Finite Group Databasebeta

← #14738886

Subgroups — #14738886

Order 2816.

572 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#13079989C211yesmaximal, characteristic
2#13078996C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic
4#13068196C211yesmaximal, characteristic, complemented
5#13068189C211yesmaximal, characteristic, complemented
6#13068168C211yesmaximal, characteristic, complemented
7#13068161C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068065C211yesmaximal, characteristic, complemented
10#13068044C211yesmaximal, characteristic, complemented
11#13068037C211yesmaximal, characteristic, complemented
12#13067384C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067301C211yesmaximal, characteristic, complemented
15C11×#3239C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#501—21no—
20C11×#489—21no—
21C11×#484—21no—
22C11×#481—21no—
23C11×#475C2211yescharacteristic
24C11×#475C2211yescharacteristic
25C11×#474C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#432C2211yescharacteristic
28#10622838—21no—
29#10622838—21no—
30#10622695—21no—
31#10622695—21no—
32#10622694C2211yescharacteristic
33#10622694C2211yescharacteristic
34#10622694C2211yescharacteristic
35#10622694C2211yescharacteristic
36#10622676—21no—
37#10622667—21no—
38#10622665—21no—
39#10622655—21no—
40#10622644C2211yescharacteristic
41#10622637C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622634C2211yescharacteristic
44#10622632C2211yescharacteristic
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622120C2211yescharacteristic
60#10622120C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C22×Q8×C11—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#126—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×#121D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4324—21no—
88#66979—21no—
89#66977—21no—
90#66977—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C22×C11⋊C8—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99C4×Dic22—21no—
100C4×Dic22—21no—
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#66899—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126#66874—21no—
127#66874—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#19381—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—42no—
148C2×Q8×C11—42no—
149C2×Q8×C11—41no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—41no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×Dic22—21no—
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—41no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4C2×D411yescharacteristic
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11—21no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—41no—
185#4326—81no—
186#4324—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193C4×Dic11—41no—
194#4318—41no—
195#4318—41no—
196#4318—42no—
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#3252—111no—
208#3239D1111yescharacteristic
209#3139—111no—
210#2969—111no—
211#1704—111no—
212#1703—111no—
213#1700—111no—
214#1699—111no—
215#1684—111no—
216#1683—111no—
217#1680—111no—
218#1679—111no—
219#1569—111no—
220#1554—111no—
221#1549—111no—
222C23×C11—21no—
223C23×C11#12111yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
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
253C2×Dic11—41no—
254C2×Dic11—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—81no—
258C8×C11—41no—
259C8×C11—41no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270#529C2×D1111yescharacteristic
271#501—21no—
272#491—221no—
273#491—221no—
274#489—21no—
275#487—111no—
276#487—111no—
277#487—111no—
278#487—111no—
279#484—21no—
280#481—21no—
281#479—221no—
282#477—111no—
283#476—111no—
284#475C2×D1111yescharacteristic
285#475C2×D1111yescharacteristic
286#474C2×D1111yescharacteristic
287#474C2×D1111yescharacteristic
288#470—221no—
289#468—221no—
290#464—221no—
291#462—111no—
292#461—111no—
293#446—111no—
294C8×Q8—111no—
295#436—111no—
296#436—221no—
297#435—221no—
298C8×D4—111no—
299#433—221no—
300#432C2×D1111yescharacteristic
301#431—111no—
302#423—111no—
303#419—221no—
304#419—221no—
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#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×#12111yescharacteristic
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#57511yescharacteristic
336C4×C11#57511yescharacteristic
337C4×C11#57711yescharacteristic
338C4×C11#57811yescharacteristic
339Dic11—81no—
340Dic11—81no—
341C22×Q8—21no—
342C2×Q16—221no—
343C2×SD16—221no—
344C2×M16—111no—
345C2×M16—111no—
346C2×M16—221no—
347C2×M16—221no—
348C22×C8—221no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—111no—
353C4⋊Q8—111no—
354C4⋊Q8C22×D1111yescharacteristic
355C4⋊Q8C22×D1111yescharacteristic
356#126—21no—
357#125—221no—
358#125C22⋊D1111yescharacteristic
359#124C22⋊D1111yescharacteristic
360#123—21no—
361C22⋊Q8—221no—
362C22⋊Q8—221no—
363C22⋊Q8C22⋊D1111yescharacteristic
364#121C22⋊D1111yescharacteristic
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1111yescharacteristic
370#117—21no—
371#117—221no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C42C22×D1111yescharacteristic
375#107—21no—
376#107—21no—
377#107—221no—
378#106—21no—
379#106—21no—
380#106—221no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390#103—21no—
391#103—21no—
392#103—221no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#102—21no—
404#102—21no—
405#102—221no—
406C22⋊C8—21no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410#97—21no—
411#97—111no—
412#97—111no—
413#97—221no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C2×C11—41no—
419C2×C11—81no—
420C2×C11#304011yescharacteristic
421C2×C11#306311yescharacteristic
422C2×C11#306911yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—41no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×Q8C2×C22⋊D1111yescharacteristic
431C2×D4—21no—
432C2×D4C2×C22⋊D1111yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—881no—
439SD16—881no—
440M16—441no—
441M16—441no—
442M16—442no—
443M16—881no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—442no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4C2×C22⋊D1111yescharacteristic
472C4⋊C4C2×C22⋊D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—441no—
479C42—21no—
480C42—441no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1938111yescharacteristic, complemented, Sylow
486C23—21no—
487C23#6699211yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—82no—
495Q8—441no—
496Q8—441no—
497Q8—881no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—82no—
514C2×C4—441no—
515C2×C4—441no—
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—221no—
525C8—221no—
526C8—221no—
527C8—221no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#6699211yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—881no—
549C4—881no—
550C4#1062330411yescharacteristic
551C4#1062330411yescharacteristic
552C4#1062336811yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—81no—
556C2#1307810811yescharacteristic
557C2#1307830311yescharacteristic
558C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3239C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#3239D11
hypocenterC11#19381
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3239

Complements

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

NH ≅ G/Ntype
2. #13078996C2semidirect
4. #13068196C2semidirect
5. #13068189C2semidirect
6. #13068168C2semidirect
7. #13068161C2semidirect
8. #13068072C2semidirect
9. #13068065C2semidirect
10. #13068044C2semidirect
11. #13068037C2semidirect
12. #13067384C2semidirect
13. #13067327C2semidirect
14. #13067301C2semidirect
485. C11#19381semidirect

Maximal subgroups

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

subgroupindex
#130799892
#130789962
#130776212
#130681962
#130681892
#130681682
#130681612
#130680722
#130680652
#130680442
#130680372
#130673842
#130673272
#130673012
C11×#32392
#1938111