Finite Group Databasebeta

← D11×#2608 #14925200

Subgroups — D11×#2608 #14925200

Order 2816.

2270 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074286C211yesmaximal, characteristic, complemented
2#13074285C214yesmaximal, complemented
3#13074284C214yesmaximal, complemented
4#13074283C212yesmaximal, complemented
5#13074282C214yesmaximal, complemented
6D11×#396C214yesmaximal
7D11×#389C214yesmaximal, complemented
8D11×#387C214yesmaximal, complemented
9D11×#381C211yesmaximal, characteristic
10C4×C22⋊C4×D11C212yesmaximal
11C11×#2608C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C2×C4⋊C4×D11C2214yes—
14C2×C4⋊C4×D11C2214yes—
15C2×C4⋊C4×D11C2214yes—
16C2×C22⋊C4×D11C2214yes—
17C2×C22⋊C4×D11C2212yes—
18C2×C42×D11C2212yes—
19C2×C42×D11C2212yes—
20C11×#396C2214yes—
21C11×#389C2214yescomplemented
22C11×#387C2214yescomplemented
23C11×#381C2211yescharacteristic
24C4×C11×C22⋊C4C2212yes—
25#10622824C2211yescharacteristic
26C4×C22⋊Dic11C2212yes—
27#10622607C2214yes—
28#10622607C2214yes—
29#10622607C2214yes—
30#10622598C2214yescomplemented
31#10622594C2214yescomplemented
32#10622591C2214yescomplemented
33#10622586C2214yescomplemented
34#10622585C2214yescomplemented
35#10622585C2214yescomplemented
36#10622561C2214yes—
37#10622561C2214yes—
38#10622561C2214yes—
39#10622556C2212yes—
40C22⋊C4×Dic11C2214yes—
41C4×(C2×D11)⋊C4C2212yes—
42C4×(C2×D11)⋊C4C2212yes—
43#10622546C2214yescomplemented
44#10622541C2214yescomplemented
45#10622289C2214yes—
46#10622279C2214yes—
47#10622277C2214yes—
48D11×#95C2214yes—
49D11×#95C2214yes—
50D11×#95C2214yes—
51#10622268C2214yescomplemented
52#10622267C2214yescomplemented
53#10622266C2214yescomplemented
54#10622265C2214yescomplemented
55#10622260C2214yescomplemented
56#10622260C2214yescomplemented
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—44no—
61C22×C4×D11Q818yes—
62C22×C4×D11C2314yes—
63C22×C4×D11C2314yes—
64C22×C4×D11C2312yes—
65C22×C4×D11C2314yes—
66C22×C4×D11C2312yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2312yes—
72C2×C42×C11C2312yes—
73C2×C42×C11C2312yes—
74C2×C22⋊Dic11C2314yes—
75C2×C22⋊Dic11C2312yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×C4⋊Dic11C2314yes—
80C2×C4⋊Dic11C2314yes—
81C2×C4⋊Dic11C2314yes—
82C2×Dic11⋊C4C2314yes—
83C2×Dic11⋊C4C2314yes—
84C2×Dic11⋊C4C2314yes—
85C2×Dic11⋊C4C2314yes—
86C2×Dic11⋊C4C2314yes—
87C2×Dic11⋊C4C2314yes—
88C2×C4×Dic11C2312yes—
89C2×C4×Dic11C2314yes—
90C2×C4×Dic11C2312yes—
91C2×C4×Dic11C2314yes—
92C4⋊C4×D11—216no—
93C4⋊C4×D11—216no—
94C4⋊C4×D11—48no—
95C22⋊C4×D11—216no—
96C22⋊C4×D11—44no—
97C42×D11—44no—
98C42×D11—44no—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C2×#2608—111nomaximal, Sylow
112C24×C11C2411yescharacteristic
113C23×D11—28no—
114C23×D11—24no—
115C23×D11C2×Q814yes—
116C23×D11C2411yescharacteristic
117C23×D11C2411yescharacteristic
118C22×C4×C11—42no—
119C22×C4×C11C2×Q814yes—
120C22×C4×C11C2414yes—
121C22×C4×C11C2414yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2414yes—
124C22×Dic11—42no—
125C22×Dic11C2×Q814yes—
126C22×Dic11C2414yes—
127C22×Dic11C2414yes—
128C22×Dic11C2412yes—
129C22×Dic11C2414yes—
130C2×C4×D11—28no—
131C2×C4×D11—28no—
132C2×C4×D11—28no—
133C2×C4×D11—28no—
134C2×C4×D11—28no—
135C2×C4×D11—28no—
136C2×C4×D11—24no—
137C2×C4×D11—24no—
138C2×C4×D11—28no—
139C2×C4×D11—28no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—416no—
143C2×C4×D11C2×Q818yes—
144C2×C4×D11C2×Q818yes—
145C2×C4×D11#41116yes—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—44no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—42no—
151C42×C11—42no—
152C42×C11—42no—
153C22⋊Dic11—28no—
154C22⋊Dic11—42no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—44no—
158C4⋊Dic11—28no—
159C4⋊Dic11—28no—
160C4⋊Dic11—44no—
161Dic11⋊C4—28no—
162Dic11⋊C4—28no—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—44no—
166Dic11⋊C4—44no—
167C4×Dic11—44no—
168C4×Dic11—42no—
169C4×Dic11—42no—
170C4×Dic11—44no—
171#2608—114no—
172#2608—114no—
173#2608—114no—
174#2608—111no—
175#2608—112no—
176#2608D1111yescharacteristic, direct product factor
177C2×#396—114no—
178C2×#389—114no—
179C2×#387—114no—
180C2×#381—111no—
181C2×C4×C22⋊C4—112no—
182C23×C11—24no—
183C23×C11—22no—
184C23×C11C22×Q812yes—
185C23×C11C2511yescharacteristic
186C22×D11—24no—
187C22×D11—22no—
188C22×D11—216no—
189C22×D11—28no—
190C22×D11—416no—
191C22×D11C22×Q812yes—
192C22×D11C22×Q812yes—
193C22×D11C2×#4118yes—
194C22×D11H(5,𝔽2)14yes—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—44no—
206C2×C4×C11C22×Q814yes—
207C2×C4×C11C2×#4118yes—
208C2×Dic11—24no—
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—24no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—44no—
219C2×Dic11C22×Q814yes—
220C2×Dic11C2×#4118yes—
221C4×D11—216no—
222C4×D11—232no—
223C4×D11—48no—
224C4×D11—416no—
225C4×D11—416no—
226C24×C4—111no—
227C22×C4⋊C4—114no—
228C22×C4⋊C4—114no—
229C22×C4⋊C4—114no—
230C22×C22⋊C4—114no—
231C22×C22⋊C4—112no—
232C22×C42—112no—
233C22×C42—112no—
234#396—114no—
235#396—114no—
236#396—114no—
237#396—114no—
238#396—114no—
239#396—114no—
240#396—114no—
241#396C2×D1114yes—
242#389—114no—
243#389—114no—
244#389—114no—
245#389—114no—
246#389—114no—
247#389—114no—
248#389—114no—
249#389C2×D1114yescomplemented
250#387—114no—
251#387—114no—
252#387—114no—
253#387—114no—
254#387—114no—
255#387—114no—
256#387—114no—
257#387C2×D1114yescomplemented
258#381—111no—
259#381—112no—
260#381—114no—
261#381C2×D1111yescharacteristic
262C4×C22⋊C4—112no—
263C4×C22⋊C4—114no—
264C4×C22⋊C4—112no—
265C4×C22⋊C4—112no—
266C4×C22⋊C4—114no—
267C4×C22⋊C4C2×D1112yes—
268C2×#95—114no—
269C2×#95—114no—
270C2×#95—114no—
271C22×C11—24no—
272C22×C11—22no—
273C22×C11—44no—
274C22×C11C23×Q811yescharacteristic
275C22×C11C22×#4114yes—
276C22×C11C2×H(5,𝔽2)12yes—
277C2×D11—24no—
278C2×D11—22no—
279C2×D11—44no—
280C2×D11—416no—
281C2×D11#53318yes—
282C2×D11#54314yes—
283C2×D11#553116yes—
284C4×C11—24no—
285C4×C11—28no—
286C4×C11—44no—
287C4×C11—44no—
288Dic11—24no—
289Dic11—28no—
290Dic11—44no—
291Dic11—44no—
292C25—111no—
293C23×C4—111no—
294C23×C4—114no—
295C23×C4—112no—
296C23×C4—118no—
297C23×C4—112no—
298C23×C4—114no—
299C23×C4—114no—
300C23×C4—444no—
301C23×C4C22×D1111yescharacteristic
302C2×C4⋊C4—114no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—114no—
306C2×C4⋊C4—114no—
307C2×C4⋊C4—114no—
308C2×C4⋊C4—114no—
309C2×C4⋊C4—114no—
310C2×C4⋊C4—114no—
311C2×C4⋊C4—2216no—
312C2×C4⋊C4—2216no—
313C2×C4⋊C4—448no—
314C2×C4⋊C4C22×D1114yes—
315C2×C4⋊C4C22×D1114yes—
316C2×C4⋊C4C22×D1114yes—
317C2×C22⋊C4—114no—
318C2×C22⋊C4—114no—
319C2×C22⋊C4—114no—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—114no—
322C2×C22⋊C4—2216no—
323C2×C22⋊C4—444no—
324C2×C22⋊C4C22×D1114yes—
325C2×C22⋊C4C22×D1112yes—
326C2×C42—114no—
327C2×C42—112no—
328C2×C42—114no—
329C2×C42—112no—
330C2×C42—444no—
331C2×C42—444no—
332C2×C42C22×D1112yes—
333C2×C42C22×D1112yes—
334#95—114no—
335#95—114no—
336#95—114no—
337#95—114no—
338#95—114no—
339#95—114no—
340#95—114no—
341#95—114no—
342#95—114no—
343#95C22×D1114yes—
344#95C22×D1114yes—
345#95C22×D1114yes—
346C2×C11—42no—
347C2×C11C2×#53312yes—
348C2×C11C2×#54311yescharacteristic
349C2×C11C2×#55314yes—
350D11—42no—
351D11#260818yesdirect product factor
352C24—111no—
353C24—114no—
354C24—111no—
355C24—228no—
356C24—224no—
357C24C23×D1111yescharacteristic
358C22×C4—42no—
359C22×C4—112no—
360C22×C4—114no—
361C22×C4—114no—
362C22×C4—118no—
363C22×C4—1116no—
364C22×C4—118no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—228no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—228no—
371C22×C4—228no—
372C22×C4—228no—
373C22×C4—228no—
374C22×C4—228no—
375C22×C4—228no—
376C22×C4—228no—
377C22×C4—442no—
378C22×C4—442no—
379C22×C4—4416no—
380C22×C4—442no—
381C22×C4Q8×D1114yes—
382C22×C4C23×D1114yes—
383C22×C4C23×D1114yes—
384C22×C4C23×D1112yes—
385C22×C4C23×D1114yes—
386C4⋊C4—28no—
387C4⋊C4—28no—
388C4⋊C4—44no—
389C4⋊C4—228no—
390C4⋊C4—228no—
391C4⋊C4—228no—
392C4⋊C4—228no—
393C4⋊C4—228no—
394C4⋊C4—228no—
395C4⋊C4—444no—
396C4⋊C4—444no—
397C4⋊C4—444no—
398C22⋊C4—28no—
399C22⋊C4—42no—
400C22⋊C4—228no—
401C22⋊C4—228no—
402C22⋊C4—228no—
403C22⋊C4—444no—
404C22⋊C4—442no—
405C42—42no—
406C42—42no—
407C42—444no—
408C42—442no—
409C42—442no—
410C42—444no—
411C11C2×#260811yescharacteristic, complemented, Sylow
412C23—24no—
413C23—22no—
414C23—112no—
415C23—118no—
416C23—114no—
417C23—112no—
418C23—228no—
419C23—2216no—
420C23—224no—
421C23—222no—
422C23—4416no—
423C23C2×Q8×D1112yes—
424C23C24×D1111yescharacteristic
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—44no—
436C2×C4—114no—
437C2×C4—118no—
438C2×C4—2216no—
439C2×C4—2232no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—224no—
445C2×C4—224no—
446C2×C4—224no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—448no—
451C2×C4—4416no—
452C2×C4—4416no—
453C2×C4—444no—
454C2×C4C2×Q8×D1114yes—
455C2×C4#41×D1118yes—
456C22—24no—
457C22—22no—
458C22—44no—
459C22—1116no—
460C22—118no—
461C22—114no—
462C22—224no—
463C22—222no—
464C22—4416no—
465C22—444no—
466C22C22×Q8×D1111yescharacteristic
467C22C2×#41×D1114yes—
468C22D11×H(5,𝔽2)12yes—
469C4—28no—
470C4—24no—
471C4—44no—
472C4—44no—
473C4—228no—
474C4—224no—
475C4—444no—
476C4—444no—
477C2—42no—
478C2—118no—
479C2—442no—
480C2D11×#53312yes—
481C2D11×#54311yescharacteristic
482C2D11×#55314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2608C2
prime radicalC24×D11C23
hypercenter#2608D11
hypocenterC11C2×#2608
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2608

Complements

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

NH ≅ G/Ntype
1. #13074286C2semidirect
2. #13074285C2semidirect
3. #13074284C2semidirect
4. #13074283C2semidirect
5. #13074282C2semidirect
7. D11×#389C2semidirect
8. D11×#387C2semidirect
11. C11×#2608C2semidirect
21. C11×#389C22semidirect
22. C11×#387C22semidirect
30. #10622598C22semidirect
31. #10622594C22semidirect
32. #10622591C22semidirect
33. #10622586C22semidirect
34. #10622585C22semidirect
35. #10622585C22semidirect
43. #10622546C22semidirect
44. #10622541C22semidirect
51. #10622268C22semidirect
52. #10622267C22semidirect
53. #10622266C22semidirect
54. #10622265C22semidirect
55. #10622260C22semidirect
56. #10622260C22semidirect
176. #2608D11direct (N × H)
249. #389C2×D11semidirect
257. #387C2×D11semidirect
351. D11#2608direct (N × H)
411. C11C2×#2608semidirect

Maximal subgroups

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

subgroupindex
#130742862
#130742852
#130742842
#130742832
#130742822
D11×#3962
D11×#3892
D11×#3872
D11×#3812
C4×C22⋊C4×D112
C11×#26082
C2×#260811