Finite Group Databasebeta

← D11×#2913 #15617441

Subgroups — D11×#2913 #15617441

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#131C211yesmaximal, characteristic
2D11×#520C212yesmaximal
3#13077216C211yesmaximal, characteristic, complemented
4#13077215C216yesmaximal, complemented
5#13077214C212yesmaximal, complemented
6#13077213C213yesmaximal, complemented
7#13077212C213yesmaximal, complemented
8D11×#428C216yesmaximal, complemented
9D11×#427C213yesmaximal, complemented
10C2×D11×#107C213yesmaximal, complemented
11C11×#2913C211yesmaximal, characteristic, complemented
12C2×#41×D11C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#520C2212yes—
15#10623358C2212yes—
16C2×#67001C2211yescharacteristic
17D11×#131C4116yescomplemented
18C2×#66960C2213yes—
19C2×M16×D11C2213yes—
20C2×#66954C2213yes—
21C22×C8×D11C2213yes—
22#10623105—22no—
23C4×Q8×D11—22no—
24#10623077—26no—
25C4×D4×D11—26no—
26#10623054C2216yes—
27D11×#117C2216yes—
28#10623035C2216yes—
29C2×C4⋊C4×D11C2216yes—
30C11×#428C2216yescomplemented
31C11×#427C2213yescomplemented
32C2×C11×#107C2213yescomplemented
33#10622734C2216yescomplemented
34#10622719C2213yescomplemented
35C2×#66882C2213yescomplemented
36#10622611C2216yescomplemented
37#10622608C2216yescomplemented
38#10622577C2216yescomplemented
39C2×#66871C2216yescomplemented
40#10622494C22112yescomplemented
41#10622493C2213yescomplemented
42#10622493C2213yescomplemented
43D11×#107C2213yes—
44D11×#107C2216yes—
45D11×#107C2211yescharacteristic
46D11×#107C2216yescomplemented
47D11×#107C2216yescomplemented
48#10622474C22112yescomplemented
49#10622473C2216yescomplemented
50D11×#106C2216yes—
51C2×C11×#41C2311yescharacteristic
52#41×D11C2×C418yes—
53#41×D11Q818yes—
54C2×#4343D411yescharacteristic
55C2×Q8×D11D411yescharacteristic
56C2×#4341D413yes—
57C2×D4×D11D413yes—
58C2×#4339C2313yes—
59C22×C4×D11—26no—
60C22×C4×D11C2313yes—
61C11×#131C2×C418yescomplemented
62C2×C11×M16C2313yes—
63C22×C8×C11C2313yes—
64C4×Q8×C11—22no—
65C4×D4×C11—26no—
66C11×#117C2316yes—
67C2×C11×C4⋊C4C2316yes—
68#67001C2×C418yescomplemented
69Q8×Dic11—22no—
70D4×Dic11—26no—
71C4×C22⋊D11—212no—
72#66979C2316yes—
73C2×C4⋊Dic11C2316yes—
74C2×Dic11⋊C4—26no—
75C2×#4318C2313yes—
76C22×C11⋊C8C2313yes—
77#66960C2×C4124yescomplemented
78M16×D11C2×C4124yescomplemented
79#66954C2×C4124yescomplemented
80C2×#4313C2316yes—
81C2×C8×D11C2×C4124yescomplemented
82C2×C8×D11C2313yes—
83C2×C8×D11C2311yescharacteristic
84C2×C8×D11C2313yes—
85C2×C8×D11C2313yes—
86#66946—26no—
87#66945C2316yes—
88#66945C2316yes—
89C4⋊C4×D11—26no—
90C4⋊C4×D11—26no—
91C4⋊C4×D11C2312yes—
92C4⋊C4×D11C2316yes—
93C4⋊C4×D11C23112yes—
94#66940—26no—
95(C22⋊D11)⋊C4—212no—
96C22⋊C4×D11—26no—
97#66930—26no—
98C4×D44—26no—
99#66925—26no—
100C42×D11—26no—
101C4×Dic22—26no—
102C11×#107C2313yes—
103C11×#107C2316yes—
104C11×#107C2311yescharacteristic
105C11×#106C2316yes—
106#66882C2316yes—
107#66882C2313yes—
108#66882C2311yescharacteristic
109#66881C2316yes—
110#66872C2316yes—
111#66872C2316yes—
112#66871C2312yes—
113#66871C2316yes—
114#66871C23112yes—
115C2×#2913—111nomaximal, Sylow
116C23×D11C2×D413yes—
117C11×#41C22×C414yes—
118C11×#41C2×Q814yes—
119C2×Q8×C11C2×D411yescharacteristic
120C2×D4×C11C2×D413yes—
121C22×C4×C11—26no—
122C22×C4×C11C2413yes—
123C2×C22⋊D11C2×D416yes—
124C22×Dic11—26no—
125C22×Dic11C2×D413yes—
126#4343C4⋊C418yes—
127Q8×D11C4⋊C418yes—
128#4341C4⋊C4124yes—
129D4×D11C4⋊C4124yes—
130#4339C22×C4112yes—
131#4339C2×Q8112yes—
132C2×D44C2×D413yes—
133C2×C4×D11—22no—
134C2×C4×D11—26no—
135C2×C4×D11—212no—
136C2×C4×D11—812no—
137C2×C4×D11C22×C4112yes—
138C2×C4×D11C2×D413yes—
139C2×C4×D11C2×D413yes—
140C2×C4×D11C2×Q8112yes—
141C2×C4×D11C2411yescharacteristic
142C2×C4×D11C2413yes—
143C2×Dic22C2×D413yes—
144C11×M16C22×C4112yescomplemented
145C2×C8×C11C22×C4112yescomplemented
146C2×C8×C11C2413yes—
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—26no—
149C11×C4⋊C4C2416yes—
150C11×C4⋊C4C2412yes—
151C11×C22⋊C4—26no—
152C42×C11—26no—
153C22⋊Dic11—26no—
154(C2×D11)⋊C4—26no—
155(C2×D11)⋊C4—26no—
156C4⋊Dic11—26no—
157C4⋊Dic11C2416yes—
158C4⋊Dic11C2412yes—
159Dic11⋊C4—212no—
160Dic11⋊C4—22no—
161Dic11⋊C4—26no—
162C4×Dic11—26no—
163C4×Dic11—26no—
164C4×Dic11—26no—
165#4318C22×C4112yescomplemented
166C2×C11⋊C8C22×C4112yescomplemented
167C2×C11⋊C8C2411yescharacteristic
168C2×C11⋊C8C2413yes—
169#4313C22×C4124yescomplemented
170C8×D11C22×C414yes—
171C8×D11C22×C4112yes—
172C8×D11C22×C4112yescomplemented
173C8×D11C22×C4112yescomplemented
174C22×#131—111no—
175C2×#520—112no—
176#2913—116no—
177#2913—113no—
178#2913—113no—
179#2913—111no—
180#2913—112no—
181#2913D1111yescharacteristic, direct product factor
182C2×#428—116no—
183C2×#427—113no—
184C22×#107—113no—
185C23×C11C22×D413yes—
186C22×D11—26no—
187C22×D11—26no—
188C22×D11C2×C4⋊C4112yes—
189C22×D11C22×D413yes—
190C22×D11C22×D411yescharacteristic
191Q8×C11C2×C4⋊C414yes—
192D4×C11C2×C4⋊C4112yes—
193C2×C4×C11—22no—
194C2×C4×C11—26no—
195C2×C4×C11—86no—
196C2×C4×C11C23×C416yes—
197C2×C4×C11C22×D413yes—
198C2×C4×C11C22×Q816yes—
199C2×C4×C11C2511yescharacteristic
200C22⋊D11C2×C4⋊C4124yes—
201C2×Dic11—22no—
202C2×Dic11—26no—
203C2×Dic11—86no—
204C2×Dic11C2×C4⋊C4112yes—
205C2×Dic11C22×D413yes—
206C2×Dic11C22×D411yescharacteristic
207D44C2×C4⋊C4112yes—
208C4×D11—412no—
209C4×D11—44no—
210C4×D11—812no—
211C4×D11C2×C4⋊C4112yes—
212C4×D11C2×C4⋊C4112yes—
213C4×D11C23×C412yes—
214C4×D11C23×C416yes—
215C4×D11C22×Q812yes—
216C4×D11C22×Q816yes—
217Dic22C2×C4⋊C4112yes—
218C8×C11C23×C412yes—
219C8×C11C23×C416yes—
220C11⋊C8C23×C412yes—
221C11⋊C8C23×C416yes—
222C22×#41—111no—
223C2×#131—111no—
224C2×#131—1116no—
225C2×#131—113no—
226C2×#131—113no—
227C2×#131C2×D1111yescharacteristic
228C22×M16—113no—
229C23×C8—113no—
230#520—112no—
231#520—116no—
232#520—116no—
233#520—226no—
234#520—222no—
235#520C2×D1112yes—
236C2×C4×Q8—222no—
237C2×C4×D4—226no—
238C2×#117—116no—
239C22×C4⋊C4—116no—
240#428—116no—
241#428—116no—
242#428—116no—
243#428—1112no—
244#428—1112no—
245#428C2×D1116yescomplemented
246#427—113no—
247#427—116no—
248#427—113no—
249#427—113no—
250#427—116no—
251#427C2×D1113yescomplemented
252C2×#107—113no—
253C2×#107—116no—
254C2×#107—113no—
255C2×#107—116no—
256C2×#107—111no—
257C2×#107—116no—
258C2×#107—116no—
259C2×#107C2×D1113yescomplemented
260C2×#106—116no—
261C22×C11—23no—
262C22×C11—23no—
263C22×C11C22×C4⋊C416yes—
264C22×C11C23×D411yescharacteristic
265C2×D11—23no—
266C2×D11—23no—
267C2×D11—224no—
268C2×D11C22×C4⋊C416yes—
269C2×D11C22×C4⋊C412yes—
270C2×D11#57612yes—
271C2×D11#57812yes—
272C4×C11—46no—
273C4×C11—42no—
274C4×C11C22×C4⋊C416yes—
275C4×C11C24×C411yescharacteristic
276C4×C11C23×Q811yescharacteristic
277Dic11—46no—
278Dic11—42no—
279Dic11C22×C4⋊C416yes—
280Dic11C22×C4⋊C412yes—
281C2×#41—118no—
282C2×#41—118no—
283C2×#41—111no—
284C2×#41—113no—
285C2×#41—113no—
286C2×#41C22×D1111yescharacteristic
287C22×Q8—111no—
288C22×D4—113no—
289C23×C4—113no—
290C23×C4—226no—
291#131—118no—
292#131—1124no—
293#131—1124no—
294#131C4×D1118yescomplemented
295C2×M16—113no—
296C2×M16—1124no—
297C2×M16—116no—
298C2×M16C22×D1113yes—
299C22×C8—113no—
300C22×C8—1124no—
301C22×C8—111no—
302C22×C8—113no—
303C22×C8—113no—
304C22×C8—113no—
305C22×C8C22×D1113yes—
306C4×Q8—22no—
307C4×Q8—226no—
308C4×Q8—226no—
309C4×Q8—222no—
310C4×D4—26no—
311C4×D4—226no—
312C4×D4—2212no—
313C4×D4—226no—
314C4×D4—2212no—
315C4×D4—226no—
316#117—116no—
317#117—116no—
318#117—116no—
319#117—226no—
320#117—226no—
321#117C22×D1116yes—
322C2×C4⋊C4—116no—
323C2×C4⋊C4—116no—
324C2×C4⋊C4—1112no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—226no—
327C2×C4⋊C4—226no—
328C2×C4⋊C4—226no—
329C2×C4⋊C4C22×D1116yes—
330C2×C22⋊C4—226no—
331C2×C42—226no—
332#107—113no—
333#107—116no—
334#107—111no—
335#107—116no—
336#107—1112no—
337#107—112no—
338#107C22×D1113yes—
339#107C22×D1116yes—
340#107C22×D1111yescharacteristic
341#106—116no—
342#106—116no—
343#106—116no—
344#106C22×D1116yes—
345C2×C11—26no—
346C2×C11C23×C4⋊C411yescharacteristic
347C2×C11C2×#57611yescharacteristic
348C2×C11C2×#57811yescharacteristic
349D11—26no—
350D11#291314yesdirect product factor
351C24—113no—
352#41—118no—
353#41—1124no—
354#41—1112no—
355#41—1112no—
356#41C2×C4×D1114yes—
357#41Q8×D1114yes—
358C2×Q8—118no—
359C2×Q8—113no—
360C2×Q8D4×D1111yescharacteristic
361C2×D4—116no—
362C2×D4—1124no—
363C2×D4—113no—
364C2×D4D4×D1113yes—
365C22×C4—26no—
366C22×C4—113no—
367C22×C4—1112no—
368C22×C4—113no—
369C22×C4—113no—
370C22×C4—1112no—
371C22×C4—111no—
372C22×C4—113no—
373C22×C4—222no—
374C22×C4—226no—
375C22×C4—2212no—
376C22×C4—226no—
377C22×C4—8812no—
378C22×C4C23×D1113yes—
379M16—1112no—
380M16—1124no—
381M16C2×C4×D11112yescomplemented
382C2×C8—1112no—
383C2×C8—113no—
384C2×C8—111no—
385C2×C8—114no—
386C2×C8—1112no—
387C2×C8—1112no—
388C2×C8—1112no—
389C2×C8C2×C4×D11112yescomplemented
390C2×C8C23×D1113yes—
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—26no—
393C4⋊C4—112no—
394C4⋊C4—116no—
395C4⋊C4—226no—
396C4⋊C4—2212no—
397C4⋊C4—222no—
398C4⋊C4—226no—
399C4⋊C4C23×D1112yes—
400C4⋊C4C23×D1116yes—
401C22⋊C4—26no—
402C22⋊C4—226no—
403C22⋊C4—226no—
404C22⋊C4—226no—
405C42—26no—
406C42—226no—
407C42—226no—
408C42—226no—
409C11C2×#291311yescharacteristic, complemented, Sylow
410C23—111no—
411C23—1112no—
412C23—113no—
413C23—226no—
414C23—226no—
415C23C2×D4×D1113yes—
416Q8—1112no—
417Q8C4⋊C4×D1114yes—
418D4—1124no—
419D4—1112no—
420D4C4⋊C4×D11112yes—
421C2×C4—22no—
422C2×C4—26no—
423C2×C4—86no—
424C2×C4—1112no—
425C2×C4—113no—
426C2×C4—111no—
427C2×C4—1112no—
428C2×C4—1112no—
429C2×C4—112no—
430C2×C4—116no—
431C2×C4—112no—
432C2×C4—116no—
433C2×C4—222no—
434C2×C4—226no—
435C2×C4—4412no—
436C2×C4—444no—
437C2×C4—8812no—
438C2×C4—886no—
439C2×C4C22×C4×D1116yes—
440C2×C4C2×D4×D1113yes—
441C2×C4C2×Q8×D1116yes—
442C2×C4C24×D1111yescharacteristic
443C8—112no—
444C8—116no—
445C8C22×C4×D1112yes—
446C8C22×C4×D1116yes—
447C22—23no—
448C22—23no—
449C22—112no—
450C22—112no—
451C22—112no—
452C22—116no—
453C22—2224no—
454C22—223no—
455C22—223no—
456C22C2×C4⋊C4×D1116yes—
457C22C22×D4×D1111yescharacteristic
458C4—46no—
459C4—42no—
460C4—112no—
461C4—116no—
462C4—446no—
463C4—442no—
464C4C2×C4⋊C4×D1116yes—
465C4C23×C4×D1111yescharacteristic
466C4C22×Q8×D1111yescharacteristic
467C2—26no—
468C2—114no—
469C2—226no—
470C2C22×C4⋊C4×D1111yescharacteristic
471C2D11×#57611yescharacteristic
472C2D11×#57811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2913C2
socleC22×C11C23×D4
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2913D11
hypocenterC11C2×#2913
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2913

Complements

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

NH ≅ G/Ntype
3. #13077216C2semidirect
4. #13077215C2semidirect
5. #13077214C2semidirect
6. #13077213C2semidirect
7. #13077212C2semidirect
8. D11×#428C2semidirect
9. D11×#427C2semidirect
10. C2×D11×#107C2semidirect
11. C11×#2913C2semidirect
17. D11×#131C4semidirect
30. C11×#428C22semidirect
31. C11×#427C22semidirect
32. C2×C11×#107C22semidirect
33. #10622734C22semidirect
34. #10622719C22semidirect
35. C2×#66882C22semidirect
36. #10622611C22semidirect
37. #10622608C22semidirect
38. #10622577C22semidirect
39. C2×#66871C22semidirect
40. #10622494C22semidirect
41. #10622493C22semidirect
42. #10622493C22semidirect
46. D11×#107C22semidirect
47. D11×#107C22semidirect
48. #10622474C22semidirect
49. #10622473C22semidirect
61. C11×#131C2×C4semidirect
68. #67001C2×C4semidirect
77. #66960C2×C4semidirect
78. M16×D11C2×C4semidirect
79. #66954C2×C4semidirect
81. C2×C8×D11C2×C4semidirect
144. C11×M16C22×C4semidirect
145. C2×C8×C11C22×C4semidirect
165. #4318C22×C4semidirect
166. C2×C11⋊C8C22×C4semidirect
169. #4313C22×C4semidirect
172. C8×D11C22×C4semidirect
173. C8×D11C22×C4semidirect
181. #2913D11direct (N × H)
245. #428C2×D11semidirect
251. #427C2×D11semidirect
259. C2×#107C2×D11semidirect
294. #131C4×D11semidirect
350. D11#2913direct (N × H)
381. M16C2×C4×D11semidirect
389. C2×C8C2×C4×D11semidirect
409. C11C2×#2913semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1312
D11×#5202
#130772162
#130772152
#130772142
#130772132
#130772122
D11×#4282
D11×#4272
C2×D11×#1072
C11×#29132
C2×#291311