Finite Group Databasebeta

← #14738909

Subgroups — #14738909

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068200C211yesmaximal, characteristic, complemented
5#13068193C211yesmaximal, characteristic, complemented
6#13068158C211yesmaximal, characteristic, complemented
7#13068151C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068069C211yesmaximal, characteristic, complemented
10#13068034C211yesmaximal, characteristic, complemented
11#13068027C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067322C211yesmaximal, characteristic, complemented
14#13067297C211yesmaximal, characteristic, complemented
15C11×#3238C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#501—21no—
20C11×#489—21no—
21C11×#483—21no—
22C11×#480—21no—
23C11×#477C2211yescharacteristic
24C11×#477C2211yescharacteristic
25C11×#476C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#432C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622706C2211yescharacteristic
30#10622702—21no—
31#10622702—21no—
32#10622701C2211yescharacteristic
33#10622701C2211yescharacteristic
34#10622679—21no—
35#10622670—21no—
36#10622662—21no—
37#10622652—21no—
38#10622640C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622628C2211yescharacteristic
43#10622625—21no—
44#10622625C2211yescharacteristic
45#10622624—21no—
46D4×C11⋊C8C2211yescharacteristic
47#10622620C2211yescharacteristic
48#10622613—21no—
49#10622610—21no—
50#10622579—21no—
51#10622579—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622123C2211yescharacteristic
62#10622123C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×#4339—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124D411yescharacteristic
77C11×#123—21no—
78C11×C22⋊Q8D411yescharacteristic
79C11×#121D411yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4325—21no—
88C2×#4323—21no—
89#66983—21no—
90#66983—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C22×C11⋊C8—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44—21no—
100#66922C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#106—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8—21no—
112C11×#97—21no—
113#66899—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66874—21no—
121#66874—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19382—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—41no—
148C2×Q8×C11—82no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—41no—
158#4339—42no—
159#4339—42no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11—21no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189#4325—81no—
190#4323—81no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195#4318—41no—
196#4318—41no—
197#4318—42no—
198#4318—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3251—111no—
209#3238D1111yescharacteristic, complemented
210#3141—111no—
211#2969—111no—
212#1704—111no—
213#1703—111no—
214#1698—111no—
215#1697—111no—
216#1684—111no—
217#1683—111no—
218#1678—111no—
219#1677—111no—
220#1569—111no—
221#1553—111no—
222#1548—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225C22×D11—41no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—81no—
229Q8×C11—81no—
230Q8×C11—82no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—81no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—82no—
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—82no—
254C2×Dic11—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—81no—
260C4×D11—82no—
261Dic22—41no—
262Dic22—41no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#532—111no—
274C2×C4⋊Q8C2×D1111yescharacteristic
275#529C2×D1111yescharacteristic
276#501—21no—
277#489—21no—
278#489—221no—
279#489—221no—
280#487—111no—
281#487—111no—
282#486—111no—
283#486—111no—
284#483—21no—
285#480—21no—
286#478—221no—
287#477C2×D1111yescharacteristic
288#477C2×D1111yescharacteristic
289#476C2×D1111yescharacteristic
290#476C2×D1111yescharacteristic
291#475—111no—
292#474—111no—
293#469—221no—
294#468—221no—
295#463—221no—
296#460—111no—
297#459—111no—
298#446—111no—
299C8×Q8—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304#433—221no—
305#432C2×D1111yescharacteristic
306#431—111no—
307#423—111no—
308#417—221no—
309#417—221no—
310#405—221no—
311C4×M16—111no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#333—111no—
317#333—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#331—111no—
323#331—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#57511yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—81no—
348C2×#41—221no—
349C22×Q8—21no—
350C2×SD16—221no—
351C2×D8—221no—
352C2×M16—111no—
353C2×M16—111no—
354C2×M16—221no—
355C2×M16—221no—
356C22×C8—221no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—111no—
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363#127—111no—
364#126—21no—
365#125C22⋊D1111yescharacteristic
366#124—221no—
367#124C22⋊D1111yescharacteristic
368#123—21no—
369C22⋊Q8C22⋊D1111yescharacteristic
370#121—221no—
371#121—221no—
372#121C22⋊D1111yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×D4—21no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—21no—
384#107—221no—
385#106—21no—
386#106—21no—
387#106—221no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397#103—21no—
398#103—21no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—21no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—21no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#97—21no—
418#97—111no—
419#97—111no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C2×C11—41no—
426C2×C11—81no—
427C2×C11#304011yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#306811yescharacteristic
430D11—161no—
431#41—442no—
432#41—442no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—82no—
437C2×Q8—221no—
438C2×Q8C2×C22⋊D1111yescharacteristic
439C2×D4—21no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—441no—
444C2×D4C2×C22⋊D1111yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—441no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451SD16—881no—
452D8—881no—
453M16—441no—
454M16—441no—
455M16—442no—
456M16—881no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—111no—
462C2×C8—111no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4C2×C22⋊D1111yescharacteristic
481C4⋊C4C2×C22⋊D1111yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C42—21no—
490C42D4×D1111yescharacteristic
491C42#434111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1938211yescharacteristic, complemented, Sylow
495C23—21no—
496C23—441no—
497C23#6699211yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—81no—
501Q8—81no—
502Q8—82no—
503Q8—441no—
504Q8—441no—
505D4—21no—
506D4—21no—
507D4—81no—
508D4—441no—
509D4—441no—
510D4—441no—
511D4—441no—
512D4—881no—
513D4—882no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—82no—
527C2×C4—441no—
528C2×C4—882no—
529C2×C4#6699211yescharacteristic
530C2×C4#6699211yescharacteristic
531C2×C4#6699211yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—41no—
536C8—41no—
537C8—221no—
538C8—221no—
539C8—221no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22C2×#6699211yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—881no—
565C4#1062330811yescharacteristic
566C4#1062330811yescharacteristic
567C4#1062336811yescharacteristic
568C4#1062336911yescharacteristic
569C2—41no—
570C2—81no—
571C2—1761no—
572C2#1307811211yescharacteristic
573C2#1307830311yescharacteristic
574C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3238C2
socleC22×C11C2×#121
prime radical#13079978C2
hypercenter#3238D11
hypocenterC11#19382
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. #13079012C2semidirect
3. #13077621C2semidirect
4. #13068200C2semidirect
5. #13068193C2semidirect
6. #13068158C2semidirect
7. #13068151C2semidirect
8. #13068076C2semidirect
9. #13068069C2semidirect
10. #13068034C2semidirect
11. #13068027C2semidirect
12. #13067384C2semidirect
13. #13067322C2semidirect
14. #13067297C2semidirect
15. C11×#3238C2semidirect
209. #3238D11semidirect
494. C11#19382semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130790122
#130776212
#130682002
#130681932
#130681582
#130681512
#130680762
#130680692
#130680342
#130680272
#130673842
#130673222
#130672972
C11×#32382
#1938211