Finite Group Databasebeta

← C11×#11571 #14588764

Subgroups — C11×#11571 #14588764

Order 2816.

350 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2565C211yesmaximal, characteristic
2C11×#1467C211yesmaximal, characteristic
3C11×#1461C211yesmaximal, characteristic
4C11×#1325C212yesmaximal
5C11×#1324C212yesmaximal
6C2×C11×#125C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#432—21no—
9C11×#431—21no—
10C11×#398—21no—
11C11×#398—21no—
12C11×#391C411yescharacteristic
13C11×#391C411yescharacteristic
14C11×#387—21no—
15C11×#387—21no—
16C11×#384C2211yescharacteristic
17C11×#382C2211yescharacteristic
18C4×C11×C4⋊C4C411yescharacteristic
19C11×#324—21no—
20C11×#324—21no—
21C11×#324C2212yes—
22C11×#324C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C11×#125—41no—
25C11×#125—41no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C11×C4⋊C8—41no—
44C11×C4⋊C8—41no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×#97—41no—
48C4×C8×C11—41no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56#11571C1111yesmaximal, characteristic, direct product factor, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—22no—
59C2×Q8×C11—41no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
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
71C2×C8×C11—42no—
72C2×C8×C11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—22no—
91C42×C11—22no—
92#2565C2×C1111yescharacteristic
93#1467C2×C1111yescharacteristic
94#1461C2×C1111yescharacteristic
95#1325C2×C1112yes—
96#1324C2×C1112yes—
97C23×C11C2×C22⋊C411yescharacteristic
98Q8×C11—44no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11#9911yescharacteristic
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#10112yes—
127C2×C4×C11#13112yes—
128C8×C11—82no—
129C8×C11—82no—
130C2×#125C4×C1111yescharacteristic
131C2×C4×Q8C22×C1111yescharacteristic
132#432—21no—
133#431—21no—
134#398—21no—
135#398—21no—
136#391C4×C1111yescharacteristic
137#391C4×C1111yescharacteristic
138#387—21no—
139#387—21no—
140#384C22×C1111yescharacteristic
141#382C22×C1111yescharacteristic
142C4×C4⋊C4C4×C1111yescharacteristic
143#324—21no—
144#324—21no—
145#324C22×C1112yes—
146#324C22×C1112yes—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#40811yescharacteristic
150C22×C11C2×#9911yescharacteristic
151C22×C11C2×#10111yescharacteristic
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—22no—
155C4×C11—22no—
156C4×C11—42no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—81no—
162C4×C11—81no—
163C4×C11—81no—
164C22×Q8C2×C4×C1111yescharacteristic
165#125—41no—
166#125—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4C2×C4×C1111yescharacteristic
175C2×C4⋊C4C2×C4×C1111yescharacteristic
176C2×C4⋊C4D4×C1111yescharacteristic
177C2×C4⋊C4D4×C1111yescharacteristic
178C2×C4⋊C4C23×C1111yescharacteristic
179C2×C42C2×C4×C1111yescharacteristic
180C2×C42C2×C4×C1111yescharacteristic
181C2×C42C2×C4×C1111yescharacteristic
182C2×C42D4×C1111yescharacteristic
183C2×C42D4×C1111yescharacteristic
184C4⋊C8—41no—
185C4⋊C8—41no—
186C22⋊C8—22no—
187C22⋊C8—22no—
188#97—41no—
189C4×C8—41no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11#147211yescharacteristic
200C2×C11#212611yescharacteristic
201C2×C11#213311yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C11×C22⋊C411yescharacteristic
210C22×C4C11×C22⋊C411yescharacteristic
211C22×C4C11×C22⋊C411yescharacteristic
212C22×C4C11×C22⋊C411yescharacteristic
213C22×C4C22×C4×C1111yescharacteristic
214C22×C4C2×D4×C1111yescharacteristic
215C22×C4C2×D4×C1111yescharacteristic
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—22no—
236C42—22no—
237C11#1157111yescharacteristic, direct product factor, Sylow
238C23C2×C11×C22⋊C411yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4C11×#9911yescharacteristic
266C2×C4C11×#9911yescharacteristic
267C2×C4C11×#10112yes—
268C2×C4C11×#13112yes—
269C8—82no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22C11×#40811yescharacteristic
274C22C2×C11×#9911yescharacteristic
275C22C2×C11×#10111yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—42no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2C11×#147211yescharacteristic
291C2C11×#212611yescharacteristic
292C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×C11C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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
56. #11571C11direct (N × H)
237. C11#11571direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25652
C11×#14672
C11×#14612
C11×#13252
C11×#13242
#1157111