Finite Group Databasebeta

← #25084209

Subgroups — #25084209

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145932C211yesmaximal, characteristic
2#19145748C211yesmaximal, characteristic, complemented
3#19145619C211yesmaximal, characteristic
4#19134149C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134113C211yesmaximal, characteristic, complemented
7#19134108C211yesmaximal, characteristic, complemented
8#19134025C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19133989C211yesmaximal, characteristic, complemented
11#19133984C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133293C211yesmaximal, characteristic, complemented
14C2×#14582644C211yesmaximal, characteristic, complemented
15C43×#2994C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583294—21no—
21#14583269—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583235—21no—
25#14583235—21no—
26#14583203—21no—
27#14583195—21no—
28#14583195—21no—
29#14583184C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583138—21no—
32#14583126—21no—
33#14583118—21no—
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583109C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583104C2211yescharacteristic
39#14583104C2211yescharacteristic
40#14583054—21no—
41#14583037—21no—
42#14582956C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582644C2211yescharacteristic
51#14582644C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
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
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C22×C43⋊C8—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063317—21no—
83#13063304—21no—
84#13063304—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87#13063284—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063259—21no—
91#13063259—21no—
92#13063259—21no—
93#13063259—21no—
94#13063258—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#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063248—21no—
112#13063246—21no—
113C22⋊(C43⋊C8)—21no—
114#13063236—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
151C22×Dic43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86—81no—
158C2×Dic86—81no—
159M16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—81no—
163C2×C8×C43—81no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C42×C43—21no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—81no—
186#10621885—81no—
187#10621885—81no—
188#10621883—81no—
189#10621883—81no—
190#10621883—81no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—81no—
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—21no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—42no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—82no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—82no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#19590—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43#47312yes—
263C22×C43C2×#12111yescharacteristic
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43#57611yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—81no—
276Dic43—81no—
277Dic43—81no—
278Dic43—81no—
279#3248—431no—
280#3230—431no—
281#3218—431no—
282#2994D4311yescharacteristic
283#1700—431no—
284#1699—431no—
285#1694—431no—
286#1693—431no—
287#1680—431no—
288#1679—431no—
289#1674—431no—
290#1673—431no—
291#1573—431no—
292#1552—431no—
293C2×#332—431no—
294C2×C43—22no—
295C2×C43—81no—
296C2×C43#304611yescharacteristic
297C2×C43#306211yescharacteristic
298C2×C43C2×#47311yescharacteristic
299#533—431no—
300C2×C4⋊Q8—431no—
301#529C2×D4311yescharacteristic
302#500—431no—
303#500—431no—
304#497—861no—
305#491—861no—
306#487—431no—
307#487—431no—
308#484—861no—
309#484—861no—
310#479—861no—
311#477—861no—
312#477—861no—
313#475—431no—
314#474—431no—
315#467—861no—
316#465—861no—
317#464—861no—
318#462—431no—
319#462—431no—
320#462—431no—
321#461—431no—
322#461—431no—
323#461—431no—
324#451—861no—
325#448—861no—
326#446C2×D4311yescharacteristic
327C8×Q8C2×D4311yescharacteristic
328#436C2×D4311yescharacteristic
329#435—21no—
330C8×D4—21no—
331C8×D4C2×D4311yescharacteristic
332#433—21no—
333#432—431no—
334#431C2×D4311yescharacteristic
335#424—21no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338#335—431no—
339#335—431no—
340#334—431no—
341#334—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350C43#1959011yescharacteristic, complemented, Sylow
351C22×Q8—861no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—861no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369#126—21no—
370#125—861no—
371#125D17211yescharacteristic
372#124D17211yescharacteristic
373#123—21no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376C22⋊Q8D17211yescharacteristic
377#121D17211yescharacteristic
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4C22×D4311yescharacteristic
383#117—21no—
384#117—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C42C22×D4311yescharacteristic
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8C22⋊D4311yescharacteristic
403C4⋊C8C22⋊D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8C22⋊D4311yescharacteristic
422C22⋊C8C22⋊D4311yescharacteristic
423#97—21no—
424#97—861no—
425C4×C8—21no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—3441no—
433C2×Q8—3441no—
434C2×Q8—1721no—
435C2×Q8C2×D17211yescharacteristic
436C2×D4—21no—
437C2×D4C2×D17211yescharacteristic
438C22×C4—21no—
439C22×C4—1721no—
440C22×C4C2×D17211yescharacteristic
441C22×C4#1062189811yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446SD16—3441no—
447SD16—3441no—
448SD16—3441no—
449M16—81no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8—81no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4C2×D17211yescharacteristic
480C4⋊C4C2×D17211yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1721no—
487C42—21no—
488C42—1721no—
489C42C2×D17211yescharacteristic
490C42#1062189811yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—21no—
494C23#1306329911yescharacteristic
495Q8—21no—
496Q8—21no—
497Q8—3442no—
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—21no—
507D4—21no—
508D4—42no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—3442no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4#1306329911yescharacteristic
525C2×C4#1306329911yescharacteristic
526C2×C4#1306329911yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4C22×D17211yescharacteristic
529C2×C4C2×#1062189811yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#1458317412yes—
546C22C2×#1306329911yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—3441no—
555C4—3441no—
556C4—3441no—
557C4—3441no—
558C4#1458370411yescharacteristic
559C4#1458371011yescharacteristic
560C4#1458371111yescharacteristic
561C4#1458371411yescharacteristic
562C2—22no—
563C2—81no—
564C2#1914414511yescharacteristic
565C2#1914427511yescharacteristic
566C2C2×#1458317411yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2994C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2994D43
hypocenterC43#19590
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
2. #19145748C2semidirect
4. #19134149C2semidirect
5. #19134142C2semidirect
6. #19134113C2semidirect
7. #19134108C2semidirect
8. #19134025C2semidirect
9. #19134018C2semidirect
10. #19133989C2semidirect
11. #19133984C2semidirect
12. #19133380C2semidirect
13. #19133293C2semidirect
14. C2×#14582644C2semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191457482
#191456192
#191341492
#191341422
#191341132
#191341082
#191340252
#191340182
#191339892
#191339842
#191333802
#191332932
C2×#145826442
C43×#29942
#1959043