Finite Group Databasebeta

← D11×#2817 #14959908

Subgroups — D11×#2817 #14959908

Order 2816.

2478 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C212yesmaximal
2#13076654C214yesmaximal, complemented
3#13076653C211yesmaximal, characteristic, complemented
4#13076652C214yesmaximal, complemented
5#13076651C212yesmaximal, complemented
6#13076650C214yesmaximal, complemented
7D11×#400C214yesmaximal, complemented
8D11×#397C214yesmaximal
9D11×#395C214yesmaximal, complemented
10D11×#381C211yesmaximal, characteristic
11C11×#2817C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×#66999C2212yes—
16C2×#66977C2212yes—
17D11×C22⋊Q8—216no—
18C2×#66950C2212yes—
19C2×#66949C2214yes—
20C2×C4⋊C4×D11C2214yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4⋊C4×D11C2214yes—
23C2×C22⋊C4×D11C2214yes—
24C2×C22⋊C4×D11C2212yes—
25C2×#66931C2214yes—
26C11×#400C2214yescomplemented
27C11×#397C2214yes—
28C11×#395C2214yescomplemented
29C11×#381C2211yescharacteristic
30#10622842C2214yescomplemented
31#10622824C2211yescharacteristic
32#10622606C2214yes—
33#10622599C2214yescomplemented
34#10622595C2214yescomplemented
35#10622592C2218yescomplemented
36#10622592C2214yescomplemented
37#10622566C2214yes—
38#10622565C2218yes—
39#10622556C2212yes—
40#10622288C2218yes—
41#10622287C2214yes—
42#10622277C2214yes—
43D11×#95C2214yes—
44D11×#95C2218yes—
45D11×#95C2214yes—
46#10622273C2218yescomplemented
47#10622272C2214yescomplemented
48#10622271C2218yescomplemented
49#10622269C2214yescomplemented
50#10622269C2218yescomplemented
51C24×D11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C2×Q8×D11—28no—
56C2×Q8×D11—48no—
57C22×C4×D11—44no—
58C22×C4×D11D418yes—
59C22×C4×D11C2314yes—
60C22×C4×D11C2314yes—
61C22×C4×D11C2314yes—
62C22×C4×D11C2312yes—
63C22×C4×D11C2312yes—
64C22×Dic22C2314yes—
65C22×Dic22C2312yes—
66C11×C22⋊Q8—28no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2312yes—
72C2×C22⋊Dic11C2314yes—
73C2×C22⋊Dic11C2312yes—
74#66999—28no—
75C2×(C2×D11)⋊C4C2314yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×C4⋊Dic11C2314yes—
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2314yes—
81#66977—28no—
82C2×Dic11⋊C4C2314yes—
83C2×Dic11⋊C4C2314yes—
84C2×Dic11⋊C4C2314yes—
85C2×Dic11⋊C4C2318yes—
86#66950—28no—
87#66949—216no—
88C4⋊C4×D11—28no—
89C4⋊C4×D11—216no—
90C4⋊C4×D11—48no—
91C22⋊C4×D11—216no—
92C22⋊C4×D11—44no—
93#66931—216no—
94C11×#95C2318yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C11⋊#95C2318yes—
100C11⋊#95C2314yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2314yes—
104C2×#2817—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C23×D11—24no—
107C23×D11—28no—
108C23×D11C2×D414yes—
109C23×D11C2411yescharacteristic
110C23×D11C2411yescharacteristic
111C2×Q8×C11—24no—
112C2×Q8×C11—44no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D414yes—
115C22×C4×C11C2414yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2414yes—
118C22×C4×C11C2412yes—
119C22×Dic11—42no—
120C22×Dic11C2×D414yes—
121C22×Dic11C2414yes—
122C22×Dic11C2414yes—
123C22×Dic11C2414yes—
124C22×Dic11C2412yes—
125Q8×D11—432no—
126C2×C4×D11—28no—
127C2×C4×D11—28no—
128C2×C4×D11—28no—
129C2×C4×D11—28no—
130C2×C4×D11—216no—
131C2×C4×D11—216no—
132C2×C4×D11—216no—
133C2×C4×D11—44no—
134C2×C4×D11—416no—
135C2×C4×D11C2×D418yes—
136C2×C4×D11C2×D418yes—
137C2×Dic22—28no—
138C2×Dic22—24no—
139C2×Dic22—44no—
140C2×Dic22—48no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—44no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—42no—
146C22⋊Dic11—28no—
147C22⋊Dic11—42no—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—44no—
151C4⋊Dic11—28no—
152C4⋊Dic11—24no—
153C4⋊Dic11—44no—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157Dic11⋊C4—48no—
158C22×C22⋊Q8—112no—
159#2817—114no—
160#2817—114no—
161#2817—114no—
162#2817—111no—
163#2817—112no—
164#2817D1111yescharacteristic, direct product factor
165C2×#400—114no—
166C2×#397—114no—
167C2×#395—114no—
168C2×#381—111no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11C22×D412yes—
172C23×C11C2511yescharacteristic
173C22×D11—22no—
174C22×D11—24no—
175C22×D11—28no—
176C22×D11—216no—
177C22×D11—416no—
178C22×D11C22×D412yes—
179C22×D11C22×D412yes—
180C22×D11H(5,𝔽2)14yes—
181C22×D112−1+418yes—
182Q8×C11—48no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—28no—
187C2×C4×C11—24no—
188C2×C4×C11—28no—
189C2×C4×C11—28no—
190C2×C4×C11—44no—
191C2×C4×C11C22×D414yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—28no—
197C2×Dic11—28no—
198C2×Dic11—28no—
199C2×Dic11—44no—
200C2×Dic11C22×D414yes—
201C4×D11—216no—
202C4×D11—48no—
203C4×D11—416no—
204C4×D11—416no—
205C4×D11—416no—
206Dic22—416no—
207Dic22—48no—
208C23×Q8—112no—
209C24×C4—111no—
210C2×C22⋊Q8—112no—
211C2×C22⋊Q8—112no—
212C2×C22⋊Q8—114no—
213C2×C22⋊Q8—112no—
214C2×C22⋊Q8—114no—
215C2×C22⋊Q8—2216no—
216C2×C22⋊Q8C2×D1112yes—
217C22×C4⋊C4—114no—
218C22×C4⋊C4—112no—
219C22×C4⋊C4—114no—
220C22×C22⋊C4—114no—
221C22×C22⋊C4—112no—
222#400—114no—
223#400—114no—
224#400—118no—
225#400—114no—
226#400—118no—
227#400C2×D1114yescomplemented
228#397—114no—
229#397—118no—
230#397—114no—
231#397—114no—
232#397—118no—
233#397C2×D1114yes—
234#395—114no—
235#395—118no—
236#395—114no—
237#395—118no—
238#395—114no—
239#395C2×D1114yescomplemented
240#381—111no—
241#381—112no—
242#381—114no—
243#381C2×D1111yescharacteristic
244C2×#95—118no—
245C2×#95—114no—
246C2×#95—114no—
247C22×C11—22no—
248C22×C11—24no—
249C22×C11—44no—
250C22×C11C23×D411yescharacteristic
251C22×C11C2×H(5,𝔽2)12yes—
252C22×C11C2×2−1+414yes—
253C2×D11—22no—
254C2×D11—24no—
255C2×D11—44no—
256C2×D11—416no—
257C2×D11#53414yes—
258C2×D11#53618yes—
259C2×D11#563116yes—
260C4×C11—24no—
261C4×C11—44no—
262C4×C11—44no—
263C4×C11—44no—
264Dic11—24no—
265Dic11—44no—
266Dic11—44no—
267Dic11—44no—
268C25—111no—
269C22×Q8—114no—
270C22×Q8—112no—
271C22×Q8—228no—
272C22×Q8—448no—
273C22×Q8C22×D1112yes—
274C23×C4—111no—
275C23×C4—112no—
276C23×C4—118no—
277C23×C4—112no—
278C23×C4—114no—
279C23×C4—114no—
280C23×C4—114no—
281C23×C4—444no—
282C23×C4C22×D1111yescharacteristic
283C22⋊Q8—28no—
284C22⋊Q8—2216no—
285C22⋊Q8—2216no—
286C22⋊Q8—228no—
287C22⋊Q8—228no—
288C22⋊Q8—228no—
289C2×C4⋊C4—114no—
290C2×C4⋊C4—114no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4—114no—
293C2×C4⋊C4—112no—
294C2×C4⋊C4—118no—
295C2×C4⋊C4—114no—
296C2×C4⋊C4—228no—
297C2×C4⋊C4—2216no—
298C2×C4⋊C4—448no—
299C2×C4⋊C4C22×D1114yes—
300C2×C4⋊C4C22×D1112yes—
301C2×C4⋊C4C22×D1114yes—
302C2×C22⋊C4—114no—
303C2×C22⋊C4—114no—
304C2×C22⋊C4—114no—
305C2×C22⋊C4—112no—
306C2×C22⋊C4—114no—
307C2×C22⋊C4—2216no—
308C2×C22⋊C4—444no—
309C2×C22⋊C4C22×D1114yes—
310C2×C22⋊C4C22×D1112yes—
311#95—118no—
312#95—114no—
313#95—118no—
314#95—118no—
315#95—118no—
316#95—118no—
317#95—114no—
318#95C22×D1114yes—
319#95C22×D1118yes—
320#95C22×D1114yes—
321C2×C11—42no—
322C2×C11C2×#53411yescharacteristic
323C2×C11C2×#53612yes—
324C2×C11C2×#56314yes—
325D11—42no—
326D11#281718yesdirect product factor
327C24—111no—
328C24—114no—
329C24—111no—
330C24—224no—
331C24—228no—
332C24C23×D1111yescharacteristic
333C2×Q8—24no—
334C2×Q8—44no—
335C2×Q8—228no—
336C2×Q8—224no—
337C2×Q8—444no—
338C2×Q8—448no—
339C2×Q8—4432no—
340C22×C4—42no—
341C22×C4—112no—
342C22×C4—114no—
343C22×C4—118no—
344C22×C4—118no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—114no—
348C22×C4—228no—
349C22×C4—228no—
350C22×C4—228no—
351C22×C4—228no—
352C22×C4—2216no—
353C22×C4—2216no—
354C22×C4—2216no—
355C22×C4—444no—
356C22×C4—4416no—
357C22×C4—442no—
358C22×C4D4×D1114yes—
359C22×C4C23×D1114yes—
360C22×C4C23×D1114yes—
361C22×C4C23×D1114yes—
362C22×C4C23×D1112yes—
363C4⋊C4—24no—
364C4⋊C4—28no—
365C4⋊C4—44no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—228no—
369C4⋊C4—228no—
370C4⋊C4—224no—
371C4⋊C4—448no—
372C4⋊C4—444no—
373C22⋊C4—28no—
374C22⋊C4—42no—
375C22⋊C4—228no—
376C22⋊C4—228no—
377C22⋊C4—228no—
378C22⋊C4—444no—
379C22⋊C4—442no—
380C11C2×#281711yescharacteristic, complemented, Sylow
381C23—22no—
382C23—24no—
383C23—112no—
384C23—114no—
385C23—118no—
386C23—112no—
387C23—228no—
388C23—2216no—
389C23—222no—
390C23—224no—
391C23—4416no—
392C23C2×D4×D1112yes—
393C23C24×D1111yescharacteristic
394Q8—48no—
395Q8—448no—
396Q8—4416no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—28no—
404C2×C4—44no—
405C2×C4—114no—
406C2×C4—2216no—
407C2×C4—224no—
408C2×C4—224no—
409C2×C4—224no—
410C2×C4—224no—
411C2×C4—228no—
412C2×C4—228no—
413C2×C4—228no—
414C2×C4—448no—
415C2×C4—4416no—
416C2×C4—4416no—
417C2×C4—4416no—
418C2×C4—444no—
419C2×C4C2×D4×D1114yes—
420C22—22no—
421C22—24no—
422C22—44no—
423C22—114no—
424C22—118no—
425C22—1116no—
426C22—222no—
427C22—224no—
428C22—4416no—
429C22—444no—
430C22C22×D4×D1111yescharacteristic
431C22D11×H(5,𝔽2)12yes—
432C22D11×2−1+414yes—
433C4—24no—
434C4—44no—
435C4—44no—
436C4—44no—
437C4—224no—
438C4—444no—
439C4—444no—
440C4—444no—
441C2—42no—
442C2—118no—
443C2—442no—
444C2D11×#53411yescharacteristic
445C2D11×#53612yes—
446C2D11×#56314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2817C2
prime radicalC24×D11C23
hypercenter#2817D11
hypocenterC11C2×#2817
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2817

Complements

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

NH ≅ G/Ntype
2. #13076654C2semidirect
3. #13076653C2semidirect
4. #13076652C2semidirect
5. #13076651C2semidirect
6. #13076650C2semidirect
7. D11×#400C2semidirect
9. D11×#395C2semidirect
11. C11×#2817C2semidirect
26. C11×#400C22semidirect
28. C11×#395C22semidirect
30. #10622842C22semidirect
33. #10622599C22semidirect
34. #10622595C22semidirect
35. #10622592C22semidirect
36. #10622592C22semidirect
46. #10622273C22semidirect
47. #10622272C22semidirect
48. #10622271C22semidirect
49. #10622269C22semidirect
50. #10622269C22semidirect
164. #2817D11direct (N × H)
227. #400C2×D11semidirect
239. #395C2×D11semidirect
326. D11#2817direct (N × H)
380. C11C2×#2817semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
#130766542
#130766532
#130766522
#130766512
#130766502
D11×#4002
D11×#3972
D11×#3952
D11×#3812
C11×#28172
C2×#281711