Finite Group Databasebeta

← Dic11×D4⋊C8 #14644367

Subgroups — Dic11×D4⋊C8 #14644367

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic11C211yesmaximal, characteristic
2C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
3C4×C8×Dic11C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×D4×Dic11C412yes—
10C22×C4×Dic11—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C4×C22⋊Dic11—21no—
14C2×C8×Dic11—22no—
15C2×C8×Dic11—21no—
16C4⋊C4×Dic11C412yes—
17C22⋊C4×Dic11—22no—
18C4×C4⋊Dic11C2211yescharacteristic
19C42×Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C11×D4⋊C8C414yescomplemented
23#10622188—21no—
24D4⋊(C11⋊C8)C414yescomplemented
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×Dic11—22no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—21no—
32C4×D4×C11C2×C412yes—
33C4×D4×C11C2×C412yes—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—22no—
38D4×Dic11—24no—
39D4×Dic11C818yescomplemented
40C2×C4⋊Dic11C2×C412yes—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—22no—
43C2×C4×Dic11—42no—
44C2×C4×Dic11—42no—
45C2×C4×Dic11C2×C412yes—
46C2×C4×Dic11D412yes—
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8C2×C412yescomplemented
53C4×C8×C11—21no—
54C4×C8×C11C2×C412yescomplemented
55C11⋊#95—21no—
56C11⋊#95—22no—
57C8×Dic11—28no—
58C8×Dic11—42no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)C2×C412yescomplemented
61C4×C11⋊C8—21no—
62C4×C11⋊C8C2×C412yescomplemented
63C4×D4⋊C8—111nomaximal, Sylow
64C24×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—22no—
67C2×D4×C11C4212yes—
68C2×D4×C11C2×C814yes—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—28no—
80C22×Dic11—22no—
81C22×Dic11—44no—
82C22×Dic11—44no—
83C22×Dic11C22⋊C412yes—
84C22×Dic11C22⋊C412yes—
85C2×C8×C11—24no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4C4212yes—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C42×C11C22×C411yescharacteristic
95C42×C11C22×C411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C22⋊Dic11—28no—
99C4⋊Dic11—22no—
100C4⋊Dic11C2×C814yes—
101C4×Dic11—24no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—44no—
105C4×Dic11—41no—
106C4×Dic11—41no—
107C4×Dic11C2×C814yes—
108C4×Dic11M1614yes—
109C4×Dic11D812yes—
110C4×Dic11SD1612yes—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C42×D4—111no—
117C4×C4⋊C8—111no—
118C42×C8—111no—
119C2×D4⋊C8—111no—
120C2×D4⋊C8D1111yescharacteristic
121#1279—111no—
122#1279—111no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—42no—
128C23×C11C2×C22⋊C411yescharacteristic
129D4×C11—22no—
130D4×C11—24no—
131D4×C11C4×C814yescomplemented
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11C2×C4211yescharacteristic
141C2×C4×C11#11711yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11C22×C812yes—
147C2×C4×C11C2×M1612yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×SD1611yescharacteristic
150C2×C4×C11#13511yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—24no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—416no—
158C2×Dic11C22⋊C814yes—
159C2×Dic11C22⋊C814yes—
160C2×Dic11#10214yes—
161C2×Dic11#10414yes—
162C8×C11—24no—
163C8×C11—42no—
164C11⋊C8—24no—
165C11⋊C8—42no—
166C2×C4×D4—112no—
167C2×C4×D4C2×D1111yescharacteristic
168C22×C42—221no—
169C2×C4⋊C8—111no—
170C2×C4⋊C8C2×D1111yescharacteristic
171C2×C4×C8—111no—
172C2×C4×C8—222no—
173C2×C4×C8—221no—
174C2×C4×C8C2×D1111yescharacteristic
175C4×C4⋊C4—112no—
176C4×C4⋊C4—111no—
177C4×C22⋊C4—222no—
178C4×C22⋊C4—221no—
179C43—111no—
180#336—221no—
181D4⋊C8—114no—
182D4⋊C8Dic1114yesdirect product factor
183C22×C11—24no—
184C22×C11—44no—
185C22×C11—44no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11C4×C22⋊C411yescharacteristic
189C22×C11C2×C22⋊C812yes—
190C22×C11C2×#10211yescharacteristic
191C22×C11#41611yescharacteristic
192C22×C11C2×#10412yes—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—42no—
196C4×C11C2×C4×C811yescharacteristic
197C4×C11C4×M1611yescharacteristic
198C4×C11#43112yes—
199C4×C11C4×D811yescharacteristic
200C4×C11C4×D811yescharacteristic
201C4×C11C4×SD1611yescharacteristic
202C4×C11C4×SD1611yescharacteristic
203Dic11—24no—
204Dic11—44no—
205Dic11D4⋊C818yesdirect product factor
206C22×D4C4×D1111yescharacteristic
207C23×C4—21no—
208C23×C4—222no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—221no—
212C22×C8—221no—
213C4×D4—21no—
214C4×D4—21no—
215C4×D4—118no—
216C4×D4—224no—
217C4×D4C4×D1112yes—
218C4×D4C2×Dic1112yes—
219C2×C4⋊C4—112no—
220C2×C4⋊C4C4×D1111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—222no—
223C2×C42—112no—
224C2×C42—111no—
225C2×C42—112no—
226C2×C42—111no—
227C2×C42—222no—
228C2×C42—221no—
229C2×C42—442no—
230C2×C42—442no—
231C2×C42C22×D1111yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—112no—
234C4⋊C8—221no—
235C4⋊C8C2×Dic1112yescomplemented
236C4×C8—21no—
237C4×C8—112no—
238C4×C8—228no—
239C4×C8—221no—
240C4×C8—442no—
241C4×C8C2×Dic1112yescomplemented
242#95—222no—
243#95—221no—
244C2×C11—44no—
245C2×C11C2×D4⋊C812yes—
246C2×C11#147612yes—
247C2×C11C4×C22⋊C811yescharacteristic
248C2×C11C4×#10411yescharacteristic
249C2×C11C4×#10211yescharacteristic
250C24—21no—
251C2×D4—21no—
252C2×D4—22no—
253C2×D4C8×D1114yes—
254C2×D4C4×Dic1112yes—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—112no—
263C22×C4—112no—
264C22×C4—228no—
265C22×C4—222no—
266C22×C4—444no—
267C22×C4—444no—
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C2×C8—24no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—224no—
277C2×C8—222no—
278C2×C8—222no—
279C2×C8—441no—
280C2×C8—441no—
281C4⋊C4—21no—
282C4⋊C4—114no—
283C4⋊C4—222no—
284C4⋊C4C4×Dic1112yes—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—228no—
288C42—114no—
289C42—114no—
290C42—112no—
291C42—112no—
292C42—224no—
293C42—221no—
294C42—221no—
295C42—444no—
296C42—441no—
297C42—441no—
298C42C2×C4×D1111yescharacteristic
299C42#434111yescharacteristic
300C42#434111yescharacteristic
301C42C22×Dic1111yescharacteristic
302C11C4×D4⋊C811yescharacteristic, complemented, Sylow
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—42no—
308C23C22⋊C4×D1111yescharacteristic
309D4—22no—
310D4—24no—
311D4C8×Dic1114yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—114no—
321C2×C4—114no—
322C2×C4—114no—
323C2×C4—114no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—224no—
327C2×C4—4416no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4#6693011yescharacteristic
331C2×C4(C22⋊D11)⋊C411yescharacteristic
332C2×C4(C22⋊D11)⋊C411yescharacteristic
333C2×C4C2×C8×D1112yes—
334C2×C4M16×D1112yes—
335C2×C4D8×D1111yescharacteristic
336C2×C4#6696511yescharacteristic
337C2×C4SD16×D1111yescharacteristic
338C2×C4#6696911yescharacteristic
339C2×C4C2×C4×Dic1111yescharacteristic
340C2×C4D4×Dic1111yescharacteristic
341C2×C4D4×Dic1111yescharacteristic
342C8—24no—
343C8—42no—
344C8—224no—
345C8—442no—
346C22—24no—
347C22—42no—
348C22—42no—
349C22—44no—
350C22—44no—
351C22D11×C22⋊C812yes—
352C22D11×#10211yescharacteristic
353C22#1062238511yescharacteristic
354C22D11×#10412yes—
355C22C22⋊C4×Dic1111yescharacteristic
356C4—21no—
357C4—21no—
358C4—42no—
359C4—118no—
360C4—224no—
361C4—444no—
362C4#1062233112yes—
363C4#1062236911yescharacteristic
364C4#1062237111yescharacteristic
365C4C2×C8×Dic1111yescharacteristic
366C4M16×Dic1111yescharacteristic
367C4D8×Dic1111yescharacteristic
368C4SD16×Dic1111yescharacteristic
369C2—44no—
370C2D11×D4⋊C812yes—
371C2#1306699512yes—
372C2C22⋊C8×Dic1111yescharacteristic
373C2#104×Dic1111yescharacteristic
374C2#102×Dic1111yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C2×C4×C8
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×D4⋊C8D11
hypocenterC11C4×D4⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×Dic11C2semidirect
3. C4×C8×Dic11C2semidirect
5. #13066456C2semidirect
6. #13066455C2semidirect
22. C11×D4⋊C8C4semidirect
24. D4⋊(C11⋊C8)C4semidirect
39. D4×Dic11C8semidirect
52. C11×C4⋊C8C2×C4semidirect
54. C4×C8×C11C2×C4semidirect
60. C4⋊(C11⋊C8)C2×C4semidirect
62. C4×C11⋊C8C2×C4semidirect
131. D4×C11C4×C8semidirect
182. D4⋊C8Dic11direct (N × H)
205. Dic11D4⋊C8direct (N × H)
235. C4⋊C8C2×Dic11semidirect
241. C4×C8C2×Dic11semidirect
302. C11C4×D4⋊C8semidirect
311. D4C8×Dic11semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic112
C4⋊C8×Dic112
C4×C8×Dic112
C2×D4⋊(C11⋊C8)2
#130664562
#130664552
C2×C11×D4⋊C82
C4×D4⋊C811