Finite Group Databasebeta

← #25082029

Subgroups — #25082029

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144740C211yesmaximal, characteristic, complemented
2#19144649C211yesmaximal, characteristic, complemented
3#19143703C211yesmaximal, characteristic, complemented
4#19134050C211yesmaximal, characteristic, complemented
5#19134043C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133952C211yesmaximal, characteristic, complemented
9#19133947C211yesmaximal, characteristic, complemented
10#19133940C211yesmaximal, characteristic, complemented
11#19133933C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14#19133244C211yesmaximal, characteristic, complemented
15C43×#3207C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583220—21no—
18#14583220—21no—
19#14583191C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583181C2211yescharacteristic
22#14583176C2211yescharacteristic
23#14583096C2211yescharacteristic
24#14583096C2211yescharacteristic
25#14583091C2211yescharacteristic
26#14583091C2211yescharacteristic
27#14583042—21no—
28#14583042—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31#14583009—21no—
32#14582999—21no—
33C4×#10621883—21no—
34C4×#10621882—21no—
35C8×D172C2211yescharacteristic
36C8×D172C2211yescharacteristic
37(C22⋊D43)⋊C8—21no—
38(C22⋊D43)⋊C8—21no—
39#14582956C2211yescharacteristic
40#14582952C2211yescharacteristic
41#14582951—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C4⋊C8×D43—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582643C2211yescharacteristic
53#14582643C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#493C2211yescharacteristic
59C43×#492C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#463—21no—
63C43×#463—21no—
64C43×#449—21no—
65C43×#449—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621882—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86D411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172D411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284D411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C2×#41×C43—21no—
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×D8×C43—21no—
118C2×D8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#127×C43C2311yescharacteristic
123#124×C43—21no—
124#124×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—81no—
145#41×C43—81no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×C22⋊D43—21no—
163#10621898—22no—
164#10621898—22no—
165C2×D172C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×Dic86C2×D411yescharacteristic
170SD16×C43—81no—
171SD16×C43—81no—
172D8×C43—81no—
173D8×C43—81no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—21no—
191#10621883—42no—
192#10621883—42no—
193#10621882—42no—
194#10621882—42no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197C4⋊Dic43C2×D411yescharacteristic
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—81no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43#12111yescharacteristic
216C22×D43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—81no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—41no—
227D4×C43—41no—
228D4×C43—81no—
229D4×C43—81no—
230D4×C43—82no—
231D4×C43—82no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43—82no—
241C2×C4×C43#12111yescharacteristic
242C2×C4×C43#12111yescharacteristic
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—24no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251D172—21no—
252D172#13512yes—
253C4×D43—24no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—81no—
257Dic86—21no—
258Dic86#13512yes—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19412—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43C2×#12111yescharacteristic
280C2×D43—22no—
281C2×D43—41no—
282C2×D43—41no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—81no—
288C4×C43—81no—
289C4×C43C2×#13511yescharacteristic
290C4×C43C2×#13511yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—22no—
294Dic43—41no—
295Dic43—41no—
296#3207D4311yescharacteristic, complemented
297#3115—431no—
298#3106—431no—
299#2988—431no—
300#1684—431no—
301#1683—431no—
302#1678—431no—
303#1677—431no—
304#1668—431no—
305#1667—431no—
306#1666—431no—
307#1665—431no—
308#1572—431no—
309#1551—431no—
310#1540—431no—
311C2×C43—41no—
312C2×C43—161no—
313C2×C43—161no—
314C2×C43#304511yescharacteristic
315C2×C43#305011yescharacteristic
316C2×C43#306811yescharacteristic
317D43—42no—
318#532C2×D4311yescharacteristic
319#532C2×D4311yescharacteristic
320C4×#41—431no—
321#493C2×D4311yescharacteristic
322#492C2×D4311yescharacteristic
323#487C2×D4311yescharacteristic
324#486C2×D4311yescharacteristic
325#482—861no—
326#482—861no—
327#477—431no—
328#476—431no—
329#475—431no—
330#474—431no—
331#463—21no—
332#463—21no—
333#460—431no—
334#460—431no—
335#459—431no—
336#459—431no—
337#449—21no—
338#449—21no—
339#449—861no—
340#449—861no—
341C8×Q8—431no—
342C8×Q8—431no—
343#442—861no—
344#440—861no—
345C4×SD16—861no—
346C4×D8—861no—
347C8×D4—431no—
348C8×D4—431no—
349C8×D4—861no—
350C8×D4—861no—
351#432—431no—
352#431—431no—
353#431—861no—
354#431C2×D4311yescharacteristic
355C2×C4⋊C8—431no—
356C2×C4⋊C8—861no—
357#335—431no—
358#335—431no—
359#334—431no—
360#334—431no—
361#333—431no—
362#333—431no—
363#332—431no—
364#332—431no—
365#331—431no—
366#331—431no—
367#331—431no—
368#331—431no—
369C43#1941211yescharacteristic, complemented, Sylow
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—431no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—861no—
380C2×D8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8C22×D4311yescharacteristic
385C4⋊Q8C22×D4311yescharacteristic
386#127C22×D4311yescharacteristic
387#127C22×D4311yescharacteristic
388#124—21no—
389#124—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#121—21no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C42—861no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#107—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—431no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8—861no—
421C4⋊C8C22⋊D4311yescharacteristic
422C4⋊C8C22⋊D4311yescharacteristic
423#103—21no—
424#103—21no—
425#103—861no—
426#103—861no—
427#102—21no—
428#102—21no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8C22⋊D4311yescharacteristic
440C22⋊C8C22⋊D4311yescharacteristic
441#97—861no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447#41—81no—
448#41—81no—
449#41—82no—
450#41—862no—
451#41—862no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—431no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—431no—
464C2×D4—861no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4D4×D4311yescharacteristic
471C22×C4#1062190011yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473SD16—81no—
474SD16—81no—
475SD16—1722no—
476SD16—1722no—
477D8—81no—
478D8—81no—
479D8—1722no—
480D8—1722no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—3441no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C2×C8C2×C22⋊D4311yescharacteristic
493C2×C8C2×C22⋊D4311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—431no—
499C4⋊C4—431no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—861no—
510C42—861no—
511C42—861no—
512C42D4×D4311yescharacteristic
513C42#1062190011yescharacteristic
514C42C2×C22⋊D4311yescharacteristic
515C42C23×D4311yescharacteristic
516C23—41no—
517C23—41no—
518C23—861no—
519C23#1306329611yescharacteristic
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—432no—
524Q8—861no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—81no—
535D4—82no—
536D4—82no—
537D4—432no—
538D4—864no—
539D4—861no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—864no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3441no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#1306329611yescharacteristic
557C2×C4#1306329611yescharacteristic
558C2×C4#1306329611yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C22×C22⋊D4311yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—1721no—
567C8—1721no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C8—1721no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—862no—
582C22—1721no—
583C22—1721no—
584C22C2×#1306329611yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—81no—
590C4—81no—
591C4—862no—
592C4—1721no—
593C4—1721no—
594C4#135×D4311yescharacteristic
595C4#135×D4311yescharacteristic
596C4#1458370211yescharacteristic
597C4#1458371011yescharacteristic
598C2—41no—
599C2—161no—
600C2—161no—
601C2—1722no—
602C2#1914413011yescharacteristic
603C2#1914417211yescharacteristic
604C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3207C2
socleC22×C43C2×#121
hypercenter#3207D43
hypocenterC43#19412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3207

Complements

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

NH ≅ G/Ntype
1. #19144740C2semidirect
2. #19144649C2semidirect
3. #19143703C2semidirect
4. #19134050C2semidirect
5. #19134043C2semidirect
6. #19134008C2semidirect
7. #19134001C2semidirect
8. #19133952C2semidirect
9. #19133947C2semidirect
10. #19133940C2semidirect
11. #19133933C2semidirect
12. #19133375C2semidirect
13. #19133290C2semidirect
14. #19133244C2semidirect
15. C43×#3207C2semidirect
296. #3207D43semidirect
369. C43#19412semidirect

Maximal subgroups

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

subgroupindex
#191447402
#191446492
#191437032
#191340502
#191340432
#191340082
#191340012
#191339522
#191339472
#191339402
#191339332
#191333752
#191332902
#191332442
C43×#32072
#1941243