Finite Group Databasebeta

← #14762828

Subgroups — #14762828

Order 2816.

1538 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3D11×#380C211yesmaximal, characteristic
4#13069046C214yesmaximal, complemented
5#13068920C214yesmaximal, complemented
6#13068703C211yesmaximal, characteristic, complemented
7#13068700C211yesmaximal, characteristic, complemented
8#13068551C211yesmaximal, characteristic, complemented
9C11×#1787C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C2×#66999—24no—
13C2×#66999—21no—
14C2×#66999—21no—
15C2×#66999C418yescomplemented
16C2×#66999C2212yes—
17C2×#66999C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×#4313C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C22⋊C4×D11—21no—
24C2×C11×#103C2214yescomplemented
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×#66899C2214yescomplemented
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×(C2×D11)⋊C8C2212yes—
31#10622600C2212yes—
32#10622555—21no—
33#10622339—24no—
34#10622280—21no—
35D11×#95—21no—
36#10622189C2214yescomplemented
37#10622167C2214yescomplemented
38C24×D11D411yescharacteristic
39C22×Q8×C11—22no—
40C22×Q8×C11—21no—
41C22×Q8×C11—44no—
42C22×Q8×C11C2×C414yescomplemented
43C22×Q8×C11C2312yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—44no—
50C22×C4×D11C2×C414yes—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D414yes—
54C22×C4×D11C2311yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×C8×C11C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C22⋊Dic11—21no—
60#66999—28no—
61#66999—28no—
62#66999—24no—
63#66999—24no—
64#66999C2×C418yes—
65#66999C2×C418yescomplemented
66C2×(C2×D11)⋊C4—28no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11C2×C414yescomplemented
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C22×C11⋊C8C2312yes—
80C2×#4313—24no—
81C2×#4313—44no—
82C4⋊C4×D11—44no—
83C22⋊C4×D11—44no—
84C11×#103—44no—
85C11×C22⋊C8—22no—
86C11×#95—21no—
87#66899—44no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C22⋊(C11⋊C8)—22no—
91(C2×D11)⋊C8—24no—
92#21765—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—24no—
97C23×D11—42no—
98C23×D11C22⋊C414yes—
99C23×D11C2×D411yescharacteristic
100C23×D11C2×D411yescharacteristic
101C2×Q8×C11—24no—
102C2×Q8×C11—22no—
103C2×Q8×C11—24no—
104C2×Q8×C11—24no—
105C2×Q8×C11—48no—
106C2×Q8×C11—44no—
107C2×Q8×C11—48no—
108C2×Q8×C11C22×C414yes—
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—44no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11C22⋊C414yes—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C2×C4×D11—24no—
128C2×C4×D11—24no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—48no—
132C2×C4×D11—48no—
133C2×C4×D11—44no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11C22⋊C414yes—
137C2×C4×D11C22⋊C414yes—
138C2×C4×D11C22×C412yes—
139C2×C4×D11C22×C412yes—
140C2×C4×D11C2×D412yes—
141C2×C4×D11C2×D412yes—
142C2×C8×C11—22no—
143C2×C8×C11—24no—
144C11×C4⋊C4—24no—
145C11×C22⋊C4—42no—
146C22⋊Dic11—42no—
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—44no—
150C4⋊Dic11—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—24no—
153C4⋊Dic11C22×C414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—44no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—24no—
159#4313—48no—
160C22×C22⋊Q8—111no—
161C2×#407—111no—
162C2×#380—111no—
163#1894—114no—
164#1872—114no—
165#1823—111no—
166#1823—111no—
167#1787—111no—
168#1787D1111yescharacteristic, complemented
169C23×C11—22no—
170C23×C11—22no—
171C23×C11C2×C22⋊C412yes—
172C23×C11AGL(1,ℤ/8)12yes—
173C23×C11#13712yes—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—22no—
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—22no—
182C22×D11—28no—
183C22×D11—28no—
184C22×D11—44no—
185C22×D11—48no—
186C22×D11—48no—
187C22×D11C2×C22⋊C412yes—
188C22×D11C2×C22⋊C412yes—
189C22×D11#13714yes—
190Q8×C11—24no—
191Q8×C11—24no—
192Q8×C11—48no—
193Q8×C11—44no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—48no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11H(5,𝔽2)14yes—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—48no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11C2×C22⋊C412yes—
218C2×Dic11C2×C22⋊C412yes—
219C4×D11—24no—
220C4×D11—24no—
221C4×D11—24no—
222C4×D11—24no—
223C4×D11—44no—
224C4×D11—44no—
225C4×D11—88no—
226C8×C11—42no—
227C11⋊C8—42no—
228C23×Q8C2×D1111yescharacteristic
229C24×C4—111no—
230C22×M16—112no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233C2×C22⋊Q8—118no—
234C2×C22⋊Q8—221no—
235C2×C22⋊Q8—221no—
236C2×C22⋊Q8—224no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4—112no—
239C22×C4⋊C4—221no—
240C22×C22⋊C4—221no—
241C22×C22⋊C4—221no—
242C2×#103—114no—
243C2×#103C2×D1114yescomplemented
244#407—224no—
245C2×C22⋊C8—111no—
246C2×C22⋊C8—112no—
247C2×C22⋊C8C2×D1111yescharacteristic
248#380—111no—
249#380—112no—
250#380—221no—
251#380—221no—
252#380C2×D1111yescharacteristic
253C2×#95—221no—
254#340—114no—
255#340—114no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—24no—
259C22×C11—24no—
260C22×C11#41714yes—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11#53412yes—
263C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11C2×#13712yes—
266C2×D11—22no—
267C2×D11—22no—
268C2×D11—24no—
269C2×D11—24no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—416no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11#41914yes—
277C4×C11—22no—
278C4×C11—44no—
279C4×C11—82no—
280C4×C11#51812yes—
281C4×C11#53412yes—
282Dic11—22no—
283Dic11—22no—
284Dic11—44no—
285Dic11—82no—
286C25—111no—
287C22×Q8—22no—
288C22×Q8—21no—
289C22×Q8—44no—
290C22×Q8C4×D1114yescomplemented
291C22×Q8C22×D1112yes—
292C23×C4—21no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—114no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—114no—
300C23×C4—222no—
301C23×C4—221no—
302C23×C4—444no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—224no—
305C2×M16—444no—
306C22×C8—112no—
307C22×C8C22×D1112yes—
308C22⋊Q8—118no—
309C22⋊Q8—118no—
310C22⋊Q8—228no—
311C22⋊Q8—228no—
312C22⋊Q8—224no—
313C22⋊Q8—224no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—228no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—444no—
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—228no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—444no—
332#103—44no—
333#103—444no—
334C22⋊C8—22no—
335C22⋊C8—224no—
336C22⋊C8—222no—
337#95—21no—
338#95—222no—
339#95—221no—
340C2×C11—24no—
341C2×C11#230811yescharacteristic
342C2×C11C2×#41911yescharacteristic
343C2×C11C2×#41711yescharacteristic
344C2×C11#319312yes—
345C2×C11#319512yes—
346D11—24no—
347D11—42no—
348C24—111no—
349C24—111no—
350C24—114no—
351C24—224no—
352C24—222no—
353C24—222no—
354C24—442no—
355C24D4×D1111yescharacteristic
356C2×Q8—24no—
357C2×Q8—22no—
358C2×Q8—24no—
359C2×Q8—24no—
360C2×Q8—48no—
361C2×Q8—44no—
362C2×Q8—48no—
363C2×Q8C2×C4×D1114yes—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—44no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—114no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—224no—
379C22×C4—224no—
380C22×C4—224no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—448no—
384C22×C4—448no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4C2×C4×D1112yes—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1112yes—
396C22×C4C23×D1111yescharacteristic
397M16—448no—
398C2×C8—22no—
399C2×C8—24no—
400C2×C8—222no—
401C2×C8—224no—
402C4⋊C4—24no—
403C4⋊C4—114no—
404C4⋊C4—228no—
405C4⋊C4—228no—
406C4⋊C4—224no—
407C4⋊C4—222no—
408C4⋊C4—224no—
409C4⋊C4—444no—
410C22⋊C4—42no—
411C22⋊C4—228no—
412C22⋊C4—228no—
413C22⋊C4—444no—
414C22⋊C4—442no—
415C11#2176511yescharacteristic, complemented, Sylow
416C23—22no—
417C23—22no—
418C23—112no—
419C23—114no—
420C23—112no—
421C23—228no—
422C23—221no—
423C23—221no—
424C23—222no—
425C23—221no—
426C23—221no—
427C23—222no—
428C23—222no—
429C23—228no—
430C23—444no—
431C23—448no—
432C23—448no—
433C23C22⋊C4×D1112yes—
434C23#6696712yes—
435C23#6697112yes—
436C23C2×D4×D1111yescharacteristic
437Q8—24no—
438Q8—24no—
439Q8—48no—
440Q8—44no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—48no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—224no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—444no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—448no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—888no—
469C2×C4C22⋊C4×D1112yes—
470C2×C4C22×C4×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4#6703714yes—
473C8—42no—
474C8—442no—
475C22—22no—
476C22—24no—
477C22—22no—
478C22—24no—
479C22—114no—
480C22—222no—
481C22—224no—
482C22—222no—
483C22—224no—
484C22—222no—
485C22—222no—
486C22—222no—
487C22—4416no—
488C22—442no—
489C22—442no—
490C22#1062241614yes—
491C22C2×C22⋊C4×D1111yescharacteristic
492C22#1062312012yes—
493C22C2×#6696711yescharacteristic
494C22C2×#6697111yescharacteristic
495C22D11×#13712yes—
496C4—22no—
497C4—44no—
498C4—82no—
499C4—222no—
500C4—222no—
501C4—444no—
502C4—882no—
503C4#1062301712yes—
504C4#1062312012yes—
505C2—24no—
506C2—224no—
507C2—442no—
508C2#1307119211yescharacteristic
509C2D11×#41911yescharacteristic
510C2C2×#1062241611yescharacteristic
511C2#1307942012yes—
512C2#1307943812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#21765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
4. #13069046C2semidirect
5. #13068920C2semidirect
6. #13068703C2semidirect
7. #13068700C2semidirect
8. #13068551C2semidirect
9. C11×#1787C2semidirect
15. C2×#66999C4semidirect
24. C2×C11×#103C22semidirect
27. C2×#66899C22semidirect
36. #10622189C22semidirect
37. #10622167C22semidirect
42. C22×Q8×C11C2×C4semidirect
65. #66999C2×C4semidirect
72. C2×C4⋊Dic11C2×C4semidirect
168. #1787D11semidirect
243. C2×#103C2×D11semidirect
290. C22×Q8C4×D11semidirect
415. C11#21765semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C2×#106223392
D11×#3802
#130690462
#130689202
#130687032
#130687002
#130685512
C11×#17872
#2176511