Finite Group Databasebeta

← #15622295

Subgroups — #15622295

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic, complemented
2#13078902C214yesmaximal, complemented
3#13078854C214yesmaximal, complemented
4#13078809C218yesmaximal, complemented
5#13078552C212yesmaximal, complemented
6#13078434C212yesmaximal, complemented
7#13078092C212yesmaximal, complemented
8#13077866C212yesmaximal, complemented
9C4×#66985C214yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C2×C11×#540C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C11×#540—22no—
14C11×#540—22no—
15C11×#540C2214yes—
16C11×#540C2214yescomplemented
17C2×C11×#127C2211yescharacteristic, complemented
18C2×C11×#125C2211yescharacteristic, complemented
19C2×C11×#123—22no—
20C2×C11×#121—22no—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2212yescomplemented
23C2×C11×#117C2211yescharacteristic
24C2×#66985C2214yes—
25C2×#66979C2211yescharacteristic
26#10623054C2214yescomplemented
27#10623053—22no—
28#10623052C2212yescomplemented
29D11×#117—22no—
30#10623047C2212yescomplemented
31#10623035—22no—
32#10623017—22no—
33C4×#4339C2212yes—
34C4×#4339C2212yes—
35#10622828C2214yescomplemented
36#10622820C2212yes—
37#10622688C2218yescomplemented
38#10622685C2218yescomplemented
39#10622679C2218yescomplemented
40#10622676C2218yescomplemented
41#10622653C2214yescomplemented
42#10622650C2218yescomplemented
43#10622649C2214yescomplemented
44#10622648C2218yescomplemented
45#10622647C2214yescomplemented
46#10622646C2214yescomplemented
47#10622631C2218yescomplemented
48C4×#4324C2218yescomplemented
49#10622627C2218yescomplemented
50C4×#4323C2218yescomplemented
51#10622613C2214yescomplemented
52#10622613C2214yescomplemented
53#10622579C2214yes—
54#10622577C2214yescomplemented
55#10622537C2212yescomplemented
56C4×#4318C2212yescomplemented
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11C2312yes—
60C23×C4×C11—22no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—28no—
66C2×#4339C2312yes—
67C2×#4339C2312yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×Dic22C2311yescharacteristic
71C11×#127—22no—
72C11×#127C2314yes—
73C11×#125—22no—
74C11×#125C2314yes—
75C11×#123—28no—
76C11×#123—28no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—28no—
80C11×#121—28no—
81C11×#121C2314yes—
82C11×#121C2314yes—
83C4×D4×C11—24no—
84C4×D4×C11C2318yes—
85C11×#117D412yes—
86C11×#117D412yes—
87C11×#117C2312yes—
88C11×#117C2312yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×#4324C2318yes—
99#66985—216no—
100C2×#4323C2318yes—
101C4×C22⋊D11—24no—
102C4×C22⋊D11—24no—
103#66979—21no—
104#66979—21no—
105#66979C2312yes—
106#66979C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4×Dic11—21no—
109C2×#4318C2314yes—
110#66946—24no—
111#66945—24no—
112C4⋊C4×D11—24no—
113#66940—24no—
114(C22⋊D11)⋊C4—24no—
115(C22⋊D11)⋊C4—24no—
116C22⋊C4×D11—24no—
117#66930—24no—
118C4×D44C2314yes—
119C4×D44C2314yes—
120#66925—22no—
121#66925—22no—
122C42×D11—22no—
123C42×D11—22no—
124C4×Dic22C2314yes—
125C4×Dic22C2314yes—
126#66896C2318yes—
127#66896C2318yes—
128C22⋊(C11⋊C8)C2314yes—
129C22⋊(C11⋊C8)C2314yes—
130#66874C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2318yes—
135#66867C2314yes—
136C4×C11⋊C8C2314yes—
137#60568—111nomaximal, Sylow
138C24×C11—22no—
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—22no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—84no—
147C2×D4×C11—84no—
148C2×D4×C11C2414yes—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—84no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—28no—
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166#4339—28no—
167#4339—28no—
168#4339—24no—
169#4339—24no—
170#4339—24no—
171#4339#4118yes—
172C2×D44—24no—
173C2×D44—21no—
174C2×D44C2412yes—
175C2×C4×D11—28no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×Dic22—24no—
181C2×Dic22—21no—
182C2×Dic22C2412yes—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4C2×D414yes—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2414yes—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4C2×D414yes—
192C11×C22⋊C4C2×D414yes—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195C42×C11C2412yes—
196C42×C11C2412yes—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199#4324—216no—
200#4323—216no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203C4⋊Dic11—22no—
204C4⋊Dic11C2414yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—24no—
207C4×Dic11—24no—
208C4×Dic11—24no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211#4318—28no—
212C2×C11⋊C8C2418yes—
213C2×#540D1111yescharacteristic, complemented
214#3428—111no—
215#3126—114no—
216#3122—114no—
217#3119—118no—
218#3094—112no—
219#3080—112no—
220#3038—112no—
221#3006—112no—
222C4×AGL(1,ℤ/8)—114no—
223#2921—111no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—42no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11—44no—
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—24no—
235C22×D11—82no—
236D4×C11—28no—
237D4×C11—44no—
238D4×C11—88no—
239D4×C11—84no—
240D4×C11—84no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—88no—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D414yes—
253C2×C4×C11C22×D414yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2511yescharacteristic
258C22⋊D11—28no—
259C22⋊D11—28no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—82no—
264D44—24no—
265D44—22no—
266D44C2×#4114yes—
267C4×D11—28no—
268C4×D11—28no—
269C4×D11—84no—
270C4×D11—84no—
271Dic22—24no—
272Dic22—22no—
273Dic22C2×#4114yes—
274C11⋊C8—28no—
275C22×#41—111no—
276C2×AGL(1,ℤ/8)—114no—
277#540—22no—
278#540—22no—
279#540C2×D1114yes—
280#540C2×D1114yescomplemented
281C2×#127C2×D1111yescharacteristic, complemented
282C2×#125C2×D1111yescharacteristic, complemented
283C2×#123—22no—
284C2×#121—22no—
285C2×#121C2×D1112yes—
286#520—114no—
287#520—222no—
288#519—112no—
289#518—112no—
290#518—222no—
291C4×#41—112no—
292C4×#41—112no—
293C4×#41—222no—
294C2×C4×D4C2×D1112yescomplemented
295C2×#117—111no—
296C2×#117—222no—
297C2×#117C2×D1111yescharacteristic
298#482—118no—
299#481—114no—
300#480—114no—
301#479—118no—
302#478—118no—
303#460—118no—
304#459—118no—
305#449—118no—
306#448—114no—
307#447—114no—
308#442—118no—
309#440—118no—
310C4×SD16—118no—
311C4×D8—118no—
312#433—114no—
313#433—114no—
314#428—114no—
315#423—112no—
316#418—114no—
317#417—114no—
318#407—112no—
319C4×M16—112no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—82no—
329C22×C11—88no—
330C22×C11#52512yes—
331C22×C11C23×D411yescharacteristic
332C2×D11—24no—
333C2×D11—44no—
334C2×D11—84no—
335C4×C11—24no—
336C4×C11—24no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—44no—
340C4×C11#52512yes—
341C4×C11C22×#4112yes—
342Dic11—24no—
343Dic11—44no—
344C2×#41—112no—
345C2×#41—112no—
346C2×#41—228no—
347C2×#41—221no—
348C2×#41—221no—
349C22×Q8—111no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—111no—
353C22×D4—221no—
354C22×D4C22×D1112yes—
355C23×C4—22no—
356C23×C4—221no—
357C23×C4C22×D1111yescharacteristic
358AGL(1,ℤ/8)—2216no—
359C2×SD16—118no—
360C2×D8—118no—
361C2×M16—114no—
362#127—22no—
363#127C22×D1114yes—
364#125—22no—
365#125C22×D1114yes—
366#123—28no—
367#123—28no—
368#121—22no—
369#121—22no—
370#121—28no—
371#121—28no—
372#121C22×D1114yes—
373#121C22×D1114yes—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—224no—
377C4×D4—24no—
378C4×D4—114no—
379C4×D4—114no—
380C4×D4—224no—
381C4×D4—224no—
382C4×D4—224no—
383C4×D4—224no—
384C4×D4—224no—
385C4×D4C22×D1118yes—
386#117—112no—
387#117—112no—
388#117—221no—
389#117—221no—
390#117—224no—
391#117—224no—
392#117—222no—
393#117—222no—
394#117C22⋊D1112yes—
395#117C22⋊D1112yes—
396#117C22×D1112yes—
397#117C22×D1112yes—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4C22⋊D1112yes—
402C2×C4⋊C4C22×D1112yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4C22⋊D1112yes—
408C2×C42—221no—
409C2×C42—222no—
410C2×C42—222no—
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#107—118no—
414#106—118no—
415C4⋊C8—118no—
416#103—118no—
417#102—118no—
418#102—118no—
419#102—118no—
420C22⋊C8—114no—
421C22⋊C8—114no—
422#97—114no—
423C4×C8—114no—
424C2×C11—22no—
425C2×C11—41no—
426C2×C11—41no—
427C2×C11—84no—
428C2×C11C2×#52511yescharacteristic
429C2×C11#358512yes—
430D11—44no—
431C24—22no—
432C24—221no—
433C24C2×C22⋊D1111yescharacteristic
434#41—118no—
435#41—224no—
436#41—224no—
437#41—228no—
438#41—228no—
439#41—224no—
440C2×Q8—112no—
441C2×Q8—224no—
442C2×Q8—221no—
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—28no—
446C2×D4—22no—
447C2×D4—28no—
448C2×D4—84no—
449C2×D4—84no—
450C2×D4—112no—
451C2×D4—224no—
452C2×D4—228no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4C23×D1114yes—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—28no—
460C22×C4—84no—
461C22×C4—228no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C23×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476SD16—2216no—
477D8—2216no—
478M16—228no—
479C2×C8—118no—
480C4⋊C4—28no—
481C4⋊C4—22no—
482C4⋊C4—114no—
483C4⋊C4—222no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4C2×C22⋊D1114yes—
487C4⋊C4C2×C22⋊D1114yes—
488C4⋊C4C23×D1114yes—
489C22⋊C4—28no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4C2×C22⋊D1114yes—
497C22⋊C4C2×C22⋊D1114yes—
498C42—222no—
499C42—222no—
500C42—224no—
501C42—224no—
502C42C2×C22⋊D1112yes—
503C42C2×C22⋊D1112yes—
504C42C23×D1112yes—
505C42C23×D1112yes—
506C11#6056811yescharacteristic, complemented, Sylow
507C23—22no—
508C23—24no—
509C23—42no—
510C23—44no—
511C23—44no—
512C23—44no—
513C23—224no—
514C23—222no—
515C23—882no—
516C23C22×C22⋊D1111yescharacteristic
517C23C22×C22⋊D1111yescharacteristic
518C23C22×C22⋊D1111yescharacteristic
519Q8—114no—
520Q8—224no—
521Q8—222no—
522D4—28no—
523D4—44no—
524D4—88no—
525D4—84no—
526D4—84no—
527D4—114no—
528D4—224no—
529D4—228no—
530D4—228no—
531D4—222no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—88no—
542C2×C4—228no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—228no—
546C2×C4—224no—
547C2×C4—884no—
548C2×C4—884no—
549C2×C4—882no—
550C2×C4#41×D1114yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C22×C22⋊D1114yes—
553C2×C4C22×C22⋊D1114yes—
554C2×C4C22×C22⋊D1111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C2×C4C24×D1111yescharacteristic
557C8—228no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—21no—
562C22—21no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—82no—
567C22—88no—
568C22—224no—
569C22—444no—
570C22—884no—
571C22#1062335912yes—
572C22C23×C22⋊D1111yescharacteristic
573C4—24no—
574C4—24no—
575C4—21no—
576C4—21no—
577C4—44no—
578C4—224no—
579C4—444no—
580C4#1062335912yes—
581C4C2×#41×D1112yes—
582C2—22no—
583C2—41no—
584C2—41no—
585C2—84no—
586C2—444no—
587C2C2×#1062335911yescharacteristic
588C2#1308339612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#540C2
socleC22×C11C23×D4
hypercenterC2×#540D11
hypocenterC11#60568
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13081817C2semidirect
2. #13078902C2semidirect
3. #13078854C2semidirect
4. #13078809C2semidirect
5. #13078552C2semidirect
6. #13078434C2semidirect
7. #13078092C2semidirect
8. #13077866C2semidirect
9. C4×#66985C2semidirect
10. #13077254C2semidirect
11. C2×C11×#540C2semidirect
16. C11×#540C22semidirect
17. C2×C11×#127C22semidirect
18. C2×C11×#125C22semidirect
22. C2×C4×D4×C11C22semidirect
26. #10623054C22semidirect
28. #10623052C22semidirect
30. #10623047C22semidirect
35. #10622828C22semidirect
37. #10622688C22semidirect
38. #10622685C22semidirect
39. #10622679C22semidirect
40. #10622676C22semidirect
41. #10622653C22semidirect
42. #10622650C22semidirect
43. #10622649C22semidirect
44. #10622648C22semidirect
45. #10622647C22semidirect
46. #10622646C22semidirect
47. #10622631C22semidirect
48. C4×#4324C22semidirect
49. #10622627C22semidirect
50. C4×#4323C22semidirect
51. #10622613C22semidirect
52. #10622613C22semidirect
54. #10622577C22semidirect
55. #10622537C22semidirect
56. C4×#4318C22semidirect
213. C2×#540D11semidirect
280. #540C2×D11semidirect
281. C2×#127C2×D11semidirect
282. C2×#125C2×D11semidirect
294. C2×C4×D4C2×D11semidirect
506. C11#60568semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130789022
#130788542
#130788092
#130785522
#130784342
#130780922
#130778662
C4×#669852
#130772542
C2×C11×#5402
#6056811