Finite Group Databasebeta

← #14770907

Subgroups — #14770907

Order 2816.

1218 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
1C22×#66873C211yesmaximal, characteristic
2#13071485C211yesmaximal, characteristic, complemented
3#13071436C211yesmaximal, characteristic
4#13069300C212yesmaximal, complemented
5#13069234C212yesmaximal, complemented
6#13068864C212yesmaximal, complemented
7#13068643C211yesmaximal, characteristic, complemented
8#13068548C211yesmaximal, characteristic
9#13068430C212yesmaximal, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979—21no—
15C23×C11⋊C8C2211yescharacteristic
16C2×#66946C2212yes—
17C2×C22⋊C4×D11—21no—
18C2×C11×C22⋊C8C2211yescharacteristic
19C11×#380C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622824—21no—
22C4×C22⋊Dic11C2211yescharacteristic
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×C8×Dic11C2212yescomplemented
26#10622601C2212yes—
27#10622598C2212yescomplemented
28#10622594—22no—
29C4⋊C4×Dic11C2212yescomplemented
30C2×#66873C418yescomplemented
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66871C2212yescomplemented
36#10622568—21no—
37#10622278—22no—
38C11×#340C2212yescomplemented
39C11×#340C2212yescomplemented
40#10622188C2212yescomplemented
41#10622167C2212yescomplemented
42C24×D11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×D44—24no—
46C22×D44—21no—
47C22×D44—22no—
48C22×D44—42no—
49C22×D44C2×C414yes—
50C22×D44C2311yescharacteristic
51C22×D44C2311yescharacteristic
52C22×C4×D11—22no—
53C22×C8×C11C2312yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yescomplemented
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11D411yescharacteristic
63C2×C22⋊Dic11D411yescharacteristic
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67#66979—44no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11C2312yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8—42no—
73C22×C11⋊C8C2×C414yescomplemented
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66946—24no—
77#66946—42no—
78C22⋊C4×D11—44no—
79C11×C22⋊C8—22no—
80C11×#95—21no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95D412yes—
85#66885—24no—
86#66885—42no—
87C8×Dic11—42no—
88#66873C2×C414yes—
89#66873C2×C414yes—
90#66873C2×C414yescomplemented
91#66873C2×C414yescomplemented
92#66871—42no—
93#22570—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—24no—
98C23×D11—44no—
99C23×D11—42no—
100C23×D11—42no—
101C23×D11—82no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—24no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4112yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×D44—28no—
118C2×D44—24no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—44no—
125C2×D44—44no—
126C2×D44—48no—
127C2×D44C22×C412yes—
128C2×D44C22×C412yes—
129C2×D44#4114yes—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—82no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C22×C412yes—
143C11×C22⋊C4—42no—
144C22⋊Dic11—22no—
145C22⋊Dic11—42no—
146C22⋊Dic11D814yes—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—44no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—44no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—44no—
159C2×C11⋊C8C22×C412yes—
160C2×C11⋊C8C22×C412yes—
161C22×#102—111no—
162#2344—111no—
163D4×C22⋊C4—111no—
164#1934—112no—
165#1925—112no—
166#1862—112no—
167#1823D1111yescharacteristic, complemented
168#1808—111no—
169#1786—111no—
170C4×#102—112no—
171C8×C22⋊C4—111no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C4×D412yes—
175C23×C11C2×D812yes—
176C23×C11#13512yes—
177C23×C11C22×D411yescharacteristic
178C22×D11—22no—
179C22×D11—24no—
180C22×D11—22no—
181C22×D11—48no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—42no—
189C22×D11—48no—
190C22×D11—84no—
191C22×D11—88no—
192C22×D11—88no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11C4×D412yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4112yes—
211C2×C4×C11H(5,𝔽2)12yes—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11C2×D814yes—
221D44—22no—
222D44—22no—
223D44—22no—
224D44—24no—
225D44—48no—
226D44—42no—
227D44#11714yescomplemented
228C4×D11—88no—
229C8×C11—42no—
230C11⋊C8—22no—
231C11⋊C8—22no—
232C23×D4—111no—
233C23×C8—111no—
234C2×C4×D4—112no—
235C2×#117—221no—
236C22×C4⋊C4C2×D1111yescharacteristic
237C22×C22⋊C4—221no—
238C2×#107—112no—
239C2×#102—111no—
240C2×#102—111no—
241C2×#102—111no—
242C2×#102—111no—
243C2×#102—118no—
244C2×#102—112no—
245C2×#102—112no—
246C2×C22⋊C8C2×D1111yescharacteristic
247C2×C4×C8—112no—
248#390—112no—
249#389—112no—
250#387—222no—
251#386—222no—
252#381—221no—
253#380—111no—
254#380C2×D1111yescharacteristic
255#379—221no—
256C4×C4⋊C4—112no—
257C4×C22⋊C4—111no—
258#340—112no—
259#340C2×D1112yescomplemented
260#340C2×D1112yescomplemented
261#336—112no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—24no—
265C22×C11—24no—
266C22×C11C4×D814yes—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11#54612yes—
269C22×C11C22×D811yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11#57712yes—
272C2×D11—24no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—816no—
281C2×D11—82no—
282C2×D11—82no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11C2×#11711yescharacteristic
288C4×C11#51811yescharacteristic
289C4×C11#55112yes—
290Dic11—24no—
291Dic11—42no—
292Dic11—82no—
293C25—221no—
294C22×D4—114no—
295C22×D4—111no—
296C22×D4—111no—
297C22×D4—224no—
298C22×D4—221no—
299C22×D4—222no—
300C22×D4—442no—
301C23×C4—21no—
302C23×C4—222no—
303C23×C4C22×D1111yescharacteristic
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—114no—
307C22×C8—442no—
308C22×C8C22×D1112yes—
309C4×D4—224no—
310C4×D4—442no—
311#117—444no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4C4×D1114yescomplemented
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C4⋊C4C22×D1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—111no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—222no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—444no—
328C2×C42—112no—
329C2×C42—222no—
330#107—442no—
331#102—114no—
332#102—114no—
333#102—114no—
334#102—114no—
335#102—224no—
336#102—442no—
337C22⋊C8—22no—
338C4×C8—442no—
339#95—21no—
340#95—112no—
341#95—222no—
342#95—222no—
343#95—221no—
344C2×C11—24no—
345C2×C11#234211yescharacteristic
346C2×C11C2×C4×D811yescharacteristic
347C2×C11#294911yescharacteristic
348C2×C11#329412yes—
349C2×C11#329612yes—
350D11—44no—
351D11—82no—
352C24—221no—
353C24—221no—
354C24—224no—
355C24—444no—
356C24—442no—
357C24—442no—
358C24—882no—
359C24D4×D1111yescharacteristic
360C2×D4—112no—
361C2×D4—112no—
362C2×D4—114no—
363C2×D4—228no—
364C2×D4—224no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—222no—
369C2×D4—222no—
370C2×D4—444no—
371C2×D4—448no—
372C2×D4—444no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—112no—
382C22×C4—112no—
383C22×C4—222no—
384C22×C4—444no—
385C22×C4—444no—
386C22×C4—882no—
387C22×C4C2×C4×D1112yes—
388C22×C4D4×D1111yescharacteristic
389C22×C4#434112yes—
390C22×C4C23×D1111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—444no—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—444no—
407C4⋊C4C2×C4×D1112yes—
408C4⋊C4C2×C4×D1112yes—
409C22⋊C4—42no—
410C22⋊C4—114no—
411C22⋊C4—222no—
412C22⋊C4—444no—
413C22⋊C4—444no—
414C22⋊C4—442no—
415C22⋊C4—882no—
416C42—222no—
417C42—222no—
418C42—444no—
419C11#2257011yescharacteristic, complemented, Sylow
420C23—22no—
421C23—22no—
422C23—222no—
423C23—224no—
424C23—222no—
425C23—448no—
426C23—441no—
427C23—441no—
428C23—442no—
429C23—441no—
430C23—441no—
431C23—442no—
432C23—448no—
433C23—442no—
434C23—884no—
435C23—888no—
436C23—888no—
437C23(C22⋊D11)⋊C412yes—
438C23D8×D1112yes—
439C23#6696912yes—
440C23C2×D4×D1111yescharacteristic
441D4—114no—
442D4—222no—
443D4—222no—
444D4—222no—
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—48no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—114no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—888no—
472C2×C4(C22⋊D11)⋊C412yes—
473C2×C4C22×C4×D1111yescharacteristic
474C2×C4C2×#434111yescharacteristic
475C2×C4#41×D1112yes—
476C2×C4#6704212yes—
477C8—42no—
478C8—222no—
479C8—222no—
480C22—22no—
481C22—24no—
482C22—24no—
483C22—22no—
484C22—224no—
485C22—444no—
486C22—442no—
487C22—444no—
488C22—442no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—8816no—
493C22—882no—
494C22—882no—
495C22#1062236914yes—
496C22C2×(C22⋊D11)⋊C411yescharacteristic
497C22#1062318512yes—
498C22C2×D8×D1111yescharacteristic
499C22C2×#6696911yescharacteristic
500C22#1062330912yes—
501C4—22no—
502C4—42no—
503C4—42no—
504C4—82no—
505C4—224no—
506C4—442no—
507C4—882no—
508C4D11×#11711yescharacteristic
509C4#1062305211yescharacteristic
510C4#1062318912yes—
511C2—24no—
512C2—444no—
513C2—882no—
514C2#1307145811yescharacteristic
515C2C2×#1062236911yescharacteristic
516C2#1307747111yescharacteristic
517C2#1308042712yes—
518C2#1308044912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#22570
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #13071485C2semidirect
4. #13069300C2semidirect
5. #13069234C2semidirect
6. #13068864C2semidirect
7. #13068643C2semidirect
9. #13068430C2semidirect
10. #13068390C2semidirect
11. C11×#1823C2semidirect
25. C2×C8×Dic11C22semidirect
27. #10622598C22semidirect
29. C4⋊C4×Dic11C22semidirect
30. C2×#66873C4semidirect
35. C2×#66871C22semidirect
38. C11×#340C22semidirect
39. C11×#340C22semidirect
40. #10622188C22semidirect
41. #10622167C22semidirect
56. C2×C11×C4⋊C4C2×C4semidirect
73. C22×C11⋊C8C2×C4semidirect
90. #66873C2×C4semidirect
91. #66873C2×C4semidirect
167. #1823D11semidirect
227. D44#117semidirect
259. #340C2×D11semidirect
260. #340C2×D11semidirect
316. C2×C4⋊C4C4×D11semidirect
419. C11#22570semidirect

Maximal subgroups

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

subgroupindex
C22×#668732
#130714852
#130714362
#130693002
#130692342
#130688642
#130686432
#130685482
#130684302
#130683902
C11×#18232
#2257011