Finite Group Databasebeta

← #14680853

Subgroups — #14680853

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622274C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic
3C2×#10622265C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic
5#13066879C212yesmaximal
6#13066868C212yesmaximal
7#13066866C211yesmaximal, characteristic
8#13066845C212yesmaximal
9#13066841C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic
11C11×#1444C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622586—24no—
36#10622274C418yescomplemented
37#10622265—24no—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—24no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4—42no—
53C2×C11×C4⋊C4—42no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—42no—
57C2×C4⋊Dic11—42no—
58C2×C4⋊Dic11C2×C414yes—
59C2×C4⋊Dic11C2×C418yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—42no—
65C2×Dic11⋊C4—42no—
66C2×Dic11⋊C4—42no—
67C2×Dic11⋊C4C2×C414yes—
68C2×C4×Dic11—42no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11—42no—
71C2×C4×Dic11D414yes—
72C2×C4×Dic11Q818yes—
73C11×#95—22no—
74C11×#95—24no—
75C11×#95C2×C414yes—
76C11⋊#95—24no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—24no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95C2×C418yes—
87#14328—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C414yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×Q814yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4114yes—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11C22×C412yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C22×C412yes—
150C22×Dic11C2×D412yes—
151C22×Dic11C2×D412yes—
152C22×Dic11C2×Q814yes—
153C22×Dic11C2×Q814yes—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—48no—
156C4⋊Dic11—28no—
157C4⋊Dic11—48no—
158Dic11⋊C4—28no—
159Dic11⋊C4—44no—
160Dic11⋊C4—48no—
161C4×Dic11—44no—
162C4×Dic11—48no—
163C2×#398—111no—
164C2×#389—111no—
165C2×#387—111no—
166#1445—111no—
167#1444—112no—
168#1444D1111yescharacteristic
169#1441—112no—
170#1441—111no—
171C4⋊#95—112no—
172#1434—112no—
173C4×#95—111no—
174C23×C11C23×C411yescharacteristic
175C23×C11C22×D411yescharacteristic
176C23×C11C22×Q812yes—
177C23×C11C2×#4112yes—
178C23×C11C2×#4111yescharacteristic
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)12yes—
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C11H(5,𝔽2)11yescharacteristic
183C23×C112−1+411yescharacteristic
184C23×C112−1+412yes—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
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—42no—
212C2×C4×C11C4×D414yes—
213C2×C4×C11C4×Q818yes—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—22no—
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234C2×Dic11—41no—
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—41no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11C4⋊Q814yes—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—112no—
253C22×C4⋊C4—112no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4C2×D1112yes—
256C22×C4⋊C4C2×D1111yescharacteristic
257C22×C42—112no—
258C22×C42—111no—
259#398—118no—
260#389—224no—
261#387—224no—
262C2×#95—112no—
263C2×#95—112no—
264C2×#95—111no—
265C2×#95—111no—
266C2×#95—112no—
267C2×#95—111no—
268C2×#95—111no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95C2×D1112yes—
274C2×#95C2×D1111yescharacteristic
275C2×#95C2×D1111yescharacteristic
276C22×C11C2×C4×D411yescharacteristic
277C22×C11C2×C4×Q812yes—
278C22×C11#51811yescharacteristic
279C22×C11#52012yes—
280C22×C11#52011yescharacteristic
281C22×C11C2×C4⋊Q811yescharacteristic
282C22×C11#53211yescharacteristic
283C22×C11#53312yes—
284C22×C11#53411yescharacteristic
285C22×C11#53511yescharacteristic
286C22×C11#53611yescharacteristic
287C22×C11#53711yescharacteristic
288C22×C11#53812yes—
289C22×C11#53912yes—
290C22×C11#53912yes—
291C22×C11#54012yes—
292C22×C11#54011yescharacteristic
293C22×C11#54112yes—
294C22×C11#54211yescharacteristic
295C22×C11#54312yes—
296C22×C11#54412yes—
297C22×C11#54412yes—
298C22×C11#54412yes—
299C4×C11—24no—
300C4×C11—28no—
301C4×C11—81no—
302C4×C11—82no—
303C4×C11—81no—
304Dic11—24no—
305Dic11—42no—
306Dic11—42no—
307Dic11—44no—
308Dic11—42no—
309Dic11—44no—
310C23×C4—111no—
311C23×C4—112no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—112no—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1112yes—
318C23×C4C22×D1111yescharacteristic
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1112yes—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—442no—
336C2×C4⋊C4—442no—
337C2×C4⋊C4—442no—
338C2×C4⋊C4—442no—
339C2×C4⋊C4—442no—
340C2×C42—114no—
341C2×C42—118no—
342C2×C42—442no—
343C2×C42—442no—
344C2×C42—442no—
345#95—22no—
346#95—24no—
347#95—118no—
348#95—222no—
349#95—222no—
350#95—222no—
351#95—224no—
352#95—224no—
353#95—222no—
354#95—442no—
355#95—442no—
356#95—442no—
357#95—442no—
358#95C4×D1114yes—
359C2×C11C4×C4⋊Q811yescharacteristic
360C2×C11#232211yescharacteristic
361C2×C11#232411yescharacteristic
362C2×C11#232912yes—
363C2×C11#233012yes—
364C2×C11#265911yescharacteristic
365C2×C11#266011yescharacteristic
366C2×C11#266111yescharacteristic
367C2×C11#266411yescharacteristic
368C2×C11#266612yes—
369C2×C11#266712yes—
370C24C23×D1111yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
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—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—112no—
395C22×C4—114no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—114no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4C2×C4×D1114yes—
431C22×C4C2×C4×D1112yes—
432C22×C4D4×D1112yes—
433C22×C4#434114yes—
434C22×C4Q8×D1114yes—
435C22×C4#434312yes—
436C4⋊C4—44no—
437C4⋊C4—48no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C4⋊C4—448no—
441C4⋊C4—444no—
442C4⋊C4—448no—
443C42—444no—
444C42—448no—
445C11#1432811yescharacteristic, complemented, Sylow
446C23C22×C4×D1111yescharacteristic
447C23C2×D4×D1111yescharacteristic
448C23C2×#434112yes—
449C23#6703712yes—
450C23#6703711yescharacteristic
451C23C2×Q8×D1112yes—
452C23C2×#434311yescharacteristic
453C23#6704011yescharacteristic
454C23#6704211yescharacteristic
455C23#6704211yescharacteristic
456C23#6704312yes—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—42no—
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—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—114no—
485C2×C4—224no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—224no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—441no—
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—441no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—441no—
519C2×C4—442no—
520C2×C4#6694018yes—
521C2×C4#6694614yes—
522C22C2×#6694012yes—
523C22C2×#6694611yescharacteristic
524C22#1062307611yescharacteristic
525C22#1062307712yes—
526C22#1062310511yescharacteristic
527C22#1062312011yescharacteristic
528C22#1062312412yes—
529C22#1062313811yescharacteristic
530C22#1062315012yes—
531C22#1062315412yes—
532C22#1062315612yes—
533C22#1062316011yescharacteristic
534C22#1062316512yes—
535C22#1062317612yes—
536C22#1062317911yescharacteristic
537C22#1062319612yes—
538C22#1062322012yes—
539C22#1062322911yescharacteristic
540C22#1062324711yescharacteristic
541C22D11×C4⋊Q811yescharacteristic
542C22#1062325912yes—
543C22#1062326012yes—
544C22#1062326411yescharacteristic
545C4—24no—
546C4—28no—
547C4—82no—
548C4—81no—
549C4—81no—
550C4—224no—
551C4—442no—
552C4—444no—
553C4—442no—
554C4—442no—
555C4—444no—
556C2#1307118311yescharacteristic
557C2#1307128411yescharacteristic
558C2#1307130711yescharacteristic
559C2#1307134712yes—
560C2#1307135612yes—
561C2#1307472911yescharacteristic
562C2#1307473911yescharacteristic
563C2#1307474711yescharacteristic
564C2#1307478011yescharacteristic
565C2#1307480212yes—
566C2#1307481512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11#14328
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
36. #10622274C4semidirect
445. C11#14328semidirect

Maximal subgroups

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

subgroupindex
C2×#106222742
C2×#106225862
C2×#106222652
#130668832
#130668792
#130668682
#130668662
#130668452
#130668412
#95×Dic112
C11×#14442
#1432811