Finite Group Databasebeta

← #25082131

Subgroups — #25082131

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145726C211yesmaximal, characteristic, complemented
2#19144756C211yesmaximal, characteristic, complemented
3#19144654C211yesmaximal, characteristic
4#19143705C211yesmaximal, characteristic, complemented
5#19134029C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19134003C211yesmaximal, characteristic, complemented
8#19133999C211yesmaximal, characteristic, complemented
9#19133995C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133969C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133287C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1682C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×#10621902C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583238—21no—
23#14583222—21no—
24#14583221—21no—
25#14583221—21no—
26#14583197—21no—
27#14583197—21no—
28#14583194C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583101C2211yescharacteristic
33#14583091C2211yescharacteristic
34#14583060—21no—
35#14583043—21no—
36Q8×C43⋊C8C2211yescharacteristic
37#14583006—21no—
38#14583002—21no—
39SD16×Dic43—21no—
40#14582979—21no—
41C8×D172—21no—
42C8×D172C2211yescharacteristic
43#14582964—21no—
44#14582964C2211yescharacteristic
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950—21no—
48#14582950C2211yescharacteristic
49C4⋊C8×D43—21no—
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×#10621900—21no—
69C2×#10621884—21no—
70C2×#10621882—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063312—21no—
78#13063305—21no—
79#13063301—21no—
80#13063296—21no—
81#13063296—21no—
82Q8×Dic43—21no—
83Q8×Dic43D411yescharacteristic
84#13063290—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87D4×Dic43—21no—
88D4×Dic43—21no—
89#13063287—21no—
90#13063287D411yescharacteristic
91#13063283—21no—
92#13063283—21no—
93#13063283D411yescharacteristic
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063247—21no—
115#13063247—21no—
116#13063246—21no—
117#13063246—21no—
118#13063246—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8—21no—
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151#10621902—22no—
152#10621902—22no—
153#10621900—82no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164Q16×C43—42no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179#10621884—42no—
180#10621882—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C8×D43—81no—
205C8×D43—81no—
206C8×D43—81no—
207C23×C43—41no—
208C22×D43—21no—
209C22×D43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43#13512yes—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—82no—
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—82no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233D172—24no—
234D172—21no—
235D172#13512yes—
236C4×D43—24no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—81no—
245Dic86—81no—
246Dic86—81no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—21no—
263C2×D43—22no—
264C2×D43—21no—
265C2×D43—21no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—22no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13511yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106—431no—
285#2988—431no—
286#1682D4311yescharacteristic, complemented
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—161no—
298C2×C43#304611yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306811yescharacteristic
301D43—41no—
302D43—42no—
303#533—431no—
304#532—431no—
305C4×#41—431no—
306#500—431no—
307#498—431no—
308#486—431no—
309#486C2×D4311yescharacteristic
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476—431no—
320#462C2×D4311yescharacteristic
321#461—431no—
322#460C2×D4311yescharacteristic
323#459—431no—
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8C2×D4311yescharacteristic
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432—431no—
337#431—431no—
338#431—431no—
339#431—861no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335C2×D4311yescharacteristic
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332C2×D4311yescharacteristic
352#331—431no—
353#331C2×D4311yescharacteristic
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—431no—
356C2×#41—861no—
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8C22×D4311yescharacteristic
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4—861no—
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—431no—
421C22⋊C8—431no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427C4×C8—21no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432#41—862no—
433#41—862no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8D4×D4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—431no—
443C2×D4—861no—
444C2×D4—1721no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—1721no—
452Q16—42no—
453SD16—42no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—3441no—
465C2×C8—3441no—
466C2×C8—3441no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—431no—
489C42—431no—
490C42—431no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—41no—
496C23—431no—
497C23—861no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—3441no—
502Q8—3441no—
503Q8#1306334412yes—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—432no—
510D4—864no—
511D4—861no—
512D4—3442no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—431no—
517C2×C4—431no—
518C2×C4—431no—
519C2×C4—864no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3441no—
526C2×C4—3442no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4#41×D4311yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—861no—
541C8—861no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—861no—
549C22—861no—
550C22—862no—
551C22—861no—
552C22—1721no—
553C22—1721no—
554C22#121×D4311yescharacteristic
555C4—21no—
556C4—22no—
557C4—41no—
558C4—81no—
559C4—861no—
560C4—861no—
561C4—861no—
562C4—3441no—
563C4—3441no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4C2×#1306334411yescharacteristic
567C4#1458370611yescharacteristic
568C4#1458371511yescharacteristic
569C2—161no—
570C2—1721no—
571C2—1722no—
572C2#1914414811yescharacteristic
573C2#1914417411yescharacteristic
574C2#1914431811yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1682C2
socleC22×C43C2×#121
prime radical#19144654C2
hypercenter#1682D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
1. #19145726C2semidirect
2. #19144756C2semidirect
4. #19143705C2semidirect
5. #19134029C2semidirect
6. #19134009C2semidirect
7. #19134003C2semidirect
8. #19133999C2semidirect
9. #19133995C2semidirect
10. #19133975C2semidirect
11. #19133969C2semidirect
12. #19133374C2semidirect
13. #19133287C2semidirect
14. #19133251C2semidirect
15. C43×#1682C2semidirect
286. #1682D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457262
#191447562
#191446542
#191437052
#191340292
#191340092
#191340032
#191339992
#191339952
#191339752
#191339692
#191333742
#191332872
#191332512
C43×#16822
#1941943