Finite Group Databasebeta

← #14760410

Subgroups — #14760410

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622748C211yesmaximal, characteristic
2C2×#10622485C211yesmaximal, characteristic, complemented
3C2×M16×Dic11C211yesmaximal, characteristic, complemented
4#13071122C212yesmaximal, complemented
5#13069490C211yesmaximal, characteristic, complemented
6#13069357C211yesmaximal, characteristic, complemented
7#13069311C212yesmaximal, complemented
8#13069052C212yesmaximal, complemented
9#106×Dic11C211yesmaximal, characteristic, complemented
10#13068430C212yesmaximal, complemented
11C11×#1809C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×#66983C2212yes—
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×#66946C2212yes—
18C2×(C22⋊D11)⋊C4—22no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C11×#380C2212yes—
22#10622748C418yescomplemented
23M16×Dic11—24no—
24C2×#66885C2212yes—
25C2×#66881C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622601C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622586C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35#10622571—22no—
36#10622485—24no—
37#10622282—22no—
38#10622279—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16C2×C414yescomplemented
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56#66983—24no—
57#66983C2×C418yescomplemented
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×D88—22no—
77C2×D88—22no—
78C2×D88C2×C414yescomplemented
79#66946—24no—
80#66946—24no—
81(C22⋊D11)⋊C4—48no—
82C11×#107—22no—
83C11×#106—22no—
84C11×#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885C2×C418yescomplemented
88#66881C2×C414yescomplemented
89#66879—22no—
90#66879—22no—
91C8×Dic11—22no—
92C8×Dic11D414yescomplemented
93#66873—24no—
94#66873—24no—
95C4×#469—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C23×D11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4112yes—
107C22×C4×C11C2411yescharacteristic
108C2×C22⋊D11—28no—
109C2×C22⋊D11—44no—
110C2×C22⋊D11—44no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—24no—
114C22×Dic11—22no—
115C22×Dic11—42no—
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44C22×C414yes—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C11×M16—28no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C2×D412yes—
135C2×C8×C11#4112yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C22⋊C4—44no—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—44no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—44no—
145C4⋊Dic11—22no—
146C4⋊Dic11C22×C414yes—
147Dic11⋊C4—44no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—44no—
153C4×Dic11C2×D412yes—
154C4×Dic11#4112yes—
155#4318—28no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8C2×D412yes—
161C2×C11⋊C8#4112yes—
162D88—28no—
163C2×#469—111no—
164C2×C4×D8—111no—
165C2×C4×M16—111no—
166C4×#121—112no—
167#1972—111no—
168#1944—111no—
169#1936—112no—
170#1895—112no—
171#1809D1111yescharacteristic, complemented
172C4×#106—111no—
173C4×#102—112no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11C4×D412yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C4×D412yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C22⋊D11—416no—
207C2×Dic11—22no—
208C2×Dic11—24no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—44no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—44no—
217C2×Dic11#12112yes—
218C2×Dic11#12112yes—
219C2×Dic11AGL(1,ℤ/8)14yes—
220D44—24no—
221D44—24no—
222D44—42no—
223D44—42no—
224C4×D11—88no—
225C8×C11—22no—
226C8×C11C4×D414yescomplemented
227C11⋊C8—22no—
228C11⋊C8—22no—
229C22×D8—111no—
230C22×M16—111no—
231C22×M16C2×D1111yescharacteristic
232C2×#121—112no—
233C2×C4×D4—112no—
234C2×C4×D4—222no—
235C22×C42—111no—
236#469—118no—
237C4×D8—224no—
238C2×#107C2×D1111yescharacteristic
239C2×#106—111no—
240C2×#106C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102—112no—
244C4×M16—224no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8—111no—
249#390—112no—
250#389—112no—
251#388—222no—
252#386—222no—
253#380C2×D1112yes—
254C4×C4⋊C4—112no—
255C4×C22⋊C4—222no—
256#340—112no—
257#340—112no—
258#340C2×D1112yes—
259C22×C11—24no—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11C2×#12111yescharacteristic
266C22×C11#53211yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)12yes—
268C22×C11#57512yes—
269C2×D11—44no—
270C2×D11—44no—
271C2×D11—44no—
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—82no—
275C2×D11—82no—
276C4×C11—22no—
277C4×C11—82no—
278C4×C11—82no—
279C4×C11C2×C4×D411yescharacteristic
280C4×C11C4×#4111yescharacteristic
281C4×C11#52511yescharacteristic
282C4×C11#52911yescharacteristic
283Dic11—22no—
284Dic11—44no—
285Dic11—41no—
286Dic11—41no—
287Dic11#46914yescomplemented
288C22×D4—112no—
289C22×D4—222no—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—222no—
293C23×C4C22×D1111yescharacteristic
294C2×D8—114no—
295C2×D8—222no—
296C2×D8—222no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16C4×D1114yescomplemented
303C22×C8—111no—
304C22×C8—111no—
305C22×C8C22×D1111yescharacteristic
306C22×C8C22×D1111yescharacteristic
307#121—118no—
308#121—224no—
309C4×D4—224no—
310C4×D4—224no—
311C4×D4—448no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22×D1112yes—
315C2×C4⋊C4C22×D1112yes—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—111no—
322C2×C42—111no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—222no—
326C2×C42—222no—
327C2×C42—222no—
328#107—22no—
329#106—22no—
330#106—114no—
331#102—118no—
332#102—224no—
333#102—224no—
334#97—222no—
335#97—222no—
336C4×C8—114no—
337C4×C8—222no—
338#95—22no—
339#95—222no—
340#95—222no—
341C2×C11—42no—
342C2×C11C4×#12111yescharacteristic
343C2×C11C4×AGL(1,ℤ/8)12yes—
344C2×C11C2×#46911yescharacteristic
345C2×C11#305411yescharacteristic
346C2×C11#317112yes—
347D11—84no—
348C24—222no—
349C24D4×D1111yescharacteristic
350C2×D4—114no—
351C2×D4—228no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—444no—
358C2×D4—444no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—224no—
372C22×C4—222no—
373C22×C4—444no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4—442no—
377C22×C4C2×C4×D1112yes—
378C22×C4D4×D1111yescharacteristic
379C22×C4#434312yes—
380C22×C4C23×D1111yescharacteristic
381D8—228no—
382M16—28no—
383M16—228no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—112no—
387C2×C8—112no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8C2×C4×D1112yes—
393C2×C8C2×C4×D1112yes—
394C2×C8D4×D1112yes—
395C2×C8#434112yes—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—114no—
401C4⋊C4—222no—
402C4⋊C4—444no—
403C22⋊C4—44no—
404C22⋊C4—228no—
405C22⋊C4—444no—
406C22⋊C4—444no—
407C22⋊C4—444no—
408C42—112no—
409C42—112no—
410C42—222no—
411C42—222no—
412C42—221no—
413C42—221no—
414C42—444no—
415C11C4×#46911yescharacteristic, complemented, Sylow
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—224no—
421C23—442no—
422C23—442no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23#6694612yes—
428C23C2×D4×D1111yescharacteristic
429D4—224no—
430D4—224no—
431D4—4416no—
432D4—442no—
433D4—442no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—114no—
447C2×C4—112no—
448C2×C4—112no—
449C2×C4—222no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—444no—
456C2×C4—444no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—888no—
460C2×C4#6694612yes—
461C2×C4C22×C4×D1111yescharacteristic
462C2×C4C2×D4×D1111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C2×C4C2×#434311yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4#41×D1111yescharacteristic
467C8—22no—
468C8—222no—
469C8—222no—
470C8(C22⋊D11)⋊C414yescomplemented
471C22—22no—
472C22—24no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—444no—
477C22—444no—
478C22—444no—
479C22—882no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22C2×#6694611yescharacteristic
484C22#1062312711yescharacteristic
485C22D11×#12111yescharacteristic
486C22D11×AGL(1,ℤ/8)12yes—
487C22#1062330812yes—
488C4—22no—
489C4—82no—
490C4—82no—
491C4—114no—
492C4—222no—
493C4—444no—
494C4—441no—
495C4—441no—
496C4C2×(C22⋊D11)⋊C411yescharacteristic
497C4#1062305311yescharacteristic
498C4#1062315511yescharacteristic
499C4#1062315811yescharacteristic
500C2—42no—
501C2—884no—
502C2#1307112211yescharacteristic
503C2#1307742312yes—
504C2D11×#46911yescharacteristic
505C2#1307822711yescharacteristic
506C2#1307920412yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC2×#10622748C2
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11C4×#469
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622485C2semidirect
3. C2×M16×Dic11C2semidirect
4. #13071122C2semidirect
5. #13069490C2semidirect
6. #13069357C2semidirect
7. #13069311C2semidirect
8. #13069052C2semidirect
9. #106×Dic11C2semidirect
10. #13068430C2semidirect
11. C11×#1809C2semidirect
22. #10622748C4semidirect
50. C2×C11×M16C2×C4semidirect
57. #66983C2×C4semidirect
78. C2×D88C2×C4semidirect
87. #66885C2×C4semidirect
88. #66881C2×C4semidirect
92. C8×Dic11D4semidirect
171. #1809D11semidirect
226. C8×C11C4×D4semidirect
287. Dic11#469semidirect
302. C2×M16C4×D11semidirect
415. C11C4×#469semidirect
470. C8(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106227482
C2×#106224852
C2×M16×Dic112
#130711222
#130694902
#130693572
#130693112
#130690522
#106×Dic112
#130684302
C11×#18092
C4×#46911