Finite Group Databasebeta

← #15622302

Subgroups — #15622302

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
1C2×#10623066C211yesmaximal, characteristic, complemented
2#13081817C211yesmaximal, characteristic, complemented
3#13078908C214yesmaximal, complemented
4#13078860C214yesmaximal, complemented
5#13078817C218yesmaximal, complemented
6#13078557C212yesmaximal, complemented
7#13078439C212yesmaximal, complemented
8#13078097C212yesmaximal, complemented
9#13077870C212yesmaximal, complemented
10C4×#66961C214yesmaximal, complemented
11C11×#2921C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66983C2212yes—
15C2×#66979C2211yescharacteristic
16C2×#66961C2214yes—
17#10623066—22no—
18#10623066—22no—
19#10623066C2214yes—
20#10623066C2214yescomplemented
21#10623054C2214yescomplemented
22#10623053—22no—
23#10623052C2212yescomplemented
24D11×#117—22no—
25#10623047C2212yescomplemented
26C2×#66947—22no—
27#10623035—22no—
28C2×#66937—22no—
29#10623017—22no—
30C2×#66927C2211yescharacteristic, complemented
31C4×#4339C2212yes—
32C4×#4339C2212yes—
33C2×C4×D44C2212yescomplemented
34C2×#66923C2211yescharacteristic, complemented
35C11×#433C2214yescomplemented
36C11×#433C2214yescomplemented
37C11×#423C2212yescomplemented
38C11×#407C2212yes—
39C4×C11×M16C2212yescomplemented
40#10622746C2214yes—
41#10622744C2214yescomplemented
42#10622734C2214yescomplemented
43#10622461C2218yescomplemented
44#10622460C2218yescomplemented
45#10622456C2218yescomplemented
46#10622442C2218yescomplemented
47#10622351C2214yescomplemented
48#10622350C2218yescomplemented
49#10622349C2214yescomplemented
50#10622348C2214yescomplemented
51#10622347C2218yescomplemented
52#10622345C2214yescomplemented
53#10622324C2218yescomplemented
54#10622323C2218yescomplemented
55C4×D88C2218yescomplemented
56C4×#4314C2218yescomplemented
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C22×C22⋊D11—22no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—28no—
63C2×#4339C2312yes—
64C2×#4339C2312yes—
65C22×D44—22no—
66C22×D44C2312yes—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×Dic22C2311yescharacteristic
71C2×C11×M16C2314yes—
72C11×#117D412yes—
73C11×#117D412yes—
74C11×#117C2312yes—
75C11×#117C2312yes—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81#66983—22no—
82#66983—22no—
83#66983C2314yes—
84#66983C2314yes—
85C4×C22⋊D11—24no—
86C4×C22⋊D11—24no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89#66979—21no—
90#66979—21no—
91#66979C2312yes—
92#66979C2312yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2312yes—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—21no—
97#66961—216no—
98C2×D88C2318yes—
99C2×#4314C2318yes—
100#66947—28no—
101#66947—28no—
102#66946—24no—
103#66945—24no—
104C4⋊C4×D11—24no—
105#66940—24no—
106#66937—28no—
107#66937—28no—
108(C22⋊D11)⋊C4—24no—
109(C22⋊D11)⋊C4—24no—
110C22⋊C4×D11—24no—
111#66930—24no—
112#66927—22no—
113#66927C2314yes—
114C4×D44—24no—
115C4×D44C2318yes—
116C4×D44C2314yes—
117C4×D44C2314yes—
118#66925—22no—
119#66925—22no—
120C42×D11—22no—
121C42×D11—22no—
122#66923—22no—
123#66923C2314yes—
124C4×Dic22C2314yes—
125C4×Dic22C2314yes—
126C11×C4⋊C8C2318yes—
127C11×C22⋊C8C2314yes—
128C11×C22⋊C8C2314yes—
129C11×#97C2314yes—
130C4×C8×C11C2314yes—
131#66885C2318yes—
132#66885C2318yes—
133#66885C2318yes—
134#66882C2318yes—
135#66881C2318yes—
136#66880C2318yes—
137#60568—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C23×D11—22no—
141C22×C4×C11—24no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—28no—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—22no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—84no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159#4339—28no—
160#4339—28no—
161#4339—24no—
162#4339—24no—
163#4339—24no—
164#4339#4118yes—
165C2×D44—24no—
166C2×D44—21no—
167C2×D44—22no—
168C2×D44—28no—
169C2×D44—28no—
170C2×D44—84no—
171C2×D44C2414yes—
172C2×D44C2412yes—
173C2×C4×D11—28no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—28no—
179C2×C4×D11—84no—
180C2×Dic22—24no—
181C2×Dic22—21no—
182C2×Dic22C2412yes—
183C11×M16—28no—
184C2×C8×C11C2418yes—
185C11×C4⋊C4C2×D414yes—
186C11×C4⋊C4C2×D414yes—
187C11×C22⋊C4C2×D414yes—
188C11×C22⋊C4C2×D414yes—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C42×C11C2412yes—
192C42×C11C2412yes—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11C2414yes—
203C4⋊Dic11C2414yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—24no—
206Dic11⋊C4—28no—
207C4×Dic11—24no—
208C4×Dic11—24no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211D88—216no—
212#4314—216no—
213C2×#540—111no—
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#2921D1111yescharacteristic, complemented
224C23×C11—22no—
225C23×C11—42no—
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—82no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D414yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—28no—
251C22⋊D11—28no—
252C22⋊D11—84no—
253C22⋊D11—84no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—44no—
259C2×Dic11—82no—
260D44—24no—
261D44—22no—
262D44—28no—
263D44—44no—
264D44—88no—
265D44C2×#4114yes—
266C4×D11—28no—
267C4×D11—28no—
268C4×D11—84no—
269C4×D11—84no—
270C4×D11—88no—
271Dic22—24no—
272Dic22—22no—
273Dic22C2×#4114yes—
274C8×C11—28no—
275C22×#41—111no—
276C2×AGL(1,ℤ/8)—114no—
277#540—114no—
278#540—114no—
279#540—222no—
280#540—222no—
281C2×#127—111no—
282C2×#125—111no—
283C2×#123—222no—
284C2×#121—112no—
285C2×#121—222no—
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×D4—112no—
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#433C2×D1114yescomplemented
313#433C2×D1114yescomplemented
314#428—114no—
315#423C2×D1112yescomplemented
316#418—114no—
317#417—114no—
318#407C2×D1112yes—
319C4×M16C2×D1112yescomplemented
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—82no—
326C22×C11#52512yes—
327C22×C11C23×D411yescharacteristic
328C2×D11—24no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—84no—
334C2×D11—88no—
335C4×C11—24no—
336C4×C11—24no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11#52512yes—
340C4×C11C22×#4112yes—
341Dic11—24no—
342Dic11—44no—
343Dic11—44no—
344C2×#41—112no—
345C2×#41—112no—
346C2×#41—228no—
347C2×#41—221no—
348C2×#41—221no—
349C22×Q8—111no—
350C22×D4—112no—
351C22×D4—111no—
352C22×D4—221no—
353C22×D4—222no—
354C22×D4—222no—
355C23×C4—221no—
356C23×C4—222no—
357C23×C4C22×D1111yescharacteristic
358AGL(1,ℤ/8)—2216no—
359C2×SD16—118no—
360C2×D8—118no—
361C2×M16C22×D1114yes—
362#127—114no—
363#127—222no—
364#125—114no—
365#125—222no—
366#123—228no—
367#123—228no—
368#121—114no—
369#121—114no—
370#121—222no—
371#121—222no—
372#121—228no—
373#121—228no—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—224no—
377C4×D4—118no—
378C4×D4—114no—
379C4×D4—114no—
380C4×D4—224no—
381C4×D4—224no—
382C4×D4—224no—
383C4×D4—224no—
384C4×D4—224no—
385C4×D4—224no—
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#117D4412yes—
395#117D4412yes—
396#117C22×D1112yes—
397#117C22×D1112yes—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—224no—
402C2×C4⋊C4D4412yes—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4D4412yes—
408C2×C42—221no—
409C2×C42—222no—
410C2×C42—222no—
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#107—118no—
414#106—118no—
415C4⋊C8C22×D1118yes—
416#103—118no—
417#102—118no—
418#102—118no—
419#102—118no—
420C22⋊C8C22×D1114yes—
421C22⋊C8C22×D1114yes—
422#97C22×D1114yes—
423C4×C8C22×D1114yes—
424C2×C11—22no—
425C2×C11—41no—
426C2×C11—41no—
427C2×C11C2×#52511yescharacteristic
428C2×C11#358512yes—
429D11—44no—
430D11—84no—
431C24—221no—
432C24—222no—
433C24C2×D4411yescharacteristic
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—112no—
444C2×D4—114no—
445C2×D4—224no—
446C2×D4—228no—
447C2×D4—222no—
448C2×D4—222no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—221no—
452C2×D4—222no—
453C2×D4—228no—
454C2×D4—228no—
455C2×D4—884no—
456C2×D4—884no—
457C22×C4—24no—
458C22×C4—228no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—228no—
467C22×C4—884no—
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4412yes—
472C22×C4C2×D4412yes—
473C22×C4C23×D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476SD16—2216no—
477D8—2216no—
478M16—28no—
479C2×C8C23×D1118yes—
480C4⋊C4—114no—
481C4⋊C4—114no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—228no—
487C4⋊C4C2×D4414yes—
488C4⋊C4C2×D4414yes—
489C22⋊C4—222no—
490C22⋊C4—222no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4C2×D4414yes—
497C22⋊C4C2×D4414yes—
498C42—222no—
499C42—222no—
500C42—224no—
501C42—224no—
502C42C2×D4412yes—
503C42C2×D4412yes—
504C42C23×D1112yes—
505C42C23×D1112yes—
506C11#6056811yescharacteristic, complemented, Sylow
507C23—22no—
508C23—42no—
509C23—224no—
510C23—222no—
511C23—224no—
512C23—444no—
513C23—444no—
514C23—444no—
515C23—882no—
516C23C22×D4411yescharacteristic
517C23C22×D4411yescharacteristic
518C23C22×D4411yescharacteristic
519Q8—114no—
520Q8—224no—
521Q8—222no—
522D4—114no—
523D4—224no—
524D4—228no—
525D4—228no—
526D4—222no—
527D4—228no—
528D4—444no—
529D4—888no—
530D4—884no—
531D4—884no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—228no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—444no—
546C2×C4—888no—
547C2×C4—884no—
548C2×C4—884no—
549C2×C4—882no—
550C2×C4C22×D4411yescharacteristic
551C2×C4C22×D4414yes—
552C2×C4C22×D4414yes—
553C2×C4C22×D4411yescharacteristic
554C2×C4C22×D4411yescharacteristic
555C2×C4#41×D1114yes—
556C2×C4C24×D1111yescharacteristic
557C8—28no—
558C22—22no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—82no—
564C22—224no—
565C22—444no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—888no—
570C22—884no—
571C22#1062305512yes—
572C22C23×D4411yescharacteristic
573C4—21no—
574C4—21no—
575C4—24no—
576C4—24no—
577C4—224no—
578C4—444no—
579C4—444no—
580C4#1062305512yes—
581C4C2×#41×D1112yes—
582C2—22no—
583C2—41no—
584C2—41no—
585C2—444no—
586C2—884no—
587C2C2×#1062305511yescharacteristic
588C2#1308339712yes—
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2921C2
socleC22×C11C23×D4
hypercenter#2921D11
hypocenterC11#60568
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. C2×#10623066C2semidirect
2. #13081817C2semidirect
3. #13078908C2semidirect
4. #13078860C2semidirect
5. #13078817C2semidirect
6. #13078557C2semidirect
7. #13078439C2semidirect
8. #13078097C2semidirect
9. #13077870C2semidirect
10. C4×#66961C2semidirect
11. C11×#2921C2semidirect
20. #10623066C22semidirect
21. #10623054C22semidirect
23. #10623052C22semidirect
25. #10623047C22semidirect
30. C2×#66927C22semidirect
33. C2×C4×D44C22semidirect
34. C2×#66923C22semidirect
35. C11×#433C22semidirect
36. C11×#433C22semidirect
37. C11×#423C22semidirect
39. C4×C11×M16C22semidirect
41. #10622744C22semidirect
42. #10622734C22semidirect
43. #10622461C22semidirect
44. #10622460C22semidirect
45. #10622456C22semidirect
46. #10622442C22semidirect
47. #10622351C22semidirect
48. #10622350C22semidirect
49. #10622349C22semidirect
50. #10622348C22semidirect
51. #10622347C22semidirect
52. #10622345C22semidirect
53. #10622324C22semidirect
54. #10622323C22semidirect
55. C4×D88C22semidirect
56. C4×#4314C22semidirect
223. #2921D11semidirect
312. #433C2×D11semidirect
313. #433C2×D11semidirect
315. #423C2×D11semidirect
319. C4×M16C2×D11semidirect
506. C11#60568semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
#130818172
#130789082
#130788602
#130788172
#130785572
#130784392
#130780972
#130778702
C4×#669612
C11×#29212
#6056811