Finite Group Databasebeta

← C11×#11792 #14588985

Subgroups — C11×#11792 #14588985

Order 2816.

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

normal subgroups only

This group has 378 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×#2581C211yesmaximal, characteristic
2C4×C11×#101C211yesmaximal, characteristic
3C11×#1467C211yesmaximal, characteristic
4C11×#1354C212yesmaximal
5C11×#1353C212yesmaximal
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#432—21no—
9C2×C11×#101—21no—
10C4×C11×M16—21no—
11C11×#400C411yescharacteristic
12C11×#400C2211yescharacteristic
13C11×#395C411yescharacteristic
14C11×#395C2211yescharacteristic
15C11×#391—21no—
16C11×#389—21no—
17C11×#387—21no—
18C11×#387—21no—
19C11×#382C411yescharacteristic
20C11×#343C2212yes—
21C11×#324—21no—
22C11×#324C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C2×C11×M16—22no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C4×Q8×C11—41no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
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×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11×#95C2×C411yescharacteristic
57#11792C1111yesmaximal, characteristic, direct product factor, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C2×Q8×C11—42no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C11×M16—24no—
75C11×M16—42no—
76C2×C8×C11—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—42no—
94#2581C2×C1111yescharacteristic
95C4×#101C2×C1111yescharacteristic
96#1467C2×C1111yescharacteristic
97#1354C2×C1112yes—
98#1353C2×C1112yes—
99C23×C11C2×C22⋊C411yescharacteristic
100Q8×C11—44no—
101Q8×C11—42no—
102Q8×C11—42no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
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—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#10412yes—
131C2×C4×C11#13712yes—
132C8×C11—44no—
133C8×C11—82no—
134C2×C4×Q8C4×C1111yescharacteristic
135C2×C4×Q8C22×C1111yescharacteristic
136#432—21no—
137C2×#101—21no—
138C4×M16—21no—
139#400C4×C1111yescharacteristic
140#400C22×C1111yescharacteristic
141#395C4×C1111yescharacteristic
142#395C22×C1111yescharacteristic
143#391—21no—
144#389—21no—
145#387—21no—
146#387—21no—
147#382C4×C1111yescharacteristic
148#343C22×C1112yes—
149#324—21no—
150#324C22×C1112yes—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11C2×#9911yescharacteristic
154C22×C11#41911yescharacteristic
155C22×C11C2×#10411yescharacteristic
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—42no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—81no—
166C4×C11—81no—
167C4×C11—81no—
168C22×Q8C2×C4×C1111yescharacteristic
169C22×Q8D4×C1111yescharacteristic
170C2×M16—22no—
171C4×Q8—41no—
172C4×Q8—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4C2×C4×C1111yescharacteristic
180C2×C4⋊C4C2×C4×C1111yescharacteristic
181C2×C4⋊C4D4×C1111yescharacteristic
182C2×C4⋊C4C23×C1111yescharacteristic
183C2×C42—21no—
184C2×C42C2×C4×C1111yescharacteristic
185C2×C42D4×C1111yescharacteristic
186C2×C42D4×C1111yescharacteristic
187C4⋊C8—41no—
188#101—24no—
189C22⋊C8—22no—
190#97—41no—
191#97—41no—
192C4×C8—41no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95C2×C4×C1111yescharacteristic
201#95C2×C4×C1111yescharacteristic
202C2×C11—21no—
203C2×C11—21no—
204C2×C11#150811yescharacteristic
205C2×C11#212011yescharacteristic
206C2×C11#213311yescharacteristic
207C2×Q8—22no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—42no—
211C2×Q8—41no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4C11×C22⋊C411yescharacteristic
217C22×C4C11×C22⋊C411yescharacteristic
218C22×C4C11×C22⋊C411yescharacteristic
219C22×C4C11×C22⋊C411yescharacteristic
220C22×C4C22×C4×C1111yescharacteristic
221C22×C4C2×D4×C1111yescharacteristic
222C22×C4C2×D4×C1111yescharacteristic
223M16—24no—
224M16—42no—
225C2×C8—42no—
226C2×C8—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—42no—
243C11#1179211yescharacteristic, direct product factor, Sylow
244C23C2×C11×C22⋊C411yescharacteristic
245Q8—44no—
246Q8—42no—
247Q8—42no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4C11×#9911yescharacteristic
274C2×C4C11×#9911yescharacteristic
275C2×C4C11×#10412yes—
276C2×C4C11×#13712yes—
277C8—44no—
278C8—82no—
279C22—21no—
280C22—21no—
281C22C2×C11×#9911yescharacteristic
282C22C11×#41911yescharacteristic
283C22C2×C11×#10411yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C2—21no—
297C2—21no—
298C2C11×#150811yescharacteristic
299C2C11×#212011yescharacteristic
300C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC23×C11C2×C22⋊C4
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
57. #11792C11direct (N × H)
243. C11#11792direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25812
C4×C11×#1012
C11×#14672
C11×#13542
C11×#13532
#1179211