Finite Group Databasebeta

← #14684686

Subgroups — #14684686

Order 2816.

1226 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622562C211yesmaximal, characteristic
2#13066877C212yesmaximal, complemented
3#13066868C212yesmaximal, complemented
4#13066867C212yesmaximal, complemented
5#13066863C212yesmaximal
6#13066859C212yesmaximal
7#13066853C211yesmaximal, characteristic
8#13066851C212yesmaximal, complemented
9C11×#1440C211yesmaximal, characteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C22⋊Dic11C2212yes—
14C22×C22⋊Dic11C2212yes—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×#95C2212yes—
20C2×C11×#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622562C418yescomplemented
32C25×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C22⋊C4—41no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4—41no—
44C2×C11×C22⋊C4—42no—
45C2×C11×C22⋊C4—42no—
46C2×C11×C22⋊C4—41no—
47C2×C11×C22⋊C4C2×C414yes—
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—42no—
50C2×C22⋊Dic11—42no—
51C2×C22⋊Dic11—42no—
52C2×C22⋊Dic11—42no—
53C2×C22⋊Dic11C2×C418yes—
54C2×C4⋊Dic11—41no—
55C2×C4⋊Dic11—41no—
56C2×C4⋊Dic11C2×C414yes—
57C2×Dic11⋊C4—42no—
58C2×Dic11⋊C4—42no—
59C2×Dic11⋊C4—42no—
60C2×Dic11⋊C4—42no—
61C2×Dic11⋊C4—42no—
62C2×Dic11⋊C4C2×C418yes—
63C2×C4×Dic11—41no—
64C2×C4×Dic11—42no—
65C11×#95—42no—
66C11×#95—42no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—41no—
76C11⋊#95C2×C414yes—
77#14646—111nomaximal, Sylow
78C24×C11—22no—
79C24×C11—22no—
80C24×C11—22no—
81C24×C11—22no—
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11C22×C412yes—
87C24×C11C2411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
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×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×Dic11—22no—
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×Dic11C22×C414yes—
138C22×Dic11C22×C414yes—
139C22×Dic11#4114yes—
140C11×C22⋊C4—44no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—44no—
143C22⋊Dic11—48no—
144C22⋊Dic11—48no—
145C4⋊Dic11—44no—
146Dic11⋊C4—48no—
147Dic11⋊C4—48no—
148C4×Dic11—44no—
149C2×#399—111no—
150#1443—112no—
151#1441—112no—
152#1441—112no—
153#1440—112no—
154#1440D1111yescharacteristic
155#1439—112no—
156#1437—111no—
157#1436—112no—
158C23×C11—22no—
159C23×C11—24no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—24no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—42no—
172C23×C11—41no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—41no—
178C23×C11—42no—
179C23×C11C23×C411yescharacteristic
180C23×C11C2×#4112yes—
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C11H(5,𝔽2)12yes—
183C23×C11H(5,𝔽2)11yescharacteristic
184C23×C11H(5,𝔽2)12yes—
185C23×C11H(5,𝔽2)12yes—
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—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
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—42no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
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—
240C22×C4⋊C4—112no—
241C22×C4⋊C4—111no—
242C22×C4⋊C4—112no—
243C22×C22⋊C4—112no—
244C22×C22⋊C4—112no—
245C22×C22⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4C2×D1111yescharacteristic
247C22×C22⋊C4C2×D1111yescharacteristic
248C22×C42—111no—
249#399—118no—
250C2×#95—111no—
251C2×#95—112no—
252C2×#95—112no—
253C2×#95—112no—
254C2×#95—112no—
255C2×#95—111no—
256C2×#95—112no—
257C2×#95—112no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95C2×D1112yes—
261C2×#95C2×D1112yes—
262C22×C11—42no—
263C22×C11—44no—
264C22×C11—42no—
265C22×C11—44no—
266C22×C11—42no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C4×#4111yescharacteristic
272C22×C11#51811yescharacteristic
273C22×C11#51812yes—
274C22×C11#51911yescharacteristic
275C22×C11#52012yes—
276C22×C11#53812yes—
277C22×C11#53912yes—
278C22×C11#53912yes—
279C22×C11#54012yes—
280C22×C11#54212yes—
281C22×C11#54212yes—
282C22×C11#56011yescharacteristic
283C22×C11#56011yescharacteristic
284C22×C11#56012yes—
285C22×C11#56011yescharacteristic
286C22×C11#56212yes—
287C22×C11#56212yes—
288C22×C11#56212yes—
289C22×C11#56312yes—
290C22×C11#56311yescharacteristic
291C22×C11#56312yes—
292C4×C11—42no—
293C4×C11—42no—
294C4×C11—82no—
295C4×C11—82no—
296Dic11—44no—
297Dic11—44no—
298Dic11—44no—
299Dic11—82no—
300C25C22×D1111yescharacteristic
301C23×C4—112no—
302C23×C4—112no—
303C23×C4—112no—
304C23×C4—112no—
305C23×C4C22×D1112yes—
306C23×C4C22×D1112yes—
307C23×C4C22×D1111yescharacteristic
308C23×C4C22×D1111yescharacteristic
309C2×C4⋊C4—118no—
310C2×C4⋊C4—114no—
311C2×C4⋊C4—442no—
312C2×C4⋊C4—442no—
313C2×C4⋊C4—442no—
314C2×C4⋊C4—442no—
315C2×C4⋊C4—442no—
316C2×C4⋊C4—441no—
317C2×C4⋊C4—441no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—41no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—118no—
325C2×C22⋊C4—224no—
326C2×C22⋊C4—442no—
327C2×C22⋊C4—442no—
328C2×C22⋊C4—442no—
329C2×C22⋊C4—442no—
330C2×C22⋊C4C4×D1114yes—
331C2×C42—441no—
332C2×C42—442no—
333#95—42no—
334#95—42no—
335#95—114no—
336#95—224no—
337#95—224no—
338#95—442no—
339#95—441no—
340#95—442no—
341#95—442no—
342#95—442no—
343#95—442no—
344#95—442no—
345C2×C11—82no—
346C2×C11#233211yescharacteristic
347C2×C11#233512yes—
348C2×C11#237611yescharacteristic
349C2×C11#237812yes—
350C2×C11#238011yescharacteristic
351C2×C11#282712yes—
352C2×C11#282912yes—
353C2×C11#283712yes—
354C2×C11#283812yes—
355C24—21no—
356C24—21no—
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24C2×C4×D1112yes—
364C24C23×D1111yescharacteristic
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
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—114no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—222no—
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×C4C2×C4×D1112yes—
416C22×C4C2×C4×D1112yes—
417C4⋊C4—448no—
418C4⋊C4—444no—
419C4⋊C4—448no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—448no—
424C22⋊C4—448no—
425C42—444no—
426C11#1464611yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—24no—
431C23—24no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—41no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23C22×C4×D1111yescharacteristic
449C23#6703711yescharacteristic
450C23#6703711yescharacteristic
451C23#6703712yes—
452C23#6703712yes—
453C23#41×D1112yes—
454C23#6704212yes—
455C23#6704312yes—
456C23#6704312yes—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
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—224no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—442no—
497C2×C4—442no—
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—
509C22—42no—
510C22—44no—
511C22—42no—
512C22—44no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22#1062301711yescharacteristic
519C22#1062304711yescharacteristic
520C22#1062305311yescharacteristic
521C22#1062307612yes—
522C22#1062307712yes—
523C22#1062312611yescharacteristic
524C22#1062312611yescharacteristic
525C22#1062314612yes—
526C22#1062315112yes—
527C22#1062315212yes—
528C22#1062315212yes—
529C22#1062318211yescharacteristic
530C22#1062319112yes—
531C22#1062319312yes—
532C22#1062319312yes—
533C22#1062319711yescharacteristic
534C22#1062319812yes—
535C22#1062320312yes—
536C22#1062320912yes—
537C22#1062323812yes—
538C22#1062324312yes—
539C4—42no—
540C4—42no—
541C4—82no—
542C4—82no—
543C4—444no—
544C4—444no—
545C4—444no—
546C4—882no—
547C2—82no—
548C2#1307136911yescharacteristic
549C2#1307140412yes—
550C2#1307175911yescharacteristic
551C2#1307177612yes—
552C2#1307179111yescharacteristic
553C2#1307672112yes—
554C2#1307675112yes—
555C2#1307682312yes—
556C2#1307684412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#14646
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066868C2semidirect
4. #13066867C2semidirect
8. #13066851C2semidirect
31. #10622562C4semidirect
426. C11#14646semidirect

Maximal subgroups

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

subgroupindex
C2×#106225622
#130668772
#130668682
#130668672
#130668632
#130668592
#130668532
#130668512
C11×#14402
#1464611