Finite Group Databasebeta

← #15622301

Subgroups — #15622301

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#13078907C214yesmaximal, complemented
3#13078859C214yesmaximal, complemented
4#13078815C218yesmaximal, complemented
5#13078556C212yesmaximal, complemented
6#13078438C212yesmaximal, complemented
7#13078096C212yesmaximal, complemented
8#13077868C212yesmaximal, complemented
9C4×#67002C214yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C11×#3428C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C11×#520—22no—
14C11×#520C2214yescomplemented
15C11×#519C2212yescomplemented
16C11×#518—22no—
17C11×#518C2212yescomplemented
18C4×C11×#41—22no—
19C4×C11×#41C2212yes—
20C4×C11×#41C2212yes—
21C2×C11×#117—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C2×#67002C2214yes—
25C2×#66983C2212yes—
26#10623066—22no—
27#10623066—22no—
28#10623066C2214yes—
29#10623066C2214yescomplemented
30C2×#66947—22no—
31C2×#66937—22no—
32C2×#66927C2211yescharacteristic, complemented
33C2×C4×D44C2212yescomplemented
34C2×#66923C2211yescharacteristic, complemented
35#10622851C2218yescomplemented
36#10622845C2214yes—
37#10622840C2214yescomplemented
38#10622830C2214yescomplemented
39#10622820C2212yes—
40#10622640C2218yescomplemented
41#10622639C2218yescomplemented
42C4×#4325C2218yescomplemented
43#10622635C2218yescomplemented
44#10622628C2218yescomplemented
45#10622627C2218yescomplemented
46C4×#4323C2218yescomplemented
47#10622622C2218yescomplemented
48#10622616C2218yescomplemented
49#10622614C2214yescomplemented
50#10622613C2214yescomplemented
51#10622613C2214yescomplemented
52#10622608C2214yescomplemented
53#10622581C2214yescomplemented
54#10622580C2214yescomplemented
55#10622537C2212yescomplemented
56C4×#4318C2212yescomplemented
57C2×C11×#41—28no—
58C2×C11×#41—21no—
59C2×C11×#41—21no—
60C2×C11×#41C2312yes—
61C2×C11×#41C2312yes—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×D44—22no—
69C22×D44C2312yes—
70C22×C4×D11—22no—
71C4×Q8×C11—24no—
72C4×Q8×C11C2314yes—
73C4×Q8×C11C2314yes—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C4×D4×C11—24no—
78C4×D4×C11—24no—
79C4×D4×C11C2314yes—
80C4×D4×C11C2314yes—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—24no—
84C11×#117—24no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117D412yes—
88C11×#117D412yes—
89C11×#117C2312yes—
90C11×#117C2312yes—
91C11×#117C2312yes—
92C11×#117C2312yes—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4D412yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11—21no—
100C2×C42×C11—22no—
101C2×C42×C11—22no—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104#67002—216no—
105C2×#4325C2318yes—
106C2×#4323C2318yes—
107#66983—22no—
108#66983—22no—
109#66983C2314yes—
110#66983C2314yes—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×C4⋊Dic11C2312yes—
114C2×Dic11⋊C4—22no—
115C2×#4318C2314yes—
116#66947—28no—
117#66947—28no—
118#66937—28no—
119#66937—28no—
120#66927—22no—
121#66927C2314yes—
122C4×D44—24no—
123C4×D44C2318yes—
124#66923—22no—
125#66923C2314yes—
126#66899C2318yes—
127#66896C2318yes—
128C22⋊(C11⋊C8)C2314yes—
129C22⋊(C11⋊C8)C2314yes—
130#66873C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2318yes—
135#66867C2314yes—
136C4×C11⋊C8C2314yes—
137#60568—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C23×D11—22no—
141C11×#41—28no—
142C11×#41—28no—
143C11×#41—24no—
144C11×#41—24no—
145C11×#41—24no—
146C11×#41#4118yes—
147C2×Q8×C11—24no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2412yes—
150C2×D4×C11—28no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11C2412yes—
156C22×C4×C11—28no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—24no—
161C22×C4×C11—22no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—84no—
175C22×Dic11—22no—
176C2×D44—22no—
177C2×D44—28no—
178C2×D44—28no—
179C2×D44—84no—
180C2×D44C2414yes—
181C2×C4×D11—28no—
182C2×C4×D11—84no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2×D414yes—
188C11×C4⋊C4C2414yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4C2×D414yes—
194C11×C22⋊C4C2×D414yes—
195C42×C11—22no—
196C42×C11—24no—
197C42×C11—24no—
198C42×C11—22no—
199C42×C11C2×D412yes—
200C42×C11C2×D412yes—
201C42×C11C2412yes—
202C42×C11C2412yes—
203#4325—216no—
204#4323—216no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—24no—
208C4⋊Dic11—22no—
209C4⋊Dic11C2414yes—
210Dic11⋊C4—28no—
211#4318—28no—
212C2×C11⋊C8C2418yes—
213C2×#540—111no—
214#3428D1111yescharacteristic, complemented
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—24no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—82no—
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—44no—
236Q8×C11—24no—
237Q8×C11—22no—
238Q8×C11C2×#4114yes—
239D4×C11—28no—
240D4×C11—24no—
241D4×C11—28no—
242D4×C11—22no—
243D4×C11C2×#4114yes—
244C2×C4×C11—24no—
245C2×C4×C11—28no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—84no—
257C2×C4×C11—84no—
258C2×C4×C11—82no—
259C2×C4×C11C22×D414yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D414yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4114yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—84no—
267C22⋊D11—84no—
268C2×Dic11—24no—
269C2×Dic11—44no—
270D44—28no—
271D44—44no—
272D44—88no—
273C4×D11—88no—
274C11⋊C8—28no—
275C22×#41C2×D1111yescharacteristic
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—22no—
287#520C2×D1114yescomplemented
288#519C2×D1112yescomplemented
289#518—22no—
290#518C2×D1112yescomplemented
291C4×#41—22no—
292C4×#41C2×D1112yes—
293C4×#41C2×D1112yes—
294C2×C4×D4—112no—
295C2×#117—22no—
296C2×#117C2×D1111yescharacteristic
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—24no—
326C22×C11—44no—
327C22×C11—82no—
328C22×C11—84no—
329C22×C11#52512yes—
330C22×C11C23×D411yescharacteristic
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—88no—
335C4×C11—24no—
336C4×C11—24no—
337C4×C11—21no—
338C4×C11—24no—
339C4×C11—21no—
340C4×C11—44no—
341C4×C11#52512yes—
342C4×C11C22×#4112yes—
343Dic11—44no—
344C2×#41—28no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41C22×D1112yes—
348C2×#41C22×D1112yes—
349C22×Q8C22×D1111yescharacteristic
350C22×D4—21no—
351C22×D4—112no—
352C22×D4—222no—
353C22×D4—222no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—222no—
357C23×C4C22×D1111yescharacteristic
358AGL(1,ℤ/8)—2216no—
359C2×SD16—118no—
360C2×D8—118no—
361C2×M16—114no—
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—24no—
375C4×Q8C22×D1114yes—
376C4×Q8C22×D1114yes—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—24no—
381C4×D4—24no—
382C4×D4—118no—
383C4×D4—224no—
384C4×D4C22×D1114yes—
385C4×D4C22×D1114yes—
386#117—21no—
387#117—21no—
388#117—24no—
389#117—24no—
390#117—22no—
391#117—22no—
392#117C22⋊D1112yes—
393#117C22⋊D1112yes—
394#117C22×D1112yes—
395#117C22×D1112yes—
396#117C22×D1112yes—
397#117C22×D1112yes—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4C22⋊D1112yes—
402C2×C4⋊C4C22×D1112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4C22⋊D1112yes—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—22no—
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—44no—
428C2×C11C2×#52511yescharacteristic
429C2×C11#358512yes—
430D11—84no—
431C24—21no—
432C24—222no—
433C24C2×C22⋊D1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—24no—
437#41—24no—
438#41—24no—
439#41#433918yes—
440C2×Q8—24no—
441C2×Q8—21no—
442C2×Q8C23×D1112yes—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—114no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—228no—
452C2×D4—222no—
453C2×D4—228no—
454C2×D4—884no—
455C2×D4—884no—
456C2×D4C23×D1112yes—
457C22×C4—28no—
458C22×C4—21no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—222no—
466C22×C4—228no—
467C22×C4—884no—
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—22no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—114no—
484C4⋊C4—222no—
485C4⋊C4—228no—
486C4⋊C4C2×C22⋊D1114yes—
487C4⋊C4C2×C22⋊D1114yes—
488C4⋊C4C23×D1114yes—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—228no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4C2×C22⋊D1114yes—
497C22⋊C4C2×C22⋊D1114yes—
498C42—22no—
499C42—24no—
500C42—24no—
501C42—22no—
502C42C2×C22⋊D1112yes—
503C42C2×C22⋊D1112yes—
504C42C23×D1112yes—
505C42C23×D1112yes—
506C11#6056811yescharacteristic, complemented, Sylow
507C23—24no—
508C23—22no—
509C23—22no—
510C23—42no—
511C23—82no—
512C23—224no—
513C23—444no—
514C23—444no—
515C23—444no—
516C23C22×C22⋊D1111yescharacteristic
517C23C22×C22⋊D1111yescharacteristic
518C23C22×C22⋊D1111yescharacteristic
519Q8—24no—
520Q8—22no—
521Q8C2×#433914yes—
522D4—28no—
523D4—24no—
524D4—28no—
525D4—22no—
526D4—228no—
527D4—444no—
528D4—888no—
529D4—884no—
530D4—884no—
531D4C2×#433914yes—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—28no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—84no—
545C2×C4—84no—
546C2×C4—82no—
547C2×C4—224no—
548C2×C4—444no—
549C2×C4—888no—
550C2×C4C2×#433914yes—
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—21no—
560C22—21no—
561C22—24no—
562C22—22no—
563C22—22no—
564C22—44no—
565C22—82no—
566C22—84no—
567C22—444no—
568C22—444no—
569C22—444no—
570C22—888no—
571C22#1062332212yes—
572C22C23×C22⋊D1111yescharacteristic
573C4—21no—
574C4—24no—
575C4—21no—
576C4—24no—
577C4—24no—
578C4—44no—
579C4—444no—
580C4#1062332212yes—
581C4C22×#433912yes—
582C2—22no—
583C2—41no—
584C2—41no—
585C2—44no—
586C2—884no—
587C2C2×#1062332211yescharacteristic
588C2#1308339512yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3428C2
socleC22×C11C23×D4
hypercenter#3428D11
hypocenterC11#60568
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C2×#10623066C2semidirect
2. #13078907C2semidirect
3. #13078859C2semidirect
4. #13078815C2semidirect
5. #13078556C2semidirect
6. #13078438C2semidirect
7. #13078096C2semidirect
8. #13077868C2semidirect
9. C4×#67002C2semidirect
10. #13077254C2semidirect
11. C11×#3428C2semidirect
14. C11×#520C22semidirect
15. C11×#519C22semidirect
17. C11×#518C22semidirect
29. #10623066C22semidirect
32. C2×#66927C22semidirect
33. C2×C4×D44C22semidirect
34. C2×#66923C22semidirect
35. #10622851C22semidirect
37. #10622840C22semidirect
38. #10622830C22semidirect
40. #10622640C22semidirect
41. #10622639C22semidirect
42. C4×#4325C22semidirect
43. #10622635C22semidirect
44. #10622628C22semidirect
45. #10622627C22semidirect
46. C4×#4323C22semidirect
47. #10622622C22semidirect
48. #10622616C22semidirect
49. #10622614C22semidirect
50. #10622613C22semidirect
51. #10622613C22semidirect
52. #10622608C22semidirect
53. #10622581C22semidirect
54. #10622580C22semidirect
55. #10622537C22semidirect
56. C4×#4318C22semidirect
214. #3428D11semidirect
287. #520C2×D11semidirect
288. #519C2×D11semidirect
290. #518C2×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
#130789072
#130788592
#130788152
#130785562
#130784382
#130780962
#130778682
C4×#670022
#130772542
C11×#34282
#6056811