Finite Group Databasebeta

← #25082035

Subgroups — #25082035

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#19145530C211yesmaximal, characteristic, complemented
2#19144746C211yesmaximal, characteristic, complemented
3#19144655C211yesmaximal, characteristic, complemented
4#19134053C211yesmaximal, characteristic, complemented
5#19134046C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133955C211yesmaximal, characteristic, complemented
9#19133950C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133936C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133288C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C43×#2988C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583276C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583223—21no—
23#14583223—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583184C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583115—21no—
29#14583115—21no—
30#14583099C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583094C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583046—21no—
35#14583046—21no—
36#14583044—21no—
37#14583044—21no—
38#14583009—21no—
39#14582997—21no—
40C4×#10621884—21no—
41C4×#10621882—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582642C2211yescharacteristic
53#14582642C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—21no—
74C2×D344—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063313—21no—
82#13063313—21no—
83#13063299—21no—
84#13063299—21no—
85#13063299—21no—
86#13063299—21no—
87C4×D172—21no—
88C4×D172—21no—
89C4×D172—21no—
90C4×D172—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063247—21no—
104#13063247—21no—
105#13063246—21no—
106#13063246—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43D411yescharacteristic
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157#10621898—81no—
158#10621898—81no—
159#10621898—82no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×C4×D43—41no—
167C2×C4×D43—41no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—81no—
173C2×C8×C43—81no—
174C2×C8×C43—81no—
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43C2×D411yescharacteristic
182C4⋊C4×C43C2×D411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43#4111yescharacteristic
192C42×C43C2411yescharacteristic
193#10621884—42no—
194#10621884—42no—
195#10621882—42no—
196#10621882—42no—
197(C2×D43)⋊C4—41no—
198(C2×D43)⋊C4—41no—
199(C2×D43)⋊C4—41no—
200(C2×D43)⋊C4—41no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209D344—81no—
210D344—81no—
211#10621873—81no—
212#10621873—81no—
213C23×C43—21no—
214C23×C43#12111yescharacteristic
215C22×D43—41no—
216C22×D43—41no—
217Q8×C43—21no—
218Q8×C43#13512yes—
219D4×C43—24no—
220D4×C43—21no—
221D4×C43#13512yes—
222C2×C4×C43—24no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—81no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—82no—
241C22⋊D43—82no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—41no—
249D172—41no—
250D172—41no—
251D172—41no—
252D172—81no—
253D172—81no—
254C4×D43—82no—
255C4×D43—82no—
256Dic86—41no—
257Dic86—41no—
258Dic86—81no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—41no—
264C8×C43—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19412—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—22no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43C2×#12111yescharacteristic
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—22no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43C2×#13511yescharacteristic
291C4×C43C2×#13511yescharacteristic
292C4×C43#57611yescharacteristic
293C4×C43#57711yescharacteristic
294Dic43—81no—
295Dic43—81no—
296#3207—431no—
297#3115—431no—
298#3106—431no—
299#2988D4311yescharacteristic, complemented
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—42no—
313C2×C43#304511yescharacteristic
314C2×C43#305011yescharacteristic
315C2×C43#306811yescharacteristic
316D43—161no—
317D43—161no—
318#532—431no—
319#532—431no—
320C4×#41C2×D4311yescharacteristic
321#493—431no—
322#492—431no—
323#487—431no—
324#486—431no—
325#482—861no—
326#482—861no—
327#477—431no—
328#476—431no—
329#475—431no—
330#474—431no—
331#463—861no—
332#463—861no—
333#460—431no—
334#460—431no—
335#459—431no—
336#459—431no—
337#449—861no—
338#449—861no—
339#449—861no—
340#449—861no—
341C8×Q8C2×D4311yescharacteristic
342C8×Q8C2×D4311yescharacteristic
343#442—861no—
344#440—861no—
345C4×SD16—861no—
346C4×D8—861no—
347C8×D4—21no—
348C8×D4—21no—
349C8×D4C2×D4311yescharacteristic
350C8×D4C2×D4311yescharacteristic
351#432—431no—
352#431—21no—
353#431—431no—
354#431C2×D4311yescharacteristic
355C2×C4⋊C8—21no—
356C2×C4⋊C8C2×D4311yescharacteristic
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—861no—
371C2×#41—861no—
372C2×#41D17211yescharacteristic
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—861no—
378C2×D8—861no—
379C2×D8—861no—
380C2×D8—861no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386#127—431no—
387#127—431no—
388#124—861no—
389#124—861no—
390#121—861no—
391#121—861no—
392#121—861no—
393#121—861no—
394C4×Q8D17211yescharacteristic
395C4×Q8C22×D4311yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4D17211yescharacteristic
403C4×D4C22×D4311yescharacteristic
404#117—21no—
405#117D17211yescharacteristic
406C2×C42—21no—
407C2×C42C22×D4311yescharacteristic
408#107—861no—
409#107—861no—
410#106—861no—
411#106—861no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—431no—
418C4⋊C8—431no—
419C4⋊C8C22⋊D4311yescharacteristic
420C4⋊C8C22⋊D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—861no—
424#103—861no—
425#103—861no—
426#103—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8C22⋊D4311yescharacteristic
440C22⋊C8C22⋊D4311yescharacteristic
441#97—861no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—861no—
445C4×C8C22×D4311yescharacteristic
446C4×C8C22×D4311yescharacteristic
447#41—22no—
448#41—22no—
449#41—3441no—
450#41—3441no—
451#41—3442no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8C2×D17211yescharacteristic
455C2×D4—21no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4C2×D17211yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4C2×D17211yescharacteristic
471C22×C4#1062189811yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473SD16—3441no—
474SD16—3441no—
475SD16—1722no—
476SD16—1722no—
477D8—3441no—
478D8—3441no—
479D8—1722no—
480D8—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8C2×C22⋊D4311yescharacteristic
491C2×C8C2×C22⋊D4311yescharacteristic
492C2×C8C2×C22⋊D4311yescharacteristic
493C2×C8C2×C22⋊D4311yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4C2×D17211yescharacteristic
501C4⋊C4C2×D17211yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D17211yescharacteristic
513C42#1062189811yescharacteristic
514C42C2×C22⋊D4311yescharacteristic
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—1721no—
518C23—1721no—
519C23#1306329911yescharacteristic
520Q8—21no—
521Q8—3441no—
522Q8—1721no—
523Q8—1721no—
524Q8#1306334712yes—
525D4—24no—
526D4—21no—
527D4—3441no—
528D4—3441no—
529D4—3442no—
530D4—3442no—
531D4—1721no—
532D4—1721no—
533D4—1721no—
534D4—1721no—
535D4—1721no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539D4#1306334712yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—81no—
552C2×C4—3442no—
553C2×C4—3442no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4#1306329911yescharacteristic
557C2×C4#1306329911yescharacteristic
558C2×C4#1306329911yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C2×C4C22×D17211yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—1721no—
569C8—1721no—
570C8—1721no—
571C8—1721no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—3441no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—3441no—
584C22C2×#1306329911yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—3441no—
593C4—3441no—
594C4C2×#1306334711yescharacteristic
595C4C2×#1306334711yescharacteristic
596C4#1458370211yescharacteristic
597C4#1458370711yescharacteristic
598C2—41no—
599C2—42no—
600C2—6881no—
601C2—6881no—
602C2#1914413411yescharacteristic
603C2#1914417611yescharacteristic
604C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
hypercenter#2988D43
hypocenterC43#19412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145530C2semidirect
2. #19144746C2semidirect
3. #19144655C2semidirect
4. #19134053C2semidirect
5. #19134046C2semidirect
6. #19134011C2semidirect
7. #19134004C2semidirect
8. #19133955C2semidirect
9. #19133950C2semidirect
10. #19133943C2semidirect
11. #19133936C2semidirect
12. #19133375C2semidirect
13. #19133288C2semidirect
14. #19133245C2semidirect
15. C43×#2988C2semidirect
299. #2988D43semidirect
369. C43#19412semidirect

Maximal subgroups

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

subgroupindex
#191455302
#191447462
#191446552
#191340532
#191340462
#191340112
#191340042
#191339552
#191339502
#191339432
#191339362
#191333752
#191332882
#191332452
C43×#29882
#1941243