Finite Group Databasebeta

← C11×#11780 #14588973

Subgroups — C11×#11780 #14588973

Order 2816.

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

normal subgroups only

This group has 464 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×#2486C211yesmaximal, characteristic
2C4×C11×#100C211yesmaximal, characteristic
3C11×#1465C211yesmaximal, characteristic
4C11×#1346C214yesmaximal, complemented
5C2×C11×#123—21no—
6C2×C4×D4×C11C2211yescharacteristic
7C22×C11×C4⋊C4C411yescharacteristic
8C2×C11×#100—21no—
9C11×#407—21no—
10C4×C11×M16—21no—
11C11×#398C2212yes—
12C11×#397C412yes—
13C11×#389—21no—
14C11×#381—21no—
15C11×#380—21no—
16C11×#380C411yescharacteristic
17C11×#343C2212yes—
18C11×#324C2212yes—
19C11×#323—21no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C2×C11×M16—22no—
25C2×C11×M16—41no—
26C11×#123—44no—
27C4×D4×C11—41no—
28C4×D4×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—41no—
33C2×C11×C4⋊C4—41no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C11×#100—24no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—41no—
44C11×#97—41no—
45C4×C8×C11—41no—
46C11×#95—22no—
47C11×#95—22no—
48C11×#95C2×C412yes—
49#11780C1111yesmaximal, characteristic, direct product factor, Sylow
50C24×C11C22⋊C411yescharacteristic
51C24×C11C22⋊C411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
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—
73C11×M16—82no—
74C2×C8×C11—42no—
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—44no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—44no—
86C42×C11—21no—
87C42×C11—21no—
88#2486C2×C1111yescharacteristic
89C4×#100C2×C1111yescharacteristic
90#1465C2×C1111yescharacteristic
91#1346C2×C1114yescomplemented
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11#10412yes—
102C23×C11C2×C22⋊C411yescharacteristic
103D4×C11—44no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—81no—
123C2×C4×C11—84no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)12yes—
127C8×C11—44no—
128C8×C11—82no—
129C2×#123—21no—
130C2×C4×D4C22×C1111yescharacteristic
131C22×C4⋊C4C4×C1111yescharacteristic
132C2×#100—21no—
133#407—21no—
134C4×M16—21no—
135#398C22×C1112yes—
136#397C4×C1112yes—
137#389—21no—
138#381—21no—
139#380—21no—
140#380C4×C1111yescharacteristic
141#343C22×C1112yes—
142#324C22×C1112yes—
143#323—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—22no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11C2×#9911yescharacteristic
157C22×C11#41811yescharacteristic
158C22×C11C2×#10411yescharacteristic
159C4×C11—21no—
160C4×C11—22no—
161C4×C11—41no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—82no—
165C4×C11—82no—
166C4×C11#35212yes—
167C22×D4D4×C1111yescharacteristic
168C23×C4—21no—
169C23×C4C2×C4×C1111yescharacteristic
170C23×C4D4×C1111yescharacteristic
171C2×M16—22no—
172C2×M16—41no—
173#123—44no—
174C4×D4—41no—
175C4×D4—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×C4×C1112yes—
182C2×C4⋊C4C23×C1111yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4C2×C4×C1111yescharacteristic
186C2×C22⋊C4D4×C1111yescharacteristic
187C2×C42D4×C1111yescharacteristic
188#100—24no—
189C22⋊C8—22no—
190C22⋊C8—41no—
191#97—41no—
192C4×C8—41no—
193#95—22no—
194#95—22no—
195#95C2×C4×C1112yes—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11—81no—
200C2×C11#150711yescharacteristic
201C2×C11C2×#35211yescharacteristic
202C2×C11#213511yescharacteristic
203C24C11×C22⋊C411yescharacteristic
204C24C11×C22⋊C411yescharacteristic
205C2×D4—22no—
206C2×D4—22no—
207C2×D4—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4C11×C22⋊C411yescharacteristic
220C22×C4C11×C22⋊C411yescharacteristic
221C22×C4C22×C4×C1111yescharacteristic
222C22×C4C2×D4×C1111yescharacteristic
223C22×C4C2×D4×C1111yescharacteristic
224M16—24no—
225M16—42no—
226M16—82no—
227C2×C8—42no—
228C2×C8—42no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—44no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—42no—
238C22⋊C4—44no—
239C42—21no—
240C42—21no—
241C11#1178011yescharacteristic, direct product factor, Sylow
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23C11×#10412yes—
252C23C2×C11×C22⋊C411yescharacteristic
253D4—44no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—81no—
273C2×C4—84no—
274C2×C4C11×#9911yescharacteristic
275C2×C4C11×#9911yescharacteristic
276C2×C4C11×AGL(1,ℤ/8)12yes—
277C8—44no—
278C8—82no—
279C22—21no—
280C22—21no—
281C22—22no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—81no—
291C22C2×C11×#9911yescharacteristic
292C22C11×#41811yescharacteristic
293C22C2×C11×#10411yescharacteristic
294C4—22no—
295C4—21no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C4—82no—
301C4C11×#35212yes—
302C2—21no—
303C2—21no—
304C2—42no—
305C2—81no—
306C2C11×#150711yescharacteristic
307C2C2×C11×#35211yescharacteristic
308C2C11×#213511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1346C2semidirect
49. #11780C11direct (N × H)
91. #1346C2×C11semidirect
241. C11#11780direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#24862
C4×C11×#1002
C11×#14652
C11×#13462
#1178011