Finite Group Databasebeta

← #25084203

Subgroups — #25084203

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#19145926C211yesmaximal, characteristic
2#19145622C211yesmaximal, characteristic
3#19143757C211yesmaximal, characteristic
4#19134146C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134110C211yesmaximal, characteristic, complemented
7#19134105C211yesmaximal, characteristic, complemented
8#19134022C211yesmaximal, characteristic, complemented
9#19134015C211yesmaximal, characteristic, complemented
10#19133986C211yesmaximal, characteristic, complemented
11#19133981C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14C2×#14582645C211yesmaximal, characteristic, complemented
15C43×#3230C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583291—21no—
18#14583267—21no—
19#14583206—21no—
20#14583181C2211yescharacteristic
21#14583176C2211yescharacteristic
22#14583138—21no—
23#14583130—21no—
24#14583121—21no—
25#14583106C2211yescharacteristic
26#14583106C2211yescharacteristic
27#14583106C2211yescharacteristic
28#14583101C2211yescharacteristic
29#14583101C2211yescharacteristic
30#14583101C2211yescharacteristic
31#14583055—21no—
32#14583038—21no—
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582967—21no—
37C8×D172C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582959—21no—
40#14582956C2211yescharacteristic
41#14582924—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#500C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#484—21no—
63C43×#484—21no—
64C43×#477—21no—
65C43×#477—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063319—21no—
78#13063317D411yescharacteristic
79#13063313D411yescharacteristic
80#13063308—21no—
81#13063304D411yescharacteristic
82#13063299D411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2311yescharacteristic
85C4×C22⋊D43—21no—
86#13063282—21no—
87#13063258—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063248—21no—
106#13063245—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111#13063235—21no—
112C8×Dic43—21no—
113C22×Q8×C43—21no—
114C4⋊Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126#117×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—41no—
149C2×Q8×C43—81no—
150C2×Q8×C43—81no—
151C22×C4×C43—41no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C42×C43—41no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621885—81no—
183#10621885—81no—
184#10621885—81no—
185#10621884—81no—
186#10621884—81no—
187#10621884—81no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C2×D411yescharacteristic
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—81no—
206C2×C43⋊C8—81no—
207#10621872—81no—
208C8×D43—81no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—82no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—82no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—42no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240D172—21no—
241D172—21no—
242C4×D43—41no—
243C4×D43—41no—
244Dic86—21no—
245Dic86—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C43⋊C8—41no—
251C43⋊C8—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#47312yes—
260C22×C43C2×#12111yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43#57611yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3248—431no—
280#3230D4311yescharacteristic, complemented
281#3218—431no—
282#2994—431no—
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#304611yescharacteristic
296C2×C43#306211yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—81no—
299#533C2×D4311yescharacteristic
300C2×C4⋊Q8C2×D4311yescharacteristic
301#529—431no—
302#500C2×D4311yescharacteristic
303#500C2×D4311yescharacteristic
304#497—861no—
305#491—861no—
306#487C2×D4311yescharacteristic
307#487C2×D4311yescharacteristic
308#484—21no—
309#484—21no—
310#479—861no—
311#477—21no—
312#477—21no—
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#446—431no—
327C8×Q8—431no—
328#436—431no—
329#435—861no—
330C8×D4—431no—
331C8×D4—861no—
332#433—861no—
333#432—431no—
334#431C2×D4311yescharacteristic
335#424—861no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—431no—
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—21no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—861no—
359C22×C8—861no—
360C22×C8—861no—
361C22×C8—861no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—861no—
370#125—21no—
371#125—431no—
372#124—431no—
373#123—861no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—431no—
377#121—431no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—431no—
381C4×D4—431no—
382C4×D4—861no—
383#117—21no—
384#117—861no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C22×D4311yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22⋊D4311yescharacteristic
405C4⋊C8C22⋊D4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
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—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8C22⋊D4311yescharacteristic
422C22⋊C8C22⋊D4311yescharacteristic
423#97—861no—
424#97—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8—431no—
436C2×D4—431no—
437C2×D4—861no—
438C22×C4—41no—
439C22×C4—861no—
440C22×C4D4×D4311yescharacteristic
441C22×C4#1062190011yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446SD16—3441no—
447SD16—3441no—
448SD16—3441no—
449M16—3441no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—3441no—
457C2×C8—3441no—
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—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C22⋊C4—41no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C42—41no—
488C42—861no—
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—861no—
494C23#1306329611yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—82no—
504Q8—861no—
505Q8—861no—
506D4—861no—
507D4—861no—
508D4—1722no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4#1306329611yescharacteristic
525C2×C4#1306329611yescharacteristic
526C2×C4#1306329611yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C22×C22⋊D4311yescharacteristic
529C2×C4C2×#1062190011yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—1721no—
543C22—1721no—
544C22—1721no—
545C22#1458317112yes—
546C22C2×#1306329611yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#1458370311yescharacteristic
559C4#1458370711yescharacteristic
560C4#1458370911yescharacteristic
561C4#1458371411yescharacteristic
562C2—22no—
563C2—3441no—
564C2#1914414111yescharacteristic
565C2#1914426911yescharacteristic
566C2C2×#1458317111yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3230C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#3230D43
hypocenterC43#19590
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #19134146C2semidirect
5. #19134139C2semidirect
6. #19134110C2semidirect
7. #19134105C2semidirect
8. #19134022C2semidirect
9. #19134015C2semidirect
10. #19133986C2semidirect
11. #19133981C2semidirect
12. #19133380C2semidirect
13. #19133295C2semidirect
14. C2×#14582645C2semidirect
15. C43×#3230C2semidirect
280. #3230D43semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191459262
#191456222
#191437572
#191341462
#191341392
#191341102
#191341052
#191340222
#191340152
#191339862
#191339812
#191333802
#191332952
C2×#145826452
C43×#32302
#1959043