Finite Group Databasebeta

← #25082023

Subgroups — #25082023

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145544C211yesmaximal, characteristic, complemented
2#19144403C211yesmaximal, characteristic
3#19144384C211yesmaximal, characteristic
4#19143702C211yesmaximal, characteristic
5#19134056C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19134048C211yesmaximal, characteristic, complemented
8#19133966C211yesmaximal, characteristic, complemented
9#19133964C211yesmaximal, characteristic, complemented
10#19133960C211yesmaximal, characteristic, complemented
11#19133958C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#332×D43C211yesmaximal, characteristic, complemented
15C43×#1683C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583279C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583209—21no—
23#14583201—21no—
24#14583193—21no—
25#14583191C2211yescharacteristic
26#14583187—21no—
27#14583185C2211yescharacteristic
28#14583185C2211yescharacteristic
29#14583181C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583108—21no—
33#14583108—21no—
34#14583056—21no—
35#14583056—21no—
36C8×Dic86C2211yescharacteristic
37#14583023C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41#14582950C2211yescharacteristic
42#14582949—21no—
43#14582940—21no—
44#14582934—21no—
45#14582921C2211yescharacteristic
46C2×Dic43⋊C8—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582897—21no—
50#14582892—21no—
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063323—21no—
82#13063316—21no—
83#13063305—21no—
84#13063301—21no—
85Q8×Dic43—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290D411yescharacteristic
89D4×Dic43D411yescharacteristic
90C4×C22⋊D43—21no—
91(C22⋊D43)⋊C4—21no—
92#13063283—21no—
93#13063283D411yescharacteristic
94#13063281—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C2×C4×Dic43—21no—
98C42×D43C2311yescharacteristic
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063257—21no—
103#13063257—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115#13063250—21no—
116#13063250—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063248—21no—
121#13063246—21no—
122#13063246—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151Q8×D43—81no—
152Q8×D43—81no—
153#10621900—22no—
154#10621900Q1614yescomplemented
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86C2×D411yescharacteristic
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177#10621885—81no—
178#10621885—81no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
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⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—81no—
206Dic172—81no—
207#10621872—42no—
208C8×D43—42no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43#12111yescharacteristic
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215D4×C43—21no—
216D4×C43C2×Q1612yes—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—24no—
226C2×Dic43—21no—
227C2×Dic43—24no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—81no—
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—41no—
238C4×D43—82no—
239C4×D43C2×Q1612yes—
240C4×D43#13512yes—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—82no—
247Dic86C2×Q1612yes—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19411—431nomaximal, Sylow
259C22×C43—22no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—21no—
264C2×D43—21no—
265C2×D43#46712yes—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C22×Q1611yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43#57611yescharacteristic
273C4×C43#57711yescharacteristic
274Dic43—21no—
275Dic43—22no—
276Dic43—21no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Dic43#46712yes—
281#3209—431no—
282#3079—431no—
283#3076—431no—
284#2988—431no—
285#1684—431no—
286#1684—431no—
287#1683—431no—
288#1683D4311yescharacteristic, complemented
289#1670—431no—
290#1670—431no—
291#1669—431no—
292#1669—431no—
293#1571—431no—
294#1550—431no—
295C2×#332—431no—
296C2×C43—42no—
297C2×C43#304511yescharacteristic
298C2×C43C2×#46711yescharacteristic
299C2×C43#306911yescharacteristic
300D43—22no—
301#533—431no—
302C2×C4⋊Q8—431no—
303C4×#41—431no—
304#494—431no—
305#494—431no—
306#487—431no—
307#487C2×D4311yescharacteristic
308#479—861no—
309#478—861no—
310#477—431no—
311#477—861no—
312#476—861no—
313#476C2×D4311yescharacteristic
314#475—431no—
315#475—431no—
316#475—431no—
317#474—431no—
318#474—431no—
319#474C2×D4311yescharacteristic
320#462—861no—
321#462—861no—
322#451—861no—
323#451—861no—
324C8×Q8—431no—
325C8×Q8—431no—
326C8×D4—431no—
327C8×D4—861no—
328C8×D4—861no—
329C8×D4C2×D4311yescharacteristic
330#431—431no—
331#431—861no—
332#428—861no—
333#427—861no—
334#423—431no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—861no—
338#417—861no—
339#416—861no—
340#335—431no—
341#335—431no—
342#335—431no—
343#335C2×D4311yescharacteristic
344#333—431no—
345#333C2×D4311yescharacteristic
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350#332—431no—
351#332C2×D4311yescharacteristic
352C43#1941111yescharacteristic, complemented, Sylow
353C2×#41—431no—
354C22×Q8—861no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×M16—861no—
360C22×C8—21no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#125—861no—
372C22⋊Q8—861no—
373C22⋊Q8—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—861no—
380C4×D4—861no—
381C4×D4C22×D4311yescharacteristic
382#117—431no—
383#117—861no—
384#117—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—21no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#102—21no—
419#102—21no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—431no—
424C22⋊C8—431no—
425C22⋊C8—861no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—434no—
431#41—862no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—3441no—
438C2×Q8—3441no—
439C2×Q8—1721no—
440C2×D4—861no—
441C2×D4D4×D4311yescharacteristic
442C22×C4—21no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449Q16—3441no—
450Q16—3441no—
451Q16—3441no—
452Q16—3441no—
453M16—1722no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—3441no—
464C2×C8—3441no—
465C2×C8—1722no—
466C2×C8D4×D4311yescharacteristic
467C2×C8D4×D4311yescharacteristic
468C4⋊C4—21no—
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—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—1721no—
488C42—431no—
489C42—431no—
490C42—431no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1721no—
495C42C23×D4311yescharacteristic
496C23—21no—
497C23—431no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—432no—
502Q8—861no—
503Q8—3442no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508D4—21no—
509D4—864no—
510D4Q16×D4312yes—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—431no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—864no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—3442no—
527C2×C4—3441no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—432no—
548C22—861no—
549C22—861no—
550C22#121×D4311yescharacteristic
551C4—21no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—432no—
556C4—861no—
557C4—861no—
558C4—862no—
559C4—3441no—
560C4—3441no—
561C4—1721no—
562C4C2×Q16×D4311yescharacteristic
563C4#135×D4311yescharacteristic
564C4#1458370311yescharacteristic
565C4#1458370611yescharacteristic
566C2—42no—
567C2—862no—
568C2#1914413511yescharacteristic
569C2#467×D4311yescharacteristic
570C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1683C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1683D43
hypocenterC43#19411
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

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

NH ≅ G/Ntype
1. #19145544C2semidirect
5. #19134056C2semidirect
6. #19134050C2semidirect
7. #19134048C2semidirect
8. #19133966C2semidirect
9. #19133964C2semidirect
10. #19133960C2semidirect
11. #19133958C2semidirect
12. #19133368C2semidirect
13. #19133282C2semidirect
14. #332×D43C2semidirect
15. C43×#1683C2semidirect
154. #10621900Q16semidirect
288. #1683D43semidirect
352. C43#19411semidirect

Maximal subgroups

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

subgroupindex
#191455442
#191444032
#191443842
#191437022
#191340562
#191340502
#191340482
#191339662
#191339642
#191339602
#191339582
#191333682
#191332822
#332×D432
C43×#16832
#1941143