Finite Group Databasebeta

← #15634946

Subgroups — #15634946

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082500C211yesmaximal, characteristic, complemented
2#13082490C211yesmaximal, characteristic, complemented
3#13081674C214yesmaximal, complemented
4#13081641C214yesmaximal, complemented
5#13081617C214yesmaximal, complemented
6#13081594C214yesmaximal, complemented
7#13079086C212yesmaximal, complemented
8#13078134C212yesmaximal, complemented
9#13078125C212yesmaximal, complemented
10#13078099C211yesmaximal, characteristic, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13077550C211yesmaximal, characteristic, complemented
13#13077476C212yesmaximal, complemented
14C4×#66957C211yesmaximal, characteristic, complemented
15C2×C11×#492C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2212yes—
17C22×C11×SD16C2212yes—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#127C2211yescharacteristic
20#10623347C2212yes—
21#10623343C2212yes—
22C2×#66995C2212yes—
23#10623337—24no—
24#10623336C2212yes—
25#10623329C2212yes—
26C2×#66985C2212yes—
27C2×#66957C2211yescharacteristic
28#10623263C2214yescomplemented
29#10623262—22no—
30#10623259—22no—
31#10623252C2214yescomplemented
32#10623250—22no—
33#10623249C2214yes—
34#10623247—22no—
35#10623244C2214yes—
36#10623044—24no—
37C4×#4339C2211yescharacteristic
38C4×#4339C2211yescharacteristic
39#10623001C2211yescharacteristic
40C11×#492C2214yes—
41C11×#492C2214yes—
42C2×C4×C8×C11C2211yescharacteristic
43#10622838C2212yes—
44#10622828C2212yes—
45#10622789C2214yescomplemented
46#10622788C2214yescomplemented
47#10622781C2214yescomplemented
48#10622780C2214yescomplemented
49#10622779C2218yescomplemented
50#10622778C2218yescomplemented
51#10622777C2218yescomplemented
52#10622776C2218yescomplemented
53#10622775C2218yescomplemented
54SD16×Dic11C2218yescomplemented
55#10622726C2211yescharacteristic
56#10622726C2211yescharacteristic
57#10622719C2211yescharacteristic
58#10622715C2212yes—
59#10622714C2212yes—
60#10622703C2214yescomplemented
61#10622696C2214yescomplemented
62#10622688C2214yes—
63#10622685C2214yes—
64#10622537C2211yescharacteristic
65C4×Dic44C2212yescomplemented
66C4×D88C2212yescomplemented
67C4×#4314C2212yescomplemented
68C4×#4314C2212yescomplemented
69#10622292C2214yescomplemented
70C8×Dic22C2214yescomplemented
71C22×Q8×C11C2312yes—
72C22×D4×C11—22no—
73C22×D4×C11C2312yes—
74C2×#4341—24no—
75C2×#4339C2311yescharacteristic
76C2×#4339C2311yescharacteristic
77C2×C11×SD16—28no—
78C2×C11×SD16—44no—
79C2×C11×SD16C2314yes—
80C2×C11×SD16C2314yes—
81C2×C11×SD16C2318yes—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C11×C4⋊Q8—21no—
85C11×C4⋊Q8—21no—
86C11×C4⋊Q8C2314yes—
87C11×#127—21no—
88C11×#127—21no—
89C11×#127C2314yes—
90C2×C11×C4⋊C4—22no—
91C2×C42×C11C2311yescharacteristic
92#67006—24no—
93C2×C22⋊Dic11—24no—
94#67000C2314yes—
95#66999—24no—
96Q8×Dic11—24no—
97Q8×Dic11C2318yes—
98#66997C2314yes—
99C2×#4326C2314yes—
100#66995—44no—
101C2×#4325C2314yes—
102#66993C2314yes—
103#66992—28no—
104#66991—24no—
105#66991—24no—
106#66989—24no—
107#66989C2314yes—
108#66988—28no—
109D4×Dic11—24no—
110D4×Dic11—24no—
111D4×Dic11C2318yes—
112C2×#4324C2314yes—
113#66985—44no—
114C2×#4323C2314yes—
115#66982—24no—
116C4×C22⋊D11—22no—
117C4×C22⋊D11—22no—
118#66979—24no—
119#66979C2311yescharacteristic
120#66979C2311yescharacteristic
121#66979C2312yes—
122#66977D414yes—
123C2×#4318C2312yes—
124C2×Dic44C2311yescharacteristic
125#66957—24no—
126C2×D88C2311yescharacteristic
127C2×#4314C2311yescharacteristic
128C2×#4314C2311yescharacteristic
129#66951—28no—
130#66950—24no—
131#66945—24no—
132#66943—24no—
133#66942—28no—
134#66940—24no—
135C4×D44C2312yes—
136C4×D44C2312yes—
137#66925—21no—
138#66925—21no—
139C42×D11—21no—
140C42×D11—21no—
141#66923D412yes—
142#66922D412yes—
143C4×Dic22C2312yes—
144C4×Dic22C2312yes—
145C4×Dic22C2314yes—
146C4×C8×C11C2312yes—
147C4×C8×C11C2312yes—
148#66899C2318yes—
149#66896C2318yes—
150#66885C2312yes—
151#66885C2312yes—
152#66882C2312yes—
153#66881C2312yes—
154#66880C2312yes—
155#66880C2312yes—
156#66879C2314yes—
157Dic11⋊C8C2318yes—
158C8×Dic11C2314yes—
159C4⋊(C11⋊C8)C2314yes—
160#61410—111nomaximal, Sylow
161C24×C11—22no—
162C2×Q8×C11—22no—
163C2×Q8×C11—24no—
164C2×Q8×C11—24no—
165C2×Q8×C11C2414yes—
166C2×D4×C11—22no—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—84no—
172C2×D4×C11C2414yes—
173C22×C4×C11—22no—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—28no—
177C2×C22⋊D11—21no—
178C2×C22⋊D11—21no—
179C22×Dic11—28no—
180#4341—88no—
181#4339—22no—
182#4339—22no—
183#4339—22no—
184#4339—22no—
185C2×D44C2411yescharacteristic
186C2×D44C2411yescharacteristic
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×Dic22C2×D414yes—
192C2×Dic22C2411yescharacteristic
193C2×Dic22C2411yescharacteristic
194C11×SD16—28no—
195C11×SD16—28no—
196C11×SD16—48no—
197C2×C8×C11—22no—
198C2×C8×C11#4114yescomplemented
199C2×C8×C11C2412yes—
200C2×C8×C11C2411yescharacteristic
201C2×C8×C11C2411yescharacteristic
202C11×C4⋊C4—24no—
203C11×C4⋊C4—24no—
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2412yes—
207C22⋊Dic11—28no—
208C22⋊Dic11—28no—
209C22⋊Dic11—21no—
210C22⋊Dic11—21no—
211C22⋊Dic11C2×D414yes—
212#4326—44no—
213#4325—44no—
214#4324—44no—
215#4323—44no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219C4⋊Dic11—28no—
220C4⋊Dic11C2×D414yes—
221C4⋊Dic11C2×D414yes—
222C4⋊Dic11C2412yes—
223C4⋊Dic11C2412yes—
224Dic11⋊C4—28no—
225Dic11⋊C4—22no—
226Dic11⋊C4—22no—
227Dic11⋊C4C2×D418yes—
228C4×Dic11—28no—
229C4×Dic11—22no—
230C4×Dic11—22no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11C2414yes—
234#4318—24no—
235C2×C11⋊C8C2414yes—
236Dic44—22no—
237D88—22no—
238#4314—22no—
239#4314—22no—
240#3509—111no—
241#3508—111no—
242#3400—114no—
243#3397—114no—
244#3394—114no—
245#3392—114no—
246#3154—112no—
247C2×#492D1111yescharacteristic, complemented
248#3043—112no—
249#3042—112no—
250#3039—111no—
251#3038—111no—
252#2960—111no—
253#2949—112no—
254C4×#135—111no—
255C23×C11—24no—
256C23×C11—44no—
257C23×C11—84no—
258C23×C11C22×D411yescharacteristic
259C22×D11—21no—
260C22×D11—21no—
261Q8×C11—24no—
262Q8×C11—24no—
263Q8×C11—44no—
264D4×C11—24no—
265D4×C11—24no—
266D4×C11—44no—
267D4×C11—48no—
268D4×C11—84no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—44no—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D412yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11H(5,𝔽2)12yes—
277C2×C4×C11C2511yescharacteristic
278C22⋊D11—42no—
279C22⋊D11—42no—
280C22⋊D11—88no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—88no—
286C2×Dic11C22×D418yes—
287D44—21no—
288D44—21no—
289D44—21no—
290D44—21no—
291C4×D11—42no—
292C4×D11—42no—
293C4×D11—44no—
294C4×D11—44no—
295Dic22—28no—
296Dic22—21no—
297Dic22—21no—
298Dic22—21no—
299Dic22—21no—
300C8×C11—22no—
301C8×C11C2×#4112yes—
302C8×C11C2×#4112yes—
303C11⋊C8—24no—
304C2×#137—112no—
305C2×AGL(1,ℤ/8)—112no—
306C2×#135—111no—
307C22×SD16C2×D1112yes—
308C22×SD16C2×D1112yes—
309#559—114no—
310#557—114no—
311#556—114no—
312#552—224no—
313#550—114no—
314#546—224no—
315#541—222no—
316#540—222no—
317#536—112no—
318#535—112no—
319#533—111no—
320#533—222no—
321#532—222no—
322C2×C4⋊Q8C2×D1111yescharacteristic
323C2×#127C2×D1111yescharacteristic
324#519—112no—
325#518—112no—
326C4×#41—111no—
327C4×#41—111no—
328#497—114no—
329#496—114no—
330#495—114no—
331#492—114no—
332#492C2×D1114yes—
333#492C2×D1114yes—
334#464—118no—
335#463—118no—
336#462—114no—
337#461—118no—
338#461—114no—
339#460—118no—
340#460—114no—
341#459—114no—
342#446—114no—
343C8×Q8—114no—
344#440—118no—
345C4×Q16—112no—
346C4×SD16—118no—
347C4×SD16—112no—
348C4×SD16—112no—
349C4×D8—112no—
350#427—111no—
351#424—112no—
352#423—111no—
353#419—112no—
354#418—112no—
355#416—111no—
356#416—111no—
357#405—112no—
358C2×C4×C8C2×D1111yescharacteristic
359C22×C11—22no—
360C22×C11—44no—
361C22×C11—48no—
362C22×C11—164no—
363C22×C11#55012yes—
364C22×C11C23×D411yescharacteristic
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—42no—
368C2×D11—42no—
369C4×C11—22no—
370C4×C11—44no—
371C4×C11#55012yes—
372C4×C11#57714yes—
373C4×C11C22×#4111yescharacteristic
374C4×C11C2×H(5,𝔽2)11yescharacteristic
375Dic11—28no—
376Dic11—41no—
377Dic11—41no—
378Dic11—42no—
379Dic11—42no—
380C2×#41—111no—
381C2×#41—111no—
382C2×#41—224no—
383C22×Q8C22×D1112yes—
384C22×D4—22no—
385C22×D4C22×D1112yes—
386#137—444no—
387AGL(1,ℤ/8)—444no—
388#135—224no—
389C2×Q16—114no—
390C2×Q16—111no—
391C2×SD16—28no—
392C2×SD16—44no—
393C2×SD16—114no—
394C2×SD16—114no—
395C2×SD16—111no—
396C2×SD16—111no—
397C2×SD16C22×D1114yes—
398C2×SD16C22×D1114yes—
399C2×SD16C22×D1118yes—
400C2×D8—114no—
401C2×D8—111no—
402C2×M16—112no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—21no—
406C4⋊Q8—21no—
407C4⋊Q8—114no—
408C4⋊Q8—112no—
409C4⋊Q8C22×D1114yes—
410#127—21no—
411#127—21no—
412#127—114no—
413#127C22×D1114yes—
414#126—228no—
415#125—112no—
416#125—224no—
417#125—228no—
418#124—114no—
419#124—114no—
420#124—224no—
421#123—224no—
422#123—228no—
423C22⋊Q8—114no—
424C22⋊Q8—224no—
425C22⋊Q8—224no—
426#121—224no—
427#121—224no—
428#121—228no—
429#120—224no—
430C4×Q8—114no—
431C4×Q8—118no—
432C4×Q8—112no—
433C4×Q8—112no—
434C4×Q8—224no—
435C4×Q8—224no—
436C4×D4—118no—
437C4×D4—112no—
438C4×D4—112no—
439C4×D4—224no—
440C4×D4—224no—
441C4×D4—222no—
442C4×D4—222no—
443#117—112no—
444#117—111no—
445#117—111no—
446#117—224no—
447#117—224no—
448#117—221no—
449#117—221no—
450C2×C4⋊C4—22no—
451C2×C22⋊C4—224no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#107—112no—
456#106—112no—
457C4⋊C8—118no—
458C4⋊C8—114no—
459#103—118no—
460#103—112no—
461#103—112no—
462#102—118no—
463#102—112no—
464#102—112no—
465#97—114no—
466C4×C8—114no—
467C4×C8C22×D1112yes—
468C4×C8C22×D1112yes—
469C2×C11—22no—
470C2×C11—84no—
471C2×C11C2×#55011yescharacteristic
472C2×C11C2×#57712yes—
473D11—81no—
474D11—81no—
475C24—22no—
476#41—222no—
477#41—222no—
478#41—222no—
479#41—222no—
480#41—888no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—114no—
485C2×Q8—111no—
486C2×Q8—111no—
487C2×Q8C23×D1114yes—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—84no—
494C2×D4—111no—
495C2×D4—111no—
496C2×D4—228no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4C23×D1114yes—
500C22×C4—22no—
501C22×C4—228no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—222no—
506C22×C4D4×D1112yes—
507C22×C4C23×D1111yescharacteristic
508Q16—222no—
509Q16—444no—
510SD16—28no—
511SD16—28no—
512SD16—48no—
513SD16—222no—
514SD16—222no—
515SD16—444no—
516SD16—444no—
517D8—222no—
518D8—444no—
519M16—224no—
520C2×C8—22no—
521C2×C8—114no—
522C2×C8#434114yescomplemented
523C2×C8C23×D1112yes—
524C2×C8C23×D1111yescharacteristic
525C2×C8C23×D1111yescharacteristic
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—114no—
529C4⋊C4—114no—
530C4⋊C4—118no—
531C4⋊C4—112no—
532C4⋊C4—112no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C22⋊C4—114no—
538C22⋊C4—228no—
539C22⋊C4—228no—
540C22⋊C4—228no—
541C22⋊C4—221no—
542C22⋊C4—221no—
543C22⋊C4—222no—
544C22⋊C4—222no—
545C42—114no—
546C42—228no—
547C42—221no—
548C42—221no—
549C42—222no—
550C42—222no—
551C42D4×D1111yescharacteristic
552C42D4×D1111yescharacteristic
553C42C23×D1112yes—
554C11#6141011yescharacteristic, complemented, Sylow
555C23—24no—
556C23—44no—
557C23—84no—
558C23—221no—
559C23—221no—
560C23C2×D4×D1111yescharacteristic
561Q8—24no—
562Q8—24no—
563Q8—44no—
564Q8—228no—
565Q8—221no—
566Q8—221no—
567Q8—221no—
568Q8—221no—
569D4—24no—
570D4—24no—
571D4—44no—
572D4—48no—
573D4—84no—
574D4—221no—
575D4—221no—
576D4—221no—
577D4—221no—
578D4—442no—
579D4—442no—
580D4—888no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—44no—
584C2×C4—118no—
585C2×C4—222no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—221no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—444no—
592C2×C4—444no—
593C2×C4—888no—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×D4×D1112yes—
597C2×C4C2×#434112yes—
598C2×C4#6703712yes—
599C2×C4C24×D1111yescharacteristic
600C8—22no—
601C8—224no—
602C8C2×#434112yes—
603C8C2×#434112yes—
604C22—22no—
605C22—48no—
606C22—44no—
607C22—164no—
608C22—442no—
609C22—442no—
610C22—441no—
611C22—441no—
612C22#1062324912yes—
613C22C22×D4×D1111yescharacteristic
614C4—22no—
615C4—44no—
616C4—228no—
617C4—442no—
618C4—442no—
619C4—441no—
620C4—441no—
621C4#1062324912yes—
622C4#1062329314yes—
623C4C22×#434111yescharacteristic
624C4C2×#6703711yescharacteristic
625C2—22no—
626C2—84no—
627C2—881no—
628C2—881no—
629C2C2×#1062324911yescharacteristic
630C2C2×#1062329312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#492C2
socleC22×C11C23×D4
hypercenterC2×#492D11
hypocenterC11#61410
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13082500C2semidirect
2. #13082490C2semidirect
3. #13081674C2semidirect
4. #13081641C2semidirect
5. #13081617C2semidirect
6. #13081594C2semidirect
7. #13079086C2semidirect
8. #13078134C2semidirect
9. #13078125C2semidirect
10. #13078099C2semidirect
11. #13078092C2semidirect
12. #13077550C2semidirect
13. #13077476C2semidirect
14. C4×#66957C2semidirect
15. C2×C11×#492C2semidirect
28. #10623263C22semidirect
31. #10623252C22semidirect
45. #10622789C22semidirect
46. #10622788C22semidirect
47. #10622781C22semidirect
48. #10622780C22semidirect
49. #10622779C22semidirect
50. #10622778C22semidirect
51. #10622777C22semidirect
52. #10622776C22semidirect
53. #10622775C22semidirect
54. SD16×Dic11C22semidirect
60. #10622703C22semidirect
61. #10622696C22semidirect
65. C4×Dic44C22semidirect
66. C4×D88C22semidirect
67. C4×#4314C22semidirect
68. C4×#4314C22semidirect
69. #10622292C22semidirect
70. C8×Dic22C22semidirect
198. C2×C8×C11#41semidirect
247. C2×#492D11semidirect
522. C2×C8#4341semidirect
554. C11#61410semidirect

Maximal subgroups

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

subgroupindex
#130825002
#130824902
#130816742
#130816412
#130816172
#130815942
#130790862
#130781342
#130781252
#130780992
#130780922
#130775502
#130774762
C4×#669572
C2×C11×#4922
#6141011