Finite Group Databasebeta

← #25084169

Subgroups — #25084169

Order 11008.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145970C211yesmaximal, characteristic
2#19145772C211yesmaximal, characteristic
3#19145749C211yesmaximal, characteristic, complemented
4#19143756C211yesmaximal, characteristic
5#19134148C211yesmaximal, characteristic, complemented
6#19134122C211yesmaximal, characteristic, complemented
7#19134094C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19133992C211yesmaximal, characteristic, complemented
11#19133978C211yesmaximal, characteristic, complemented
12#19133382C211yesmaximal, characteristic, complemented
13#19133284C211yesmaximal, characteristic, complemented
14#19133249C211yesmaximal, characteristic, complemented
15C43×#1703C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583300—21no—
21#14583297C2211yescharacteristic
22#14583252—21no—
23#14583249C2211yescharacteristic
24#14583242—21no—
25#14583238—21no—
26#14583238—21no—
27#14583221—21no—
28#14583209—21no—
29#14583204—21no—
30#14583204—21no—
31#14583195C2211yescharacteristic
32#14583191C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583181C2211yescharacteristic
35#14583158—21no—
36#14583144—21no—
37#14583120—21no—
38#14583110C2211yescharacteristic
39#14583104C2211yescharacteristic
40#14583026C2211yescharacteristic
41C8×Dic86C2211yescharacteristic
42#14582968—21no—
43D4×C43⋊C8C2211yescharacteristic
44(C22⋊D43)⋊C8—21no—
45#14582957—21no—
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582927—21no—
49#14582921C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621883—21no—
69C2×#10621872—21no—
70C22×C43⋊C8—21no—
71C2×C8×D43—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063318—21no—
75#13063316—21no—
76#13063316—21no—
77#13063316D411yescharacteristic
78#13063312D411yescharacteristic
79#13063307—21no—
80#13063305—21no—
81#13063305—21no—
82#13063305D411yescharacteristic
83#13063301—21no—
84#13063301—21no—
85#13063296D411yescharacteristic
86Q8×Dic43—21no—
87Q8×Dic43—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90#13063290—21no—
91C4×C22⋊D43—21no—
92#13063284—21no—
93#13063283—21no—
94#13063283—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063246—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8D411yescharacteristic
124(C2×D43)⋊C8D411yescharacteristic
125#13063235—21no—
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×M16×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—
149C2×C4×D43C2×D411yescharacteristic
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43#4111yescharacteristic
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155M16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C2×D411yescharacteristic
166C22⋊C4×C43—21no—
167C42×C43C2411yescharacteristic
168C22⋊Dic43—21no—
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171#10621883—81no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183C4⋊Dic43C2×D411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—21no—
189C4×Dic43—41no—
190C4×Dic43—41no—
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43#4111yescharacteristic
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—81no—
201#10621872—81no—
202C8×D43—81no—
203C23×C43—21no—
204C22×D43#12111yescharacteristic
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—81no—
208D4×C43—21no—
209D4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C22⋊D43—42no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12111yescharacteristic
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—21no—
230C4×D43—41no—
231Dic86—21no—
232Dic86—21no—
233Dic86—41no—
234Dic86—41no—
235Dic86—81no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—41no—
239C8×C43—41no—
240C8×C43—41no—
241C43⋊C8—21no—
242C43⋊C8—21no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19587—431nomaximal, Sylow
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43C2×#12111yescharacteristic
251C2×D43—21no—
252C2×D43—21no—
253C2×D43—21no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43#57711yescharacteristic
259C4×C43#57711yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262Dic43—21no—
263Dic43—21no—
264Dic43—21no—
265Dic43—41no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269#3252—431no—
270#3233—431no—
271#3231—431no—
272#2994—431no—
273#1703D4311yescharacteristic, complemented
274#1700—431no—
275#1696—431no—
276#1691—431no—
277#1684—431no—
278#1679—431no—
279#1675—431no—
280#1672—431no—
281#1574—431no—
282#1550—431no—
283#1542—431no—
284C2×C43—81no—
285C2×C43#304611yescharacteristic
286C2×C43#306311yescharacteristic
287C2×C43#306711yescharacteristic
288D43—41no—
289#533—431no—
290#533—431no—
291#529—431no—
292#500—431no—
293#499—861no—
294#498—431no—
295#488—861no—
296#487—431no—
297#487C2×D4311yescharacteristic
298#485—861no—
299#485—861no—
300#485—861no—
301#482—861no—
302#479—861no—
303#479—861no—
304#479—861no—
305#477—431no—
306#477—431no—
307#476—431no—
308#476C2×D4311yescharacteristic
309#475—431no—
310#474C2×D4311yescharacteristic
311#470—861no—
312#468—861no—
313#464—861no—
314#462—431no—
315#461—431no—
316#446—431no—
317C8×Q8—431no—
318#436C2×D4311yescharacteristic
319#435—861no—
320C8×D4—431no—
321C8×D4—861no—
322#433—861no—
323#431—431no—
324#431—431no—
325#424—861no—
326#423—431no—
327C2×C4⋊C8—431no—
328#335—431no—
329#335—431no—
330#334—431no—
331#334C2×D4311yescharacteristic
332#333—431no—
333#333—431no—
334#333—431no—
335#333C2×D4311yescharacteristic
336#332—431no—
337#332—431no—
338#332—431no—
339#332C2×D4311yescharacteristic
340C43#1958711yescharacteristic, complemented, Sylow
341C2×Q16—861no—
342C2×SD16—861no—
343C2×M16—21no—
344C2×M16—861no—
345C22×C8—861no—
346C22×C8—861no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8C22×D4311yescharacteristic
350C4⋊Q8C22×D4311yescharacteristic
351#126—861no—
352#125—431no—
353#125—861no—
354#125—861no—
355#124—431no—
356#123—861no—
357C22⋊Q8—431no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—861no—
362#121—431no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×D4—861no—
369C4×D4C22×D4311yescharacteristic
370#117—861no—
371#117—861no—
372#117—861no—
373C2×C42—431no—
374#107—21no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#106—21no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#102—21no—
406#102—21no—
407#102—861no—
408C22⋊C8—21no—
409C22⋊C8—431no—
410C22⋊C8—431no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—861no—
414C4×C8—431no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—431no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—861no—
424C2×D4D4×D4311yescharacteristic
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429Q16—3441no—
430SD16—3441no—
431M16—81no—
432M16—3441no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—431no—
437C2×C8—431no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—3441no—
442C2×C8—3441no—
443C2×C8D4×D4311yescharacteristic
444C2×C8D4×D4311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—431no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4D4×D4311yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—861no—
465C22⋊C4—861no—
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—431no—
471C42—431no—
472C42—431no—
473C42—861no—
474C42—1721no—
475C42—1721no—
476C42C23×D4311yescharacteristic
477C23—21no—
478C23—431no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—861no—
483Q8—861no—
484Q8—3441no—
485Q8—1721no—
486Q8—1721no—
487D4—21no—
488D4—21no—
489D4—1722no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—431no—
496C2×C4—431no—
497C2×C4—431no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C2×D4×D4311yescharacteristic
509C2×C4#41×D4311yescharacteristic
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—861no—
516C8—861no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—861no—
524C22—861no—
525C22—861no—
526C22#121×D4311yescharacteristic
527C4—21no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—861no—
532C4—861no—
533C4—861no—
534C4—3441no—
535C4—3441no—
536C4—1721no—
537C4—1721no—
538C4#1458370811yescharacteristic
539C4#1458370911yescharacteristic
540C4#1458371311yescharacteristic
541C4#1458371511yescharacteristic
542C2—81no—
543C2—1721no—
544C2#1914414611yescharacteristic
545C2#1914428311yescharacteristic
546C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1703C2
socleC22×C43C2×#121
prime radical#13063296D4
hypercenter#1703D43
hypocenterC43#19587
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
3. #19145749C2semidirect
5. #19134148C2semidirect
6. #19134122C2semidirect
7. #19134094C2semidirect
8. #19134050C2semidirect
9. #19134016C2semidirect
10. #19133992C2semidirect
11. #19133978C2semidirect
12. #19133382C2semidirect
13. #19133284C2semidirect
14. #19133249C2semidirect
15. C43×#1703C2semidirect
273. #1703D43semidirect
340. C43#19587semidirect

Maximal subgroups

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

subgroupindex
#191459702
#191457722
#191457492
#191437562
#191341482
#191341222
#191340942
#191340502
#191340162
#191339922
#191339782
#191333822
#191332842
#191332492
C43×#17032
#1958743