Finite Group Databasebeta

← #14680432

Subgroups — #14680432

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic
4#13066882C212yesmaximal
5#13066882C212yesmaximal
6#13066868C212yesmaximal
7#13066867C212yesmaximal
8#13066851C211yesmaximal, characteristic
9#13066849C211yesmaximal, characteristic
10#13066848C211yesmaximal, characteristic
11C11×#1436C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×#66942—24no—
23C2×#66942—24no—
24C2×#66942C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×Dic11⋊C4—24no—
39#10622264—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C42×C11—22no—
55C2×C42×C11—42no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2×C414yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×Dic11⋊C4C2×C414yes—
73C2×Dic11⋊C4C2×C414yes—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11D414yes—
78C2×C4×Dic11D414yes—
79#66942—232no—
80C11×#95—22no—
81C11×#95—24no—
82C11×#95—42no—
83C11⋊#95—22no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93#14289—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
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×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11#4114yes—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
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—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C412yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D412yes—
157C22×Dic11#4114yes—
158C11×C4⋊C4—28no—
159C42×C11—44no—
160C4⋊Dic11—28no—
161Dic11⋊C4—216no—
162Dic11⋊C4—28no—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—28no—
166C4×Dic11—44no—
167C4×Dic11C22⋊C4116yes—
168C22×#125—111no—
169C2×#383—111no—
170C2×C4×C4⋊C4—111no—
171#1445—112no—
172#1445—112no—
173#1441—112no—
174#1441—112no—
175#1436—111no—
176#1436—111no—
177#1436—111no—
178#1436D1111yescharacteristic
179C23×C11C23×C411yescharacteristic
180C23×C11C22×D411yescharacteristic
181C23×C11C22×D411yescharacteristic
182C23×C11C2×#4112yes—
183C23×C11C2×#4112yes—
184C23×C11H(5,𝔽2)12yes—
185C23×C112−1+412yes—
186C23×C112−1+412yes—
187C23×C112−1+412yes—
188C2×C4×C11—24no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
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×C4×C11—42no—
216C2×C4×C11C2×C22⋊C414yes—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—41no—
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—42no—
248C2×Dic11—42no—
249C2×Dic11C2×C22⋊C414yes—
250C2×Dic11C2×C22⋊C414yes—
251C2×#125—118no—
252C2×#125—224no—
253C2×#125—224no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4C2×D1111yescharacteristic
261C22×C42—111no—
262C22×C42—111no—
263C22×C42C2×D1111yescharacteristic
264#383—224no—
265C4×C4⋊C4—224no—
266C2×#95—111no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95C2×D1111yescharacteristic
277C2×#95C2×D1112yes—
278C2×#95C2×D1112yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11C4×#4111yescharacteristic
281C22×C11C4×#4111yescharacteristic
282C22×C11#51912yes—
283C22×C11#52012yes—
284C22×C11#52512yes—
285C22×C11#53212yes—
286C22×C11#53511yescharacteristic
287C22×C11#53611yescharacteristic
288C22×C11#53612yes—
289C22×C11#53611yescharacteristic
290C22×C11#53611yescharacteristic
291C22×C11#53712yes—
292C22×C11#53912yes—
293C22×C11#53912yes—
294C22×C11#53912yes—
295C22×C11#53912yes—
296C22×C11#54112yes—
297C22×C11#54112yes—
298C22×C11#54112yes—
299C22×C11#54112yes—
300C4×C11—24no—
301C4×C11—42no—
302C4×C11—44no—
303C4×C11—42no—
304C4×C11—82no—
305Dic11—24no—
306Dic11—24no—
307Dic11—42no—
308Dic11—44no—
309Dic11—42no—
310Dic11—82no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4—112no—
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1112yes—
321C23×C4C22×D1111yescharacteristic
322#125—2232no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—224no—
339C2×C4⋊C4—224no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4C4×D1114yes—
344C2×C42—22no—
345C2×C42—42no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—114no—
349C2×C42—222no—
350C2×C42—442no—
351#95—24no—
352#95—22no—
353#95—42no—
354#95—224no—
355#95—224no—
356#95—224no—
357#95—224no—
358#95—224no—
359#95—224no—
360#95—222no—
361#95—442no—
362#95—442no—
363#95—442no—
364C2×C11#229711yescharacteristic
365C2×C11#231011yescharacteristic
366C2×C11#231111yescharacteristic
367C2×C11#233612yes—
368C2×C11#233612yes—
369C2×C11#263312yes—
370C2×C11#263412yes—
371C2×C11#266412yes—
372C2×C11#266412yes—
373C24C23×D1111yescharacteristic
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
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—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—114no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—222no—
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×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4C2×C4×D1112yes—
432C22×C4C2×C4×D1112yes—
433C22×C4C2×C4×D1112yes—
434C22×C4#433914yes—
435C22×C4D4×D1112yes—
436C22×C4D4×D1112yes—
437C4⋊C4—28no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C4⋊C4—228no—
441C4⋊C4—228no—
442C4⋊C4—2216no—
443C4⋊C4—228no—
444C42—44no—
445C42—1116no—
446C42—444no—
447C11#1428911yescharacteristic, complemented, Sylow
448C23C22×C4×D1111yescharacteristic
449C23C2×#433912yes—
450C23C2×D4×D1111yescharacteristic
451C23C2×D4×D1111yescharacteristic
452C23#6703712yes—
453C23#6704012yes—
454C23#41×D1112yes—
455C23#6704312yes—
456C23#6704312yes—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—114no—
486C2×C4—114no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4C22⋊C4×D1114yes—
520C22C4×#433911yescharacteristic
521C22C2×C22⋊C4×D1111yescharacteristic
522C22#1062304612yes—
523C22#1062304912yes—
524C22#1062305311yescharacteristic
525C22#1062307712yes—
526C22#1062307812yes—
527C22#1062307912yes—
528C22#1062309512yes—
529C22#1062310312yes—
530C22#1062311412yes—
531C22#1062312311yescharacteristic
532C22#1062312812yes—
533C22#1062315912yes—
534C22#1062316912yes—
535C22#1062317911yescharacteristic
536C22#1062319112yes—
537C22#1062320611yescharacteristic
538C22#1062322712yes—
539C22#1062323212yes—
540C22#1062325511yescharacteristic
541C4—24no—
542C4—44no—
543C4—42no—
544C4—42no—
545C4—82no—
546C4—224no—
547C4—224no—
548C4—444no—
549C4—442no—
550C4—442no—
551C4—882no—
552C2#1307110211yescharacteristic
553C2#1307119911yescharacteristic
554C2#1307120311yescharacteristic
555C2#1307141512yes—
556C2#1307141812yes—
557C2#1307448812yes—
558C2#1307449612yes—
559C2#1307477912yes—
560C2#1307478112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14289
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
24. C2×#66942C4semidirect
447. C11#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
C2×#106222642
C2×C4×Dic11⋊C42
#130668822
#130668682
#130668672
#130668512
#130668492
#130668482
C11×#14362
#1428911