Finite Group Databasebeta

← #14738766

Subgroups — #14738766

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic
2#13079335C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic, complemented
4#13068196C211yesmaximal, characteristic, complemented
5#13068158C211yesmaximal, characteristic, complemented
6#13068142C211yesmaximal, characteristic, complemented
7#13068090C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13068018C211yesmaximal, characteristic, complemented
11#13067966C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067312C211yesmaximal, characteristic
14#13067306C211yesmaximal, characteristic, complemented
15C11×#3237C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#501—21no—
20C11×#491—21no—
21C11×#485—21no—
22C11×#485—21no—
23C11×#477C2211yescharacteristic
24C11×#477C2211yescharacteristic
25C11×#475C2211yescharacteristic
26C11×#475C2211yescharacteristic
27C11×#432C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622700—21no—
30#10622698C2211yescharacteristic
31#10622696—21no—
32#10622694C2211yescharacteristic
33#10622691C2211yescharacteristic
34#10622662—21no—
35#10622662—21no—
36#10622662—21no—
37#10622662—21no—
38#10622640C2211yescharacteristic
39#10622640C2211yescharacteristic
40#10622639—21no—
41#10622639—21no—
42#10622637—21no—
43#10622637—21no—
44#10622637C2211yescharacteristic
45#10622637C2211yescharacteristic
46Q8×C11⋊C8C2211yescharacteristic
47Q8×C11⋊C8C2211yescharacteristic
48#10622634C2211yescharacteristic
49#10622634C2211yescharacteristic
50#10622612—21no—
51#10622610—21no—
52#10622537C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×#4339—21no—
68C11×C4⋊Q8D411yescharacteristic
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×C22⋊Q8D411yescharacteristic
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11C2311yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91#66983—21no—
92#66983—21no—
93C2×#4318—21no—
94C2×#4318D411yescharacteristic
95C2×#4318D411yescharacteristic
96C22×C11⋊C8—21no—
97#66928—21no—
98#66927C2311yescharacteristic
99C4×D44—21no—
100C4×D44—21no—
101#66922C2311yescharacteristic
102C11×#107—21no—
103C11×#107—21no—
104C11×#106—21no—
105C11×#106—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×C22⋊C8—21no—
113C11×#97—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66873—21no—
119#66873—21no—
120#66873—21no—
121#66873—21no—
122#66871—21no—
123#66871—21no—
124#66871—21no—
125#66871—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19373—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C2×C22⋊D11—41no—
154#4339—82no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×C4×D11—41no—
159C2×Dic22—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—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—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—41no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—41no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4325—42no—
188#4325—42no—
189#4325—81no—
190#4325—81no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195#4318—22no—
196#4318—41no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#3254—111no—
208#3237D1111yescharacteristic, complemented
209#3182—111no—
210#2962—111no—
211#1704—111no—
212#1698—111no—
213#1696—111no—
214#1686—111no—
215#1684—111no—
216#1678—111no—
217#1676—111no—
218#1666—111no—
219#1569—111no—
220#1551—111no—
221#1550—111no—
222C23×C11#12111yescharacteristic
223C22×D11—41no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231Q8×C11—81no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
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—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—82no—
250C2×Dic11—41no—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—41no—
255D44—81no—
256C4×D11—82no—
257Dic22—81no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8#13712yes—
268#533C2×D1111yescharacteristic
269#533C2×D1111yescharacteristic
270#532—111no—
271#501—21no—
272#500—111no—
273#492—111no—
274#491—21no—
275#487—111no—
276#486—111no—
277#485—21no—
278#485—21no—
279#477—111no—
280#477—111no—
281#477C2×D1111yescharacteristic
282#477C2×D1111yescharacteristic
283#475C2×D1111yescharacteristic
284#475C2×D1111yescharacteristic
285#474—221no—
286#468—221no—
287#468—221no—
288#468—221no—
289#468—221no—
290#461—221no—
291#460—111no—
292#460—111no—
293#446—111no—
294#446—111no—
295#446—221no—
296#446—221no—
297C8×Q8—111no—
298C8×Q8—111no—
299#440—221no—
300#440—221no—
301#432C2×D1111yescharacteristic
302#424—221no—
303#423—111no—
304C2×C4⋊C8—111no—
305#405—221no—
306C4×M16—111no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#331—111no—
318#331—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11C2×#12111yescharacteristic
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#13711yescharacteristic
337C4×C11#57511yescharacteristic
338C4×C11#57711yescharacteristic
339C4×C11#57811yescharacteristic
340Dic11—81no—
341C2×#41—221no—
342C2×SD16—221no—
343C2×SD16—221no—
344C2×SD16—221no—
345C2×SD16—221no—
346C2×M16—111no—
347C2×M16—111no—
348C2×M16—221no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8C22⋊D1111yescharacteristic
352C4⋊Q8C22⋊D1111yescharacteristic
353C4⋊Q8C22×D1111yescharacteristic
354C4⋊Q8C22×D1111yescharacteristic
355#127—111no—
356#125—21no—
357#125—21no—
358#124—221no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8C22⋊D1111yescharacteristic
363C22⋊Q8C22⋊D1111yescharacteristic
364#121—221no—
365#121—221no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C22×D1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—221no—
372C4×D4—221no—
373#117—21no—
374#117—21no—
375C2×C42C22×D1111yescharacteristic
376#107—21no—
377#107—21no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—21no—
383#106—21no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—221no—
405#102—221no—
406#102—221no—
407#102—221no—
408C22⋊C8—21no—
409#97—21no—
410#97—111no—
411#97—111no—
412#97—221no—
413#97—221no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C2×C11—41no—
419C2×C11#303711yescharacteristic
420C2×C11#306311yescharacteristic
421C2×C11#306811yescharacteristic
422D11—161no—
423#41—882no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—221no—
428C2×Q8C2×C22⋊D1111yescharacteristic
429C2×Q8C2×C22⋊D1111yescharacteristic
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—441no—
434C22×C4—441no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438SD16—442no—
439SD16—442no—
440SD16—881no—
441SD16—881no—
442M16—222no—
443M16—441no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—442no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C4⋊C4C2×C22⋊D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—41no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1937311yescharacteristic, complemented, Sylow
486C23—441no—
487C23#6699211yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—881no—
497D4—441no—
498D4—441no—
499D4—441no—
500D4—441no—
501D4—881no—
502D4—882no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—441no—
515C2×C4—882no—
516C2×C4#6699211yescharacteristic
517C2×C4#6699211yescharacteristic
518C2×C4#6699211yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—41no—
523C8—41no—
524C8—112no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22C2×#6699211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—881no—
550C4D11×#13711yescharacteristic
551C4#1062330811yescharacteristic
552C4#1062336811yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—1761no—
556C2#1307808511yescharacteristic
557C2#1307830311yescharacteristic
558C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3237C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3237D11
hypocenterC11#19373
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3237

Complements

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

NH ≅ G/Ntype
3. #13077565C2semidirect
4. #13068196C2semidirect
5. #13068158C2semidirect
6. #13068142C2semidirect
7. #13068090C2semidirect
8. #13068072C2semidirect
9. #13068034C2semidirect
10. #13068018C2semidirect
11. #13067966C2semidirect
12. #13067384C2semidirect
14. #13067306C2semidirect
15. C11×#3237C2semidirect
208. #3237D11semidirect
485. C11#19373semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130793352
#130775652
#130681962
#130681582
#130681422
#130680902
#130680722
#130680342
#130680182
#130679662
#130673842
#130673122
#130673062
C11×#32372
#1937311