Finite Group Databasebeta

← #15634950

Subgroups — #15634950

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082503C211yesmaximal, characteristic, complemented
2#13081647C214yesmaximal, complemented
3#13081643C214yesmaximal, complemented
4#13081619C214yesmaximal, complemented
5#13081600C214yesmaximal, complemented
6#13079107C212yesmaximal
7C2×#10622705C211yesmaximal, characteristic, complemented
8#13078146C212yesmaximal, complemented
9#13078142C212yesmaximal, complemented
10#13078103C211yesmaximal, characteristic, complemented
11#13078099C211yesmaximal, characteristic, complemented
12#13077551C211yesmaximal, characteristic, complemented
13#13077482C212yesmaximal, complemented
14C4×#67003C211yesmaximal, characteristic
15C11×#3509C211yesmaximal, characteristic, complemented
16C11×#557C2214yes—
17C11×#556C2214yes—
18C11×#552—24no—
19C11×#541—22no—
20C11×#536C2212yes—
21C11×#533—22no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#519C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67004C2212yes—
27C2×#67003C2211yescharacteristic
28C22×#4326C2212yes—
29C22×#4326C2212yes—
30C2×#66995C2212yes—
31#10623259—22no—
32#10623228—22no—
33#10623173—24no—
34#10623115C2214yes—
35#10623101C2214yes—
36#10623057C2212yes—
37#10623047C2212yes—
38C4×#4339C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40#10622846C2211yescharacteristic
41#10622838C2212yes—
42#10622705C2214yes—
43#10622705C2214yes—
44#10622705C2214yes—
45#10622703C2218yes—
46#10622703C2214yes—
47#10622699C2214yes—
48#10622696C2214yes—
49#10622673C2214yes—
50#10622672C2214yes—
51#10622667C2218yes—
52#10622644C2214yes—
53#10622644C2218yes—
54#10622643C2218yes—
55C4×#4326C2218yes—
56C4×#4326C2212yes—
57#10622641C2218yes—
58C4×#4325C2212yes—
59#10622637C2214yes—
60Q8×C11⋊C8C2214yes—
61#10622632C2214yes—
62C4×#4324C2212yes—
63C4×#4323C2212yes—
64#10622617C2212yes—
65#10622615C2211yescharacteristic
66#10622612C2212yes—
67#10622611C2211yescharacteristic
68#10622610C2212yes—
69#10622537C2211yescharacteristic
70C2×C4×C11⋊C8C2211yescharacteristic
71C2×C11×#41C2311yescharacteristic
72C22×Q8×C11C2312yes—
73C2×#4339C2311yescharacteristic
74C22×Dic22C2312yes—
75C11×C4⋊Q8—21no—
76C11×C4⋊Q8—21no—
77C11×C4⋊Q8D412yes—
78C11×C4⋊Q8C2314yes—
79C11×C4⋊Q8C2314yes—
80C11×#126—28no—
81C11×#125—24no—
82C11×#125—28no—
83C11×#125D412yes—
84C11×#124C2314yes—
85C11×#123—24no—
86C11×C22⋊Q8—24no—
87C11×C22⋊Q8—24no—
88C11×C22⋊Q8D414yes—
89C4×Q8×C11—24no—
90C4×Q8×C11—24no—
91C4×Q8×C11C2312yes—
92C4×Q8×C11C2318yes—
93C4×Q8×C11C2314yes—
94C4×D4×C11—22no—
95C4×D4×C11C2312yes—
96C11×#117—24no—
97C11×#117—24no—
98C11×#117—21no—
99C11×#117C2311yescharacteristic
100C11×#117C2312yes—
101C2×C11×C4⋊C4—22no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104#67004—44no—
105#67003—24no—
106#66999—24no—
107Q8×Dic11—24no—
108C2×#4326—28no—
109C2×#4326—44no—
110C2×#4326C2314yes—
111C2×#4326C2314yes—
112C2×#4326C2311yescharacteristic
113C2×#4326C2314yes—
114C2×#4326C2318yes—
115C2×#4326C2314yes—
116#66995—44no—
117C2×#4325C2311yescharacteristic
118C2×#4325C2314yes—
119C2×#4324C2311yescharacteristic
120C2×#4324C2314yes—
121C2×#4323C2311yescharacteristic
122C4×C22⋊D11—22no—
123#66979C2311yescharacteristic
124C2×C4⋊Dic11—22no—
125C2×#4318C2312yes—
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66951—28no—
129#66950—24no—
130#66945—24no—
131#66943—24no—
132#66943—28no—
133#66940—24no—
134#66939—24no—
135#66930—24no—
136#66928C2314yes—
137C4×D44C2312yes—
138#66925—21no—
139C42×D11—21no—
140#66922—21no—
141#66922—21no—
142#66922C2314yes—
143#66922C2314yes—
144C4×Dic22C2312yes—
145C4×Dic22C2318yes—
146#66899C2318yes—
147#66899C2312yes—
148#66896C2312yes—
149#66874C2312yes—
150#66874C2318yes—
151#66873C2312yes—
152#66872C2312yes—
153#66871C2312yes—
154C4⋊(C11⋊C8)C2314yes—
155C4⋊(C11⋊C8)C2318yes—
156#66867C2314yes—
157C4×C11⋊C8C2312yes—
158C4×C11⋊C8C2312yes—
159C4×C11⋊C8C2314yes—
160#61411—111nomaximal, Sylow
161C11×#41—22no—
162C11×#41—22no—
163C2×Q8×C11—22no—
164C2×Q8×C11—24no—
165C2×Q8×C11—24no—
166C2×Q8×C11C2×D414yes—
167C2×Q8×C11C2414yes—
168C2×Q8×C11C2411yescharacteristic
169C2×D4×C11—21no—
170C2×D4×C11C2411yescharacteristic
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—21no—
177C22×Dic11—22no—
178#4339—22no—
179#4339—22no—
180C2×D44C2411yescharacteristic
181C2×C4×D11—21no—
182C2×C4×D11—22no—
183C2×Dic22—22no—
184C2×Dic22—24no—
185C2×Dic22—24no—
186C2×Dic22C2411yescharacteristic
187C2×Dic22C2414yes—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—28no—
192C11×C4⋊C4—28no—
193C11×C4⋊C4C2×D414yes—
194C11×C4⋊C4C2×D414yes—
195C11×C4⋊C4C2×D418yes—
196C11×C4⋊C4C2412yes—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4C2×D414yes—
201C42×C11—21no—
202C42×C11—22no—
203C42×C11—28no—
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2412yes—
207C42×C11C2414yes—
208C22⋊Dic11—21no—
209#4326—28no—
210#4326—28no—
211#4326—22no—
212#4326—44no—
213#4326—48no—
214#4326—44no—
215#4325—22no—
216#4325—44no—
217#4324—22no—
218#4324—44no—
219#4323—22no—
220(C2×D11)⋊C4—22no—
221(C2×D11)⋊C4—28no—
222C4⋊Dic11—24no—
223C4⋊Dic11—24no—
224C4⋊Dic11—28no—
225C4⋊Dic11C2412yes—
226Dic11⋊C4—22no—
227Dic11⋊C4—28no—
228C4×Dic11—22no—
229C4×Dic11—28no—
230C4×Dic11—21no—
231#4318—24no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8#4114yes—
234C2×C11⋊C8C2412yes—
235C2×C11⋊C8C2414yes—
236C2×C11⋊C8C2411yescharacteristic
237C2×C11⋊C8C2411yescharacteristic
238#3509—111no—
239#3509D1111yescharacteristic, complemented
240#3398—114no—
241#3398—114no—
242#3395—114no—
243#3393—114no—
244#3156—112no—
245C2×#494—111no—
246#3044—112no—
247#3044—112no—
248#3039—111no—
249#3039—111no—
250#2960—111no—
251#2950—112no—
252C4×#135—111no—
253C23×C11—21no—
254C23×C11C22×D411yescharacteristic
255C22×D11—21no—
256Q8×C11—28no—
257Q8×C11—21no—
258Q8×C11—24no—
259Q8×C11—24no—
260Q8×C11—21no—
261Q8×C11—44no—
262D4×C11—21no—
263D4×C11—21no—
264D4×C11—42no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—21no—
269C2×C4×C11—44no—
270C2×C4×C11—42no—
271C2×C4×C11—44no—
272C2×C4×C11C22×D418yes—
273C2×C4×C11C22×D412yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D412yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11H(5,𝔽2)12yes—
278C2×C4×C11C2511yescharacteristic
279C22⋊D11—42no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—24no—
283C2×Dic11—44no—
284D44—21no—
285D44—21no—
286C4×D11—42no—
287C4×D11—44no—
288Dic22—21no—
289Dic22—24no—
290Dic22—24no—
291Dic22—21no—
292Dic22—44no—
293C11⋊C8—22no—
294C11⋊C8—24no—
295C11⋊C8C2×#4112yes—
296C11⋊C8C2×#4112yes—
297C2×#137—112no—
298C2×#137—112no—
299C2×#135—111no—
300C22×Q16—112no—
301C22×Q16—112no—
302#557—114no—
303#557C2×D1114yes—
304#556—114no—
305#556C2×D1114yes—
306#552—24no—
307#552—224no—
308#541—22no—
309#541—222no—
310#536—112no—
311#536C2×D1112yes—
312#533—22no—
313#533—222no—
314#533C2×D1111yescharacteristic
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8C2×D1111yescharacteristic
317#519—112no—
318#519C2×D1112yes—
319C4×#41—111no—
320C4×#41C2×D1111yescharacteristic
321#497—114no—
322#497—114no—
323#495—114no—
324#494—114no—
325#494—114no—
326#494—114no—
327#464—118no—
328#464—118no—
329#462—114no—
330#462—118no—
331#462—114no—
332#462—118no—
333#461—114no—
334#461—114no—
335#446—114no—
336C8×Q8—114no—
337#441—118no—
338C4×Q16—118no—
339C4×Q16—112no—
340C4×SD16—112no—
341C4×SD16—112no—
342C4×D8—112no—
343#427—111no—
344#424—112no—
345#423—111no—
346#419—112no—
347#419—112no—
348#416—111no—
349#416—111no—
350#405—112no—
351C2×C4×C8—111no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—42no—
355C22×C11#55012yes—
356C22×C11C23×D411yescharacteristic
357C2×D11—41no—
358C2×D11—42no—
359C4×C11—22no—
360C4×C11—28no—
361C4×C11—41no—
362C4×C11—44no—
363C4×C11—42no—
364C4×C11#55012yes—
365C4×C11#57814yes—
366C4×C11C22×#4111yescharacteristic
367C4×C11C2×H(5,𝔽2)11yescharacteristic
368Dic11—44no—
369Dic11—41no—
370Dic11—42no—
371C2×#41—111no—
372C2×#41C22×D1111yescharacteristic
373C22×Q8—112no—
374C22×Q8C22×D1112yes—
375#137—444no—
376#137—444no—
377#135—224no—
378C2×Q16—114no—
379C2×Q16—114no—
380C2×Q16—111no—
381C2×Q16—118no—
382C2×Q16—114no—
383C2×Q16—114no—
384C2×Q16—228no—
385C2×Q16—444no—
386C2×SD16—111no—
387C2×SD16—111no—
388C2×SD16—114no—
389C2×SD16—114no—
390C2×D8—111no—
391C2×M16—112no—
392C22×C8—111no—
393C22×C8—111no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—114no—
397C4⋊Q8—114no—
398C4⋊Q8—221no—
399C4⋊Q8—221no—
400C4⋊Q8C22⋊D1112yes—
401C4⋊Q8C22×D1114yes—
402C4⋊Q8C22×D1114yes—
403#126—28no—
404#126—228no—
405#125—24no—
406#125—28no—
407#125—224no—
408#125—228no—
409#125C22⋊D1112yes—
410#124—114no—
411#124C22×D1114yes—
412#123—24no—
413#123—224no—
414C22⋊Q8—24no—
415C22⋊Q8—24no—
416C22⋊Q8—224no—
417C22⋊Q8—224no—
418C22⋊Q8C22⋊D1114yes—
419C4×Q8—24no—
420C4×Q8—24no—
421C4×Q8—112no—
422C4×Q8—118no—
423C4×Q8—224no—
424C4×Q8—224no—
425C4×Q8C22×D1112yes—
426C4×Q8C22×D1118yes—
427C4×Q8C22×D1114yes—
428C4×D4—22no—
429C4×D4—112no—
430C4×D4—222no—
431C4×D4C22×D1112yes—
432#117—24no—
433#117—24no—
434#117—21no—
435#117—111no—
436#117—224no—
437#117—224no—
438#117—221no—
439#117C22×D1111yescharacteristic
440#117C22×D1112yes—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—222no—
443C2×C42—21no—
444C2×C42—221no—
445C2×C42C22×D1111yescharacteristic
446#107—112no—
447#106—112no—
448C4⋊C8—114no—
449C4⋊C8—118no—
450#103—112no—
451#103—118no—
452#103—112no—
453#103—118no—
454#102—112no—
455#102—112no—
456#97—114no—
457C4×C8—112no—
458C4×C8—112no—
459C4×C8—114no—
460C2×C11—22no—
461C2×C11—81no—
462C2×C11C2×#55011yescharacteristic
463C2×C11C2×#57812yes—
464D11—81no—
465#41—22no—
466#41—22no—
467#41—222no—
468#41—222no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—114no—
473C2×Q8—111no—
474C2×Q8—222no—
475C2×Q8—224no—
476C2×Q8—224no—
477C2×Q8C2×C22⋊D1114yes—
478C2×Q8C23×D1114yes—
479C2×Q8C23×D1111yescharacteristic
480C2×D4—21no—
481C2×D4—111no—
482C2×D4—221no—
483C2×D4C23×D1111yescharacteristic
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4C2×C22⋊D1112yes—
491C22×C4C23×D1111yescharacteristic
492Q16—228no—
493Q16—228no—
494Q16—222no—
495Q16—448no—
496Q16—444no—
497Q16—444no—
498SD16—222no—
499SD16—222no—
500SD16—444no—
501SD16—444no—
502D8—222no—
503M16—224no—
504C2×C8—114no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—112no—
508C2×C8—114no—
509C2×C8—222no—
510C4⋊C4—24no—
511C4⋊C4—24no—
512C4⋊C4—22no—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—224no—
518C4⋊C4—222no—
519C4⋊C4—228no—
520C4⋊C4—228no—
521C4⋊C4C2×C22⋊D1114yes—
522C4⋊C4C2×C22⋊D1114yes—
523C4⋊C4C2×C22⋊D1118yes—
524C4⋊C4C23×D1112yes—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—28no—
528C22⋊C4—221no—
529C22⋊C4—222no—
530C22⋊C4—228no—
531C22⋊C4C2×C22⋊D1114yes—
532C42—21no—
533C42—22no—
534C42—28no—
535C42—221no—
536C42—222no—
537C42—228no—
538C42C2×C22⋊D1111yescharacteristic
539C42C2×C22⋊D1111yescharacteristic
540C42C23×D1112yes—
541C42C23×D1114yes—
542C11#6141111yescharacteristic, complemented, Sylow
543C23—21no—
544C23—221no—
545C23C22×C22⋊D1111yescharacteristic
546Q8—28no—
547Q8—21no—
548Q8—24no—
549Q8—24no—
550Q8—21no—
551Q8—44no—
552Q8—221no—
553Q8—224no—
554Q8—224no—
555Q8—221no—
556Q8—444no—
557D4—21no—
558D4—21no—
559D4—42no—
560D4—221no—
561D4—221no—
562D4—442no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—221no—
573C2×C4—444no—
574C2×C4—442no—
575C2×C4—444no—
576C2×C4#41×D1112yes—
577C2×C4#6704212yes—
578C2×C4C22×C22⋊D1118yes—
579C2×C4C22×C22⋊D1112yes—
580C2×C4C22×C22⋊D1111yescharacteristic
581C2×C4C22×C22⋊D1112yes—
582C2×C4C24×D1111yescharacteristic
583C8—112no—
584C8—112no—
585C8—222no—
586C8—224no—
587C22—22no—
588C22—41no—
589C22—42no—
590C22—441no—
591C22—442no—
592C22#1062336512yes—
593C22C23×C22⋊D1111yescharacteristic
594C4—22no—
595C4—28no—
596C4—41no—
597C4—44no—
598C4—42no—
599C4—441no—
600C4—444no—
601C4—442no—
602C4#1062336512yes—
603C4#1062336914yes—
604C4C2×#41×D1111yescharacteristic
605C4C2×#6704211yescharacteristic
606C2—22no—
607C2—81no—
608C2—881no—
609C2C2×#1062336511yescharacteristic
610C2C2×#1062336912yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3509C2
socleC22×C11C23×D4
prime radicalC2×#67003C22
hypercenter#3509D11
hypocenterC11#61411
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13082503C2semidirect
2. #13081647C2semidirect
3. #13081643C2semidirect
4. #13081619C2semidirect
5. #13081600C2semidirect
7. C2×#10622705C2semidirect
8. #13078146C2semidirect
9. #13078142C2semidirect
10. #13078103C2semidirect
11. #13078099C2semidirect
12. #13077551C2semidirect
13. #13077482C2semidirect
15. C11×#3509C2semidirect
239. #3509D11semidirect
542. C11#61411semidirect

Maximal subgroups

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

subgroupindex
#130825032
#130816472
#130816432
#130816192
#130816002
#130791072
C2×#106227052
#130781462
#130781422
#130781032
#130780992
#130775512
#130774822
C4×#670032
C11×#35092
#6141111