Finite Group Databasebeta

← #14769793

Subgroups — #14769793

Order 2816.

1384 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623300C211yesmaximal, characteristic
2C2×#10622809C211yesmaximal, characteristic, complemented
3#13077139C212yesmaximal, complemented
4#13069526C211yesmaximal, characteristic, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069122C212yesmaximal, complemented
7#13068992C212yesmaximal, complemented
8#13068681C211yesmaximal, characteristic, complemented
9#13068568C212yesmaximal, complemented
10#13068455C211yesmaximal, characteristic, complemented
11C11×#2951C211yesmaximal, characteristic, complemented
12C2×#67042C2212yes—
13C2×C11×#135C2211yescharacteristic
14C11×#520C2212yescomplemented
15C2×#67002C2212yes—
16C2×#67001C2212yescomplemented
17#10623300—24no—
18#10623300C418yescomplemented
19C2×#66972—21no—
20C2×#66967—22no—
21C2×D8×D11—21no—
22C22×D88C2211yescharacteristic
23C2×#66954C2211yescharacteristic
24C11×#440—22no—
25C4×C11×Q16—21no—
26C4×C11×D8—21no—
27C2×C11×#107C2211yescharacteristic, complemented
28C11×#417C2212yescomplemented
29C11×#405C2211yescharacteristic, complemented
30C2×#66901C2212yescomplemented
31#10622809—24no—
32C2×#66889C2211yescharacteristic
33C2×#66887C2212yescomplemented
34C2×#66883C2211yescharacteristic, complemented
35C2×C8×Dic11C2211yescharacteristic, complemented
36#10622615—22no—
37#10622615C2211yescharacteristic
38#10622614—22no—
39#10622614C2212yescomplemented
40#10622601C2212yescomplemented
41#10622579—22no—
42#10622579C2212yes—
43C2×#66873—22no—
44C2×#66873C2212yescomplemented
45#10622196C2211yescharacteristic, complemented
46#10622170C2211yescharacteristic, complemented
47#10622168C2212yescomplemented
48C2×C11×#41C2312yes—
49#67042—24no—
50#67042—24no—
51#67042—42no—
52#67042C2×C418yescomplemented
53C2×#4343—22no—
54C2×D4×D11—22no—
55C2×D4×D11—42no—
56C2×#4339—22no—
57C2×#4339C2311yescharacteristic
58C22×D44—22no—
59C22×D44C2312yes—
60C11×#135C2×C414yes—
61C11×#135D414yes—
62C2×C11×Q16D411yescharacteristic
63C2×C11×SD16D412yes—
64C2×C11×D8D411yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—42no—
70C11×#117—22no—
71C11×#117C2311yescharacteristic
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4C2312yes—
74#67002—24no—
75#67002C2×C418yescomplemented
76#67001—24no—
77#67001—42no—
78C2×#4325—22no—
79C2×#4323—22no—
80C2×(C2×D11)⋊C4—42no—
81C2×C4×Dic11C2311yescharacteristic
82C2×#4318—22no—
83C2×#4318C2312yes—
84C2×#4318C2311yescharacteristic
85C22×C11⋊C8—22no—
86C22×C11⋊C8C2311yescharacteristic
87#66972—28no—
88#66967—216no—
89D8×D11—28no—
90C2×D88—21no—
91C2×D88—21no—
92C2×D88—22no—
93C2×D88C2×C414yescomplemented
94#66954—22no—
95#66954C2×C414yescomplemented
96C2×#4313—21no—
97C2×C8×D11—21no—
98C11×#107—21no—
99C11×#107—21no—
100C11×#103—22no—
101C11×#102—22no—
102C11×#97—21no—
103C4×C8×C11—21no—
104#66901—24no—
105#66889—22no—
106#66887—42no—
107#66883—22no—
108C8×Dic11—22no—
109#66874—22no—
110#66874D411yescharacteristic
111#66874D411yescharacteristic
112#66873—22no—
113#66873—22no—
114#66873—22no—
115#66873—22no—
116#66873—22no—
117#66873D411yescharacteristic
118#66873D411yescharacteristic
119#22466—111nomaximal, Sylow
120C23×D11—22no—
121C23×D11—42no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41C22×C414yes—
125C11×#41C2×D414yes—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—22no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—21no—
134C2×C22⋊D11—42no—
135C22×Dic11—21no—
136#4343—28no—
137#4343—44no—
138D4×D11—28no—
139D4×D11—48no—
140D4×D11—44no—
141D4×D11—48no—
142#4339—28no—
143#4339—21no—
144#4339—21no—
145#4339—44no—
146#4339C22×C412yes—
147#4339#4112yes—
148C2×D44—28no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—42no—
155C2×D44—44no—
156C2×D44C22×C414yes—
157C2×D44C2×D411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—42no—
160C2×Dic22C2×D411yescharacteristic
161C11×Q16C22⋊C414yescomplemented
162C11×SD16C22⋊C418yescomplemented
163C11×D8C22⋊C414yescomplemented
164C11×M16—21no—
165C11×M16—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C2×C8×C11C2×D412yes—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—42no—
178C42×C11—21no—
179C42×C11—42no—
180#4325—28no—
181#4323—28no—
182(C2×D11)⋊C4—84no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185#4318—21no—
186#4318—22no—
187#4318—22no—
188#4318—44no—
189#4318C22×C412yes—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—44no—
195C2×C11⋊C8C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197D88—24no—
198D88—24no—
199#4313—24no—
200C8×D11—24no—
201C2×#576—111no—
202C2×#443—111no—
203#2951D1111yescharacteristic, complemented
204#2897—112no—
205#1978—111no—
206#1970—111no—
207#1907—112no—
208#1883—112no—
209#1816—111no—
210#1792—112no—
211#1764—111no—
212C23×C11—22no—
213C23×C11H(5,𝔽2)11yescharacteristic
214C22×D11—21no—
215C22×D11—24no—
216C22×D11—48no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—82no—
220C22×D11—82no—
221C22×D11—162no—
222C22×D11—162no—
223Q8×C11—22no—
224Q8×C11C2×C22⋊C414yes—
225D4×C11—24no—
226D4×C11—24no—
227D4×C11—22no—
228D4×C11C2×C22⋊C414yes—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—42no—
235C2×C4×C11—82no—
236C2×C4×C11—162no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C22⋊D11—22no—
244C22⋊D11—22no—
245C22⋊D11—48no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250D44—24no—
251D44—24no—
252D44—21no—
253D44—48no—
254D44—42no—
255D44—42no—
256D44C4×D412yes—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—48no—
260Dic22—21no—
261Dic22C4×D412yes—
262C8×C11—41no—
263C8×C11C2×C22⋊C412yes—
264C8×C11C2×C22⋊C412yes—
265C11⋊C8—22no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—42no—
269C2×H(5,𝔽2)—112no—
270#576—118no—
271#576—224no—
272C2×AGL(1,ℤ/8)—112no—
273C2×AGL(1,ℤ/8)—222no—
274C2×#135—221no—
275C2×#135C2×D1111yescharacteristic
276C22×D8—111no—
277C22×D8—221no—
278C2×#131—112no—
279C2×#131—111no—
280#520C2×D1112yescomplemented
281#443—224no—
282#440—22no—
283C4×Q16—21no—
284C4×D8—21no—
285C2×#108—111no—
286C2×#107C2×D1111yescharacteristic, complemented
287C2×#104—112no—
288C2×#104—111no—
289#418—112no—
290#418—222no—
291#417—112no—
292#417—222no—
293#417C2×D1112yescomplemented
294#416—111no—
295#416—222no—
296C2×#102—112no—
297C2×#102—222no—
298C2×#100—112no—
299#405C2×D1111yescharacteristic, complemented
300C2×C4×C8—111no—
301#390—112no—
302#343—112no—
303#341—111no—
304#339—111no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—24no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11#51811yescharacteristic
311C22×C11D4211yescharacteristic
312C22×C11#54611yescharacteristic
313C2×D11—22no—
314C2×D11—41no—
315C2×D11—41no—
316C2×D11—44no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—84no—
320C2×D11—168no—
321C2×D11—162no—
322C4×C11—24no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—82no—
326C4×C11C22×C22⋊C411yescharacteristic
327C4×C11C2×C4×D411yescharacteristic
328C4×C11D4211yescharacteristic
329C4×C11#54611yescharacteristic
330Dic11—22no—
331Dic11—42no—
332H(5,𝔽2)—118no—
333H(5,𝔽2)—224no—
334H(5,𝔽2)—224no—
335H(5,𝔽2)—442no—
336C2×#41—111no—
337C2×#41—222no—
338C2×#41—222no—
339C2×#41C22×D1112yes—
340C22×D4—112no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—442no—
344AGL(1,ℤ/8)—118no—
345AGL(1,ℤ/8)—224no—
346AGL(1,ℤ/8)—2216no—
347#135—228no—
348#135C4×D1114yes—
349#135D4414yes—
350C2×Q16C22⋊D1111yescharacteristic
351C2×SD16—222no—
352C2×SD16C22⋊D1112yes—
353C2×D8—114no—
354C2×D8—222no—
355C2×D8—228no—
356C2×D8—222no—
357C2×D8—221no—
358C2×D8—221no—
359C2×D8C22⋊D1111yescharacteristic
360#131—114no—
361#131—222no—
362#131—224no—
363#131—442no—
364C2×M16—111no—
365C2×M16—112no—
366C2×M16—222no—
367C2×M16—221no—
368C2×M16C22×D1111yescharacteristic
369C22×C8—111no—
370C22×C8—222no—
371C22×C8—221no—
372C22×C8C22×D1111yescharacteristic
373C4×Q8—22no—
374C4×D4—22no—
375C4×D4—42no—
376#117—22no—
377#117C22×D1111yescharacteristic
378C2×C4⋊C4—22no—
379C2×C4⋊C4C22×D1112yes—
380C2×C22⋊C4—442no—
381C2×C42—111no—
382#108—222no—
383#107—21no—
384#107—21no—
385#104—222no—
386#104—224no—
387#103—22no—
388#103—111no—
389#103—111no—
390#103—222no—
391#102—22no—
392#102—111no—
393#102—111no—
394#102—222no—
395#102—222no—
396#102—222no—
397#102—222no—
398#102—222no—
399#100—442no—
400#97—21no—
401C4×C8—21no—
402C4×C8—222no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—44no—
406C2×C11D4×C22⋊C411yescharacteristic
407C2×C11#329011yescharacteristic
408C2×C11#329211yescharacteristic
409D11—42no—
410D11—84no—
411C24—222no—
412C24—442no—
413#41—22no—
414#41—22no—
415#41—112no—
416#41—112no—
417#41—228no—
418#41—221no—
419#41—221no—
420#41—228no—
421#41—444no—
422#41—444no—
423#41C2×C4×D1114yes—
424#41C2×D4414yes—
425C2×Q8—111no—
426C2×Q8C2×C22⋊D1112yes—
427C2×D4—22no—
428C2×D4—114no—
429C2×D4—111no—
430C2×D4—228no—
431C2×D4—221no—
432C2×D4—228no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—444no—
439C2×D4—442no—
440C2×D4—444no—
441C2×D4—442no—
442C2×D4—448no—
443C2×D4—448no—
444C2×D4C2×C22⋊D1112yes—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—42no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—442no—
451C22×C4C23×D1111yescharacteristic
452Q16(C2×D11)⋊C414yescomplemented
453SD16—228no—
454SD16(C2×D11)⋊C418yescomplemented
455D8—228no—
456D8—224no—
457D8—224no—
458D8(C2×D11)⋊C414yescomplemented
459M16—21no—
460M16—21no—
461M16—112no—
462M16—221no—
463M16—224no—
464M16—222no—
465M16—222no—
466M16—444no—
467C2×C8—21no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—224no—
474C2×C8—222no—
475C2×C8—444no—
476C2×C8C2×C4×D1112yes—
477C2×C8C2×D4412yes—
478C2×C8C2×C22⋊D1111yescharacteristic
479C2×C8C2×C22⋊D1111yescharacteristic
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—42no—
483C4⋊C4D4×D1111yescharacteristic
484C4⋊C4D4×D1111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—42no—
487C22⋊C4—884no—
488C42—21no—
489C42—42no—
490C42—221no—
491C42—221no—
492C11#2246611yescharacteristic, complemented, Sylow
493C23—22no—
494C23—221no—
495C23—224no—
496C23—448no—
497C23—442no—
498C23—442no—
499C23—882no—
500C23—882no—
501C23—1762no—
502C23—1762no—
503C23#6703711yescharacteristic
504Q8—22no—
505Q8—112no—
506Q8—221no—
507Q8C2×(C2×D11)⋊C414yes—
508D4—24no—
509D4—24no—
510D4—22no—
511D4—112no—
512D4—222no—
513D4—222no—
514D4—224no—
515D4—224no—
516D4—221no—
517D4—448no—
518D4—448no—
519D4—442no—
520D4—442no—
521D4C2×(C2×D11)⋊C414yes—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—162no—
530C2×C4—221no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—448no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4C22×C4×D1111yescharacteristic
538C2×C4C22×D4411yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#6704211yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—41no—
544C8—222no—
545C8—221no—
546C8—221no—
547C8—442no—
548C8C2×(C2×D11)⋊C412yes—
549C8C2×(C2×D11)⋊C412yes—
550C22—21no—
551C22—21no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—222no—
556C22—441no—
557C22—441no—
558C22—444no—
559C22—884no—
560C22—882no—
561C22—882no—
562C22—1762no—
563C22—1768no—
564C22#1062307611yescharacteristic
565C22#1062308511yescharacteristic
566C22D4×C22⋊D1111yescharacteristic
567C4—24no—
568C4—41no—
569C4—41no—
570C4—82no—
571C4—222no—
572C4—442no—
573C4C4×D4×D1111yescharacteristic
574C4D4×D4411yescharacteristic
575C4C22×(C2×D11)⋊C411yescharacteristic
576C4#1062336011yescharacteristic
577C2—21no—
578C2—21no—
579C2—44no—
580C2—442no—
581C2—884no—
582C2D4×(C2×D11)⋊C411yescharacteristic
583C2#1308040211yescharacteristic
584C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2951C2
socleC22×C11D42
prime radicalC2×#10623300C2
cosocleC22×C4×C11C24
hypercenter#2951D11
hypocenterC11#22466
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#10622809C2semidirect
3. #13077139C2semidirect
4. #13069526C2semidirect
5. #13069480C2semidirect
6. #13069122C2semidirect
7. #13068992C2semidirect
8. #13068681C2semidirect
9. #13068568C2semidirect
10. #13068455C2semidirect
11. C11×#2951C2semidirect
14. C11×#520C22semidirect
16. C2×#67001C22semidirect
18. #10623300C4semidirect
27. C2×C11×#107C22semidirect
28. C11×#417C22semidirect
29. C11×#405C22semidirect
30. C2×#66901C22semidirect
33. C2×#66887C22semidirect
34. C2×#66883C22semidirect
35. C2×C8×Dic11C22semidirect
39. #10622614C22semidirect
40. #10622601C22semidirect
44. C2×#66873C22semidirect
45. #10622196C22semidirect
46. #10622170C22semidirect
47. #10622168C22semidirect
52. #67042C2×C4semidirect
75. #67002C2×C4semidirect
93. C2×D88C2×C4semidirect
95. #66954C2×C4semidirect
161. C11×Q16C22⋊C4semidirect
162. C11×SD16C22⋊C4semidirect
163. C11×D8C22⋊C4semidirect
203. #2951D11semidirect
280. #520C2×D11semidirect
286. C2×#107C2×D11semidirect
293. #417C2×D11semidirect
299. #405C2×D11semidirect
452. Q16(C2×D11)⋊C4semidirect
454. SD16(C2×D11)⋊C4semidirect
458. D8(C2×D11)⋊C4semidirect
492. C11#22466semidirect

Maximal subgroups

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

subgroupindex
C2×#106233002
C2×#106228092
#130771392
#130695262
#130694802
#130691222
#130689922
#130686812
#130685682
#130684552
C11×#29512
#2246611