Finite Group Databasebeta

← C11×#9508 #14586701

Subgroups — C11×#9508 #14586701

Order 2816.

542 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2975C211yesmaximal, characteristic
2C11×#2486C211yesmaximal, characteristic
3C11×#1821C212yesmaximal, complemented
4C11×#1465C211yesmaximal, characteristic
5C11×#1305C212yesmaximal, complemented
6C2×C11×#123C412yes—
7C2×C4×D4×C11C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C11×#436—24no—
10C11×#431—21no—
11C11×#407—21no—
12C11×#407C2212yes—
13C11×#407C2212yes—
14C11×#398—21no—
15C11×#397—21no—
16C11×#389—21no—
17C11×#381C412yes—
18C11×#380—21no—
19C11×#380C2211yescharacteristic
20C11×#343—24no—
21C11×#324—21no—
22C11×#323—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11C2×C412yes—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C2×C11×M16—22no—
28C2×C11×M16—22no—
29C2×C11×M16D414yes—
30C11×#123—44no—
31C4×D4×C11—22no—
32C4×D4×C11—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4C2×C411yescharacteristic
42C2×C11×C22⋊C4C2×C412yes—
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C42×C11D411yescharacteristic
45C11×C4⋊C8—22no—
46C11×C22⋊C8—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—22no—
51C4×C8×C11—22no—
52C11×#95—22no—
53C11×#95—22no—
54C11×#95—21no—
55#9508C1111yesmaximal, characteristic, direct product factor, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22×C411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—24no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4112yes—
77C11×M16—44no—
78C11×M16—44no—
79C11×M16—82no—
80C2×C8×C11—24no—
81C2×C8×C11—42no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—44no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—44no—
91C11×C22⋊C4—42no—
92C42×C11—21no—
93C42×C11—21no—
94#2975C2×C1111yescharacteristic
95#2486C2×C1111yescharacteristic
96#1821C2×C1112yescomplemented
97#1465C2×C1111yescharacteristic
98#1305C2×C1112yescomplemented
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11C2×C22⋊C411yescharacteristic
109C23×C11C4×D412yes—
110D4×C11—44no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—81no—
129C2×C4×C11—84no—
130C2×C4×C11#10012yes—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12112yes—
133C2×C4×C11#12311yescharacteristic
134C8×C11—44no—
135C8×C11—82no—
136C2×#123C4×C1112yes—
137C2×C4×D4C22×C1111yescharacteristic
138C22×C4⋊C4C22×C1111yescharacteristic
139#436—24no—
140#431—21no—
141#407—21no—
142#407C22×C1112yes—
143#407C22×C1112yes—
144#398—21no—
145#397—21no—
146#389—21no—
147#381C4×C1112yes—
148#380—21no—
149#380C22×C1111yescharacteristic
150#343—24no—
151#324—21no—
152#323—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—81no—
165C22×C11#38611yescharacteristic
166C22×C11C2×#10011yescharacteristic
167C22×C11#41311yescharacteristic
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—82no—
174C4×C11—82no—
175C4×C11#45812yes—
176C22×D4C2×C4×C1111yescharacteristic
177C23×C4C2×C4×C1112yes—
178C23×C4D4×C1111yescharacteristic
179C23×C4C23×C1111yescharacteristic
180C2×M16—22no—
181C2×M16—22no—
182C2×M16D4×C1114yes—
183#123—44no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4D4×C1111yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4C2×C4×C1111yescharacteristic
195C2×C22⋊C4C2×C4×C1112yes—
196C2×C22⋊C4D4×C1111yescharacteristic
197C2×C42D4×C1111yescharacteristic
198C4⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204C4×C8—22no—
205#95—22no—
206#95—22no—
207#95—21no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—42no—
211C2×C11—81no—
212C2×C11#189011yescharacteristic
213C2×C11#190011yescharacteristic
214C2×C11#191511yescharacteristic
215C24C11×C22⋊C411yescharacteristic
216C24C22×C4×C1111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4C11×C22⋊C411yescharacteristic
230C22×C4C11×C22⋊C411yescharacteristic
231C22×C4C11×C22⋊C411yescharacteristic
232C22×C4C2×D4×C1112yes—
233C22×C4C2×D4×C1111yescharacteristic
234C22×C4C2×D4×C1111yescharacteristic
235C22×C4C11×#4112yes—
236M16—44no—
237M16—44no—
238M16—82no—
239C2×C8—24no—
240C2×C8—42no—
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—44no—
244C4⋊C4—41no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C42—21no—
252C42—21no—
253C11#950811yescharacteristic, direct product factor, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C11×C22⋊C411yescharacteristic
264C23C4×D4×C1112yes—
265D4—44no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—84no—
285C2×C4C11×#10012yes—
286C2×C4C11×#12011yescharacteristic
287C2×C4C11×#12112yes—
288C2×C4C11×#12311yescharacteristic
289C8—44no—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C11×#38611yescharacteristic
304C22C2×C11×#10011yescharacteristic
305C22C11×#41311yescharacteristic
306C4—22no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4C11×#45812yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—81no—
318C2C11×#189011yescharacteristic
319C2C11×#190011yescharacteristic
320C2C11×#191511yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC24C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1821C2semidirect
5. C11×#1305C2semidirect
55. #9508C11direct (N × H)
96. #1821C2×C11semidirect
98. #1305C2×C11semidirect
253. C11#9508direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29752
C11×#24862
C11×#18212
C11×#14652
C11×#13052
#950811