Finite Group Databasebeta

← #14780358

Subgroups — #14780358

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#13079078C211yesmaximal, characteristic
2#13069109C211yesmaximal, characteristic, complemented
3#13069107C211yesmaximal, characteristic, complemented
4#13069105C211yesmaximal, characteristic, complemented
5#13069101C211yesmaximal, characteristic, complemented
6#13069099C211yesmaximal, characteristic, complemented
7#13069090C211yesmaximal, characteristic, complemented
8#13069089C211yesmaximal, characteristic, complemented
9#13069016C211yesmaximal, characteristic, complemented
10#13069002C211yesmaximal, characteristic, complemented
11#13068999C211yesmaximal, characteristic, complemented
12#13068996C211yesmaximal, characteristic, complemented
13#13068766C211yesmaximal, characteristic, complemented
14#13068764C211yesmaximal, characteristic, complemented
15C11×#1903C211yesmaximal, characteristic, complemented
16C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
17C11×#568C2211yescharacteristic
18#10623363C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20#10623329C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×#66985C2211yescharacteristic
23C2×#66962C2211yescharacteristic
24#10623276C2211yescharacteristic
25#10623047C2211yescharacteristic
26C11×#421C2211yescharacteristic
27C11×#418C2211yescharacteristic
28C2×C11×#100C2211yescharacteristic
29#10622853C2211yescharacteristic
30#10622849C2211yescharacteristic
31#10622828C2211yescharacteristic
32#10622781C412yescomplemented
33#10622780C412yescomplemented
34#10622768C412yescomplemented
35#10622767C412yescomplemented
36#10622752C2211yescharacteristic
37#10622752C2211yescharacteristic
38C2×#66888C2211yescharacteristic
39#10622733C2211yescharacteristic
40#10622733C2211yescharacteristic
41M16×Dic11C2211yescharacteristic
42#10622619C2211yescharacteristic
43C11×#344C2211yescharacteristic
44C11×#338C2211yescharacteristic
45C11⋊#338C2211yescharacteristic
46#10622197C2211yescharacteristic
47#10622197C2211yescharacteristic
48#10622195C2211yescharacteristic
49#10622194C2211yescharacteristic
50#10622193C2211yescharacteristic
51#10622193C2211yescharacteristic
52#10622193C2211yescharacteristic
53#10622170C2211yescharacteristic
54#10622169C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C2×#4339C2311yescharacteristic
58C22×Dic22C2311yescharacteristic
59C11×AGL(1,ℤ/8)—41no—
60C11×AGL(1,ℤ/8)—41no—
61C2×C11×SD16C2×C412yes—
62C2×C11×D8C2×C412yes—
63C11×#131—41no—
64C11×#131—41no—
65C2×C11×M16—41no—
66C2×C11×M16C2311yescharacteristic
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C11×#117C2311yescharacteristic
71C2×C22⋊Dic11—41no—
72C2×C22⋊Dic11—41no—
73#67004—41no—
74#67004—41no—
75#67000C2×C411yescharacteristic, complemented
76#66997C2×C411yescharacteristic, complemented
77C2×#4326C2×C412yescomplemented
78#66993C2×C411yescharacteristic, complemented
79#66992—41no—
80#66989—41no—
81#66989C2×C412yes—
82#66989C2×C412yes—
83#66989C2×C411yescharacteristic, complemented
84D4×Dic11—41no—
85D4×Dic11—41no—
86C2×#4324C2×C412yes—
87C2×#4324C2×C412yescomplemented
88#66985—41no—
89#66985—41no—
90C2×#4323C2×C412yes—
91C4×C22⋊D11—41no—
92#66979C2311yescharacteristic
93#66979C2311yescharacteristic
94#66979C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98#66962—41no—
99#66962—41no—
100#66960—41no—
101M16×D11—41no—
102C2×Dic44C2×C412yescomplemented
103C2×#4314C2×C412yescomplemented
104#66954—41no—
105#66940—41no—
106#66930—41no—
107C4×Dic22—41no—
108C11×#104—41no—
109C11×#102—41no—
110C11×#100—41no—
111#66901—41no—
112#66898—41no—
113#66896—41no—
114#66889—41no—
115#66889—41no—
116#66888—41no—
117#66880—41no—
118#66880—41no—
119#66879C2×C412yescomplemented
120C8×Dic11C2×C412yescomplemented
121#66870—41no—
122#23362—111nomaximal, Sylow
123C24×C11—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C11×#41—21no—
128C2×Q8×C11C22×C411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C22×C412yes—
136C2×D4×C11C22×C411yescharacteristic
137C22×C4×C11—21no—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—21no—
140C2×C22⋊D11—41no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—42no—
144#4339—21no—
145#4339—21no—
146#4339—21no—
147#4339—21no—
148C2×D44C22×C411yescharacteristic
149C2×C4×D11—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C2×Dic22C22×C411yescharacteristic
157C11×SD16—42no—
158C11×D8—42no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—21no—
162C11×M16—21no—
163C11×M16—21no—
164C11×M16—21no—
165C11×M16—21no—
166C11×M16—21no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—42no—
172C2×C8×C11C22×C412yes—
173C11×C4⋊C4—21no—
174C11×C22⋊C4—21no—
175C42×C11—21no—
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178C22⋊Dic11—21no—
179C22⋊Dic11—41no—
180C22⋊Dic11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—42no—
183#4326—42no—
184#4324—42no—
185#4324—42no—
186#4323—42no—
187(C2×D11)⋊C4—41no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191Dic11⋊C4—41no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C22×C411yescharacteristic
200#4318—21no—
201#4318—21no—
202#4318—21no—
203#4318—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C412yes—
206Dic44—42no—
207#4314—42no—
208#4313—42no—
209C8×D11—42no—
210#3153—111no—
211#1905—111no—
212#1905—111no—
213#1904—111no—
214#1904—111no—
215#1903—111no—
216#1903D1111yescharacteristic, complemented
217#1902—111no—
218#1902—111no—
219#1888—111no—
220#1885—111no—
221#1884—111no—
222#1884—111no—
223#1841—111no—
224#1841—111no—
225C23×C11—22no—
226C23×C11—21no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—82no—
230C23×C11H(5,𝔽2)11yescharacteristic
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234D4×C11—22no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—22no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C22⋊D11—41no—
253C22⋊D11—41no—
254C22⋊D11—82no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—81no—
265C2×Dic11—162no—
266D44—21no—
267D44—21no—
268C4×D11—41no—
269C4×D11—41no—
270Dic22—22no—
271Dic22—21no—
272Dic22—21no—
273Dic22—22no—
274Dic22—41no—
275Dic22—41no—
276C8×C11—22no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×#137—111no—
283C2×#137—111no—
284C2×AGL(1,ℤ/8)—111no—
285C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
286#568—111no—
287#568C2×D1111yescharacteristic
288#532—111no—
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#421—111no—
299#421C2×D1111yescharacteristic
300#419—111no—
301#419—111no—
302#418—111no—
303#418C2×D1111yescharacteristic
304C2×#101—111no—
305C2×#100C2×D1111yescharacteristic
306#410—111no—
307#410—111no—
308C4×M16—111no—
309#344—111no—
310#344—111no—
311#344—111no—
312#344C2×D1111yescharacteristic
313#339—111no—
314#339—111no—
315#339—111no—
316#339—111no—
317#338—111no—
318#338C2×D1111yescharacteristic
319H(3,ℤ/4)—111no—
320H(3,ℤ/4)—111no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11—161no—
328C22×C11#51811yescharacteristic
329C22×C11#56011yescharacteristic
330C22×C11#56011yescharacteristic
331C2×D11—41no—
332C2×D11—81no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11#51811yescharacteristic
336C4×C11#51811yescharacteristic
337C4×C11#56011yescharacteristic
338C4×C11#56011yescharacteristic
339Dic11—41no—
340Dic11—41no—
341Dic11—42no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C2×#41—111no—
347C2×#41C22×D1111yescharacteristic
348C22×Q8—111no—
349C22×D4C22×D1111yescharacteristic
350#137—441no—
351#137—441no—
352#137—441no—
353#137—441no—
354AGL(1,ℤ/8)—41no—
355AGL(1,ℤ/8)—41no—
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×SD16C4×D1112yes—
364C2×D8—112no—
365C2×D8C4×D1112yes—
366#131—41no—
367#131—41no—
368#131—441no—
369#131—441no—
370C2×M16—41no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—441no—
374C2×M16C22×D1111yescharacteristic
375C2×M16C22×D1111yescharacteristic
376C2×M16C22×D1111yescharacteristic
377C2×M16C22×D1111yescharacteristic
378C4⋊Q8—111no—
379#127—111no—
380#124—111no—
381#124—112no—
382#124—112no—
383#124—111no—
384#124—441no—
385#121—441no—
386C4×Q8—441no—
387C4×Q8—441no—
388C4×D4—441no—
389C4×D4—441no—
390C4×D4—441no—
391#117—111no—
392#117—111no—
393#117—111no—
394#117—441no—
395#117C22×D1111yescharacteristic
396C2×C22⋊C4—441no—
397C2×C22⋊C4—441no—
398C2×C42—111no—
399#104—41no—
400#104—441no—
401#104—441no—
402#104—441no—
403#103—441no—
404#103—441no—
405#102—41no—
406#102—441no—
407#101—441no—
408#100—41no—
409#99—441no—
410#99—441no—
411#97—112no—
412C4×C8—112no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—81no—
417C2×C11—82no—
418C2×C11#238011yescharacteristic
419D11—81no—
420C24—21no—
421#41—21no—
422#41—21no—
423#41—21no—
424#41—21no—
425#41—221no—
426#41—221no—
427#41—221no—
428#41—221no—
429C2×Q8—112no—
430C2×Q8—111no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—111no—
444C2×D4—221no—
445C2×D4—441no—
446C2×D4C2×C4×D1112yes—
447C2×D4C2×C4×D1111yescharacteristic
448C22×C4—21no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—442no—
453C22×C4C23×D1111yescharacteristic
454Q16—442no—
455Q16—442no—
456SD16—42no—
457SD16—442no—
458SD16—442no—
459SD16—442no—
460D8—42no—
461D8—442no—
462M16—21no—
463M16—21no—
464M16—21no—
465M16—21no—
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—42no—
471M16—221no—
472M16—221no—
473M16—221no—
474M16—221no—
475M16—442no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—442no—
483C2×C8C2×C4×D1112yes—
484C4⋊C4—21no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—442no—
490C22⋊C4—21no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C22⋊C4—441no—
495C22⋊C4—442no—
496C22⋊C4—442no—
497C22⋊C4—441no—
498C22⋊C4—442no—
499C42—21no—
500C42—111no—
501C42—111no—
502C42—221no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—442no—
507C11#2336211yescharacteristic, complemented, Sylow
508C23—22no—
509C23—21no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—221no—
514C23#6704211yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—222no—
518Q8—221no—
519Q8—221no—
520Q8—222no—
521Q8—441no—
522Q8—441no—
523D4—21no—
524D4—22no—
525D4—22no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—221no—
532D4—221no—
533D4—441no—
534D4—441no—
535D4—882no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—222no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—881no—
552C2×C4—1762no—
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#6703711yescharacteristic
557C2×C4#6703711yescharacteristic
558C2×C4#6704211yescharacteristic
559C8—22no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—222no—
564C8—441no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—81no—
569C22—82no—
570C22—82no—
571C22—161no—
572C22—441no—
573C22—881no—
574C22#1062307611yescharacteristic
575C22#1062315111yescharacteristic
576C22#1062319711yescharacteristic
577C4—41no—
578C4—81no—
579C4—441no—
580C4—441no—
581C4—441no—
582C4—442no—
583C4—881no—
584C4—881no—
585C4—881no—
586C4#1062301711yescharacteristic
587C4#1062307611yescharacteristic
588C4#1062312611yescharacteristic
589C4#1062315111yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—82no—
594C2—81no—
595C2—881no—
596C2#1307179111yescharacteristic
subgroupG/H
centerC2#13071791
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1903C2
socleC2×C11#2380
prime radical#13079078C2
cosocleC22×C4×C11C24
hypercenter#1903D11
hypocenterC11#23362
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1903

Complements

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

NH ≅ G/Ntype
2. #13069109C2semidirect
3. #13069107C2semidirect
4. #13069105C2semidirect
5. #13069101C2semidirect
6. #13069099C2semidirect
7. #13069090C2semidirect
8. #13069089C2semidirect
9. #13069016C2semidirect
10. #13069002C2semidirect
11. #13068999C2semidirect
12. #13068996C2semidirect
13. #13068766C2semidirect
14. #13068764C2semidirect
15. C11×#1903C2semidirect
32. #10622781C4semidirect
33. #10622780C4semidirect
34. #10622768C4semidirect
35. #10622767C4semidirect
75. #67000C2×C4semidirect
76. #66997C2×C4semidirect
77. C2×#4326C2×C4semidirect
78. #66993C2×C4semidirect
83. #66989C2×C4semidirect
87. C2×#4324C2×C4semidirect
102. C2×Dic44C2×C4semidirect
103. C2×#4314C2×C4semidirect
119. #66879C2×C4semidirect
120. C8×Dic11C2×C4semidirect
216. #1903D11semidirect
507. C11#23362semidirect

Maximal subgroups

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

subgroupindex
#130790782
#130691092
#130691072
#130691052
#130691012
#130690992
#130690902
#130690892
#130690162
#130690022
#130689992
#130689962
#130687662
#130687642
C11×#19032
#2336211