Finite Group Databasebeta

← #25081924

Subgroups — #25081924

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145523C211yesmaximal, characteristic
2#19144716C211yesmaximal, characteristic, complemented
3#19144625C211yesmaximal, characteristic, complemented
4#19143674C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134009C211yesmaximal, characteristic, complemented
9#19133952C211yesmaximal, characteristic, complemented
10#19133942C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133297C211yesmaximal, characteristic, complemented
14#19133254C211yesmaximal, characteristic, complemented
15C43×#1668C211yesmaximal, characteristic, complemented
16#14583447C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583271C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583216—21no—
23#14583211—21no—
24#14583195C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583112—21no—
29#14583112—21no—
30#14583096C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583041—21no—
33#14583041—21no—
34#14583036—21no—
35#14583036—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14583000—21no—
42#14582996—21no—
43#14582990—21no—
44SD16×Dic43—21no—
45#14582955C2211yescharacteristic
46#14582951—21no—
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950—21no—
50#14582950C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582643C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#493C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×#10621900—21no—
69C2×Q8×D43D411yescharacteristic
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063312—21no—
77#13063312—21no—
78#13063296—21no—
79#13063296—21no—
80#13063296—21no—
81#13063296—21no—
82Q8×Dic43D411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290D411yescharacteristic
87D4×Dic43—21no—
88D4×Dic43—21no—
89D4×Dic43—21no—
90D4×Dic43—21no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43D411yescharacteristic
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×SD16×C43—21no—
131C2×D8×C43—21no—
132C2×D8×C43—21no—
133#127×C43C2311yescharacteristic
134#127×C43C2311yescharacteristic
135C4×Q8×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#102×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C22×Dic43—41no—
154C22×Dic43—41no—
155Q8×D43—22no—
156Q8×D43—22no—
157#10621900—81no—
158#10621900—81no—
159#10621900—82no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86C2×D411yescharacteristic
169SD16×C43—42no—
170SD16×C43—42no—
171D8×C43—81no—
172D8×C43—81no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D411yescharacteristic
180C42×C43—21no—
181C42×C43C2411yescharacteristic
182C22⋊Dic43—41no—
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621883—42no—
187#10621883—42no—
188#10621883—81no—
189#10621883—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43C2×D411yescharacteristic
203C4×Dic43C2×D411yescharacteristic
204C4×Dic43#4111yescharacteristic
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C23×C43—41no—
211C23×C43—41no—
212C22×D43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43#13512yes—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223D4×C43—81no—
224D4×C43—81no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—82no—
231C22⋊D43—82no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—82no—
237C2×Dic43—82no—
238C2×Dic43#12111yescharacteristic
239C2×Dic43#12111yescharacteristic
240C2×Dic43#12111yescharacteristic
241C4×D43—24no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—41no—
247C4×D43—81no—
248Dic86—24no—
249Dic86—21no—
250Dic86—41no—
251Dic86—41no—
252Dic86—81no—
253Dic86#13512yes—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19401—431nomaximal, Sylow
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—21no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—21no—
283Dic43—21no—
284Dic43—22no—
285Dic43—21no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289#3207—431no—
290#3112—431no—
291#3103—431no—
292#2982—431no—
293#1684—431no—
294#1684—431no—
295#1678—431no—
296#1678—431no—
297#1668—431no—
298#1668D4311yescharacteristic, complemented
299#1666—431no—
300#1666—431no—
301#1572—431no—
302#1553—431no—
303#1543—431no—
304C2×C43—161no—
305C2×C43—161no—
306C2×C43#304311yescharacteristic
307C2×C43#305011yescharacteristic
308C2×C43#306811yescharacteristic
309D43—41no—
310#532—431no—
311#532—431no—
312C2×C4×Q8—431no—
313#493C2×D4311yescharacteristic
314#492—431no—
315#487—431no—
316#486—431no—
317#481—861no—
318#480—861no—
319#477—431no—
320#477—431no—
321#475—431no—
322#475—431no—
323#463—861no—
324#463—861no—
325#460—431no—
326#460—431no—
327#460C2×D4311yescharacteristic
328#460C2×D4311yescharacteristic
329#449—861no—
330#449—861no—
331#448—861no—
332#448—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335C8×Q8—431no—
336C8×Q8—861no—
337C8×Q8—861no—
338C8×Q8C2×D4311yescharacteristic
339#440—861no—
340#440—861no—
341C4×SD16—861no—
342C4×SD16—861no—
343#432—431no—
344#431—431no—
345#431—431no—
346#431—431no—
347#431—861no—
348#431—861no—
349#335—431no—
350#335C2×D4311yescharacteristic
351#334—431no—
352#334—431no—
353#333—431no—
354#333—431no—
355#332—431no—
356#332—431no—
357#331—431no—
358#331—431no—
359#331C2×D4311yescharacteristic
360#331C2×D4311yescharacteristic
361C43#1940111yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C2×#41—861no—
364C22×Q8—431no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—21no—
372C2×D8—21no—
373C4⋊Q8—431no—
374C4⋊Q8—431no—
375#127C22×D4311yescharacteristic
376#127C22×D4311yescharacteristic
377#124—861no—
378#124—861no—
379#121—861no—
380#121—861no—
381#121—861no—
382#121—861no—
383C4×Q8—431no—
384C4×Q8—431no—
385C4×Q8—431no—
386C4×Q8—861no—
387C4×Q8—861no—
388C4×Q8C22×D4311yescharacteristic
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—861no—
395C2×C42—431no—
396C2×C42—861no—
397#107—861no—
398#107—861no—
399#106—861no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—21no—
420#102—21no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—431no—
426C22⋊C8—431no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430#97—861no—
431C4×C8—21no—
432C4×C8—431no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8—861no—
438C4×C8C22×D4311yescharacteristic
439#41—3441no—
440#41—3441no—
441#41—3442no—
442C2×Q8—431no—
443C2×Q8—861no—
444C2×Q8—862no—
445C2×Q8—862no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8D4×D4311yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—1721no—
456C2×D4—1721no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—1721no—
463C22×C4—1721no—
464SD16—42no—
465SD16—42no—
466SD16—3441no—
467SD16—3441no—
468SD16—1722no—
469SD16—1722no—
470D8—81no—
471D8—81no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8D4×D4311yescharacteristic
481C2×C8D4×D4311yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—431no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4D4×D4311yescharacteristic
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—21no—
498C42—431no—
499C42—431no—
500C42—431no—
501C42—861no—
502C42—861no—
503C42—861no—
504C42C23×D4311yescharacteristic
505C23—41no—
506C23—41no—
507C23—431no—
508Q8—21no—
509Q8—432no—
510Q8—864no—
511Q8—861no—
512Q8—3441no—
513Q8—1721no—
514Q8—1721no—
515Q8#1306334412yes—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—81no—
526D4—3442no—
527D4—3442no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—431no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—864no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3441no—
541C2×C4—3442no—
542C2×C4—3442no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—861no—
555C8—861no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—861no—
566C22—861no—
567C22—861no—
568C22#121×D4311yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—861no—
573C4—861no—
574C4—861no—
575C4—862no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4C2×#1306334411yescharacteristic
581C4#1458370511yescharacteristic
582C4#1458370911yescharacteristic
583C2—161no—
584C2—161no—
585C2—1721no—
586C2#1914411111yescharacteristic
587C2#1914417411yescharacteristic
588C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1668C2
socleC22×C43C2×#121
prime radical#19145523C2
hypercenter#1668D43
hypocenterC43#19401
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1668

Complements

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

NH ≅ G/Ntype
2. #19144716C2semidirect
3. #19144625C2semidirect
4. #19143674C2semidirect
5. #19134054C2semidirect
6. #19134053C2semidirect
7. #19134010C2semidirect
8. #19134009C2semidirect
9. #19133952C2semidirect
10. #19133942C2semidirect
11. #19133941C2semidirect
12. #19133374C2semidirect
13. #19133297C2semidirect
14. #19133254C2semidirect
15. C43×#1668C2semidirect
298. #1668D43semidirect
361. C43#19401semidirect

Maximal subgroups

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

subgroupindex
#191455232
#191447162
#191446252
#191436742
#191340542
#191340532
#191340102
#191340092
#191339522
#191339422
#191339412
#191333742
#191332972
#191332542
C43×#16682
#1940143