Finite Group Databasebeta

← #14675941

Subgroups — #14675941

Order 2816.

1298 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622549C211yesmaximal, characteristic
2C2×C4×Dic11⋊C4C211yesmaximal, characteristic
3C2×#10622261C211yesmaximal, characteristic
4#13066876C212yesmaximal
5#13066870C212yesmaximal
6#13066850C212yesmaximal
7#13066847C212yesmaximal
8#13066842C211yesmaximal, characteristic
9#13066841C211yesmaximal, characteristic
10#13066840C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C22×C4⋊Dic11C2212yes—
14C22×Dic11⋊C4C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×#95C2211yescharacteristic
20C2×C11×#95C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35#10622549—24no—
36C4×Dic11⋊C4C418yescomplemented
37#10622261—24no—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11C2×C414yes—
52C2×C4⋊Dic11—24no—
53C2×C4⋊Dic11—24no—
54C2×C4⋊Dic11—42no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4C2×C414yes—
59C2×Dic11⋊C4C2×C414yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—24no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11C2×C414yes—
67C2×C4×Dic11C2×C414yes—
68C11×#95—22no—
69C11×#95—24no—
70C11×#95—24no—
71C11×#95—22no—
72C11⋊#95—22no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—42no—
80C11⋊#95—42no—
81C11⋊#95C2×C414yes—
82C11⋊#95C2×C414yes—
83C11⋊#95D414yes—
84#13897—111nomaximal, Sylow
85C24×C11C2411yescharacteristic
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11#4114yes—
114C22×C4×C11#4112yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11C22×C412yes—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C412yes—
149C22×Dic11C22×C412yes—
150C22×Dic11C2×D414yes—
151C22×Dic11#4114yes—
152C22×Dic11#4114yes—
153C42×C11—28no—
154C4⋊Dic11—48no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157C4×Dic11—216no—
158C4×Dic11—28no—
159C4×Dic11—28no—
160C2×#382—111no—
161C2×C4×C4⋊C4—111no—
162C2×#376—111no—
163#1443—112no—
164#1441—112no—
165#1436—112no—
166#1436—112no—
167#1434—111no—
168#1434—111no—
169#1434—111no—
170#1434D1111yescharacteristic
171C23×C11C23×C411yescharacteristic
172C23×C11C22×D411yescharacteristic
173C23×C11C2×#4112yes—
174C23×C11C2×#4111yescharacteristic
175C23×C11C2×#4111yescharacteristic
176C23×C11C2×#4111yescharacteristic
177C23×C11C2×#4112yes—
178C23×C11C2×#4112yes—
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C112−1+412yes—
181C23×C112−1+411yescharacteristic
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11#11714yes—
212C2×C4×C11C4×D414yes—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11#11714yes—
248C2×Dic11#11714yes—
249C22×C4⋊C4—111no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—112no—
252C22×C42—111no—
253C22×C42—111no—
254C22×C42—112no—
255C22×C42C2×D1111yescharacteristic
256#382—224no—
257C4×C4⋊C4—118no—
258#376—224no—
259C2×#95—111no—
260C2×#95—111no—
261C2×#95—111no—
262C2×#95—111no—
263C2×#95—112no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95C2×D1111yescharacteristic
272C2×#95C2×D1111yescharacteristic
273C2×#95C2×D1112yes—
274C2×#95C2×D1112yes—
275C22×C11C2×#11711yescharacteristic
276C22×C11C2×#11711yescharacteristic
277C22×C11C2×#11711yescharacteristic
278C22×C11C2×C4×D411yescharacteristic
279C22×C11C4×#4111yescharacteristic
280C22×C11#51911yescharacteristic
281C22×C11#52011yescharacteristic
282C22×C11#52512yes—
283C22×C11#52912yes—
284C22×C11#52912yes—
285C22×C11#52912yes—
286C22×C11#54112yes—
287C22×C11#54212yes—
288C22×C11#54611yescharacteristic
289C22×C11#54712yes—
290C22×C11#54811yescharacteristic
291C22×C11#55212yes—
292C22×C11#55212yes—
293C22×C11#55211yescharacteristic
294C22×C11#55212yes—
295C22×C11#55311yescharacteristic
296C22×C11#55512yes—
297C22×C11#55612yes—
298C4×C11—24no—
299C4×C11—24no—
300C4×C11—44no—
301C4×C11—42no—
302C4×C11—82no—
303Dic11—24no—
304Dic11—24no—
305Dic11—42no—
306Dic11—42no—
307Dic11—44no—
308Dic11—82no—
309C23×C4—111no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—112no—
313C23×C4—111no—
314C23×C4—112no—
315C23×C4C22×D1112yes—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C2×C4⋊C4—114no—
321C2×C4⋊C4—114no—
322C2×C4⋊C4—224no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—224no—
326C2×C4⋊C4—224no—
327C2×C4⋊C4—442no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—114no—
331C2×C42—114no—
332C2×C42—224no—
333C2×C42—224no—
334C2×C42—224no—
335C2×C42—224no—
336C2×C42—222no—
337C2×C42—222no—
338C2×C42C4×D1114yes—
339#95—24no—
340#95—22no—
341#95—24no—
342#95—22no—
343#95—114no—
344#95—114no—
345#95—114no—
346#95—224no—
347#95—224no—
348#95—224no—
349#95—224no—
350#95—224no—
351#95—224no—
352#95—222no—
353#95—442no—
354#95—442no—
355C2×C11#228311yescharacteristic
356C2×C11#229011yescharacteristic
357C2×C11#232011yescharacteristic
358C2×C11#234411yescharacteristic
359C2×C11#234611yescharacteristic
360C2×C11#235211yescharacteristic
361C2×C11#235611yescharacteristic
362C2×C11#247412yes—
363C2×C11#247512yes—
364C2×C11#252812yes—
365C2×C11#252912yes—
366C24C23×D1111yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—112no—
391C22×C4—112no—
392C22×C4—114no—
393C22×C4—114no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—114no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×C4×D1112yes—
429C22×C4#433914yes—
430C22×C4D4×D1112yes—
431C22×C4#434112yes—
432C22×C4#434112yes—
433C22×C4#434312yes—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—448no—
437C42—28no—
438C42—228no—
439C42—2216no—
440C42—228no—
441C11#1389711yescharacteristic, complemented, Sylow
442C23C22×C4×D1111yescharacteristic
443C23C2×#433912yes—
444C23C2×D4×D1111yescharacteristic
445C23C2×#434111yescharacteristic
446C23C2×#434111yescharacteristic
447C23C2×#434311yescharacteristic
448C23#41×D1112yes—
449C23#41×D1112yes—
450C23#6704211yescharacteristic
451C23#6704311yescharacteristic
452C23#6704312yes—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—114no—
483C2×C4—114no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4(C22⋊D11)⋊C414yes—
519C2×C4#6694514yes—
520C22C4×#433911yescharacteristic
521C22C2×(C22⋊D11)⋊C411yescharacteristic
522C22C2×#6694511yescharacteristic
523C22#1062304711yescharacteristic
524C22D11×#11711yescharacteristic
525C22D11×#11711yescharacteristic
526C22#1062305411yescharacteristic
527C22#1062306212yes—
528C22#1062306312yes—
529C22#1062307212yes—
530C22#1062307812yes—
531C22#1062308812yes—
532C22#1062311512yes—
533C22#1062312911yescharacteristic
534C22#1062314911yescharacteristic
535C22#1062316111yescharacteristic
536C22#1062317311yescharacteristic
537C22#1062318112yes—
538C22#1062318612yes—
539C22#1062321112yes—
540C22#1062322212yes—
541C22#1062323212yes—
542C22#1062324112yes—
543C4—24no—
544C4—24no—
545C4—44no—
546C4—42no—
547C4—82no—
548C4—224no—
549C4—224no—
550C4—444no—
551C4—442no—
552C4—442no—
553C4—882no—
554C2#1307100911yescharacteristic
555C2#1307106211yescharacteristic
556C2#1307126611yescharacteristic
557C2#1307148011yescharacteristic
558C2#1307150211yescharacteristic
559C2#1307154711yescharacteristic
560C2#1307157911yescharacteristic
561C2#1307277612yes—
562C2#1307279112yes—
563C2#1307342212yes—
564C2#1307343712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#13897
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
36. C4×Dic11⋊C4C4semidirect
441. C11#13897semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
C2×C4×Dic11⋊C42
C2×#106222612
#130668762
#130668702
#130668502
#130668472
#130668422
#130668412
#130668402
C11×#14342
#1389711