Finite Group Databasebeta

← D11×#2382 #14916417

Subgroups — D11×#2382 #14916417

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#13071802C211yesmaximal, characteristic, complemented
3#13071801C212yesmaximal, complemented
4#13071800C214yesmaximal, complemented
5#13071799C214yesmaximal, complemented
6#13071798C214yesmaximal, complemented
7D11×#389C214yesmaximal
8D11×#387C214yesmaximal
9D11×#387C214yesmaximal
10D11×#382C212yesmaximal
11C11×#2382C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13D11×#125C4116yescomplemented
14C2×C4⋊C4×D11C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4⋊C4×D11C2214yes—
17C2×C4⋊C4×D11C2212yes—
18C2×C4⋊C4×D11C2214yes—
19C2×#66943C2212yes—
20C2×#66942C2214yes—
21C2×C42×D11C2214yes—
22C2×C42×D11C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C11×#389C2214yes—
25C11×#387C2214yes—
26C11×#387C2214yes—
27C11×#382C2212yes—
28#10622598C2214yes—
29#10622594C2214yes—
30#10622594C2214yes—
31#10622591C2214yes—
32#10622591C2214yes—
33#10622590C2212yes—
34#10622590C2212yes—
35#10622586C2214yes—
36#10622585C2214yes—
37#10622585C2214yes—
38#10622549C2212yes—
39#10622546C2214yes—
40#10622546C2214yes—
41#10622541C2214yes—
42D11×#95C2214yes—
43D11×#95C2214yes—
44D11×#95C2214yes—
45D11×#95C2214yes—
46#10622268C2214yes—
47#10622268C2214yes—
48#10622267C2214yes—
49#10622267C2214yes—
50#10622266C2214yes—
51#10622266C2214yes—
52#10622265C2214yes—
53#10622265C2214yes—
54#10622263C2214yes—
55#10622263C2214yes—
56#10622260C2214yes—
57#10622260C2214yes—
58C22×C4×D11C2314yes—
59C22×C4×D11C2314yes—
60C22×C4×D11C2314yes—
61C22×C4×D11C2312yes—
62C22×C4×D11C2311yescharacteristic
63C11×#125C2×C418yescomplemented
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C42×C11C2314yes—
70C2×C42×C11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×Dic11⋊C4C2314yes—
82C2×Dic11⋊C4C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2314yes—
85C2×C4×Dic11C2314yes—
86C2×C4×Dic11C2312yes—
87C2×C4×Dic11C2311yescharacteristic
88C4⋊C4×D11—48no—
89C4⋊C4×D11—44no—
90C4⋊C4×D11—44no—
91C4⋊C4×D11C2×C4132yes—
92C4⋊C4×D11C2×C4116yes—
93#66943C2×C4116yescomplemented
94#66942C2×C4132yescomplemented
95C42×D11—48no—
96C42×D11C2×C418yes—
97#66923C2×C418yescomplemented
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2314yes—
114C2×#2382—111nomaximal, Sylow
115C23×D11C2411yescharacteristic
116C22×C4×C11C2414yes—
117C22×C4×C11C2414yes—
118C22×C4×C11C2411yescharacteristic
119C22×C4×C11C2414yes—
120C22×C4×C11C2412yes—
121C22×Dic11C2414yes—
122C22×Dic11C2414yes—
123C22×Dic11C2411yescharacteristic
124C22×Dic11C2414yes—
125C22×Dic11C2412yes—
126C2×C4×D11—28no—
127C2×C4×D11—24no—
128C2×C4×D11—28no—
129C2×C4×D11—28no—
130C2×C4×D11—28no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—28no—
134C2×C4×D11—24no—
135C2×C4×D11—28no—
136C2×C4×D11—28no—
137C2×C4×D11—28no—
138C2×C4×D11C22×C418yes—
139C2×C4×D11C22×C414yes—
140C2×C4×D11C22×C4116yes—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4C22×C4116yes—
145C11×C4⋊C4C22×C418yes—
146C42×C11—44no—
147C42×C11C22×C414yes—
148C4⋊Dic11—44no—
149C4⋊Dic11—42no—
150C4⋊Dic11—42no—
151C4⋊Dic11C22×C418yes—
152C4⋊Dic11C22×C4116yes—
153Dic11⋊C4—44no—
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156Dic11⋊C4—44no—
157Dic11⋊C4C22×C4116yes—
158Dic11⋊C4C22×C4116yes—
159Dic11⋊C4C22×C4116yes—
160C4×Dic11—44no—
161C4×Dic11—44no—
162C4×Dic11—44no—
163C4×Dic11C22×C418yes—
164C4×Dic11C22×C414yes—
165C22×#125—111no—
166#2382—114no—
167#2382—114no—
168#2382—114no—
169#2382—112no—
170#2382—111no—
171#2382D1111yescharacteristic, direct product factor
172C2×#389—114no—
173C2×#387—114no—
174C2×#387—114no—
175C2×#382—112no—
176C23×C11C2511yescharacteristic
177C22×D11C23×C412yes—
178C22×D11H(5,𝔽2)14yes—
179C22×D112−1+412yes—
180C22×D112−1+412yes—
181C22×D112−1+414yes—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11C23×C414yes—
195C2×C4×C11C23×C412yes—
196C2×C4×C11C23×C418yes—
197C2×Dic11—24no—
198C2×Dic11—22no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—24no—
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—24no—
209C2×Dic11C23×C412yes—
210C2×Dic11C23×C414yes—
211C2×Dic11C23×C418yes—
212C4×D11—28no—
213C4×D11—232no—
214C4×D11—216no—
215C4×D11—416no—
216C4×D11—416no—
217C2×#125—1116no—
218C2×#125—114no—
219C2×#125—112no—
220C2×#125—111no—
221C2×#125C2×D1111yescharacteristic
222C22×C4⋊C4—112no—
223C22×C4⋊C4—114no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4—112no—
226C22×C4⋊C4—114no—
227C22×C42—111no—
228C22×C42—114no—
229#389—114no—
230#389—114no—
231#389—114no—
232#389—114no—
233#389—114no—
234#389—114no—
235#389—114no—
236#389C2×D1114yes—
237#387—114no—
238#387—114no—
239#387—114no—
240#387—114no—
241#387—114no—
242#387—114no—
243#387—114no—
244#387—114no—
245#387—114no—
246#387—114no—
247#387—114no—
248#387—114no—
249#387—114no—
250#387—114no—
251#387C2×D1114yes—
252#387C2×D1114yes—
253#382—112no—
254#382—112no—
255#382—112no—
256#382—114no—
257#382—114no—
258#382C2×D1112yes—
259C2×#95—114no—
260C2×#95—114no—
261C2×#95—114no—
262C2×#95—114no—
263C22×C11C24×C411yescharacteristic
264C22×C11C2×H(5,𝔽2)12yes—
265C22×C11C2×2−1+411yescharacteristic
266C22×C11C2×2−1+411yescharacteristic
267C22×C11C2×2−1+412yes—
268C2×D11#51914yes—
269C2×D11#52018yes—
270C2×D11#56214yes—
271C2×D11#56318yes—
272C2×D11#56414yes—
273C4×C11—22no—
274C4×C11—28no—
275C4×C11—24no—
276C4×C11—44no—
277C4×C11—44no—
278Dic11—22no—
279Dic11—28no—
280Dic11—24no—
281Dic11—44no—
282Dic11—44no—
283C23×C4—112no—
284C23×C4—114no—
285C23×C4—111no—
286C23×C4—114no—
287C23×C4—114no—
288#125—1132no—
289#125—1116no—
290#125—118no—
291#125C4×D1118yescomplemented
292C2×C4⋊C4—114no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—114no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—114no—
297C2×C4⋊C4—1116no—
298C2×C4⋊C4—1132no—
299C2×C4⋊C4—114no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—114no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—114no—
306C2×C4⋊C4—448no—
307C2×C4⋊C4—444no—
308C2×C4⋊C4—444no—
309C2×C4⋊C4C22×D1112yes—
310C2×C4⋊C4C22×D1112yes—
311C2×C4⋊C4C22×D1114yes—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1114yes—
314C2×C42—112no—
315C2×C42—111no—
316C2×C42—118no—
317C2×C42—114no—
318C2×C42—114no—
319C2×C42—114no—
320C2×C42—448no—
321C2×C42C22×D1114yes—
322C2×C42C22×D1111yescharacteristic
323#95—114no—
324#95—114no—
325#95—114no—
326#95—114no—
327#95—114no—
328#95—114no—
329#95—114no—
330#95—114no—
331#95—114no—
332#95—114no—
333#95—114no—
334#95—114no—
335#95C22×D1114yes—
336#95C22×D1114yes—
337#95C22×D1114yes—
338#95C22×D1114yes—
339C2×C11C2×#51911yescharacteristic
340C2×C11C2×#52012yes—
341C2×C11C2×#56211yescharacteristic
342C2×C11C2×#56312yes—
343C2×C11C2×#56411yescharacteristic
344D11#238218yesdirect product factor
345C24—111no—
346C22×C4—111no—
347C22×C4—112no—
348C22×C4—114no—
349C22×C4—118no—
350C22×C4—114no—
351C22×C4—1116no—
352C22×C4—114no—
353C22×C4—114no—
354C22×C4—228no—
355C22×C4—224no—
356C22×C4—224no—
357C22×C4—228no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—228no—
361C22×C4—228no—
362C22×C4—228no—
363C22×C4—228no—
364C22×C4—228no—
365C22×C4—228no—
366C22×C4C23×D1114yes—
367C22×C4C23×D1114yes—
368C22×C4C23×D1111yescharacteristic
369C22×C4C23×D1114yes—
370C22×C4C23×D1112yes—
371C4⋊C4—44no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—1116no—
375C4⋊C4—1116no—
376C4⋊C4—1116no—
377C4⋊C4—1116no—
378C4⋊C4—118no—
379C4⋊C4—444no—
380C4⋊C4—444no—
381C4⋊C4—444no—
382C4⋊C4—444no—
383C4⋊C4—444no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4C2×C4×D1118yes—
387C4⋊C4C2×C4×D11116yes—
388C42—44no—
389C42—118no—
390C42—114no—
391C42—444no—
392C42—444no—
393C42—444no—
394C42C2×C4×D1114yes—
395C11C2×#238211yescharacteristic, complemented, Sylow
396C23—112no—
397C23—114no—
398C23—112no—
399C23—112no—
400C23—114no—
401C23C24×D1111yescharacteristic
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—112no—
415C2×C4—114no—
416C2×C4—118no—
417C2×C4—228no—
418C2×C4—2216no—
419C2×C4—2232no—
420C2×C4—224no—
421C2×C4—222no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—222no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—4416no—
433C2×C4—4416no—
434C2×C4C22×C4×D1112yes—
435C2×C4C22×C4×D1114yes—
436C2×C4C22×C4×D1118yes—
437C22—114no—
438C22—118no—
439C22—114no—
440C22—114no—
441C22—118no—
442C22C23×C4×D1111yescharacteristic
443C22D11×H(5,𝔽2)12yes—
444C22D11×2−1+411yescharacteristic
445C22D11×2−1+411yescharacteristic
446C22D11×2−1+412yes—
447C4—22no—
448C4—28no—
449C4—24no—
450C4—44no—
451C4—44no—
452C4—222no—
453C4—224no—
454C4—228no—
455C4—444no—
456C4—444no—
457C2—118no—
458C2D11×#51911yescharacteristic
459C2D11×#52012yes—
460C2D11×#56211yescharacteristic
461C2D11×#56312yes—
462C2D11×#56411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2382C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2382D11
hypocenterC11C2×#2382
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
2. #13071802C2semidirect
3. #13071801C2semidirect
4. #13071800C2semidirect
5. #13071799C2semidirect
6. #13071798C2semidirect
11. C11×#2382C2semidirect
13. D11×#125C4semidirect
63. C11×#125C2×C4semidirect
93. #66943C2×C4semidirect
94. #66942C2×C4semidirect
97. #66923C2×C4semidirect
171. #2382D11direct (N × H)
291. #125C4×D11semidirect
344. D11#2382direct (N × H)
395. C11C2×#2382semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130718022
#130718012
#130718002
#130717992
#130717982
D11×#3892
D11×#3872
D11×#3822
C11×#23822
C2×#238211