Finite Group Databasebeta

← #14682324

Subgroups — #14682324

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622589C211yesmaximal, characteristic
2#13066870C212yesmaximal
3#13066869C211yesmaximal, characteristic
4#13066866C212yesmaximal
5#13066850C212yesmaximal
6#13066847C212yesmaximal
7#13066847C212yesmaximal
8#13066840C212yesmaximal
9C11×#1441C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×Dic11⋊C4C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
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⋊#95C2212yes—
31#10622589C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C11×C4⋊C4—41no—
42C2×C11×C4⋊C4—41no—
43C2×C11×C4⋊C4—42no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4C2×C414yes—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11—42no—
49C2×C4⋊Dic11—41no—
50C2×C4⋊Dic11C2×C414yes—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4C2×C418yes—
56C2×Dic11⋊C4C2×C418yes—
57C2×C4×Dic11—22no—
58C2×C4×Dic11—22no—
59C2×C4×Dic11—42no—
60C2×C4×Dic11—42no—
61C2×C4×Dic11—42no—
62C2×C4×Dic11C2×C414yes—
63C11×#95—24no—
64C11×#95—41no—
65C11×#95—42no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—24no—
69C11⋊#95—24no—
70C11⋊#95—41no—
71C11⋊#95—42no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95Q818yes—
76#14454—111nomaximal, Sylow
77C24×C11C2411yescharacteristic
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
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×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×Q814yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
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×Dic11C22×C414yes—
133C22×Dic11C22×C414yes—
134C22×Dic11C2×Q814yes—
135C22×Dic11C2×Q814yes—
136C22×Dic11#4114yes—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C4⋊Dic11—44no—
140C4⋊Dic11—44no—
141Dic11⋊C4—48no—
142Dic11⋊C4—48no—
143C4×Dic11—28no—
144C4×Dic11—48no—
145C2×#384—111no—
146#1441—112no—
147#1441—112no—
148#1441—111no—
149#1441D1111yescharacteristic
150#1436—112no—
151#1436—112no—
152#1436—112no—
153#1434—112no—
154C23×C11C23×C411yescharacteristic
155C23×C11C22×Q812yes—
156C23×C11C2×#4111yescharacteristic
157C23×C11C2×#4111yescharacteristic
158C23×C11C2×#4112yes—
159C23×C11H(5,𝔽2)11yescharacteristic
160C23×C11H(5,𝔽2)11yescharacteristic
161C23×C11H(5,𝔽2)12yes—
162C23×C11H(5,𝔽2)12yes—
163C23×C112−1+411yescharacteristic
164C23×C112−1+411yescharacteristic
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—24no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11#11714yes—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11C4×Q818yes—
224C22×C4⋊C4—112no—
225C22×C4⋊C4—112no—
226C22×C4⋊C4—111no—
227C22×C4⋊C4—111no—
228C22×C4⋊C4C2×D1111yescharacteristic
229C22×C4⋊C4C2×D1111yescharacteristic
230C22×C42—111no—
231C22×C42—112no—
232#384—118no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95—111no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95C2×D1112yes—
244C2×#95C2×D1111yescharacteristic
245C2×#95C2×D1112yes—
246C22×C11C2×#11711yescharacteristic
247C22×C11C2×C4×Q812yes—
248C22×C11#51811yescharacteristic
249C22×C11#51812yes—
250C22×C11#51911yescharacteristic
251C22×C11#53911yescharacteristic
252C22×C11#53911yescharacteristic
253C22×C11#53911yescharacteristic
254C22×C11#53911yescharacteristic
255C22×C11#54212yes—
256C22×C11#54212yes—
257C22×C11#54412yes—
258C22×C11#54412yes—
259C22×C11#55312yes—
260C22×C11#55312yes—
261C22×C11#55412yes—
262C22×C11#55412yes—
263C22×C11#55412yes—
264C22×C11#55511yescharacteristic
265C22×C11Q8211yescharacteristic
266C22×C11#56011yescharacteristic
267C22×C11#56012yes—
268C22×C11#56011yescharacteristic
269C4×C11—24no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—82no—
274Dic11—28no—
275Dic11—44no—
276Dic11—44no—
277Dic11—82no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4—112no—
281C23×C4—112no—
282C23×C4C22×D1112yes—
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1112yes—
286C23×C4C22×D1111yescharacteristic
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—118no—
292C2×C4⋊C4—118no—
293C2×C4⋊C4—114no—
294C2×C4⋊C4—442no—
295C2×C4⋊C4—442no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4—441no—
299C2×C4⋊C4—441no—
300C2×C4⋊C4—441no—
301C2×C4⋊C4—442no—
302C2×C4⋊C4C4×D1114yes—
303C2×C42—114no—
304C2×C42—222no—
305C2×C42—222no—
306C2×C42—442no—
307C2×C42—442no—
308C2×C42—442no—
309#95—24no—
310#95—41no—
311#95—42no—
312#95—118no—
313#95—224no—
314#95—224no—
315#95—224no—
316#95—224no—
317#95—441no—
318#95—442no—
319#95—442no—
320#95—442no—
321#95—442no—
322C2×C11#231311yescharacteristic
323C2×C11#233112yes—
324C2×C11#234512yes—
325C2×C11#236911yescharacteristic
326C2×C11#238011yescharacteristic
327C2×C11#279012yes—
328C2×C11#279012yes—
329C2×C11#279211yescharacteristic
330C2×C11#279211yescharacteristic
331C2×C11#279511yescharacteristic
332C2×C11#279511yescharacteristic
333C24C23×D1111yescharacteristic
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—114no—
362C22×C4—114no—
363C22×C4—114no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4C2×C4×D1112yes—
388C22×C4C2×C4×D1112yes—
389C22×C4C2×C4×D1112yes—
390C22×C4#434112yes—
391C22×C4Q8×D1114yes—
392C22×C4#434312yes—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—448no—
396C4⋊C4—448no—
397C4⋊C4—444no—
398C4⋊C4—444no—
399C42—228no—
400C42—448no—
401C11#1445411yescharacteristic, complemented, Sylow
402C23C22×C4×D1111yescharacteristic
403C23C2×#434111yescharacteristic
404C23#6703711yescharacteristic
405C23#6703712yes—
406C23#6703711yescharacteristic
407C23C2×Q8×D1112yes—
408C23C2×#434311yescharacteristic
409C23#41×D1112yes—
410C23#6704212yes—
411C23#6704311yescharacteristic
412C23#6704311yescharacteristic
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—118no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—224no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4#6694514yes—
472C22#1062301711yescharacteristic
473C22C2×#6694511yescharacteristic
474C22#1062304711yescharacteristic
475C22#1062307612yes—
476C22C4×Q8×D1112yes—
477C22#1062312611yescharacteristic
478C22#1062313311yescharacteristic
479C22#1062313311yescharacteristic
480C22#1062314512yes—
481C22#1062315112yes—
482C22#1062315412yes—
483C22#1062316612yes—
484C22#1062316712yes—
485C22#1062317611yescharacteristic
486C22#1062317611yescharacteristic
487C22#1062319312yes—
488C22#1062319711yescharacteristic
489C22#1062320111yescharacteristic
490C22#1062322012yes—
491C22#1062322612yes—
492C22#1062324112yes—
493C22#1062325311yescharacteristic
494C22#1062326112yes—
495C4—24no—
496C4—44no—
497C4—42no—
498C4—42no—
499C4—82no—
500C4—228no—
501C4—444no—
502C4—444no—
503C4—882no—
504C2#1307121811yescharacteristic
505C2#1307136112yes—
506C2#1307149212yes—
507C2#1307170411yescharacteristic
508C2#1307179111yescharacteristic
509C2#1307638812yes—
510C2#1307639212yes—
511C2#1307641611yescharacteristic
512C2#1307641711yescharacteristic
513C2#1307644911yescharacteristic
514C2#1307645011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14454
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
31. #10622589C4semidirect
401. C11#14454semidirect

Maximal subgroups

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

subgroupindex
C2×#106225892
#130668702
#130668692
#130668662
#130668502
#130668472
#130668402
C11×#14412
#1445411