Finite Group Databasebeta

← #14682963

Subgroups — #14682963

Order 2816.

1406 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×#10622556C211yesmaximal, characteristic
2#13066877C212yesmaximal, complemented
3#13066871C212yesmaximal, complemented
4#13066859C212yesmaximal
5#13066853C211yesmaximal, characteristic
6#13066847C212yesmaximal, complemented
7#13066843C212yesmaximal, complemented
8#13066838C212yesmaximal
9C11×#1437C211yesmaximal, characteristic
10C24×Dic11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622556C418yescomplemented
32C25×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×Dic11—24no—
38C23×Dic11—42no—
39C23×Dic11—41no—
40C23×Dic11—41no—
41C23×Dic11C2×C414yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C2×C11×C22⋊C4—24no—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4—41no—
49C2×C11×C22⋊C4—41no—
50C2×C11×C22⋊C4—42no—
51C2×C11×C22⋊C4C2×C414yes—
52C2×C42×C11—24no—
53C2×C42×C11—41no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—42no—
57C2×C22⋊Dic11—42no—
58C2×C22⋊Dic11C2×C414yes—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—42no—
61C2×Dic11⋊C4—42no—
62C2×C4×Dic11—41no—
63C2×C4×Dic11—42no—
64C11×#95—42no—
65C11×#95—41no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—41no—
75C11⋊#95C2×C418yes—
76C11⋊#95C2×C418yes—
77#14507—111nomaximal, Sylow
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—22no—
81C24×C11—22no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11C22×C412yes—
86C24×C11#4114yes—
87C24×C11C2411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
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×C11#4114yes—
112C22×Dic11—28no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140C22×Dic11—48no—
141C22×Dic11—48no—
142C22×Dic11C22×C414yes—
143C22×Dic11C22×C414yes—
144C22×Dic11#4114yes—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—48no—
147C42×C11—44no—
148C22⋊Dic11—44no—
149C22⋊Dic11—48no—
150Dic11⋊C4—48no—
151C4×Dic11—44no—
152C2×#381—111no—
153#1443—112no—
154#1442—112no—
155#1439—112no—
156#1437—111no—
157#1437D1111yescharacteristic
158#1436—112no—
159#1434—112no—
160C22⋊#95—112no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—24no—
165C23×C11—24no—
166C23×C11—24no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11—24no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11#11714yes—
182C23×C11C23×C411yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11C2×#4112yes—
185C23×C11C2×#4112yes—
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)12yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C112−1+412yes—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—416no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C24×C4—111no—
245C22×C4⋊C4—112no—
246C22×C22⋊C4—111no—
247C22×C22⋊C4—112no—
248C22×C22⋊C4C2×D1112yes—
249C22×C22⋊C4C2×D1111yescharacteristic
250C22×C42—111no—
251C22×C42C2×D1111yescharacteristic
252#381—118no—
253C2×#95—112no—
254C2×#95—112no—
255C2×#95—112no—
256C2×#95—112no—
257C2×#95—112no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95—112no—
261C2×#95—112no—
262C2×#95—111no—
263C2×#95—112no—
264C2×#95C2×D1112yes—
265C2×#95C2×D1111yescharacteristic
266C22×C11—24no—
267C22×C11—28no—
268C22×C11—44no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11C2×#11711yescharacteristic
276C22×C11C4×#4112yes—
277C22×C11#51811yescharacteristic
278C22×C11#51811yescharacteristic
279C22×C11#52012yes—
280C22×C11#53812yes—
281C22×C11#53812yes—
282C22×C11#53812yes—
283C22×C11#53912yes—
284C22×C11#54012yes—
285C22×C11#54212yes—
286C22×C11#55112yes—
287C22×C11#55112yes—
288C22×C11#55111yescharacteristic
289C22×C11#55212yes—
290C22×C11#55212yes—
291C22×C11#55312yes—
292C22×C11#55911yescharacteristic
293C22×C11#56011yescharacteristic
294C22×C11#56212yes—
295C22×C11#56311yescharacteristic
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—44no—
299C4×C11—82no—
300Dic11—44no—
301Dic11—44no—
302Dic11—44no—
303Dic11—82no—
304C25C22×D1111yescharacteristic
305C23×C4—112no—
306C23×C4—112no—
307C23×C4—112no—
308C23×C4—114no—
309C23×C4—112no—
310C23×C4—224no—
311C23×C4—441no—
312C23×C4—441no—
313C23×C4—442no—
314C23×C4C22×D1112yes—
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1112yes—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—442no—
320C2×C4⋊C4—442no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—41no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—114no—
327C2×C22⋊C4—224no—
328C2×C22⋊C4—224no—
329C2×C22⋊C4—442no—
330C2×C22⋊C4—442no—
331C2×C22⋊C4C4×D1114yes—
332C2×C42—24no—
333C2×C42—41no—
334C2×C42—442no—
335C2×C42—441no—
336#95—42no—
337#95—41no—
338#95—118no—
339#95—118no—
340#95—224no—
341#95—224no—
342#95—442no—
343#95—441no—
344#95—442no—
345#95—442no—
346#95—442no—
347#95—442no—
348#95—442no—
349C2×C11—44no—
350C2×C11#231211yescharacteristic
351C2×C11#233512yes—
352C2×C11#234312yes—
353C2×C11#237411yescharacteristic
354C2×C11#237611yescharacteristic
355C2×C11#274312yes—
356C2×C11#274912yes—
357C2×C11#275112yes—
358C2×C11#276512yes—
359C24—22no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24C2×C4×D1112yes—
367C24#433914yes—
368C24C23×D1111yescharacteristic
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
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—114no—
391C22×C4—114no—
392C22×C4—114no—
393C22×C4—228no—
394C22×C4—222no—
395C22×C4—222no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4—448no—
422C22×C4—448no—
423C22×C4C2×C4×D1112yes—
424C22×C4C2×C4×D1112yes—
425C22×C4#434114yes—
426C4⋊C4—448no—
427C22⋊C4—44no—
428C22⋊C4—48no—
429C22⋊C4—444no—
430C22⋊C4—448no—
431C42—44no—
432C42—444no—
433C11#1450711yescharacteristic, complemented, Sylow
434C23—22no—
435C23—24no—
436C23—22no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—24no—
444C23—42no—
445C23—41no—
446C23—41no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—41no—
451C23—42no—
452C23—41no—
453C23—42no—
454C23#6692514yes—
455C23C22×C4×D1111yescharacteristic
456C23C2×#433912yes—
457C23C2×#434112yes—
458C23#6703711yescharacteristic
459C23#6703712yes—
460C23#6703711yescharacteristic
461C23#41×D1112yes—
462C23#6704212yes—
463C23#6704312yes—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—4416no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C22—24no—
518C22—28no—
519C22—44no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—42no—
524C22—42no—
525C22—44no—
526C22C2×#6692511yescharacteristic
527C22#1062301711yescharacteristic
528C22#1062302612yes—
529C22#1062305211yescharacteristic
530C22#1062306212yes—
531C22C4×#434112yes—
532C22#1062307212yes—
533C22#1062307712yes—
534C22#1062308712yes—
535C22#1062309112yes—
536C22#1062309112yes—
537C22#1062311811yescharacteristic
538C22#1062314512yes—
539C22#1062315012yes—
540C22#1062315212yes—
541C22#1062319511yescharacteristic
542C22#1062319612yes—
543C22#1062320311yescharacteristic
544C22#1062320912yes—
545C22#1062324112yes—
546C22#1062325111yescharacteristic
547C4—44no—
548C4—42no—
549C4—42no—
550C4—82no—
551C4—444no—
552C4—444no—
553C4—444no—
554C4—882no—
555C2—44no—
556C2#1307121111yescharacteristic
557C2#1307141112yes—
558C2#1307147012yes—
559C2#1307174911yescharacteristic
560C2#1307176611yescharacteristic
561C2#1307575912yes—
562C2#1307583712yes—
563C2#1307586712yes—
564C2#1307604912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1437D11
hypocenterC11#14507
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066871C2semidirect
6. #13066847C2semidirect
7. #13066843C2semidirect
31. #10622556C4semidirect
433. C11#14507semidirect

Maximal subgroups

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

subgroupindex
C2×#106225562
#130668772
#130668712
#130668592
#130668532
#130668472
#130668432
#130668382
C11×#14372
#1450711