Finite Group Databasebeta

← C11×#11781 #14588974

Subgroups — C11×#11781 #14588974

Order 2816.

482 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2548C211yesmaximal, characteristic
2C4×C11×#101C211yesmaximal, characteristic, complemented
3C11×#1467C211yesmaximal, characteristic, complemented
4C11×#1345C214yesmaximal, complemented
5C2×C11×#127C411yescharacteristic
6C2×C11×#124—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#432—21no—
9C2×C11×#101—21no—
10C4×C11×M16—21no—
11C11×#394C412yes—
12C11×#394C2212yes—
13C11×#390—21no—
14C11×#390—21no—
15C11×#390—21no—
16C4×C11×C4⋊C4C411yescharacteristic
17C11×#343C2212yes—
18C11×#324—21no—
19C11×#324C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11—21no—
22C22×D4×C11—21no—
23C22×D4×C11C2×C412yes—
24C2×C11×M16—22no—
25C11×#127—41no—
26C11×#127—41no—
27C11×#124—44no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—22no—
38C2×C42×C11—21no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C11×C4⋊C8—41no—
43C11×#101—24no—
44C11×C22⋊C8—22no—
45C11×#97—41no—
46C11×#97—41no—
47C4×C8×C11—41no—
48C11×#95C2×C412yes—
49#11781C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11—22no—
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11—41no—
54C2×D4×C11—42no—
55C2×D4×C11—42no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—42no—
62C2×D4×C11—82no—
63C22×C4×C11—22no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C11×M16—24no—
72C11×M16—42no—
73C2×C8×C11—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—42no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—44no—
81C11×C22⋊C4—82no—
82C11×C22⋊C4—82no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—42no—
90#2548C2×C1111yescharacteristic
91C4×#101C2×C1111yescharacteristic, complemented
92#1467C2×C1111yescharacteristic, complemented
93#1345C2×C1114yescomplemented
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—44no—
103D4×C11—82no—
104D4×C11—84no—
105D4×C11—84no—
106D4×C11—82no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#10412yes—
127C2×C4×C11AGL(1,ℤ/8)12yes—
128C8×C11—44no—
129C8×C11—82no—
130C2×#127C4×C1111yescharacteristic
131C2×#124—21no—
132C2×C4×Q8C22×C1111yescharacteristic
133#432—21no—
134C2×#101—21no—
135C4×M16—21no—
136#394C4×C1112yes—
137#394C22×C1112yes—
138#390—21no—
139#390—21no—
140#390—21no—
141C4×C4⋊C4C4×C1111yescharacteristic
142#343C22×C1112yes—
143#324—21no—
144#324C22×C1112yes—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—82no—
148C22×C11—82no—
149C22×C11—82no—
150C22×C11—82no—
151C22×C11—82no—
152C22×C11—82no—
153C22×C11—82no—
154C22×C11C2×#9911yescharacteristic
155C22×C11#41811yescharacteristic
156C22×C11C2×#10411yescharacteristic
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—82no—
165C4×C11#35512yes—
166C22×Q8D4×C1111yescharacteristic
167C22×D4—21no—
168C22×D4—21no—
169C22×D4C2×C4×C1112yes—
170C2×M16—22no—
171#127—41no—
172#127—41no—
173#124—44no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C2×C4×C1111yescharacteristic
178C2×C4⋊C4D4×C1111yescharacteristic
179C2×C4⋊C4C23×C1111yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C42—21no—
185C2×C42C2×C4×C1111yescharacteristic
186C2×C42D4×C1111yescharacteristic
187C2×C42D4×C1111yescharacteristic
188C4⋊C8—41no—
189#101—24no—
190C22⋊C8—22no—
191#97—41no—
192#97—41no—
193C4×C8—41no—
194#95C2×C4×C1112yes—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—162no—
198C2×C11#150711yescharacteristic
199C2×C11#212211yescharacteristic
200C2×C11C2×#35511yescharacteristic
201C24—22no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—42no—
213C2×D4—82no—
214C22×C4—22no—
215C22×C4C11×C22⋊C411yescharacteristic
216C22×C4C11×C22⋊C411yescharacteristic
217C22×C4C11×C22⋊C411yescharacteristic
218C22×C4C11×C22⋊C411yescharacteristic
219C22×C4C22×C4×C1111yescharacteristic
220C22×C4C2×D4×C1111yescharacteristic
221C22×C4C2×D4×C1111yescharacteristic
222M16—24no—
223M16—42no—
224C2×C8—42no—
225C2×C8—42no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C22⋊C4—44no—
231C22⋊C4—44no—
232C22⋊C4—82no—
233C22⋊C4—82no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—42no—
241C11#1178111yescharacteristic, direct product factor, Sylow
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23C2×C11×C22⋊C411yescharacteristic
250Q8—44no—
251D4—82no—
252D4—84no—
253D4—84no—
254D4—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4C11×#9911yescharacteristic
273C2×C4C11×#9911yescharacteristic
274C2×C4C11×#10412yes—
275C2×C4C11×AGL(1,ℤ/8)12yes—
276C8—44no—
277C8—82no—
278C22—21no—
279C22—21no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—82no—
285C22—82no—
286C22—82no—
287C22C2×C11×#9911yescharacteristic
288C22C11×#41811yescharacteristic
289C22C2×C11×#10411yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—82no—
298C4C11×#35512yes—
299C2—21no—
300C2—21no—
301C2—162no—
302C2C11×#150711yescharacteristic
303C2C11×#212211yescharacteristic
304C2C2×C11×#35511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC2×C11×#127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#101C2semidirect
3. C11×#1467C2semidirect
4. C11×#1345C2semidirect
49. #11781C11direct (N × H)
91. C4×#101C2×C11semidirect
92. #1467C2×C11semidirect
93. #1345C2×C11semidirect
241. C11#11781direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25482
C4×C11×#1012
C11×#14672
C11×#13452
#1178111