Finite Group Databasebeta

← C2×#125×Dic11 #14912265

Subgroups — C2×#125×Dic11 #14912265

Order 2816.

2622 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×Dic11C2116yesmaximal, direct product factor
2C2×#10622598C212yesmaximal
3C2×#10622594C214yesmaximal
4C2×#10622549C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C214yesmaximal
6C2×C4⋊C4×Dic11C212yesmaximal
7C2×C42×Dic11C211yesmaximal, characteristic
8C22×C11×#125C211yesmaximal, characteristic
9C2×C11×#125C4116yescomplemented
10C2×C11×#125C2218yes—
11C22×C11×C4⋊C4C2214yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2212yes—
15C22×C4⋊Dic11C2214yes—
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2214yes—
20C22×C4×Dic11C2211yescharacteristic
21C2×C11⋊#95C2214yes—
22C2×C11⋊#95C2214yes—
23C2×C11⋊#95C2214yes—
24#10622598C22116yes—
25#10622594C22132yes—
26C4⋊C4×Dic11C22132yes—
27C4⋊C4×Dic11C22116yes—
28#10622549C2218yes—
29C42×Dic11C2218yes—
30C23×C4×C11C2312yes—
31C23×C4×C11C2314yes—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11C2314yes—
34C23×Dic11C2311yescharacteristic
35C23×Dic11C2312yes—
36C23×Dic11C2311yescharacteristic
37C11×#125C2×C4164yescomplemented
38C2×C11×C4⋊C4C2×C4132yes—
39C2×C11×C4⋊C4C2×C4116yes—
40C2×C11×C4⋊C4C23116yes—
41C2×C11×C4⋊C4C2318yes—
42C2×C42×C11C2×C418yes—
43C2×C42×C11C2314yes—
44C2×C4⋊Dic11—28no—
45C2×C4⋊Dic11—216no—
46C2×C4⋊Dic11C2318yes—
47C2×C4⋊Dic11C23116yes—
48C2×C4×Dic11—24no—
49C2×C4×Dic11—28no—
50C2×C4×Dic11—28no—
51C2×C4×Dic11—216no—
52C2×C4×Dic11Q818yes—
53C2×C4×Dic11C2318yes—
54C2×C4×Dic11C2318yes—
55C2×C4×Dic11C2314yes—
56C2×C4×Dic11C23116yes—
57C2×C4×Dic11C2314yes—
58C11⋊#95C23116yes—
59C11⋊#95C23116yes—
60C11⋊#95C23116yes—
61C2×C4×#125—111nomaximal, Sylow
62C24×C11C2411yescharacteristic
63C22×C4×C11—24no—
64C22×C4×C11—28no—
65C22×C4×C11—24no—
66C22×C4×C11—28no—
67C22×C4×C11C22×C418yes—
68C22×C4×C11C22×C4116yes—
69C22×C4×C11C22×C414yes—
70C22×C4×C11C2×Q814yes—
71C22×C4×C11#4114yes—
72C22×C4×C11C2414yes—
73C22×C4×C11C2418yes—
74C22×C4×C11C2412yes—
75C22×Dic11—24no—
76C22×Dic11—24no—
77C22×Dic11—24no—
78C22×Dic11—28no—
79C22×Dic11—28no—
80C22×Dic11—28no—
81C22×Dic11C2×Q814yes—
82C22×Dic11C2×Q814yes—
83C22×Dic11#4118yes—
84C22×Dic11#4118yes—
85C22×Dic11C2418yes—
86C22×Dic11C2412yes—
87C22×Dic11C2414yes—
88C22×Dic11C2412yes—
89C11×C4⋊C4C22×C4164yes—
90C11×C4⋊C4C22×C4132yes—
91C42×C11C22×C4116yes—
92C4⋊Dic11—232no—
93C4⋊Dic11—216no—
94C4×Dic11—216no—
95C4×Dic11—216no—
96C4×Dic11—232no—
97C4×Dic11—28no—
98C4×Dic11C2×Q8116yes—
99C22×#125D1111yescharacteristic
100C4×#125—1116no—
101C2×#389—112no—
102C2×#387—114no—
103C2×#382—111no—
104C2×C4×C4⋊C4—112no—
105C2×C4×C4⋊C4—114no—
106C2×C43—111no—
107C23×C11C23×C412yes—
108C23×C11C22×Q812yes—
109C23×C11C2×#4112yes—
110C23×C11C2×#4114yes—
111C23×C11C2×#4114yes—
112C23×C11C2511yescharacteristic
113C2×C4×C11—216no—
114C2×C4×C11—232no—
115C2×C4×C11—24no—
116C2×C4×C11—28no—
117C2×C4×C11—24no—
118C2×C4×C11—28no—
119C2×C4×C11C4×Q8116yes—
120C2×C4×C11C23×C418yes—
121C2×C4×C11C23×C4116yes—
122C2×C4×C11C23×C414yes—
123C2×C4×C11C22×Q814yes—
124C2×C4×C11C2×#4114yes—
125C2×Dic11—216no—
126C2×Dic11—28no—
127C2×Dic11—24no—
128C2×Dic11—24no—
129C2×Dic11—24no—
130C2×Dic11—28no—
131C2×Dic11—28no—
132C2×Dic11—28no—
133C2×Dic11—416no—
134C2×Dic11#125116yesdirect product factor
135C2×Dic11C22×Q814yes—
136C2×Dic11C22×Q814yes—
137C2×Dic11C2×#4118yes—
138C2×Dic11C2×#4118yes—
139C2×#125Dic11116yesdirect product factor
140C2×#125C2×D1118yes—
141C22×C4⋊C4—112no—
142C22×C4⋊C4—114no—
143C22×C4⋊C4C2×D1114yes—
144C22×C4⋊C4C2×D1112yes—
145C22×C42—111no—
146C22×C42—112no—
147C22×C42—112no—
148C22×C42—111no—
149C22×C42—114no—
150C22×C42C2×D1111yescharacteristic
151#389—1116no—
152#387—1132no—
153#382—118no—
154C4×C4⋊C4—1132no—
155C4×C4⋊C4—1116no—
156C2×#95—114no—
157C2×#95—114no—
158C2×#95—114no—
159C43—118no—
160C22×C11C2×C4×Q814yes—
161C22×C11C4×#4118yes—
162C22×C11C2×#12514yes—
163C22×C11#52918yes—
164C22×C11#53314yes—
165C22×C11C24×C411yescharacteristic
166C22×C11C23×Q811yescharacteristic
167C22×C11C22×#4111yescharacteristic
168C22×C11C22×#4112yes—
169C22×C11C22×#4112yes—
170C4×C11—28no—
171C4×C11—216no—
172C4×C11C2×C4×Q818yes—
173Dic11—28no—
174Dic11—24no—
175Dic11—48no—
176Dic11C2×#12518yesdirect product factor
177C23×C4—111no—
178C23×C4—112no—
179C23×C4—111no—
180C23×C4—114no—
181C23×C4C22×D1114yes—
182C23×C4C22×D1112yes—
183C23×C4C22×D1111yescharacteristic
184#125C2×Dic11164yesdirect product factor
185C2×C4⋊C4—118no—
186C2×C4⋊C4—1116no—
187C2×C4⋊C4—2216no—
188C2×C4⋊C4—228no—
189C2×C4⋊C4C2×Dic11132yes—
190C2×C4⋊C4C2×Dic11116yes—
191C2×C4⋊C4C22×D11116yes—
192C2×C4⋊C4C22×D1118yes—
193C2×C42—118no—
194C2×C42—114no—
195C2×C42—118no—
196C2×C42—118no—
197C2×C42—114no—
198C2×C42—1116no—
199C2×C42—228no—
200C2×C42—2216no—
201C2×C42—228no—
202C2×C42—224no—
203C2×C42C2×Dic1118yes—
204C2×C42C22×D1114yes—
205#95—1116no—
206#95—1116no—
207#95—1116no—
208C2×C11C4×#12518yescomplemented
209C2×C11C22×C4×Q811yescharacteristic
210C2×C11C2×C4×#4112yes—
211C2×C11C22×#12511yescharacteristic
212C2×C11C2×#52912yes—
213C2×C11C2×#53311yescharacteristic
214C24C23×D1111yescharacteristic
215C22×C4—28no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—28no—
219C22×C4—114no—
220C22×C4—118no—
221C22×C4—112no—
222C22×C4—114no—
223C22×C4—118no—
224C22×C4—112no—
225C22×C4—114no—
226C22×C4—118no—
227C22×C4—224no—
228C22×C4—224no—
229C22×C4—224no—
230C22×C4—228no—
231C22×C4—228no—
232C22×C4—228no—
233C22×C4Q8×D1114yes—
234C22×C4#434314yes—
235C22×C4C22×Dic1118yes—
236C22×C4C22×Dic11116yes—
237C22×C4C22×Dic1114yes—
238C22×C4C23×D1114yes—
239C22×C4C23×D1118yes—
240C22×C4C23×D1112yes—
241C4⋊C4—2232no—
242C4⋊C4—2216no—
243C4⋊C4C22×Dic11164yes—
244C4⋊C4C22×Dic11132yes—
245C42—1116no—
246C42—2216no—
247C42—2232no—
248C42—2216no—
249C42—228no—
250C42C22×Dic11116yes—
251C11C2×C4×#12511yescharacteristic, complemented, Sylow
252C23C2×Q8×D1112yes—
253C23C2×#434312yes—
254C23#41×D1114yes—
255C23#41×D1114yes—
256C23C23×Dic1112yes—
257C23C24×D1111yescharacteristic
258C2×C4—216no—
259C2×C4—232no—
260C2×C4—24no—
261C2×C4—28no—
262C2×C4—24no—
263C2×C4—28no—
264C2×C4—114no—
265C2×C4—118no—
266C2×C4—1116no—
267C2×C4—114no—
268C2×C4—118no—
269C2×C4—224no—
270C2×C4—224no—
271C2×C4—224no—
272C2×C4—228no—
273C2×C4—2216no—
274C2×C4—228no—
275C2×C4—228no—
276C2×C4—228no—
277C2×C4—4416no—
278C2×C4Q8×Dic11116yes—
279C2×C4C2×Q8×D1114yes—
280C2×C4C2×#434314yes—
281C2×C4C23×Dic1118yes—
282C2×C4C23×Dic11116yes—
283C2×C4C23×Dic1114yes—
284C22D11×#12514yes—
285C22#1062321914yes—
286C22#1062322218yes—
287C22C2×Q8×Dic1114yes—
288C22#41×Dic1118yes—
289C22C22×Q8×D1111yescharacteristic
290C22C22×#434311yescharacteristic
291C22C2×#41×D1112yes—
292C22C2×#41×D1112yes—
293C22C24×Dic1111yescharacteristic
294C4—28no—
295C4—216no—
296C4—118no—
297C4—228no—
298C4—224no—
299C4—448no—
300C4C2×Q8×Dic1118yes—
301C2#125×Dic1118yesdirect product factor
302C2C22×Q8×Dic1111yescharacteristic
303C2C2×#41×Dic1112yes—
304C2C2×D11×#12511yescharacteristic
305C2C2×#1062322212yes—
306C2C2×#1062321911yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C11×#125C2
socle, prime radicalC24×C11C24
cosocleC23×C11C25
hypercenterC22×#125D11
hypocenterC11C2×C4×#125
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #125×Dic11C2direct (N × H)
9. C2×C11×#125C4semidirect
37. C11×#125C2×C4semidirect
134. C2×Dic11#125direct (N × H)
139. C2×#125Dic11direct (N × H)
176. Dic11C2×#125direct (N × H)
184. #125C2×Dic11direct (N × H)
208. C2×C11C4×#125semidirect
251. C11C2×C4×#125semidirect
301. C2#125×Dic11direct (N × H)

Maximal subgroups

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

subgroupindex
#125×Dic112
C2×#106225982
C2×#106225942
C2×#106225492
C2×C4⋊C4×Dic112
C2×C42×Dic112
C22×C11×#1252
C2×C4×#12511