Finite Group Databasebeta

← Dic11×#424 #14751663

Subgroups — Dic11×#424 #14751663

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622612C211yesmaximal, characteristic
2C2×M16×Dic11C211yesmaximal, characteristic
3C22×C8×Dic11C211yesmaximal, characteristic
4#117×Dic11C211yesmaximal, characteristic
5#13068475C214yesmaximal, complemented
6C4⋊C8×Dic11C214yesmaximal, complemented
7#13068314C211yesmaximal, characteristic
8#13068312C211yesmaximal, characteristic
9C2×C11×#424C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#424C418yescomplemented
18C2×C11×C4⋊C8C2214yes—
19M16×Dic11—24no—
20C2×#66879C2212yes—
21C2×C8×Dic11—24no—
22C2×C8×Dic11C2212yes—
23C2×C8×Dic11C2212yes—
24C2×C8×Dic11C2212yes—
25#10622612C418yescomplemented
26C4⋊C4×Dic11C414yes—
27C22⋊C4×Dic11C414yes—
28#10622545C2212yes—
29C42×Dic11C2212yes—
30C2×C4⋊(C11⋊C8)C2214yes—
31#10622188C2214yes—
32#10622188C2214yes—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11C2×C412yes—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16C2×C414yes—
38C22×C8×C11—22no—
39C22×C8×C11—22no—
40C22×C8×C11C2×C414yes—
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C11×#117C2×C414yes—
44C11×#117C2×C414yes—
45C2×C11×C4⋊C4C2×C412yes—
46C2×C11×C22⋊C4C2×C412yes—
47C2×C42×C11C2312yes—
48C2×C22⋊Dic11C2×C412yes—
49#66979—22no—
50#66979—22no—
51C2×C4⋊Dic11C2×C412yes—
52C2×C4×Dic11C2×C418yes—
53C2×C4×Dic11C2×C412yes—
54C2×C4×Dic11D414yes—
55C2×C4×Dic11Q814yes—
56C2×C4×Dic11C2312yes—
57C2×C4×Dic11C2311yescharacteristic
58C2×C4×Dic11C2311yescharacteristic
59C2×#4318—22no—
60C2×#4318—22no—
61C2×#4318C2×C414yes—
62C22×C11⋊C8—22no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8C2×C414yes—
65C22×C11⋊C8C2312yes—
66C22×C11⋊C8C2312yes—
67C11×C4⋊C8C2×C4116yescomplemented
68C11⋊#95C2×C418yes—
69#66879—24no—
70C8×Dic11—24no—
71C8×Dic11—24no—
72C8×Dic11—24no—
73C4⋊(C11⋊C8)C2×C4116yescomplemented
74C4×#424—111nomaximal, Sylow
75C24×C11C22×C411yescharacteristic
76C22×C4×C11C22×C414yes—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C22×C412yes—
79C22×C4×C11C22×C412yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×Q812yes—
82C22×C4×C11#4112yes—
83C22×C4×C11#4112yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—28no—
86C22×Dic11C4⋊C418yes—
87C22×Dic11C22×C414yes—
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C412yes—
90C11×M16—28no—
91C2×C8×C11—28no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11C22×C414yes—
97C2×C8×C11C22×C414yes—
98C11×C4⋊C4C4218yes—
99C11×C22⋊C4C4218yes—
100C42×C11C22×C414yes—
101C42×C11C22×C414yes—
102C22⋊Dic11—24no—
103C4⋊Dic11—24no—
104C4×Dic11—216no—
105C4×Dic11—22no—
106C4×Dic11—22no—
107C4×Dic11C4⋊C418yes—
108C4×Dic11C2×D412yes—
109C4×Dic11C2×D412yes—
110C4×Dic11C2×Q812yes—
111C4×Dic11C2×Q812yes—
112#4318—28no—
113C2×C11⋊C8—28no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118C2×C11⋊C8C22×C414yes—
119C2×C11⋊C8C22×C414yes—
120C2×#424—111no—
121C2×#424D1111yescharacteristic
122C2×C4×M16—111no—
123C22×C4×C8—111no—
124C4×#117—111no—
125#1768—114no—
126C4×C4⋊C8—114no—
127#1729—111no—
128#1729—111no—
129C23×C11—24no—
130C23×C11C2×C4212yes—
131C23×C11C2×C4⋊C412yes—
132C23×C11#11712yes—
133C23×C11C23×C411yescharacteristic
134C2×C4×C11—28no—
135C2×C4×C11C2×C4218yes—
136C2×C4×C11C2×C4212yes—
137C2×C4×C11C2×C4⋊C412yes—
138C2×C4×C11#11712yes—
139C2×C4×C11C4×D414yes—
140C2×C4×C11C4×D414yes—
141C2×C4×C11C4×Q814yes—
142C2×C4×C11C4×Q814yes—
143C2×C4×C11C23×C411yescharacteristic
144C2×C4×C11C23×C411yescharacteristic
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×Q811yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×C4×C11C2×#4111yescharacteristic
149C2×Dic11—24no—
150C2×Dic11—216no—
151C2×Dic11—24no—
152C2×Dic11—28no—
153C2×Dic11C2×C4⋊C414yes—
154C2×Dic11C2×C4⋊C414yes—
155C2×Dic11#13118yes—
156C8×C11—24no—
157C8×C11—24no—
158C11⋊C8—24no—
159C11⋊C8—24no—
160C22×M16—111no—
161C22×M16C2×D1111yescharacteristic
162C23×C8—111no—
163C23×C8C2×D1111yescharacteristic
164C2×#117—111no—
165C2×#117C2×D1111yescharacteristic
166C22×C42—111no—
167#424—118no—
168#424Dic1118yesdirect product factor
169C2×C4⋊C8—114no—
170C2×C4⋊C8C2×D1114yes—
171C4×M16—224no—
172C2×#97—112no—
173C2×C4×C8—112no—
174C2×C4×C8—112no—
175C2×C4×C8—112no—
176C2×C4×C8—224no—
177C4×C4⋊C4—114no—
178C4×C22⋊C4—114no—
179#376—112no—
180C43—112no—
181#336—114no—
182#336—114no—
183C22×C11—24no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11C4×C4⋊C414yes—
187C22×C11C22×C4211yescharacteristic
188C22×C11C22×C4⋊C411yescharacteristic
189C22×C11C2×#11711yescharacteristic
190C22×C11C2×#13114yes—
191C4×C11—28no—
192C4×C11C4×C4⋊C414yes—
193C4×C11C2×C4×D411yescharacteristic
194C4×C11C2×C4×D411yescharacteristic
195C4×C11C2×C4×Q811yescharacteristic
196C4×C11C2×C4×Q811yescharacteristic
197Dic11—24no—
198Dic11—44no—
199Dic11#42418yesdirect product factor
200C23×C4—112no—
201C23×C4C22×D1111yescharacteristic
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—114no—
205C2×M16—222no—
206C2×M16—222no—
207C2×M16C2×Dic1114yes—
208C22×C8—22no—
209C22×C8—22no—
210C22×C8—114no—
211C22×C8—112no—
212C22×C8—112no—
213C22×C8—222no—
214C22×C8—222no—
215C22×C8C2×Dic1114yes—
216C22×C8C22×D1112yes—
217C22×C8C22×D1112yes—
218#117—222no—
219#117—222no—
220#117C4×D1114yes—
221#117C2×Dic1114yes—
222C2×C4⋊C4—112no—
223C2×C4⋊C4C4×D1112yes—
224C2×C22⋊C4—112no—
225C2×C22⋊C4C4×D1112yes—
226C2×C42—112no—
227C2×C42—114no—
228C2×C42—114no—
229C2×C42—111no—
230C2×C42—111no—
231C2×C42—118no—
232C2×C42—112no—
233C2×C42C22×D1112yes—
234C4⋊C8—1116no—
235C4⋊C8C2×Dic11116yescomplemented
236#97—224no—
237C4×C8—224no—
238C4×C8—224no—
239C4×C8—224no—
240#95—118no—
241C2×C11—24no—
242C2×C11C2×C4×C4⋊C411yescharacteristic
243C2×C11C4×#13112yes—
244C2×C11C2×#42412yes—
245C2×C11#292212yes—
246C24C2×C4×D1111yescharacteristic
247C22×C4—112no—
248C22×C4—118no—
249C22×C4—112no—
250C22×C4—114no—
251C22×C4—228no—
252C22×C4C2×C4×D1114yes—
253C22×C4C2×C4×D1112yes—
254C22×C4C2×C4×D1111yescharacteristic
255C22×C4D4×D1112yes—
256C22×C4#434112yes—
257C22×C4Q8×D1112yes—
258C22×C4#434312yes—
259C22×C4C22×Dic1112yes—
260C22×C4C23×D1111yescharacteristic
261M16—28no—
262M16—228no—
263C2×C8—28no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—114no—
269C2×C8—114no—
270C2×C8—228no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8C22×Dic1114yes—
276C2×C8C22×Dic1114yes—
277C4⋊C4—224no—
278C4⋊C4C4×Dic1118yes—
279C22⋊C4—224no—
280C22⋊C4C4×Dic1118yes—
281C42—118no—
282C42—112no—
283C42—112no—
284C42—112no—
285C42—112no—
286C42—2216no—
287C42—222no—
288C42—222no—
289C42C2×C4×D1114yes—
290C42C22×Dic1114yes—
291C11C4×#42411yescharacteristic, complemented, Sylow
292C23—24no—
293C23C4⋊C4×D1112yes—
294C23#6694512yes—
295C23C2×C4×Dic1112yes—
296C23C22×C4×D1111yescharacteristic
297C2×C4—28no—
298C2×C4—118no—
299C2×C4—114no—
300C2×C4—114no—
301C2×C4—2216no—
302C2×C4—224no—
303C2×C4—228no—
304C2×C4—224no—
305C2×C4#6694014yes—
306C2×C4C4⋊C4×D1112yes—
307C2×C4#6694512yes—
308C2×C4#6694614yes—
309C2×C4C2×C4×Dic1118yes—
310C2×C4C2×C4×Dic1112yes—
311C2×C4D4×Dic1114yes—
312C2×C4Q8×Dic1114yes—
313C2×C4C22×C4×D1111yescharacteristic
314C2×C4C2×D4×D1111yescharacteristic
315C2×C4C2×#434111yescharacteristic
316C2×C4C2×Q8×D1111yescharacteristic
317C2×C4C2×#434311yescharacteristic
318C2×C4C23×Dic1111yescharacteristic
319C8—24no—
320C8—24no—
321C8—224no—
322C8—224no—
323C22—24no—
324C22—24no—
325C22—24no—
326C22C4⋊C4×Dic1114yes—
327C22C2×C4⋊C4×D1111yescharacteristic
328C22C2×#6694511yescharacteristic
329C22D11×#13114yes—
330C22C22×C4×Dic1111yescharacteristic
331C4—28no—
332C4—118no—
333C4—224no—
334C4—444no—
335C4C4⋊C4×Dic1114yes—
336C4C2×#6694011yescharacteristic
337C4C2×#6694611yescharacteristic
338C4C2×D4×Dic1111yescharacteristic
339C4C2×Q8×Dic1111yescharacteristic
340C2—24no—
341C2C2×C4⋊C4×Dic1111yescharacteristic
342C2#131×Dic1112yes—
343C2D11×#42412yes—
344C2#1307725912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC2×C11×#424C2
socleC23×C11C23×C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11C4×#424
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
5. #13068475C2semidirect
6. C4⋊C8×Dic11C2semidirect
17. C11×#424C4semidirect
25. #10622612C4semidirect
67. C11×C4⋊C8C2×C4semidirect
73. C4⋊(C11⋊C8)C2×C4semidirect
168. #424Dic11direct (N × H)
199. Dic11#424direct (N × H)
235. C4⋊C8C2×Dic11semidirect
291. C11C4×#424semidirect

Maximal subgroups

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

subgroupindex
C2×#106226122
C2×M16×Dic112
C22×C8×Dic112
#117×Dic112
#130684752
C4⋊C8×Dic112
#130683142
#130683122
C2×C11×#4242
C4×#42411