Finite Group Databasebeta

← #14681976

Subgroups — #14681976

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622268C212yesmaximal
2C2×#10622591C212yesmaximal
3C2×#10622589C211yesmaximal, characteristic
4#13066882C212yesmaximal
5#13066882C212yesmaximal
6#13066869C211yesmaximal, characteristic
7#13066850C212yesmaximal
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×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11×#95C2211yescharacteristic
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622591—28no—
32#10622589C418yescomplemented
33#10622268—28no—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C2×C11×C4⋊C4—24no—
44C2×C11×C4⋊C4—41no—
45C2×C11×C4⋊C4—41no—
46C2×C11×C4⋊C4—41no—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C4⋊Dic11—24no—
49C2×C4⋊Dic11—41no—
50C2×C4⋊Dic11—41no—
51C2×C4⋊Dic11—41no—
52C2×C4⋊Dic11C2×C414yes—
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4—24no—
56C2×Dic11⋊C4—24no—
57C2×Dic11⋊C4C2×C418yes—
58C2×Dic11⋊C4C2×C418yes—
59C2×C4×Dic11—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—24no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—42no—
64C2×C4×Dic11C2×C414yes—
65C11×#95—24no—
66C11×#95—24no—
67C11×#95—41no—
68C11⋊#95—24no—
69C11⋊#95—24no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—24no—
74C11⋊#95—24no—
75C11⋊#95—42no—
76C11⋊#95—41no—
77C11⋊#95D418yes—
78#14424—111nomaximal, Sylow
79C24×C11C2411yescharacteristic
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
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×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C2×D414yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
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×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C22×C414yes—
135C22×Dic11C22×C414yes—
136C22×Dic11C2×D414yes—
137C22×Dic11C2×D414yes—
138C22×Dic11#4114yes—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—44no—
141C4⋊Dic11—44no—
142C4⋊Dic11—44no—
143Dic11⋊C4—216no—
144Dic11⋊C4—216no—
145C4×Dic11—28no—
146C4×Dic11—48no—
147C2×#387—112no—
148C2×#387—112no—
149C2×#384—111no—
150#1445—112no—
151#1445—112no—
152#1441—111no—
153#1441D1111yescharacteristic
154#1436—112no—
155#1434—112no—
156C23×C11C23×C411yescharacteristic
157C23×C11C22×D412yes—
158C23×C11C2×#4111yescharacteristic
159C23×C11C2×#4111yescharacteristic
160C23×C11C2×#4112yes—
161C23×C11H(5,𝔽2)11yescharacteristic
162C23×C11H(5,𝔽2)11yescharacteristic
163C23×C112−1+412yes—
164C23×C112−1+411yescharacteristic
165C23×C112−1+411yescharacteristic
166C23×C112−1+412yes—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
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—42no—
196C2×C4×C11—42no—
197C2×C4×C11#11714yes—
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—24no—
209C2×Dic11—24no—
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×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11C4×D418yes—
226C22×C4⋊C4—112no—
227C22×C4⋊C4—112no—
228C22×C4⋊C4—111no—
229C22×C4⋊C4—111no—
230C22×C4⋊C4C2×D1111yescharacteristic
231C22×C4⋊C4C2×D1111yescharacteristic
232C22×C42—111no—
233C22×C42—112no—
234#387—228no—
235#387—228no—
236#384—118no—
237C2×#95—112no—
238C2×#95—112no—
239C2×#95—112no—
240C2×#95—112no—
241C2×#95—112no—
242C2×#95—112no—
243C2×#95—112no—
244C2×#95—112no—
245C2×#95—112no—
246C2×#95—111no—
247C2×#95C2×D1112yes—
248C2×#95C2×D1112yes—
249C2×#95C2×D1111yescharacteristic
250C22×C11C2×#11711yescharacteristic
251C22×C11C2×C4×D412yes—
252C22×C11#51811yescharacteristic
253C22×C11#51911yescharacteristic
254C22×C11#51912yes—
255C22×C11#53612yes—
256C22×C11#53612yes—
257C22×C11#53911yescharacteristic
258C22×C11#53911yescharacteristic
259C22×C11#53911yescharacteristic
260C22×C11#53911yescharacteristic
261C22×C11#54112yes—
262C22×C11#54112yes—
263C22×C11D4211yescharacteristic
264C22×C11#54712yes—
265C22×C11#54712yes—
266C22×C11#55012yes—
267C22×C11#55212yes—
268C22×C11#55212yes—
269C22×C11#55911yescharacteristic
270C22×C11#56311yescharacteristic
271C22×C11#56312yes—
272C22×C11#56311yescharacteristic
273C4×C11—24no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—44no—
277C4×C11—82no—
278Dic11—28no—
279Dic11—44no—
280Dic11—44no—
281Dic11—82no—
282C23×C4—112no—
283C23×C4—112no—
284C23×C4—112no—
285C23×C4—112no—
286C23×C4C22×D1112yes—
287C23×C4C22×D1111yescharacteristic
288C23×C4C22×D1111yescharacteristic
289C23×C4C22×D1112yes—
290C23×C4C22×D1111yescharacteristic
291C2×C4⋊C4—24no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—118no—
296C2×C4⋊C4—118no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—224no—
299C2×C4⋊C4—224no—
300C2×C4⋊C4—224no—
301C2×C4⋊C4—224no—
302C2×C4⋊C4—224no—
303C2×C4⋊C4—441no—
304C2×C4⋊C4—441no—
305C2×C4⋊C4—441no—
306C2×C4⋊C4C4×D1114yes—
307C2×C42—114no—
308C2×C42—222no—
309C2×C42—222no—
310C2×C42—224no—
311C2×C42—224no—
312C2×C42—442no—
313#95—24no—
314#95—24no—
315#95—41no—
316#95—118no—
317#95—224no—
318#95—224no—
319#95—224no—
320#95—224no—
321#95—224no—
322#95—224no—
323#95—224no—
324#95—441no—
325#95—442no—
326C2×C11#231311yescharacteristic
327C2×C11#232712yes—
328C2×C11#234412yes—
329C2×C11#236611yescharacteristic
330C2×C11#238111yescharacteristic
331C2×C11#268011yescharacteristic
332C2×C11#268011yescharacteristic
333C2×C11#272112yes—
334C2×C11#272112yes—
335C2×C11#279411yescharacteristic
336C2×C11#279411yescharacteristic
337C24C23×D1111yescharacteristic
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
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—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—114no—
364C22×C4—114no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—114no—
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×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1112yes—
393C22×C4C2×C4×D1112yes—
394C22×C4D4×D1114yes—
395C22×C4#434112yes—
396C22×C4#434312yes—
397C4⋊C4—44no—
398C4⋊C4—44no—
399C4⋊C4—2216no—
400C4⋊C4—2216no—
401C4⋊C4—444no—
402C4⋊C4—444no—
403C42—228no—
404C42—448no—
405C11#1442411yescharacteristic, complemented, Sylow
406C23C22×C4×D1111yescharacteristic
407C23C2×D4×D1112yes—
408C23C2×#434111yescharacteristic
409C23#6703711yescharacteristic
410C23#6703711yescharacteristic
411C23C2×#434311yescharacteristic
412C23#6704012yes—
413C23#41×D1112yes—
414C23#6704311yescharacteristic
415C23#6704312yes—
416C23#6704311yescharacteristic
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—118no—
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—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
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—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4#6694514yes—
476C22#1062301711yescharacteristic
477C22C2×#6694511yescharacteristic
478C22#1062304711yescharacteristic
479C22C4×D4×D1112yes—
480C22#1062310312yes—
481C22#1062312111yescharacteristic
482C22#1062313012yes—
483C22#1062313311yescharacteristic
484C22#1062313311yescharacteristic
485C22#1062314212yes—
486C22#1062315912yes—
487C22#1062317012yes—
488C22#1062317611yescharacteristic
489C22#1062317611yescharacteristic
490C22#1062317712yes—
491C22#1062317912yes—
492C22#1062319511yescharacteristic
493C22#1062320311yescharacteristic
494C22#1062322512yes—
495C22#1062322712yes—
496C22#1062323212yes—
497C22#1062325712yes—
498C22#1062326611yescharacteristic
499C4—24no—
500C4—44no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—228no—
505C4—444no—
506C4—444no—
507C4—882no—
508C2#1307121811yescharacteristic
509C2#1307133112yes—
510C2#1307148412yes—
511C2#1307167911yescharacteristic
512C2#1307179511yescharacteristic
513C2#1307495911yescharacteristic
514C2#1307496011yescharacteristic
515C2#1307551612yes—
516C2#1307551712yes—
517C2#1307644011yescharacteristic
518C2#1307644111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#14424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
32. #10622589C4semidirect
405. C11#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#106222682
C2×#106225912
C2×#106225892
#130668822
#130668692
#130668502
#130668402
C11×#14412
#1442411