Finite Group Databasebeta

← #25082032

Subgroups — #25082032

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#19145523C211yesmaximal, characteristic, complemented
2#19144743C211yesmaximal, characteristic, complemented
3#19144652C211yesmaximal, characteristic, complemented
4#19143702C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134002C211yesmaximal, characteristic, complemented
9#19133952C211yesmaximal, characteristic, complemented
10#19133942C211yesmaximal, characteristic, complemented
11#19133934C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133287C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1667C211yesmaximal, characteristic, complemented
16#14583447C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583271C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583222—21no—
23#14583221—21no—
24#14583195C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583112—21no—
29#14583112—21no—
30#14583096C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583041—21no—
33#14583041—21no—
34#14583041—21no—
35#14583041—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583011—21no—
39#14582996—21no—
40#14582990—21no—
41D8×Dic43—21no—
42D4×C43⋊C8C2211yescharacteristic
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582949—21no—
49C2×Dic43⋊C8—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582643C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#493C2211yescharacteristic
61C43×#459C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900—21no—
69C2×#10621900D411yescharacteristic
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063312—21no—
79#13063312—21no—
80#13063296—21no—
81#13063296—21no—
82#13063296—21no—
83#13063296—21no—
84C4×Dic86C2311yescharacteristic
85#13063290D411yescharacteristic
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43D411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283D411yescharacteristic
94#13063281—21no—
95C2×C4×Dic43—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×D8×C43—21no—
130C2×D8×C43—21no—
131C2×D8×C43—21no—
132C2×D8×C43—21no—
133C22×C8×C43—21no—
134#127×C43C2311yescharacteristic
135#127×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—41no—
158C22×Dic43—41no—
159#10621900—22no—
160#10621900—22no—
161#10621900—81no—
162#10621900—81no—
163#10621900—82no—
164C2×C4×D43C2×D411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86C2×D411yescharacteristic
170D8×C43—42no—
171D8×C43—42no—
172D8×C43—81no—
173D8×C43—81no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—81no—
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—21no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188#10621883—42no—
189#10621883—42no—
190#10621883—81no—
191#10621883—81no—
192(C2×D43)⋊C4—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43#4111yescharacteristic
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—81no—
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—41no—
215C23×C43—41no—
216C22×D43#12111yescharacteristic
217D4×C43—21no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—81no—
227D4×C43—81no—
228D4×C43#13512yes—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—24no—
236C22⋊D43—82no—
237C22⋊D43—82no—
238C2×Dic43—24no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—81no—
244C2×Dic43—82no—
245C2×Dic43—82no—
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249C4×D43—21no—
250C4×D43—21no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—41no—
254Dic86—21no—
255Dic86—41no—
256Dic86—41no—
257Dic86—81no—
258Dic86#13512yes—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269#19412—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43C2×#12111yescharacteristic
280C2×D43—21no—
281C2×D43—21no—
282C2×D43—21no—
283C4×C43—21no—
284C4×C43—41no—
285C4×C43C2×#13511yescharacteristic
286C4×C43C2×#13511yescharacteristic
287C4×C43#57611yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—21no—
290Dic43—22no—
291Dic43—21no—
292Dic43—21no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296#3207—431no—
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#1667D4311yescharacteristic, complemented
306#1666—431no—
307#1665—431no—
308#1572—431no—
309#1551—431no—
310#1540—431no—
311C2×C43—42no—
312C2×C43—161no—
313C2×C43—161no—
314C2×C43#304511yescharacteristic
315C2×C43#305011yescharacteristic
316C2×C43#306811yescharacteristic
317D43—41no—
318#532—431no—
319#532—431no—
320C4×#41—431no—
321#493C2×D4311yescharacteristic
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#459C2×D4311yescharacteristic
336#459C2×D4311yescharacteristic
337#449—861no—
338#449—861no—
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—861no—
349C8×D4—861no—
350C8×D4C2×D4311yescharacteristic
351#432—431no—
352#431—431no—
353#431—431no—
354#431—861no—
355C2×C4⋊C8—431no—
356C2×C4⋊C8—861no—
357#335—431no—
358#335C2×D4311yescharacteristic
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#331C2×D4311yescharacteristic
368#331C2×D4311yescharacteristic
369C43#1941211yescharacteristic, complemented, Sylow
370C2×#41—431no—
371C2×#41—861no—
372C2×#41—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C22×C8—21no—
382C22×C8—861no—
383C22×C8—861no—
384C4⋊Q8—431no—
385C4⋊Q8—431no—
386#127C22×D4311yescharacteristic
387#127C22×D4311yescharacteristic
388#124—861no—
389#124—861no—
390#121—861no—
391#121—861no—
392#121—861no—
393#121—861no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404#117—431no—
405#117—861no—
406C2×C42—431no—
407C2×C42—861no—
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—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422C4⋊C8C22×D4311yescharacteristic
423#103—861no—
424#103—861no—
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—21no—
436C22⋊C8—431no—
437C22⋊C8—431no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441#97—861no—
442C4×C8—431no—
443C4×C8—861no—
444C4×C8—861no—
445C4×C8—861no—
446C4×C8C22×D4311yescharacteristic
447#41—862no—
448#41—862no—
449#41—3441no—
450#41—3441no—
451#41—3442no—
452C2×Q8—431no—
453C2×Q8—861no—
454C2×Q8—861no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—861no—
462C2×D4—1721no—
463C2×D4—1721no—
464C2×D4D4×D4311yescharacteristic
465C22×C4—21no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—1721no—
472C22×C4—1721no—
473SD16—3441no—
474SD16—3441no—
475SD16—1722no—
476SD16—1722no—
477D8—42no—
478D8—42no—
479D8—81no—
480D8—81no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—81no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—3441no—
491C2×C8—3441no—
492C2×C8D4×D4311yescharacteristic
493C2×C8D4×D4311yescharacteristic
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4D4×D4311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—1721no—
506C22⋊C4—1721no—
507C22⋊C4—1721no—
508C22⋊C4—1721no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—861no—
513C42—861no—
514C42—861no—
515C42C23×D4311yescharacteristic
516C23—21no—
517C23—41no—
518C23—41no—
519C23—431no—
520Q8—432no—
521Q8—861no—
522Q8—3441no—
523Q8—1721no—
524Q8—1721no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—864no—
537D4—3442no—
538D4—3442no—
539D4#1306334412yes—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—431no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—864no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3442no—
554C2×C4—3442no—
555C2×C4—3441no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—861no—
568C8—861no—
569C8—1721no—
570C8—1721no—
571C8—1721no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—861no—
582C22—861no—
583C22—861no—
584C22#121×D4311yescharacteristic
585C4—21no—
586C4—41no—
587C4—861no—
588C4—861no—
589C4—861no—
590C4—862no—
591C4—3441no—
592C4—3441no—
593C4—1721no—
594C4#135×D4311yescharacteristic
595C4C2×#1306334411yescharacteristic
596C4#1458370011yescharacteristic
597C4#1458370911yescharacteristic
598C2—42no—
599C2—161no—
600C2—161no—
601C2—1721no—
602C2#1914412911yescharacteristic
603C2#1914417411yescharacteristic
604C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1667C2
socleC22×C43C2×#121
hypercenter#1667D43
hypocenterC43#19412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #19145523C2semidirect
2. #19144743C2semidirect
3. #19144652C2semidirect
4. #19143702C2semidirect
5. #19134054C2semidirect
6. #19134046C2semidirect
7. #19134010C2semidirect
8. #19134002C2semidirect
9. #19133952C2semidirect
10. #19133942C2semidirect
11. #19133934C2semidirect
12. #19133374C2semidirect
13. #19133287C2semidirect
14. #19133241C2semidirect
15. C43×#1667C2semidirect
305. #1667D43semidirect
369. C43#19412semidirect

Maximal subgroups

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

subgroupindex
#191455232
#191447432
#191446522
#191437022
#191340542
#191340462
#191340102
#191340022
#191339522
#191339422
#191339342
#191333742
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