Finite Group Databasebeta

← #25084164

Subgroups — #25084164

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#19145968C211yesmaximal, characteristic
2#19145770C211yesmaximal, characteristic
3#19145756C211yesmaximal, characteristic, complemented
4#19134170C211yesmaximal, characteristic, complemented
5#19134149C211yesmaximal, characteristic, complemented
6#19134123C211yesmaximal, characteristic, complemented
7#19134094C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19133994C211yesmaximal, characteristic, complemented
11#19133977C211yesmaximal, characteristic, complemented
12#19133384C211yesmaximal, characteristic, complemented
13#19133283C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583298—21no—
20#14583297C2211yescharacteristic
21#14583253—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583241—21no—
25#14583241—21no—
26#14583237—21no—
27#14583220—21no—
28#14583207—21no—
29#14583207—21no—
30#14583203—21no—
31#14583194C2211yescharacteristic
32#14583194C2211yescharacteristic
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583184C2211yescharacteristic
36#14583179C2211yescharacteristic
37#14583155—21no—
38#14583143—21no—
39#14583118—21no—
40#14583109C2211yescharacteristic
41#14583104C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582923C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621877—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063317—21no—
75#13063317—21no—
76#13063304—21no—
77#13063304—21no—
78#13063304—21no—
79#13063304—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84#13063284—21no—
85#13063284—21no—
86#13063259—21no—
87#13063259—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063250—21no—
102#13063250—21no—
103#13063250—21no—
104#13063250—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8—21no—
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43D411yescharacteristic
120#124×C43D411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155M16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—81no—
159C2×C8×C43—81no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C2×D411yescharacteristic
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—21no—
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181C22⋊Dic43—41no—
182#10621885—81no—
183#10621883—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C23×C43—21no—
204C23×C43#12111yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207D4×C43—21no—
208D4×C43—21no—
209D4×C43—42no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230Dic86—41no—
231Dic86—41no—
232Dic86—41no—
233Dic86—41no—
234Dic86—81no—
235Dic86—81no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43—41no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19587—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43C2×#12111yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43#57711yescharacteristic
262C4×C43#57711yescharacteristic
263C4×C43#57811yescharacteristic
264C4×C43#57811yescharacteristic
265Dic43—81no—
266Dic43—81no—
267Dic43—81no—
268Dic43—81no—
269#3252—431no—
270#3233—431no—
271#3231—431no—
272#2994D4311yescharacteristic
273#1703—431no—
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—41no—
285C2×C43—81no—
286C2×C43#304611yescharacteristic
287C2×C43#306311yescharacteristic
288C2×C43#306711yescharacteristic
289#533—431no—
290#533—431no—
291#529C2×D4311yescharacteristic
292#500—431no—
293#499—861no—
294#498—431no—
295#488—861no—
296#487—431no—
297#487—431no—
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#476—431no—
309#475—431no—
310#474—431no—
311#470—861no—
312#468—861no—
313#464—861no—
314#462—431no—
315#461—431no—
316#446C2×D4311yescharacteristic
317C8×Q8C2×D4311yescharacteristic
318#436C2×D4311yescharacteristic
319#435—21no—
320C8×D4—21no—
321C8×D4C2×D4311yescharacteristic
322#433—21no—
323#431—431no—
324#431C2×D4311yescharacteristic
325#424—21no—
326#423—431no—
327C2×C4⋊C8C2×D4311yescharacteristic
328#335—431no—
329#335—431no—
330#334—431no—
331#334—431no—
332#333—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#332—431no—
337#332—431no—
338#332—431no—
339#332—431no—
340C43#1958711yescharacteristic, complemented, Sylow
341C2×Q16—861no—
342C2×SD16—861no—
343C2×M16—21no—
344C2×M16—861no—
345C22×C8—21no—
346C22×C8—21no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351#126—21no—
352#125—861no—
353#125—861no—
354#125D17211yescharacteristic
355#124D17211yescharacteristic
356#123—21no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8D17211yescharacteristic
362#121D17211yescharacteristic
363C4×Q8—861no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×D4—21no—
369C4×D4C22×D4311yescharacteristic
370#117—21no—
371#117—861no—
372#117—861no—
373C2×C42C22×D4311yescharacteristic
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#106—861no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8C22⋊D4311yescharacteristic
393C4⋊C8C22⋊D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#102—861no—
406#102—861no—
407#102—861no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—861no—
411C22⋊C8C22⋊D4311yescharacteristic
412C22⋊C8C22⋊D4311yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8C2×D17211yescharacteristic
423C2×D4—21no—
424C2×D4C2×D17211yescharacteristic
425C22×C4—21no—
426C22×C4C2×D17211yescharacteristic
427C22×C4#1062189811yescharacteristic
428C22×C4C2×C22⋊D4311yescharacteristic
429Q16—3441no—
430SD16—3441no—
431M16—81no—
432M16—3441no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—81no—
436C2×C8—81no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8C2×C22⋊D4311yescharacteristic
442C2×C8C2×C22⋊D4311yescharacteristic
443C2×C8C2×C22⋊D4311yescharacteristic
444C2×C8C2×C22⋊D4311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4C2×D17211yescharacteristic
462C4⋊C4C2×D17211yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—21no—
471C42—1721no—
472C42—1721no—
473C42C2×D17211yescharacteristic
474C42#1062189811yescharacteristic
475C42C2×C22⋊D4311yescharacteristic
476C42C23×D4311yescharacteristic
477C23—21no—
478C23#1306329911yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—3441no—
482Q8—3441no—
483Q8—1721no—
484Q8—1721no—
485Q8—1721no—
486Q8—1721no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4#1306329911yescharacteristic
505C2×C4#1306329911yescharacteristic
506C2×C4#1306329911yescharacteristic
507C2×C4C22×C22⋊D4311yescharacteristic
508C2×C4C22×D17211yescharacteristic
509C2×C4C2×#1062189811yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—1721no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#1306329911yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—3441no—
535C4—3441no—
536C4—3441no—
537C4—3441no—
538C4#1458371011yescharacteristic
539C4#1458371111yescharacteristic
540C4#1458371411yescharacteristic
541C4#1458371611yescharacteristic
542C2—41no—
543C2—81no—
544C2#1914414511yescharacteristic
545C2#1914428611yescharacteristic
546C2#1914431511yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2994D43
hypocenterC43#19587
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2994

Complements

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

NH ≅ G/Ntype
3. #19145756C2semidirect
4. #19134170C2semidirect
5. #19134149C2semidirect
6. #19134123C2semidirect
7. #19134094C2semidirect
8. #19134053C2semidirect
9. #19134018C2semidirect
10. #19133994C2semidirect
11. #19133977C2semidirect
12. #19133384C2semidirect
13. #19133283C2semidirect
14. #19133253C2semidirect
340. C43#19587semidirect

Maximal subgroups

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

subgroupindex
#191459682
#191457702
#191457562
#191341702
#191341492
#191341232
#191340942
#191340532
#191340182
#191339942
#191339772
#191333842
#191332832
#191332532
C43×#29942
#1958743