Finite Group Databasebeta

← #25086710

Subgroups — #25086710

Order 11008.

676 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147458C211yesmaximal, characteristic, complemented
2#19146421C211yesmaximal, characteristic, complemented
3#19146195C211yesmaximal, characteristic
4#19134220C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134004C211yesmaximal, characteristic, complemented
7#19133967C211yesmaximal, characteristic, complemented
8#19133945C211yesmaximal, characteristic, complemented
9#19133801C211yesmaximal, characteristic, complemented
10#19133746C211yesmaximal, characteristic, complemented
11#19133710C211yesmaximal, characteristic, complemented
12#19133667C211yesmaximal, characteristic, complemented
13#19133439C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic, complemented
15C43×#3335C211yesmaximal, characteristic, complemented
16C2×#13063350—21no—
17#14583609C2211yescharacteristic
18D4×D172C2211yescharacteristic
19#14583302C2211yescharacteristic, complemented
20#14583298—21no—
21#14583273C2211yescharacteristic
22#14583273C2211yescharacteristic
23#14583251C2211yescharacteristic, complemented
24#14583246C2211yescharacteristic
25#14583219—21no—
26#14583199—21no—
27#14583196—21no—
28#14583189C2211yescharacteristic
29#14583189C2211yescharacteristic, complemented
30#14583186C2211yescharacteristic
31#14583147—21no—
32#14583131—21no—
33#14583101C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583049—21no—
37#14583048—21no—
38#14583044—21no—
39Q8×C43⋊C8C2211yescharacteristic, complemented
40C4×#10621882—21no—
41C4×#10621882C2211yescharacteristic
42#14582977C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#102×D43—21no—
45#14582650C2211yescharacteristic, complemented
46#14582649C2211yescharacteristic, complemented
47#14582648C2211yescharacteristic, complemented
48#14582647C2211yescharacteristic, complemented
49#14582645C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52D4⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic, complemented
56C43×#554C2211yescharacteristic, complemented
57C43×#547C2211yescharacteristic
58C43×#498C2211yescharacteristic, complemented
59C43×#483—21no—
60C43×#481—21no—
61C43×#476C2211yescharacteristic
62C43×#475C2211yescharacteristic, complemented
63C43×#465—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic, complemented
66C2×#106×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×#10621884—41no—
75C2×#10621882—21no—
76C2×#10621882D411yescharacteristic
77C2×#10621877—21no—
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063303—41no—
83#13063301—21no—
84#13063300—21no—
85#13063299—21no—
86#13063295—41no—
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4⋊C4×D43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258D411yescharacteristic
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063249—21no—
101#13063248—41no—
102#13063247—21no—
103#13063247—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
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—
117C2×SD16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126#121×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137#106×C43D411yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#102×C43—21no—
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×C43C2×D411yescharacteristic
151C2×D4×C43—41no—
152C2×D4×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C2×C22⋊D43—41no—
159D4×D43—42no—
160D4×D43—81no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—41no—
165C2×D172—42no—
166C2×D172—81no—
167C2×D172C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—41no—
170C2×Dic86—21no—
171SD16×C43—41no—
172C2×C8×C43—21no—
173C2×C8×C43—42no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C42×C43—21no—
192C42×C43C2411yescharacteristic
193#10621884—42no—
194#10621884—42no—
195#10621884—81no—
196#10621884—81no—
197#10621884—82no—
198#10621882—42no—
199#10621882SD1614yescomplemented
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—41no—
202(C2×D43)⋊C4—41no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208#10621877—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8C2×D411yescharacteristic
214C2×C43⋊C8C2×D411yescharacteristic
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—41no—
220C22×D43—82no—
221C22×D43—82no—
222C22×D43—161no—
223Q8×C43—21no—
224Q8×C43—21no—
225Q8×C43—41no—
226Q8×C43—41no—
227Q8×C43—81no—
228D4×C43—21no—
229D4×C43—21no—
230D4×C43—21no—
231D4×C43—82no—
232D4×C43C2×SD1612yes—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—82no—
244C2×C4×C43—161no—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43H(5,𝔽2)11yescharacteristic
248C22⋊D43—82no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251D172—21no—
252D172—41no—
253D172—41no—
254D172—41no—
255D172—41no—
256D172—81no—
257D172—82no—
258D172C2×SD1612yes—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—161no—
262Dic86—81no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271C43⋊C8C2×SD1612yes—
272#19806—431nomaximal, Sylow
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43D4211yescharacteristic
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C2×D43—164no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C22×SD1611yescharacteristic
295C4×C43#57511yescharacteristic
296C4×C43#57711yescharacteristic
297C4×C43#57711yescharacteristic
298Dic43—41no—
299Dic43—81no—
300#3380—431no—
301#3335D4311yescharacteristic, complemented
302#3295—431no—
303#3272—431no—
304#1714—431no—
305#1695—431no—
306#1677—431no—
307#1671—431no—
308#1666—431no—
309#1643—431no—
310#1635—431no—
311#1629—431no—
312#1622—431no—
313#1583—431no—
314#1580—431no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43#326711yescharacteristic
318C2×C43D4×SD1611yescharacteristic
319C2×C43#328811yescharacteristic
320D43—42no—
321D43—161no—
322C2×AGL(1,ℤ/8)—861no—
323#554—431no—
324#554C2×D4311yescharacteristic, complemented
325#547C2×D4311yescharacteristic
326D42—431no—
327#500—431no—
328#499—861no—
329#498C2×D4311yescharacteristic, complemented
330#492—431no—
331#492—431no—
332#487—431no—
333#486—431no—
334#483—21no—
335#481—21no—
336#481—861no—
337#478—861no—
338#478—861no—
339#476—431no—
340#476—431no—
341#476—431no—
342#476C2×D4311yescharacteristic
343#475C2×D4311yescharacteristic, complemented
344#468—861no—
345#465—21no—
346#465—861no—
347#461—431no—
348#460—431no—
349#459—431no—
350#450—861no—
351#450—861no—
352#449—861no—
353C8×Q8—431no—
354C4×SD16C2×D4311yescharacteristic
355C4×D8—431no—
356C4×D8—861no—
357#436—431no—
358C8×D4—431no—
359C8×D4C2×D4311yescharacteristic, complemented
360C2×#106—21no—
361C2×#102—861no—
362#334—431no—
363#334—431no—
364#333—431no—
365#333—431no—
366#332—431no—
367#331—431no—
368Q8⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372#322—431no—
373C43#1980611yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C22×D4—861no—
376C22×D4—861no—
377AGL(1,ℤ/8)—1724no—
378C2×SD16—861no—
379C2×SD16—861no—
380C2×SD16—861no—
381C2×SD16—861no—
382C2×SD16—1721no—
383C2×SD16C22⋊D4311yescharacteristic
384C2×D8—431no—
385C2×D8—861no—
386C2×M16—861no—
387C22×C8—21no—
388C22×C8—861no—
389C4⋊Q8—431no—
390C4⋊Q8C22×D4311yescharacteristic
391C4⋊Q8C22×D4311yescharacteristic
392#127—431no—
393#125—21no—
394#125—861no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399C22⋊Q8—861no—
400C22⋊Q8—1721no—
401#121—21no—
402#121—861no—
403#121—861no—
404#120—1721no—
405C4×Q8C22×D4311yescharacteristic
406C4×D4—21no—
407C4×D4—431no—
408C4×D4—861no—
409C4×D4C22×D4311yescharacteristic
410C4×D4C22×D4311yescharacteristic
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—861no—
414#107—431no—
415#107—861no—
416#107—861no—
417#106—21no—
418#106—21no—
419#106—21no—
420#106—21no—
421#106—861no—
422#106—861no—
423#106—861no—
424#106C22⋊D4311yescharacteristic
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—861no—
429C4⋊C8C22×D4311yescharacteristic
430#103—21no—
431#103—861no—
432#103—1721no—
433#103C22⋊D4311yescharacteristic
434#102—21no—
435#102—431no—
436#102—431no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#102—861no—
442#102—861no—
443#102—861no—
444#102C22⋊D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—861no—
447C22⋊C8—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—861no—
451C4×C8C22×D4311yescharacteristic
452C24—1721no—
453#41—42no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—861no—
458C2×Q8C2×C22⋊D4311yescharacteristic
459C2×D4—41no—
460C2×D4—431no—
461C2×D4—861no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—3441no—
465C2×D4—3441no—
466C2×D4—1721no—
467C2×D4—1722no—
468C2×D4—1721no—
469C2×D4—1722no—
470C2×D4D4×D4311yescharacteristic
471C2×D4C2×C22⋊D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—861no—
477C22×C4—1721no—
478SD16—41no—
479SD16—3441no—
480SD16—3442no—
481SD16—3441no—
482SD16—1722no—
483SD16—1722no—
484D8—434no—
485D8—1722no—
486M16—1722no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—3441no—
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—431no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4D4×D4311yescharacteristic
512C4⋊C4C2×C22⋊D4311yescharacteristic
513C4⋊C4C2×C22⋊D4311yescharacteristic
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—861no—
519C22⋊C4—1721no—
520C22⋊C4—1721no—
521C42—21no—
522C42C23×D4311yescharacteristic
523C23—21no—
524C23—21no—
525C23—861no—
526C23—3442no—
527C23—3442no—
528C23—1721no—
529C23—6881no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—3441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—82no—
540D4—432no—
541D4—861no—
542D4—3441no—
543D4—3442no—
544D4—3442no—
545D4—1721no—
546D4—1721no—
547D4—1721no—
548D4—1721no—
549D4SD16×D4312yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—161no—
562C2×C4—861no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—6881no—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4#1306337011yescharacteristic
570C8—21no—
571C8—21no—
572C8—41no—
573C8—432no—
574C8—861no—
575C8—1721no—
576C8—1721no—
577C8—1721no—
578C8—1721no—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—862no—
586C22—3441no—
587C22—3441no—
588C22—3441no—
589C22—1721no—
590C22—1721no—
591C22—6884no—
592C22D4×C22⋊D4311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4—3441no—
601C4—1721no—
602C4C2×SD16×D4311yescharacteristic
603C4#1458369711yescharacteristic
604C4#1458370511yescharacteristic
605C4#1458370711yescharacteristic
606C2—42no—
607C2—81no—
608C2—1722no—
609C2—6881no—
610C2#1914612111yescharacteristic
611C2SD16×C22⋊D4311yescharacteristic
612C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3335C2
socleC22×C43D42
prime radical#19146195C2
hypercenter#3335D43
hypocenterC43#19806
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3335

Complements

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

NH ≅ G/Ntype
1. #19147458C2semidirect
2. #19146421C2semidirect
4. #19134220C2semidirect
5. #19134116C2semidirect
6. #19134004C2semidirect
7. #19133967C2semidirect
8. #19133945C2semidirect
9. #19133801C2semidirect
10. #19133746C2semidirect
11. #19133710C2semidirect
12. #19133667C2semidirect
13. #19133439C2semidirect
14. #19133417C2semidirect
15. C43×#3335C2semidirect
19. #14583302C22semidirect
23. #14583251C22semidirect
29. #14583189C22semidirect
39. Q8×C43⋊C8C22semidirect
45. #14582650C22semidirect
46. #14582649C22semidirect
47. #14582648C22semidirect
48. #14582647C22semidirect
49. #14582645C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
55. #14582621C22semidirect
56. C43×#554C22semidirect
58. C43×#498C22semidirect
62. C43×#475C22semidirect
65. C8×D4×C43C22semidirect
199. #10621882SD16semidirect
301. #3335D43semidirect
324. #554C2×D43semidirect
329. #498C2×D43semidirect
343. #475C2×D43semidirect
359. C8×D4C2×D43semidirect
373. C43#19806semidirect

Maximal subgroups

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

subgroupindex
#191474582
#191464212
#191461952
#191342202
#191341162
#191340042
#191339672
#191339452
#191338012
#191337462
#191337102
#191336672
#191334392
#191334172
C43×#33352
#1980643