Finite Group Databasebeta

← C11×#11381 #14588574

Subgroups — C11×#11381 #14588574

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×C11×#342C214yesmaximal
3C11×C22⋊#95C212yesmaximal
4C23×Q8×C11C411yescharacteristic, complemented
5C24×C4×C11C2211yescharacteristic
6C2×C11×C22⋊Q8—24no—
7C2×C11×C22⋊Q8—28no—
8C22×C11×C4⋊C4C411yescharacteristic, complemented
9C22×C11×C4⋊C4C412yescomplemented
10C22×C11×C22⋊C4C2214yes—
11C22×C11×C22⋊C4C2212yes—
12C2×C11×#95—24no—
13C11×#342—28no—
14C25×C11C2311yescharacteristic
15C22×Q8×C11—24no—
16C22×Q8×C11—22no—
17C22×Q8×C11—44no—
18C23×C4×C11—24no—
19C23×C4×C11—24no—
20C23×C4×C11—44no—
21C23×C4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C412yes—
23C23×C4×C11C2×C412yes—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D414yes—
26C11×C22⋊Q8—232no—
27C2×C11×C4⋊C4—24no—
28C2×C11×C4⋊C4—24no—
29C2×C11×C4⋊C4—24no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C22⋊C4—24no—
33C2×C11×C22⋊C4—24no—
34C2×C11×C22⋊C4—28no—
35C2×C11×C22⋊C4—28no—
36C2×C11×C22⋊C4—24no—
37C2×C11×C22⋊C4D418yes—
38C2×C11×C22⋊C4Q818yescomplemented
39C11×#95—48no—
40#11381C1111yesmaximal, characteristic, direct product factor, Sylow
41C24×C11—42no—
42C24×C11—42no—
43C24×C11C22×C411yescharacteristic
44C24×C11C2×D412yes—
45C24×C11C2×D414yes—
46C24×C11C2×Q814yes—
47C24×C11#4114yes—
48C2×Q8×C11—28no—
49C2×Q8×C11—416no—
50C2×Q8×C11—44no—
51C2×Q8×C11—44no—
52C22×C4×C11—22no—
53C22×C4×C11—24no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—28no—
60C22×C4×C11—28no—
61C22×C4×C11—28no—
62C22×C4×C11—42no—
63C22×C4×C11—44no—
64C22×C4×C11—416no—
65C22×C4×C11—44no—
66C22×C4×C11—44no—
67C22×C4×C11—48no—
68C22×C4×C11—48no—
69C22×C4×C11—44no—
70C22×C4×C11—44no—
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11C22⋊C412yes—
73C22×C4×C11C22⋊C414yes—
74C22×C4×C11C22⋊C414yes—
75C11×C4⋊C4—28no—
76C11×C4⋊C4—216no—
77C11×C22⋊C4—216no—
78C11×C22⋊C4—216no—
79C11×C22⋊C4—48no—
80C22×C22⋊Q8C2×C1111yescharacteristic
81C2×#342C2×C1114yes—
82C22⋊#95C2×C1112yes—
83C23×C11—22no—
84C23×C11—24no—
85C23×C11—22no—
86C23×C11—24no—
87C23×C11—44no—
88C23×C11—44no—
89C23×C11—48no—
90C23×C11—48no—
91C23×C11C2×C22⋊C412yes—
92C23×C11C2×C22⋊C411yescharacteristic
93C23×C11C4×Q814yes—
94C23×C11#12014yes—
95C23×C11C22⋊Q814yes—
96C23×C11C22⋊Q818yes—
97C23×C11#12412yes—
98C23×C11#12414yes—
99C23×C11C4⋊Q812yes—
100C23×C11C4⋊Q814yes—
101Q8×C11—416no—
102C2×C4×C11—28no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—24no—
106C2×C4×C11—24no—
107C2×C4×C11—22no—
108C2×C4×C11—24no—
109C2×C4×C11—416no—
110C2×C4×C11—44no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—44no—
114C2×C4×C11—44no—
115C2×C4×C11—44no—
116C2×C4×C11—44no—
117C2×C4×C11—416no—
118C2×C4×C11—48no—
119C2×C4×C11—88no—
120C2×C4×C11—84no—
121C2×C4×C11—84no—
122C2×C4×C11#9914yes—
123C23×Q8C4×C1111yescharacteristic, complemented
124C24×C4C22×C1111yescharacteristic
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—28no—
127C22×C4⋊C4C4×C1111yescharacteristic, complemented
128C22×C4⋊C4C4×C1112yescomplemented
129C22×C22⋊C4C22×C1114yes—
130C22×C22⋊C4C22×C1112yes—
131C2×#95—24no—
132#342—28no—
133C22×C11—28no—
134C22×C11—24no—
135C22×C11—28no—
136C22×C11—24no—
137C22×C11—22no—
138C22×C11—24no—
139C22×C11—22no—
140C22×C11—24no—
141C22×C11—48no—
142C22×C11—44no—
143C22×C11—44no—
144C22×C11#37911yescharacteristic
145C22×C11#39114yes—
146C22×C11#39112yes—
147C22×C11#39314yes—
148C22×C11#39514yes—
149C22×C11C2×#9912yes—
150C22×C11#41012yes—
151C4×C11—24no—
152C4×C11—42no—
153C4×C11—44no—
154C4×C11—44no—
155C4×C11—88no—
156C25C23×C1111yescharacteristic
157C22×Q8—24no—
158C22×Q8—22no—
159C22×Q8—44no—
160C23×C4—24no—
161C23×C4—24no—
162C23×C4—44no—
163C23×C4C2×C4×C1111yescharacteristic
164C23×C4C2×C4×C1112yes—
165C23×C4C2×C4×C1112yes—
166C23×C4C2×C4×C1111yescharacteristic
167C23×C4D4×C1114yes—
168C22⋊Q8—232no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—28no—
177C2×C22⋊C4—28no—
178C2×C22⋊C4—24no—
179C2×C22⋊C4D4×C1118yes—
180C2×C22⋊C4Q8×C1118yescomplemented
181#95—48no—
182C2×C11—24no—
183C2×C11—24no—
184C2×C11—24no—
185C2×C11#144611yescharacteristic
186C2×C11#178111yescharacteristic
187C2×C11#178211yescharacteristic
188C2×C11#199614yes—
189C24—42no—
190C24—42no—
191C24C22×C4×C1111yescharacteristic
192C24C2×D4×C1112yes—
193C24C2×D4×C1114yes—
194C24C2×Q8×C1114yes—
195C24C11×#4114yes—
196C2×Q8—28no—
197C2×Q8—416no—
198C2×Q8—44no—
199C2×Q8—44no—
200C22×C4—22no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—28no—
208C22×C4—28no—
209C22×C4—28no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4—416no—
213C22×C4—44no—
214C22×C4—44no—
215C22×C4—48no—
216C22×C4—48no—
217C22×C4—44no—
218C22×C4—44no—
219C22×C4C11×C22⋊C412yes—
220C22×C4C11×C22⋊C412yes—
221C22×C4C11×C22⋊C414yes—
222C22×C4C11×C22⋊C414yes—
223C4⋊C4—28no—
224C4⋊C4—216no—
225C22⋊C4—216no—
226C22⋊C4—216no—
227C22⋊C4—48no—
228C11#1138111yescharacteristic, direct product factor, Sylow
229C23—22no—
230C23—24no—
231C23—22no—
232C23—24no—
233C23—44no—
234C23—44no—
235C23—48no—
236C23—48no—
237C23C2×C11×C22⋊C412yes—
238C23C2×C11×C22⋊C411yescharacteristic
239C23C4×Q8×C1114yes—
240C23C11×#12014yes—
241C23C11×C22⋊Q814yes—
242C23C11×C22⋊Q818yes—
243C23C11×#12412yes—
244C23C11×#12414yes—
245C23C11×C4⋊Q812yes—
246C23C11×C4⋊Q814yes—
247Q8—416no—
248C2×C4—28no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—416no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—416no—
264C2×C4—48no—
265C2×C4—88no—
266C2×C4—84no—
267C2×C4—84no—
268C2×C4C11×#9914yes—
269C22—28no—
270C22—24no—
271C22—28no—
272C22—24no—
273C22—22no—
274C22—24no—
275C22—22no—
276C22—24no—
277C22—48no—
278C22—44no—
279C22—44no—
280C22C11×#37911yescharacteristic
281C22C11×#39114yes—
282C22C11×#39112yes—
283C22C11×#39314yes—
284C22C11×#39514yes—
285C22C2×C11×#9912yes—
286C22C11×#41012yes—
287C4—24no—
288C4—42no—
289C4—44no—
290C4—44no—
291C4—88no—
292C2—24no—
293C2—24no—
294C2—24no—
295C2C11×#144611yescharacteristic
296C2C11×#178111yescharacteristic
297C2C11×#178211yescharacteristic
298C2C11×#199614yes—
subgroupG/H
center, socleC23×C11C2×C22⋊C4
commutatorC24C22×C4×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C23×Q8×C11C4semidirect
8. C22×C11×C4⋊C4C4semidirect
9. C22×C11×C4⋊C4C4semidirect
38. C2×C11×C22⋊C4Q8semidirect
40. #11381C11direct (N × H)
123. C23×Q8C4×C11semidirect
127. C22×C4⋊C4C4×C11semidirect
128. C22×C4⋊C4C4×C11semidirect
180. C2×C22⋊C4Q8×C11semidirect
228. C11#11381direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C2×C11×#3422
C11×C22⋊#952
#1138111