteristic
120C22×C8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#123×C43—41no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C22⋊Q8×C43—41no—
128#121×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43D411yescharacteristic
142#102×C43D411yescharacteristic
143C22⋊C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C23×D43—41no—
146#41×C43—42no—
147#41×C43—81no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—41no—
151C2×Q8×C43—42no—
152C2×Q8×C43—81no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—41no—
155C2×D4×C43C2×D411yescharacteristic
156C2×D4×C43C2×D411yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C2×C22⋊D43—41no—
162D4×D43—42no—
163D4×D43—81no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—41no—
168C2×D172—42no—
169C2×D172—81no—
170C2×D172C2×D411yescharacteristic
171C2×C4×D43—21no—
172C2×C4×D43—41no—
173C2×Dic86—21no—
174SD16×C43—41no—
175SD16×C43—81no—
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×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—41no—
193C22⋊C4×C43—41no—
194C42×C43—21no—
195C42×C43C2411yescharacteristic
196#10621884—42no—
197#10621884—42no—
198#10621884—81no—
199#10621884—81no—
200#10621882—42no—
201#10621882SD1614yescomplemented
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—41no—
204(C2×D43)⋊C4—41no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C2×D411yescharacteristic
208Dic43⋊C4—41no—
209Dic43⋊C4—41no—
210#10621877—42no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C2×D411yescharacteristic
216C2×C43⋊C8C2×D411yescharacteristic
217C8×D43—81no—
218C23×C43—21no—
219C23×C43—21no—
220C22×D43—21no—
221C22×D43—41no—
222C22×D43—82no—
223C22×D43—82no—
224C22×D43—161no—
225Q8×C43—21no—
226Q8×C43—21no—
227Q8×C43—41no—
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—82no—
232D4×C43—21no—
233D4×C43—21no—
234D4×C43—21no—
235D4×C43—82no—
236D4×C43C2×SD1612yes—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—82no—
248C2×C4×C43—82no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—82no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255D172—21no—
256D172—41no—
257D172—41no—
258D172—41no—
259D172—41no—
260D172—81no—
261D172—82no—
262D172C2×SD1612yes—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—161no—
266Dic86—81no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—41no—
270C43⋊C8—21no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8C2×SD1612yes—
276#19891—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43D4211yescharacteristic
284C2×D43—22no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—164no—
291C4×C43—21no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—81no—
297C4×C43—81no—
298C4×C43C22×SD1611yescharacteristic
299C4×C43#57511yescharacteristic
300C4×C43#57611yescharacteristic
301C4×C43#57711yescharacteristic
302Dic43—41no—
303Dic43—81no—
304#3384—431no—
305#3298D4311yescharacteristic, complemented
306#3295—431no—
307#3272—431no—
308#1708—431no—
309#1691—431no—
310#1686—431no—
311#1679—431no—
312#1677—431no—
313#1643—431no—
314#1639—431no—
315#1635—431no—
316#1627—431no—
317#1590—431no—
318C8×D8—431no—
319C2×C43—42no—
320C2×C43—81no—
321C2×C43#327311yescharacteristic
322C2×C43D4×SD1611yescharacteristic
323C2×C43#329011yescharacteristic
324D43—42no—
325D43—161no—
326C2×AGL(1,ℤ/8)—861no—
327#554—431no—
328D4×Q8C2×D4311yescharacteristic, complemented
329#547C2×D4311yescharacteristic
330D42—431no—
331#501—861no—
332#498—431no—
333#492—431no—
334#487—431no—
335#487C2×D4311yescharacteristic, complemented
336#486—431no—
337#486—431no—
338#483—21no—
339#481—861no—
340#478—861no—
341#476—431no—
342#476—431no—
343#476—861no—
344#475C2×D4311yescharacteristic, complemented
345#474—431no—
346#468—861no—
347#465—21no—
348#465—861no—
349#461—431no—
350#461C2×D4311yescharacteristic
351#460—431no—
352#459—431no—
353#450—861no—
354#450—861no—
355#449—861no—
356#448—21no—
357#446—431no—
358#442—861no—
359C4×SD16C2×D4311yescharacteristic
360C4×D8—431no—
361#436—431no—
362C8×D4—431no—
363C8×D4C2×D4311yescharacteristic, complemented
364C2×#103—21no—
365C2×#102—861no—
366#335—431no—
367#334—431no—
368#333—431no—
369#332—431no—
370#332—431no—
371#331—431no—
372Q8⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376C82—431no—
377C43#1989111yescharacteristic, complemented, Sylow
378C2×#41—21no—
379C22×Q8—21no—
380C22×D4—861no—
381C22×D4—861no—
382AGL(1,ℤ/8)—1724no—
383C2×SD16—21no—
384C2×SD16—861no—
385C2×SD16—861no—
386C2×SD16—861no—
387C2×SD16—861no—
388C2×SD16C22⋊D4311yescharacteristic
389C2×D8—431no—
390C2×D8—861no—
391C2×M16—861no—
392C22×C8—21no—
393C22×C8—861no—
394C4⋊Q8—21no—
395C4⋊Q8—431no—
396C4⋊Q8C22×D4311yescharacteristic
397C4⋊Q8C22×D4311yescharacteristic
398#127—431no—
399#125—861no—
400#123—41no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—861no—
405C22⋊Q8—1721no—
406#121—21no—
407#121—861no—
408#121—861no—
409#120—1721no—
410C4×Q8C22×D4311yescharacteristic
411C4×D4—21no—
412C4×D4—431no—
413C4×D4—861no—
414C4×D4C22×D4311yescharacteristic
415C4×D4C22×D4311yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—861no—
418#107—431no—
419#107—861no—
420#106—21no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106C22⋊D4311yescharacteristic
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8C22×D4311yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—861no—
436#103—1721no—
437#103C22⋊D4311yescharacteristic
438#102—431no—
439#102—431no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102—861no—
445#102—861no—
446#102—861no—
447#102—1721no—
448#102C22⋊D4311yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452#97—861no—
453C4×C8—431no—
454C4×C8—431no—
455C4×C8C22×D4311yescharacteristic
456C24—1721no—
457#41—42no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—861no—
465C2×Q8C2×C22⋊D4311yescharacteristic
466C2×D4—41no—
467C2×D4—431no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—1721no—
474C2×D4—1722no—
475C2×D4—1721no—
476C2×D4—1722no—
477C2×D4D4×D4311yescharacteristic
478C2×D4C2×C22⋊D4311yescharacteristic
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—861no—
484C22×C4—1721no—
485SD16—41no—
486SD16—81no—
487SD16—3441no—
488SD16—3441no—
489SD16—1722no—
490SD16—1722no—
491D8—434no—
492D8—1722no—
493M16—1722no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—3441no—
503C2×C8C2×C22⋊D4311yescharacteristic
504C2×C8C2×C22⋊D4311yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1721no—
516C4⋊C4—1721no—
517C4⋊C4D4×D4311yescharacteristic
518C4⋊C4C2×C22⋊D4311yescharacteristic
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—861no—
525C22⋊C4—1721no—
526C22⋊C4—1721no—
527C42—21no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—861no—
532C23—3442no—
533C23—3442no—
534C23—1721no—
535C23—6881no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543Q8—3441no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—82no—
548D4—432no—
549D4—861no—
550D4—3441no—
551D4—3442no—
552D4—3442no—
553D4—1721no—
554D4—1721no—
555D4—1721no—
556D4—1721no—
557D4SD16×D4312yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—861no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—6881no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C22×C22⋊D4311yescharacteristic
577C2×C4#1306337011yescharacteristic
578C8—21no—
579C8—21no—
580C8—41no—
581C8—432no—
582C8—861no—
583C8—1721no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—862no—
594C22—3441no—
595C22—3441no—
596C22—3441no—
597C22—1721no—
598C22—1721no—
599C22—6884no—
600C22D4×C22⋊D4311yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—3441no—
609C4—1721no—
610C4C2×SD16×D4311yescharacteristic
611C4#1458369711yescharacteristic
612C4#1458370211yescharacteristic
613C4#1458370511yescharacteristic
614C2—42no—
615C2—81no—
616C2—1722no—
617C2—6881no—
618C2#1914620211yescharacteristic
619C2SD16×C22⋊D4311yescharacteristic
620C2#1914638111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3298C2
socleC22×C43D42
prime radical#19146195C2
hypercenter#3298D43
hypocenterC43#19891
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3298

Complements

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

NH ≅ G/Ntype
1. #19147490C2semidirect
2. #19146421C2semidirect
4. #19134198C2semidirect
5. #19134092C2semidirect
6. #19134069C2semidirect
7. #19134015C2semidirect
8. #19134004C2semidirect
9. #19133801C2semidirect
10. #19133772C2semidirect
11. #19133746C2semidirect
12. #19133698C2semidirect
13. #19133486C2semidirect
14. C8×#10621882C2semidirect
15. C43×#3298C2semidirect
20. #14583295C22semidirect
22. #14583251C22semidirect
28. #14583189C22semidirect
39. #14583030C22semidirect
45. #14582651C22semidirect
46. #14582650C22semidirect
47. #14582647C22semidirect
48. #14582645C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. C8×C43⋊C8C22semidirect
56. D4×Q8×C43C22semidirect
58. C43×#487C22semidirect
60. C43×#475C22semidirect
65. C8×D4×C43C22semidirect
201. #10621882SD16semidirect
305. #3298D43semidirect
328. D4×Q8C2×D43semidirect
335. #487C2×D43semidirect
344. #475C2×D43semidirect
363. C8×D4C2×D43semidirect
377. C43#19891semidirect

Maximal subgroups

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

subgroupindex
#191474902
#191464212
#191461952
#191341982
#191340922
#191340692
#191340152
#191340042
#191338012
#191337722
#191337462
#191336982
#191334862
C8×#106218822
C43×#32982
#1989143