Finite Group Databasebeta

← #14921015

Subgroups — #14921015

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074708C214yesmaximal, complemented
2#13074663C214yesmaximal
3#13074584C212yesmaximal, complemented
4#13074564C211yesmaximal, characteristic, complemented
5#13074449C211yesmaximal, characteristic
6#13074418C212yesmaximal
7#13074385C211yesmaximal, characteristic
8#13071920C214yesmaximal, complemented
9#13071915C214yesmaximal
10#13071183C211yesmaximal, characteristic, complemented
11#13071171C211yesmaximal, characteristic, complemented
12#13071146C212yesmaximal
13#13071087C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic
15C11×#2647C211yesmaximal, characteristic, complemented
16C2×#66950C2212yes—
17C2×#66940C2212yes—
18C2×#66925C2211yescharacteristic
19C2×#66925C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#400C2214yes—
24C11×#398C2214yes—
25C11×#389C2212yes—
26C11×#389C2212yes—
27C11×#384C2211yescharacteristic
28C11×#382C2211yescharacteristic
29C11×#376C2211yescharacteristic
30#10622607C2214yes—
31#10622606C2214yes—
32#10622602C2214yes—
33#10622600C2212yes—
34#10622599C2214yes—
35#10622598C2212yes—
36#10622597C2214yes—
37#10622596C2214yes—
38#10622595C2214yes—
39#10622591C2214yes—
40C4⋊C4×Dic11C2214yes—
41C4⋊C4×Dic11C2212yes—
42C4⋊C4×Dic11C2214yes—
43C4⋊C4×Dic11C2214yes—
44#10622587C2212yes—
45#10622587C2212yes—
46#10622586C2214yes—
47#10622586C2212yes—
48#10622545C2211yescharacteristic
49C42×Dic11C2211yescharacteristic
50C42×Dic11C2211yescharacteristic
51#10622542C2212yes—
52#10622542C2212yes—
53#10622288C2214yes—
54#10622287C2214yes—
55#10622279C2214yes—
56#10622279C2212yes—
57#10622279C2212yes—
58C11⋊#401C2214yes—
59#10622274C2214yes—
60#10622273C2214yes—
61#10622273C2214yes—
62#10622272C2214yes—
63#10622272C2214yes—
64#10622268C2214yes—
65#10622267C2214yes—
66#10622265C2214yes—
67#10622262C2212yes—
68#10622262C2214yes—
69#10622262C2212yes—
70#10622261C2214yes—
71C22×C4×D11C2311yescharacteristic
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22C2312yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×(C2×D11)⋊C4C2312yes—
84C2×(C2×D11)⋊C4C2312yes—
85C2×(C2×D11)⋊C4C2314yes—
86C2×(C2×D11)⋊C4C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2314yes—
90C2×C4⋊Dic11C2314yes—
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2312yes—
93C2×Dic11⋊C4C2312yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2312yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2311yescharacteristic
107#66950—28no—
108#66940—28no—
109#66925—24no—
110#66925—24no—
111C42×D11—24no—
112#66923—24no—
113#66922—24no—
114C11×#95C2314yes—
115C11×#95C2314yes—
116C11×#95C2312yes—
117C11×#95C2312yes—
118C11×#95C2314yes—
119C11⋊#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2312yes—
124C11⋊#95C2312yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133#34629—111nomaximal, Sylow
134C23×D11C2411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2412yes—
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11C2412yes—
143C22×Dic11C2412yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2411yescharacteristic
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2411yescharacteristic
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—24no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—42no—
155C2×C4×D11#4114yes—
156C2×Dic22—24no—
157C2×Dic22—24no—
158C2×Dic22—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—44no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—44no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11#4114yes—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—44no—
171C4⋊Dic11—28no—
172C4⋊Dic11—28no—
173C4⋊Dic11—24no—
174C4⋊Dic11—44no—
175Dic11⋊C4—24no—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178Dic11⋊C4—24no—
179Dic11⋊C4—44no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—28no—
183C4×Dic11—24no—
184C4×Dic11—24no—
185C4×Dic11—28no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C4×Dic11#4114yes—
191#2655—114no—
192#2652—114no—
193#2647D1111yescharacteristic, complemented
194#2645—112no—
195#2642—111no—
196#2629—111no—
197#2625—112no—
198#2621—111no—
199#2402—114no—
200#2401—114no—
201C4×C4⋊Q8—111no—
202C4×#125—111no—
203C4×C22⋊Q8—112no—
204#2295—112no—
205C4×#117—111no—
206C23×C11C2511yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11C2×#4112yes—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4112yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C11C2×#4112yes—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11C2×#4112yes—
247C2×Dic11C2×#4112yes—
248C2×Dic11C2×#4112yes—
249C2×Dic112−1+414yes—
250C4×D11—28no—
251C4×D11—44no—
252C4×D11—44no—
253Dic22—48no—
254C2×C4⋊Q8—111no—
255C2×#125—111no—
256C2×C22⋊Q8—112no—
257C2×C4×Q8—112no—
258C2×#117—111no—
259C2×#117—111no—
260C22×C42—111no—
261#401—114no—
262#400—114no—
263#400—114no—
264#400—114no—
265#400—114no—
266#400—114no—
267#400—114no—
268#400C2×D1114yes—
269#398—114no—
270#398—114no—
271#398—114no—
272#398C2×D1114yes—
273#397—114no—
274#397—114no—
275#397—114no—
276#396—114no—
277#391—112no—
278#391—112no—
279#391—112no—
280#391—112no—
281#389—112no—
282#389—114no—
283#389—112no—
284#389C2×D1112yes—
285#389C2×D1112yes—
286#387—114no—
287#387—114no—
288#387—114no—
289#387—114no—
290#385—114no—
291#384C2×D1111yescharacteristic
292#382C2×D1111yescharacteristic
293#380—112no—
294C4×C4⋊C4—112no—
295C4×C4⋊C4—114no—
296C4×C4⋊C4—114no—
297C4×C4⋊C4—114no—
298C4×C4⋊C4—114no—
299C4×C4⋊C4—112no—
300C4×C4⋊C4—112no—
301C4×C22⋊C4—112no—
302C4×C22⋊C4—112no—
303C4×C22⋊C4—114no—
304#376—111no—
305#376—114no—
306#376C2×D1111yescharacteristic
307C43—111no—
308C43—111no—
309C22×C11C22×#4111yescharacteristic
310C22×C11C22×#4111yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C2×2−1+412yes—
313C22×C11#58512yes—
314C2×D11—22no—
315C2×D11—24no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—42no—
319C4×C11—24no—
320C4×C11—41no—
321C4×C11—44no—
322C4×C11—41no—
323C4×C11—42no—
324C4×C11—44no—
325C4×C11#52914yes—
326Dic11—22no—
327Dic11—22no—
328Dic11—44no—
329Dic11—42no—
330Dic11—42no—
331Dic11—44no—
332Dic11#54114yes—
333C22×Q8—112no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—111no—
337C4⋊Q8—224no—
338#125—224no—
339C22⋊Q8—228no—
340C4×Q8—228no—
341#117—224no—
342#117—224no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—114no—
349C2×C4⋊C4—114no—
350C2×C4⋊C4—114no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4C22×D1112yes—
353C2×C4⋊C4C22×D1112yes—
354C2×C4⋊C4C22×D1114yes—
355C2×C4⋊C4C22×D1114yes—
356C2×C4⋊C4C22×D1114yes—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—112no—
359C2×C22⋊C4—114no—
360C2×C22⋊C4—114no—
361C2×C42—111no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—114no—
365C2×C42—112no—
366C2×C42—112no—
367C2×C42—114no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—112no—
371C2×C42—112no—
372C2×C42—224no—
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376#95—112no—
377#95—112no—
378#95—114no—
379#95—114no—
380#95—114no—
381#95—114no—
382#95—114no—
383#95—114no—
384#95—114no—
385#95—114no—
386#95—114no—
387#95—114no—
388#95—114no—
389#95—114no—
390#95C22×D1114yes—
391#95C22×D1112yes—
392#95C22×D1112yes—
393#95C22×D1114yes—
394#95C22×D1114yes—
395C2×C11C2×#52911yescharacteristic
396C2×C11C2×#54111yescharacteristic
397C2×C11#345511yescharacteristic
398C2×C11#346112yes—
399C2×C11#346112yes—
400D11—42no—
401C24—111no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—224no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—114no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—114no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—442no—
419C22×C4C23×D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421C22×C4C23×D1112yes—
422C22×C4C23×D1114yes—
423C22×C4C23×D1114yes—
424C22×C4C23×D1112yes—
425C22×C4C23×D1111yescharacteristic
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—44no—
429C4⋊C4—44no—
430C4⋊C4—44no—
431C4⋊C4—224no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—224no—
435C4⋊C4—228no—
436C4⋊C4—224no—
437C4⋊C4—228no—
438C4⋊C4—444no—
439C4⋊C4—444no—
440C22⋊C4—224no—
441C22⋊C4—228no—
442C22⋊C4—224no—
443C22⋊C4—444no—
444C42—22no—
445C42—22no—
446C42—114no—
447C42—222no—
448C42—222no—
449C42—228no—
450C42—224no—
451C42—224no—
452C42—228no—
453C42—222no—
454C42—222no—
455C42—442no—
456C42—442no—
457C42#434314yes—
458C11#3462911yescharacteristic, complemented, Sylow
459C23—112no—
460C23—221no—
461C23—221no—
462C23—222no—
463C23—222no—
464C23C24×D1111yescharacteristic
465Q8—448no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—112no—
482C2×C4—114no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—222no—
488C2×C4—228no—
489C2×C4—222no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4C2×#434314yes—
504C2×C4C2×#434312yes—
505C2×C4#41×D1112yes—
506C2×C4#41×D1112yes—
507C22—222no—
508C22—224no—
509C22—441no—
510C22—441no—
511C22—442no—
512C22C22×#434311yescharacteristic
513C22C2×#41×D1111yescharacteristic
514C22C2×#41×D1111yescharacteristic
515C22#1062345512yes—
516C22D11×2−1+412yes—
517C4—24no—
518C4—41no—
519C4—41no—
520C4—44no—
521C4—42no—
522C4—44no—
523C4—114no—
524C4—222no—
525C4—222no—
526C4—444no—
527C4—442no—
528C4—442no—
529C4—444no—
530C4#1062322214yes—
531C2—442no—
532C2C2×#1062322211yescharacteristic
533C2D11×#54111yescharacteristic
534C2#1308200011yescharacteristic
535C2#1308204212yes—
536C2#1308205012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2647C2
prime radicalC23×D11C24
hypercenter#2647D11
hypocenterC11#34629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2647

Complements

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

NH ≅ G/Ntype
1. #13074708C2semidirect
3. #13074584C2semidirect
4. #13074564C2semidirect
8. #13071920C2semidirect
10. #13071183C2semidirect
11. #13071171C2semidirect
13. #13071087C2semidirect
15. C11×#2647C2semidirect
193. #2647D11semidirect
458. C11#34629semidirect

Maximal subgroups

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

subgroupindex
#130747082
#130746632
#130745842
#130745642
#130744492
#130744182
#130743852
#130719202
#130719152
#130711832
#130711712
#130711462
#130710872
#130709552
C11×#26472
#3462911