Finite Group Databasebeta

← C11×#21307 #14598500

Subgroups — C11×#21307 #14598500

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3458C211yesmaximal, characteristic
2C11×#2873C211yesmaximal, characteristic
3C11×#2296C211yesmaximal, characteristic
4C11×#1986C218yesmaximal, complemented
5C11×#1733C212yesmaximal
6C2×C11×#339C212yesmaximal
7C22×C11×M16C2212yes—
8C11×#544—22no—
9C11×#544C418yescomplemented
10C11×#543—22no—
11C11×#533—24no—
12C11×#533C2214yes—
13C2×C11×#117C2212yes—
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#405—24no—
18C4×C11×M16C2214yes—
19C11×#389—22no—
20C11×#385—22no—
21C4×C11×C4⋊C4C2214yes—
22C11×#339C2218yes—
23C11×#339C2218yes—
24C23×C4×C11—21no—
25C23×C4×C11C2311yescharacteristic
26C2×C11×M16—22no—
27C2×C11×M16—24no—
28C2×C11×M16Q818yescomplemented
29C2×C11×M16C2314yes—
30C22×C8×C11—22no—
31C11×C4⋊Q8—28no—
32C11×C4⋊Q8C2×C418yescomplemented
33C11×#125—28no—
34C11×#125C2×C418yescomplemented
35C11×C22⋊Q8—28no—
36C11×C22⋊Q8—216no—
37C4×Q8×C11—28no—
38C11×#117—22no—
39C11×#117—22no—
40C11×#117—24no—
41C11×#117C2×C414yes—
42C11×#117C2×C414yes—
43C11×#117D414yes—
44C11×#117C2314yes—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—24no—
47C2×C11×C4⋊C4C2×C414yes—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11—22no—
53C2×C42×C11—24no—
54C2×C42×C11—21no—
55C2×C42×C11C2312yes—
56C2×C42×C11C2312yes—
57C2×C42×C11C2312yes—
58C11×#97—24no—
59C4×C8×C11—24no—
60C11×#95—24no—
61#21307C1111yesmaximal, characteristic, direct product factor, Sylow
62C24×C11C2×D411yescharacteristic
63C2×Q8×C11—28no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—22no—
67C22×C4×C11—44no—
68C22×C4×C11—42no—
69C22×C4×C11C22×C412yes—
70C22×C4×C11C2×D414yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×Q814yes—
74C22×C4×C11#4114yes—
75C22×C4×C11C2411yescharacteristic
76C11×M16—28no—
77C11×M16—24no—
78C11×M16C2×Q818yes—
79C2×C8×C11—28no—
80C2×C8×C11—24no—
81C11×C4⋊C4—24no—
82C11×C4⋊C4—28no—
83C11×C4⋊C4—216no—
84C11×C4⋊C4—48no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4C22⋊C418yes—
87C11×C4⋊C4C22×C418yes—
88C11×C22⋊C4—24no—
89C11×C22⋊C4—24no—
90C11×C22⋊C4—42no—
91C11×C22⋊C4C22⋊C418yes—
92C42×C11—24no—
93C42×C11—24no—
94C42×C11—24no—
95C42×C11—24no—
96C42×C11—42no—
97C42×C11C22×C414yes—
98C42×C11C2×D414yes—
99#3458C2×C1111yescharacteristic
100#2873C2×C1111yescharacteristic
101#2296C2×C1111yescharacteristic
102#1986C2×C1118yescomplemented
103#1733C2×C1112yes—
104C2×#339C2×C1112yes—
105C23×C11—42no—
106C23×C11C2×C22⋊C412yes—
107C23×C11#12412yes—
108C23×C11C4⋊Q812yes—
109C23×C11C22×D411yescharacteristic
110Q8×C11—88no—
111C2×C4×C11—24no—
112C2×C4×C11—28no—
113C2×C4×C11—44no—
114C2×C4×C11—42no—
115C2×C4×C11—48no—
116C2×C4×C11—42no—
117C2×C4×C11—44no—
118C2×C4×C11—42no—
119C2×C4×C11—84no—
120C2×C4×C11C2×C22⋊C418yes—
121C2×C4×C11C2×C22⋊C412yes—
122C2×C4×C11C4×Q818yes—
123C2×C4×C11C22⋊Q814yes—
124C2×C4×C11C22⋊Q814yes—
125C2×C4×C11#12412yes—
126C2×C4×C11C4⋊Q812yes—
127C2×C4×C11C23×C411yescharacteristic
128C2×C4×C11C22×D411yescharacteristic
129C2×C4×C11C22×Q812yes—
130C2×C4×C11C2×#4112yes—
131C8×C11—28no—
132C22×M16C22×C1112yes—
133#544—22no—
134#544C4×C1118yescomplemented
135#543—22no—
136#533—24no—
137#533C22×C1114yes—
138C2×#117C22×C1112yes—
139C2×#117C22×C1111yescharacteristic
140C2×#117C22×C1111yescharacteristic
141C22×C42C22×C1111yescharacteristic
142#405—24no—
143C4×M16C22×C1114yes—
144#389—22no—
145#385—22no—
146C4×C4⋊C4C22×C1114yes—
147#339C22×C1118yes—
148#339C22×C1118yes—
149C22×C11—22no—
150C22×C11—24no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11#39114yes—
154C22×C11C22×C22⋊C411yescharacteristic
155C22×C11C2×#12411yescharacteristic
156C22×C11C2×C4⋊Q811yescharacteristic
157C4×C11—28no—
158C4×C11—44no—
159C4×C11—48no—
160C4×C11—82no—
161C4×C11#39114yes—
162C4×C11C2×C4×Q812yes—
163C4×C11C2×C22⋊Q812yes—
164C23×C4—21no—
165C23×C4C23×C1111yescharacteristic
166C2×M16—22no—
167C2×M16—24no—
168C2×M16Q8×C1118yescomplemented
169C2×M16C23×C1114yes—
170C22×C8—22no—
171C4⋊Q8—28no—
172C4⋊Q8C2×C4×C1118yescomplemented
173#125—28no—
174#125C2×C4×C1118yescomplemented
175C22⋊Q8—28no—
176C22⋊Q8—216no—
177C4×Q8—28no—
178#117—22no—
179#117—22no—
180#117—24no—
181#117C2×C4×C1114yes—
182#117C2×C4×C1114yes—
183#117D4×C1114yes—
184#117C23×C1114yes—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4C2×C4×C1114yes—
188C2×C4⋊C4D4×C1112yes—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4D4×C1112yes—
192C2×C42—22no—
193C2×C42—24no—
194C2×C42—21no—
195C2×C42C23×C1112yes—
196C2×C42C23×C1112yes—
197C2×C42C23×C1112yes—
198#97—24no—
199C4×C8—24no—
200#95—24no—
201C2×C11—21no—
202C2×C11—21no—
203C2×C11—24no—
204C2×C11C2×#39111yescharacteristic
205C2×C11#290112yes—
206C24C2×D4×C1111yescharacteristic
207C2×Q8—28no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—22no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4C22×C4×C1112yes—
214C22×C4C2×D4×C1114yes—
215C22×C4C2×D4×C1111yescharacteristic
216C22×C4C2×D4×C1112yes—
217C22×C4C2×Q8×C1114yes—
218C22×C4C11×#4114yes—
219C22×C4C24×C1111yescharacteristic
220M16—28no—
221M16—24no—
222M16C2×Q8×C1118yes—
223C2×C8—28no—
224C2×C8—24no—
225C4⋊C4—24no—
226C4⋊C4—28no—
227C4⋊C4—216no—
228C4⋊C4—48no—
229C4⋊C4—42no—
230C4⋊C4C11×C22⋊C418yes—
231C4⋊C4C22×C4×C1118yes—
232C22⋊C4—24no—
233C22⋊C4—24no—
234C22⋊C4—42no—
235C22⋊C4C11×C22⋊C418yes—
236C42—24no—
237C42—24no—
238C42—24no—
239C42—24no—
240C42—42no—
241C42C22×C4×C1114yes—
242C42C2×D4×C1114yes—
243C11#2130711yescharacteristic, direct product factor, Sylow
244C23—42no—
245C23C2×C11×C22⋊C412yes—
246C23C11×#12412yes—
247C23C11×C4⋊Q812yes—
248C23C22×D4×C1111yescharacteristic
249Q8—88no—
250C2×C4—24no—
251C2×C4—28no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—48no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—84no—
259C2×C4C2×C11×C22⋊C418yes—
260C2×C4C2×C11×C22⋊C412yes—
261C2×C4C4×Q8×C1118yes—
262C2×C4C11×C22⋊Q814yes—
263C2×C4C11×C22⋊Q814yes—
264C2×C4C11×#12412yes—
265C2×C4C11×C4⋊Q812yes—
266C2×C4C23×C4×C1111yescharacteristic
267C2×C4C22×D4×C1111yescharacteristic
268C2×C4C22×Q8×C1112yes—
269C2×C4C2×C11×#4112yes—
270C8—28no—
271C22—22no—
272C22—24no—
273C22—42no—
274C22—42no—
275C22C11×#39114yes—
276C22C22×C11×C22⋊C411yescharacteristic
277C22C2×C11×#12411yescharacteristic
278C22C2×C11×C4⋊Q811yescharacteristic
279C4—28no—
280C4—44no—
281C4—48no—
282C4—82no—
283C4C11×#39114yes—
284C4C2×C4×Q8×C1112yes—
285C4C2×C11×C22⋊Q812yes—
286C2—21no—
287C2—24no—
288C2—21no—
289C2C2×C11×#39111yescharacteristic
290C2C11×#290112yes—
subgroupG/H
centerC2×C4×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1986C2semidirect
9. C11×#544C4semidirect
28. C2×C11×M16Q8semidirect
32. C11×C4⋊Q8C2×C4semidirect
34. C11×#125C2×C4semidirect
61. #21307C11direct (N × H)
102. #1986C2×C11semidirect
134. #544C4×C11semidirect
168. C2×M16Q8×C11semidirect
172. C4⋊Q8C2×C4×C11semidirect
174. #125C2×C4×C11semidirect
243. C11#21307direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C11×#28732
C11×#22962
C11×#19862
C11×#17332
C2×C11×#3392
#2130711