Finite Group Databasebeta

← #25080028

Subgroups — #25080028

Order 11008.

562 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#19145779C211yesmaximal, characteristic
2#19145778C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic, complemented
4#19143572C211yesmaximal, characteristic
5#19134121C211yesmaximal, characteristic, complemented
6#19134117C211yesmaximal, characteristic, complemented
7#19134087C211yesmaximal, characteristic, complemented
8#19134083C211yesmaximal, characteristic, complemented
9#19134053C211yesmaximal, characteristic, complemented
10#19134047C211yesmaximal, characteristic, complemented
11#19134043C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic, complemented
13#19133304C211yesmaximal, characteristic, complemented
14#19133302C211yesmaximal, characteristic, complemented
15C43×#1684C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583436C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583300—21no—
21#14583299—21no—
22#14583278C2211yescharacteristic
23#14583255—21no—
24#14583255—21no—
25#14583250C2211yescharacteristic
26#14583239—21no—
27#14583238—21no—
28#14583226—21no—
29#14583225—21no—
30#14583194C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583186C2211yescharacteristic
33#14583184C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583176C2211yescharacteristic
36#14583139—21no—
37#14583139—21no—
38#14583030C2211yescharacteristic
39#14582991—21no—
40#14582991—21no—
41#14582976C2211yescharacteristic
42#14582969—21no—
43C8×D172—21no—
44C8×D172C2211yescharacteristic
45#14582959—21no—
46#14582955C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582853—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621872—21no—
70C2×C8×D43—21no—
71C2×C8×D43D411yescharacteristic
72C2×C8×D43D411yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063320—21no—
76#13063316—21no—
77#13063316—21no—
78#13063316D411yescharacteristic
79#13063314D411yescharacteristic
80#13063310—21no—
81#13063305—21no—
82#13063305—21no—
83#13063301—21no—
84#13063301—21no—
85#13063301D411yescharacteristic
86#13063300D411yescharacteristic
87Q8×Dic43—21no—
88Q8×Dic43—21no—
89#13063290—21no—
90#13063290—21no—
91C4×D172—21no—
92C4×D172C2311yescharacteristic
93#13063283—21no—
94#13063283—21no—
95#13063282—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063247—21no—
114#13063247—21no—
115#13063245—21no—
116#13063245—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C2×D411yescharacteristic
166C42×C43—21no—
167C42×C43C2411yescharacteristic
168#10621885—42no—
169#10621885—42no—
170(C2×D43)⋊C4—21no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—41no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
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⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199#10621872—42no—
200C8×D43—22no—
201C8×D43—41no—
202C8×D43—42no—
203C22×D43—21no—
204C22×D43#12111yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—81no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×Dic43—21no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43#12111yescharacteristic
221C2×Dic43#12111yescharacteristic
222C2×Dic43#12111yescharacteristic
223D172—21no—
224D172—21no—
225D172—42no—
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—21no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—41no—
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—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8#13512yes—
246#19226—431nomaximal, Sylow
247C22×C43C2×#12111yescharacteristic
248C2×D43—21no—
249C2×D43—21no—
250C2×D43—21no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—81no—
258C4×C43—81no—
259C4×C43C2×#13511yescharacteristic
260C4×C43#57511yescharacteristic
261C4×C43#57811yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—21no—
264Dic43—21no—
265Dic43—21no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269#3233—431no—
270#3233—431no—
271#3170—431no—
272#2966—431no—
273#1696—431no—
274#1695—431no—
275#1690—431no—
276#1689—431no—
277#1684—431no—
278#1684D4311yescharacteristic, complemented
279#1683—431no—
280#1683—431no—
281#1564—431no—
282#1554—431no—
283#1554—431no—
284C2×C43#303511yescharacteristic
285C2×C43#305911yescharacteristic
286C2×C43#306711yescharacteristic
287D43—41no—
288D43—81no—
289#533—431no—
290#533—431no—
291#529—431no—
292#500—431no—
293#499—861no—
294#499—861no—
295#494—431no—
296#488—861no—
297#488—861no—
298#487—431no—
299#487C2×D4311yescharacteristic
300#485—861no—
301#485—861no—
302#482—861no—
303#482—861no—
304#477—431no—
305#477C2×D4311yescharacteristic
306#476—431no—
307#476—431no—
308#475—431no—
309#475C2×D4311yescharacteristic
310#474—431no—
311#474—431no—
312#467—861no—
313#467—861no—
314#446—431no—
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—861no—
317C4×Q16—861no—
318#436—431no—
319#435—861no—
320C8×D4—431no—
321C8×D4—861no—
322#433—861no—
323#432—431no—
324#431—431no—
325#431—431no—
326#405—861no—
327C2×C4×C8—431no—
328#335—431no—
329#335C2×D4311yescharacteristic
330#334—431no—
331#334—431no—
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#1922611yescharacteristic, complemented, Sylow
341C2×Q16—861no—
342C2×Q16—861no—
343C2×M16—861no—
344C22×C8—431no—
345C22×C8—431no—
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—861no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×D4—431no—
369C4×D4—861no—
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#107—861no—
380#106—21no—
381#106—861no—
382#106—861no—
383#106—861no—
384C4⋊C8—21no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8C22×D4311yescharacteristic
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#102—861no—
401#102—861no—
402#102—861no—
403#102—861no—
404C22⋊C8—861no—
405C22⋊C8—861no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—861no—
410#97—861no—
411C4×C8—21no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8D4×D4311yescharacteristic
423C2×D4—431no—
424C2×D4—861no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—861no—
429Q16—1722no—
430Q16—1722no—
431M16—1722no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—431no—
436C2×C8—431no—
437C2×C8—862no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—1721no—
442C2×C8—1722no—
443C2×C8D4×D4311yescharacteristic
444C2×C8D4×D4311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—431no—
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—861no—
464C22⋊C4—861no—
465C22⋊C4—861no—
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—21no—
471C42—431no—
472C42—431no—
473C42—431no—
474C42—1721no—
475C42—1721no—
476C42C23×D4311yescharacteristic
477C23—431no—
478C23—861no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—3441no—
485Q8—1721no—
486Q8—1721no—
487D4—861no—
488D4—861no—
489D4—1722no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—431no—
495C2×C4—431no—
496C2×C4—431no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—1721no—
503C2×C4—1721no—
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—432no—
516C8—861no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C22—861no—
521C22—861no—
522C22—861no—
523C22—1721no—
524C22—1721no—
525C22—1721no—
526C22#121×D4311yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—81no—
531C4—81no—
532C4—861no—
533C4—861no—
534C4—861no—
535C4—3441no—
536C4—3441no—
537C4—1721no—
538C4#135×D4311yescharacteristic
539C4#1458369811yescharacteristic
540C4#1458371211yescharacteristic
541C4#1458371311yescharacteristic
542C2—3441no—
543C2—1721no—
544C2#1914404911yescharacteristic
545C2#1914424511yescharacteristic
546C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1684C2
socleC22×C43C2×#121
prime radical#13063300D4
hypercenter#1684D43
hypocenterC43#19226
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
3. #19145180C2semidirect
5. #19134121C2semidirect
6. #19134117C2semidirect
7. #19134087C2semidirect
8. #19134083C2semidirect
9. #19134053C2semidirect
10. #19134047C2semidirect
11. #19134043C2semidirect
12. #19133342C2semidirect
13. #19133304C2semidirect
14. #19133302C2semidirect
15. C43×#1684C2semidirect
278. #1684D43semidirect
340. C43#19226semidirect

Maximal subgroups

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

subgroupindex
#191457792
#191457782
#191451802
#191435722
#191341212
#191341172
#191340872
#191340832
#191340532
#191340472
#191340432
#191333422
#191333042
#191333022
C43×#16842
#1922643