Finite Group Databasebeta

← C2×D11×#519 #15660355

Subgroups — C2×D11×#519 #15660355

Order 2816.

11230 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D11C211yesmaximal, characteristic
2C2×#10623343C211yesmaximal, characteristic, complemented
3C2×#10623047C216yesmaximal, complemented
4C2×#10623103C218yesmaximal, complemented
5D11×#519C2132yesmaximal, direct product factor
6C2×C4×Q8×D11C218yesmaximal, complemented
7C2×D11×#117C216yesmaximal
8C2×C11×#519C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×Q8×D11C4132yescomplemented
11C22×Q8×D11C2214yes—
12C22×Q8×D11C22116yes—
13C22×Q8×D11C2214yes—
14C23×C4×D11C2213yes—
15C23×Dic22C2213yes—
16C11×#519C22116yescomplemented
17C2×C4×Q8×C11C2218yescomplemented
18C2×C11×#117C2216yes—
19#10623343C22116yescomplemented
20C2×Q8×Dic11C2218yescomplemented
21C2×#66979C2216yes—
22#10623103C221128yescomplemented
23C4×Q8×D11C221128yescomplemented
24D11×#117C22196yes—
25#10623047C22196yescomplemented
26C2×#66945C22112yes—
27C2×C4⋊C4×D11C22112yes—
28C2×#66940C22124yescomplemented
29C2×C22⋊C4×D11C2214yes—
30C2×#66930C22112yes—
31C2×#66925C22112yes—
32C2×C42×D11C22112yes—
33C2×C4×Dic22C22124yescomplemented
34C24×D11C2311yescharacteristic
35C22×Q8×C11C2×C4116yescomplemented
36C22×Q8×C11C2314yes—
37C22×Q8×C11C2318yes—
38C23×C4×C11C2313yes—
39C23×Dic11C2313yes—
40C2×Q8×D11C2×C4164yes—
41C2×Q8×D11C2×C4164yescomplemented
42C2×Q8×D11C2×C41256yescomplemented
43C2×Q8×D11C23132yes—
44C2×Q8×D11C23132yes—
45C22×C4×D11C2×C4148yes—
46C22×C4×D11C2318yes—
47C22×C4×D11C2316yes—
48C22×C4×D11C2316yes—
49C22×C4×D11C23124yes—
50C22×Dic22C2×C4148yescomplemented
51C22×Dic22C23112yes—
52C22×Dic22C23124yes—
53C4×Q8×C11C23164yescomplemented
54C11×#117C23148yes—
55C2×C11×C4⋊C4C23112yes—
56C2×C11×C22⋊C4C2314yes—
57C2×C42×C11C23112yes—
58C2×C22⋊Dic11C2314yes—
59Q8×Dic11C23164yescomplemented
60C2×(C2×D11)⋊C4C2318yes—
61#66979C23148yes—
62C2×C4⋊Dic11C23112yes—
63C2×Dic11⋊C4C23124yes—
64C2×C4×Dic11C23124yes—
65C2×C4×Dic11C23112yes—
66#66945C23196yes—
67C4⋊C4×D11C23196yes—
68#66940C231192yescomplemented
69C22⋊C4×D11C23132yes—
70#66930C23196yes—
71#66925C23196yes—
72C42×D11C23196yes—
73C4×Dic22C231192yescomplemented
74C22×#519—111nomaximal, Sylow
75C24×C11C2411yescharacteristic
76C23×D11—28no—
77C23×D11C22×C418yes—
78C23×D11C2414yes—
79C23×D11C2411yescharacteristic
80C23×D11C2411yescharacteristic
81C2×Q8×C11C22×C4132yes—
82C2×Q8×C11C22×C4164yescomplemented
83C2×Q8×C11C24116yes—
84C22×C4×C11C22×C4124yes—
85C22×C4×C11C2418yes—
86C22×C4×C11C2416yes—
87C22×C4×C11C24112yes—
88C22×Dic11C22×C4124yes—
89C22×Dic11C2418yes—
90C22×Dic11C24112yes—
91C22×Dic11C2416yes—
92Q8×D11C22×C41256yes—
93Q8×D11C22×C41256yescomplemented
94C2×C4×D11—232no—
95C2×C4×D11C22×C4148yes—
96C2×C4×D11C22×C4148yes—
97C2×C4×D11C22×C41192yes—
98C2×C4×D11C24132yes—
99C2×C4×D11C24124yes—
100C2×C4×D11C24124yes—
101C2×Dic22C22×C4196yes—
102C2×Dic22C22×C41192yescomplemented
103C2×Dic22C24148yes—
104C11×C4⋊C4C24148yes—
105C11×C22⋊C4C24116yes—
106C42×C11C24148yes—
107C22⋊Dic11C24116yes—
108(C2×D11)⋊C4C24132yes—
109C4⋊Dic11C24148yes—
110Dic11⋊C4C24196yes—
111C4×Dic11C24196yes—
112C4×Dic11C24148yes—
113C24×Q8—111no—
114C2×#519—111no—
115C2×#519—1132no—
116C2×#519—118no—
117C2×#519—116no—
118C2×#519D1111yescharacteristic, direct product factor
119C22×C4×Q8—118no—
120C22×#117—116no—
121C23×C11—24no—
122C23×C11C23×C414yes—
123C23×C11C2512yes—
124C23×C11C2511yescharacteristic
125C22×D11—24no—
126C22×D11—232no—
127C22×D11—216no—
128C22×D11C23×C414yes—
129C22×D11C23×C4116yes—
130C22×D11C23×C414yes—
131C22×D112−1+418yes—
132C22×D11C2512yes—
133C22×D11C2512yes—
134Q8×C11C23×C4164yes—
135C2×C4×C11—216no—
136C2×C4×C11C23×C4124yes—
137C2×C4×C11C23×C4148yes—
138C2×C4×C11C25116yes—
139C2×C4×C11C25112yes—
140C2×Dic11—216no—
141C2×Dic11C23×C4124yes—
142C2×Dic11C23×C4148yes—
143C2×Dic11C25116yes—
144C2×Dic11C25112yes—
145C4×D11—264no—
146C4×D11C23×C4196yes—
147C4×D11C23×C4196yes—
148Dic22C23×C41192yes—
149C23×Q8—114no—
150C23×Q8—114no—
151C23×Q8—1116no—
152C23×Q8—1132no—
153C23×Q8—113no—
154C23×Q8C2×D1111yescharacteristic
155C24×C4—113no—
156#519—1116no—
157#519—11128no—
158#519—1196no—
159#519C2×D11116yesdirect product factor
160C2×C4×Q8—118no—
161C2×C4×Q8—11128no—
162C2×C4×Q8—1124no—
163C2×C4×Q8—1124no—
164C2×C4×Q8C2×D1118yescomplemented
165C2×#117—116no—
166C2×#117—1196no—
167C2×#117—1112no—
168C2×#117—1112no—
169C2×#117—1112no—
170C2×#117C2×D1116yes—
171C22×C4⋊C4—1112no—
172C22×C22⋊C4—114no—
173C22×C42—1112no—
174C22×C11—24no—
175C22×C11—28no—
176C22×C11C24×C414yes—
177C22×C11C24×C412yes—
178C22×C11C2×2−1+414yes—
179C22×C11C2611yescharacteristic
180C2×D11—24no—
181C2×D11—28no—
182C2×D11—232no—
183C2×D11#519116yesdirect product factor
184C2×D11C24×C414yes—
185C2×D11C24×C414yes—
186C2×D11C2×2−1+418yes—
187C4×C11—216no—
188C4×C11C24×C4124yes—
189Dic11—216no—
190Dic11C24×C4124yes—
191C25—111no—
192C22×Q8—1164no—
193C22×Q8—1164no—
194C22×Q8—11256no—
195C22×Q8—1132no—
196C22×Q8—1132no—
197C22×Q8—1148no—
198C22×Q8—1112no—
199C22×Q8—1124no—
200C22×Q8C4×D11116yescomplemented
201C22×Q8C22×D1114yes—
202C22×Q8C22×D1118yes—
203C23×C4—113no—
204C23×C4—1148no—
205C23×C4—116no—
206C23×C4—1124no—
207C23×C4—116no—
208C23×C4—118no—
209C23×C4C22×D1113yes—
210C4×Q8—1164no—
211C4×Q8—11192no—
212C4×Q8—11192no—
213C4×Q8C22×D11164yescomplemented
214#117—1148no—
215#117—1196no—
216#117—1196no—
217#117—1196no—
218#117C22×D11148yes—
219C2×C4⋊C4—1124no—
220C2×C4⋊C4—1112no—
221C2×C4⋊C4—1196no—
222C2×C4⋊C4C22×D11112yes—
223C2×C22⋊C4—114no—
224C2×C22⋊C4—118no—
225C2×C22⋊C4—1132no—
226C2×C22⋊C4C22×D1114yes—
227C2×C42—1124no—
228C2×C42—1112no—
229C2×C42—1196no—
230C2×C42C22×D11112yes—
231C2×C11—24no—
232C2×C11C2×#51914yescomplemented
233C2×C11C25×C411yescharacteristic
234C2×C11C22×2−1+412yes—
235D11—24no—
236D11C2×#51918yesdirect product factor
237C24—111no—
238C24—118no—
239C24—114no—
240C24—111no—
241C24—228no—
242C24C23×D1111yescharacteristic
243C2×Q8—11256no—
244C2×Q8—11256no—
245C2×Q8—1196no—
246C2×Q8—11192no—
247C2×Q8—1148no—
248C2×Q8C2×C4×D11132yes—
249C2×Q8C2×C4×D11164yescomplemented
250C2×Q8C23×D11116yes—
251C22×C4—1124no—
252C22×C4—1112no—
253C22×C4—116no—
254C22×C4—1148no—
255C22×C4—1148no—
256C22×C4—11192no—
257C22×C4—1124no—
258C22×C4—1124no—
259C22×C4—118no—
260C22×C4—1132no—
261C22×C4—2232no—
262C22×C4C2×C4×D11124yes—
263C22×C4C23×D1118yes—
264C22×C4C23×D11112yes—
265C22×C4C23×D1116yes—
266C4⋊C4—1196no—
267C4⋊C4—1148no—
268C4⋊C4C23×D11148yes—
269C22⋊C4—1116no—
270C22⋊C4—1132no—
271C22⋊C4C23×D11116yes—
272C42—1196no—
273C42—1148no—
274C42C23×D11148yes—
275C11C22×#51911yescharacteristic, complemented, Sylow
276C23—24no—
277C23—114no—
278C23—118no—
279C23—112no—
280C23—1116no—
281C23—114no—
282C23—112no—
283C23—2216no—
284C23—2232no—
285C23—224no—
286C23C22×C4×D1114yes—
287C23C24×D1112yes—
288C23C24×D1111yescharacteristic
289Q8—11192no—
290Q8C22×C4×D11164yes—
291C2×C4—216no—
292C2×C4—1148no—
293C2×C4—1124no—
294C2×C4—1112no—
295C2×C4—1196no—
296C2×C4—1196no—
297C2×C4—1116no—
298C2×C4—2264no—
299C2×C4—2216no—
300C2×C4C22×C4×D11124yes—
301C2×C4C22×C4×D11148yes—
302C2×C4C24×D11116yes—
303C2×C4C24×D11112yes—
304C22—24no—
305C22—28no—
306C22—114no—
307C22—118no—
308C22—1116no—
309C22—114no—
310C22—2232no—
311C22—224no—
312C22—228no—
313C22C23×C4×D1114yes—
314C22C23×C4×D1112yes—
315C22D11×2−1+414yes—
316C22C25×D1111yescharacteristic
317C4—216no—
318C4—1124no—
319C4—2216no—
320C4C23×C4×D11124yes—
321C2—24no—
322C2—118no—
323C2—224no—
324C2D11×#51914yesdirect product factor
325C2C24×C4×D1111yescharacteristic
326C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC2×C11×#519C2
socleC23×C11C25
prime radicalC24×D11C23
cosocleC22×C11C26
hypercenterC2×#519D11
hypocenterC11C22×#519
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#10623343C2semidirect
3. C2×#10623047C2semidirect
4. C2×#10623103C2semidirect
5. D11×#519C2direct (N × H)
6. C2×C4×Q8×D11C2semidirect
8. C2×C11×#519C2semidirect
10. C22×Q8×D11C4semidirect
16. C11×#519C22semidirect
17. C2×C4×Q8×C11C22semidirect
19. #10623343C22semidirect
20. C2×Q8×Dic11C22semidirect
22. #10623103C22semidirect
23. C4×Q8×D11C22semidirect
25. #10623047C22semidirect
28. C2×#66940C22semidirect
33. C2×C4×Dic22C22semidirect
35. C22×Q8×C11C2×C4semidirect
41. C2×Q8×D11C2×C4semidirect
42. C2×Q8×D11C2×C4semidirect
50. C22×Dic22C2×C4semidirect
53. C4×Q8×C11C23semidirect
59. Q8×Dic11C23semidirect
68. #66940C23semidirect
73. C4×Dic22C23semidirect
82. C2×Q8×C11C22×C4semidirect
93. Q8×D11C22×C4semidirect
102. C2×Dic22C22×C4semidirect
118. C2×#519D11direct (N × H)
159. #519C2×D11direct (N × H)
164. C2×C4×Q8C2×D11semidirect
183. C2×D11#519direct (N × H)
200. C22×Q8C4×D11semidirect
213. C4×Q8C22×D11semidirect
232. C2×C11C2×#519semidirect
236. D11C2×#519direct (N × H)
249. C2×Q8C2×C4×D11semidirect
275. C11C22×#519semidirect
324. C2D11×#519direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D112
C2×#106233432
C2×#106230472
C2×#106231032
D11×#5192
C2×C4×Q8×D112
C2×D11×#1172
C2×C11×#5192
C22×#51911