Finite Group Databasebeta

← #14780352

Subgroups — #14780352

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079084C211yesmaximal, characteristic
2#13069113C211yesmaximal, characteristic, complemented
3#13069107C211yesmaximal, characteristic, complemented
4#13069106C211yesmaximal, characteristic, complemented
5#13069100C211yesmaximal, characteristic, complemented
6#13069096C211yesmaximal, characteristic, complemented
7#13069094C211yesmaximal, characteristic, complemented
8#13069089C211yesmaximal, characteristic, complemented
9#13069087C211yesmaximal, characteristic, complemented
10#13069018C211yesmaximal, characteristic, complemented
11#13069003C211yesmaximal, characteristic, complemented
12#13069000C211yesmaximal, characteristic, complemented
13#13068762C211yesmaximal, characteristic, complemented
14#13068762C211yesmaximal, characteristic, complemented
15C11×#1884C211yesmaximal, characteristic, complemented
16C11×#568C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C2×#67004C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20C2×#67002C2211yescharacteristic
21C2×#67002C2211yescharacteristic
22#10623350C2211yescharacteristic
23#10623052C2211yescharacteristic
24#10623047C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C11×#421C2211yescharacteristic
27C11×#421C2211yescharacteristic
28C11×#410C2211yescharacteristic
29#10622853C2211yescharacteristic
30#10622849C2211yescharacteristic
31#10622849C2211yescharacteristic
32C2×#66888C2211yescharacteristic
33#10622744C2211yescharacteristic
34C2×#66887C2211yescharacteristic
35#10622733C2211yescharacteristic
36#10622699C412yescomplemented
37#10622687C412yescomplemented
38#10622672C412yescomplemented
39#10622672C412yescomplemented
40#10622617C2211yescharacteristic
41#10622614C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43C11×#339C2211yescharacteristic
44C11×#339C2211yescharacteristic
45C11⋊#338C2211yescharacteristic
46C11⋊#338C2211yescharacteristic
47#10622197C2211yescharacteristic
48#10622197C2211yescharacteristic
49#10622171C2211yescharacteristic
50#10622171C2211yescharacteristic
51#10622169C2211yescharacteristic
52#10622169C2211yescharacteristic
53#10622161C2211yescharacteristic
54#10622161C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C2×C11×#41C2311yescharacteristic
57C22×D44C2311yescharacteristic
58C22×Dic22C2311yescharacteristic
59C11×#131—41no—
60C11×#131—41no—
61C2×C11×M16—41no—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2311yescharacteristic
64C11×C4⋊Q8C2×C411yescharacteristic, complemented
65C11×#127C2×C411yescharacteristic, complemented
66C11×#124C2×C411yescharacteristic, complemented
67C11×#124C2×C411yescharacteristic, complemented
68C11×#121—41no—
69C4×D4×C11—41no—
70C11×#117C2311yescharacteristic
71C11×#117C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67004—41no—
74#67004—41no—
75#67004—41no—
76#67004—41no—
77#67002—41no—
78#67002—41no—
79#67002—41no—
80#67002—41no—
81#67001—41no—
82#67001—41no—
83C2×#4326C2×C412yescomplemented
84C2×#4326C2×C412yescomplemented
85C2×#4325C2×C412yes—
86C2×#4325C2×C412yes—
87C2×#4324C2×C412yescomplemented
88C2×#4324C2×C412yescomplemented
89C2×#4323C2×C412yes—
90C2×#4323C2×C412yes—
91C2×(C2×D11)⋊C4—41no—
92#66979C2311yescharacteristic
93#66979C2311yescharacteristic
94C2×#4318—41no—
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99#66946—41no—
100#66940—41no—
101C22⋊C4×D11—41no—
102#66930—41no—
103#66928—41no—
104#66928C2×C412yes—
105#66928C2×C412yes—
106C4×D44—41no—
107C4×Dic22—41no—
108C11×#104—41no—
109C11×#104—41no—
110C11×#99—41no—
111#66901—41no—
112#66901—41no—
113#66898—41no—
114#66888—41no—
115#66887—41no—
116#66885—41no—
117#66880—41no—
118#66874—41no—
119#66873—41no—
120#66867C2×C412yescomplemented
121C4×C11⋊C8C2×C412yescomplemented
122#23362—111nomaximal, Sylow
123C23×D11—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C11×#41—21no—
128C11×#41—21no—
129C11×#41—21no—
130C11×#41—21no—
131C11×#41—21no—
132C2×Q8×C11C22×C411yescharacteristic
133C2×Q8×C11C22×C411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—41no—
137C2×D4×C11C22×C411yescharacteristic
138C2×D4×C11C22×C411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C22×C412yes—
150C2×C4×D11—42no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C11×M16—21no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—42no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C22×C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179#4326—42no—
180#4326—42no—
181#4325—42no—
182#4325—42no—
183#4324—42no—
184#4324—42no—
185#4323—42no—
186#4323—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196#4318—21no—
197#4318—21no—
198#4318—21no—
199#4318—21no—
200#4318—21no—
201#4318—21no—
202#4318—21no—
203#4318—21no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8C22×C412yes—
209C2×C11⋊C8C22×C412yes—
210#3153—111no—
211#1905—111no—
212#1905—111no—
213#1904—111no—
214#1904—111no—
215#1903—111no—
216#1903—111no—
217#1902—111no—
218#1902—111no—
219#1888—111no—
220#1885—111no—
221#1884—111no—
222#1884D1111yescharacteristic, complemented
223#1841—111no—
224#1841—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11H(5,𝔽2)11yescharacteristic
228C22×D11—22no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—82no—
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—82no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—81no—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267D44—22no—
268D44—22no—
269D44—41no—
270D44—41no—
271C4×D11—162no—
272Dic22—22no—
273Dic22—22no—
274Dic22—41no—
275Dic22—41no—
276C8×C11—41no—
277C8×C11—41no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C2×#137—111no—
283C2×#137—111no—
284C2×AGL(1,ℤ/8)—111no—
285C2×AGL(1,ℤ/8)—111no—
286#568—111no—
287#568C2×D1111yescharacteristic
288#532C2×D1111yescharacteristic
289C2×#124—111no—
290#519—111no—
291#518—111no—
292#497—112no—
293#496—112no—
294#495—112no—
295#495—112no—
296#421—111no—
297#421—111no—
298#421C2×D1111yescharacteristic
299#421C2×D1111yescharacteristic
300#419—111no—
301#419—111no—
302#418—111no—
303#418—111no—
304C2×#101—111no—
305C2×#100—111no—
306#410—111no—
307#410C2×D1111yescharacteristic
308C4×M16—111no—
309#344—111no—
310#344—111no—
311#344—111no—
312#344—111no—
313#339—111no—
314#339—111no—
315#339C2×D1111yescharacteristic
316#339C2×D1111yescharacteristic
317#338—111no—
318#338—111no—
319H(3,ℤ/4)—111no—
320H(3,ℤ/4)—111no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11#51811yescharacteristic
327C22×C11#56011yescharacteristic
328C22×C11#56011yescharacteristic
329C2×D11—42no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—161no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#51811yescharacteristic
340C4×C11#51811yescharacteristic
341C4×C11#56011yescharacteristic
342C4×C11#56011yescharacteristic
343Dic11—42no—
344Dic11—81no—
345Dic11—81no—
346C2×#41C22×D1111yescharacteristic
347C2×#41C22×D1111yescharacteristic
348C22×Q8—111no—
349C22×D4—111no—
350#137—441no—
351#137—441no—
352#137—441no—
353#137—441no—
354AGL(1,ℤ/8)—441no—
355AGL(1,ℤ/8)—441no—
356AGL(1,ℤ/8)—441no—
357AGL(1,ℤ/8)—441no—
358C2×Q16—112no—
359C2×Q16—112no—
360C2×SD16—112no—
361C2×SD16—112no—
362C2×SD16—112no—
363C2×SD16—112no—
364C2×D8—112no—
365C2×D8—112no—
366#131—41no—
367#131—41no—
368#131—441no—
369#131—441no—
370C2×M16—41no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—111no—
374C2×M16—111no—
375C2×M16—441no—
376C2×M16C22×D1111yescharacteristic
377C2×M16C22×D1111yescharacteristic
378C4⋊Q8C4×D1111yescharacteristic, complemented
379#127C4×D1111yescharacteristic, complemented
380#124—112no—
381#124—112no—
382#124—441no—
383#124C4×D1111yescharacteristic, complemented
384#124C4×D1111yescharacteristic, complemented
385#121—41no—
386C4×Q8—441no—
387C4×Q8—441no—
388C4×D4—41no—
389C4×D4—441no—
390C4×D4—441no—
391#117—111no—
392#117—111no—
393#117—441no—
394#117C22×D1111yescharacteristic
395#117C22×D1111yescharacteristic
396C2×C22⋊C4—441no—
397C2×C22⋊C4—441no—
398C2×C42C22×D1111yescharacteristic
399#104—41no—
400#104—41no—
401#104—441no—
402#104—441no—
403#103—441no—
404#103—441no—
405#102—441no—
406#102—441no—
407#101—441no—
408#100—441no—
409#99—41no—
410#99—441no—
411#97—112no—
412C4×C8—112no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—81no—
417C2×C11—81no—
418C2×C11#238011yescharacteristic
419D11—82no—
420C24—221no—
421#41—21no—
422#41—21no—
423#41—21no—
424#41—21no—
425#41—21no—
426#41—21no—
427#41—21no—
428#41—21no—
429C2×Q8—112no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8C2×C4×D1111yescharacteristic
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4C2×C4×D1111yescharacteristic
447C2×D4C2×C4×D1111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—221no—
452C22×C4—442no—
453C22×C4C23×D1111yescharacteristic
454Q16—442no—
455Q16—442no—
456SD16—442no—
457SD16—442no—
458SD16—442no—
459SD16—442no—
460D8—442no—
461D8—442no—
462M16—21no—
463M16—21no—
464M16—21no—
465M16—21no—
466M16—42no—
467M16—221no—
468M16—221no—
469M16—221no—
470M16—221no—
471M16—221no—
472M16—221no—
473M16—221no—
474M16—221no—
475M16—442no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—112no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—442no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—442no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—221no—
503C42—221no—
504C42—442no—
505C42C2×C4×D1111yescharacteristic
506C42C2×C4×D1111yescharacteristic
507C11#2336211yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—222no—
511C23—441no—
512C23—441no—
513C23—882no—
514C23#6703711yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—222no—
520Q8—222no—
521Q8—441no—
522Q8—441no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—222no—
533D4—222no—
534D4—441no—
535D4—441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—222no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—1762no—
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#6703711yescharacteristic
557C2×C4#6704211yescharacteristic
558C2×C4#6704211yescharacteristic
559C8—41no—
560C8—41no—
561C8—222no—
562C8—222no—
563C8—441no—
564C8—441no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—81no—
570C22—442no—
571C22—882no—
572C22—882no—
573C22—1761no—
574C22#1062301711yescharacteristic
575C22#1062315111yescharacteristic
576C22#1062315111yescharacteristic
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—442no—
584C4—881no—
585C4—881no—
586C4#1062307611yescharacteristic
587C4#1062307611yescharacteristic
588C4#1062312611yescharacteristic
589C4#1062319711yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—81no—
594C2—81no—
595C2—882no—
596C2#1307179111yescharacteristic
subgroupG/H
centerC2#13071791
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1884C2
socleC2×C11#2380
prime radical#13079084C2
cosocleC22×C4×C11C24
hypercenter#1884D11
hypocenterC11#23362
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1884

Complements

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

NH ≅ G/Ntype
2. #13069113C2semidirect
3. #13069107C2semidirect
4. #13069106C2semidirect
5. #13069100C2semidirect
6. #13069096C2semidirect
7. #13069094C2semidirect
8. #13069089C2semidirect
9. #13069087C2semidirect
10. #13069018C2semidirect
11. #13069003C2semidirect
12. #13069000C2semidirect
13. #13068762C2semidirect
14. #13068762C2semidirect
15. C11×#1884C2semidirect
36. #10622699C4semidirect
37. #10622687C4semidirect
38. #10622672C4semidirect
39. #10622672C4semidirect
64. C11×C4⋊Q8C2×C4semidirect
65. C11×#127C2×C4semidirect
66. C11×#124C2×C4semidirect
67. C11×#124C2×C4semidirect
83. C2×#4326C2×C4semidirect
84. C2×#4326C2×C4semidirect
87. C2×#4324C2×C4semidirect
88. C2×#4324C2×C4semidirect
120. #66867C2×C4semidirect
121. C4×C11⋊C8C2×C4semidirect
222. #1884D11semidirect
378. C4⋊Q8C4×D11semidirect
379. #127C4×D11semidirect
383. #124C4×D11semidirect
384. #124C4×D11semidirect
507. C11#23362semidirect

Maximal subgroups

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

subgroupindex
#130790842
#130691132
#130691072
#130691062
#130691002
#130690962
#130690942
#130690892
#130690872
#130690182
#130690032
#130690002
#130687622
C11×#18842
#2336211