Finite Group Databasebeta

← C11×#11508 #14588701

Subgroups — C11×#11508 #14588701

Order 2816.

574 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2311C211yesmaximal, characteristic
2C11×#1463C212yesmaximal, complemented
3C11×#1319C212yesmaximal, complemented
4C11×#1318C212yesmaximal, complemented
5C22×C11×#41C411yescharacteristic
6C2×C11×#117C411yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C11×#407—22no—
9C11×#391C411yescharacteristic
10C11×#391C2211yescharacteristic
11C11×#390C411yescharacteristic
12C11×#390C2211yescharacteristic
13C11×#386—22no—
14C11×#380—22no—
15C11×#324—22no—
16C11×#324C2214yes—
17C2×C11×#41—22no—
18C2×C11×#41—22no—
19C2×C11×#41—42no—
20C2×C11×#41—42no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×D4×C11—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11—21no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D412yes—
27C2×C11×M16—42no—
28C11×#117—42no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—42no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D412yes—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C11×C22⋊C8—24no—
40C11×C22⋊C8—42no—
41C11×#95—22no—
42C11×#95—22no—
43#11508C1111yesmaximal, characteristic, direct product factor, Sylow
44C24×C11—21no—
45C24×C11C22⋊C411yescharacteristic
46C11×#41—48no—
47C11×#41—48no—
48C2×Q8×C11—21no—
49C2×Q8×C11—41no—
50C2×Q8×C11—41no—
51C2×Q8×C11M1612yescomplemented
52C2×D4×C11—24no—
53C2×D4×C11—21no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11M1612yescomplemented
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—24no—
64C22×C4×C11—22no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11—82no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D412yes—
76C11×M16—84no—
77C2×C8×C11—44no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C22⋊C4—42no—
83C11×C22⋊C4—82no—
84C11×C22⋊C4—82no—
85C42×C11—41no—
86C42×C11—41no—
87#2311C2×C1111yescharacteristic
88#1463C2×C1112yescomplemented
89#1319C2×C1112yescomplemented
90#1318C2×C1112yescomplemented
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—22no—
94C23×C11—41no—
95C23×C11—41no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#9912yes—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—42no—
103Q8×C11—42no—
104D4×C11—42no—
105D4×C11—42no—
106D4×C11—48no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—48no—
117C2×C4×C11—44no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—82no—
129C2×C4×C11#10012yes—
130C2×C4×C11C2×M1611yescharacteristic
131C2×C4×C11C2×M1611yescharacteristic
132C8×C11—84no—
133C22×#41C4×C1111yescharacteristic
134C2×#117C4×C1111yescharacteristic
135C22×C4⋊C4C22×C1111yescharacteristic
136#407—22no—
137#391C4×C1111yescharacteristic
138#391C22×C1111yescharacteristic
139#390C4×C1111yescharacteristic
140#390C22×C1111yescharacteristic
141#386—22no—
142#380—22no—
143#324—22no—
144#324C22×C1114yes—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11—44no—
153C22×C11—42no—
154C22×C11—82no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11#40711yescharacteristic
158C22×C11C2×#9911yescharacteristic
159C22×C11C2×#10011yescharacteristic
160C4×C11—22no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—42no—
164C4×C11—42no—
165C4×C11—42no—
166C4×C11—81no—
167C4×C11—81no—
168C2×#41—22no—
169C2×#41—22no—
170C2×#41—42no—
171C2×#41—42no—
172C22×Q8C2×C4×C1111yescharacteristic
173C22×D4—21no—
174C22×D4C2×C4×C1111yescharacteristic
175C23×C4—21no—
176C23×C4C2×C4×C1111yescharacteristic
177C23×C4D4×C1112yes—
178C2×M16—42no—
179#117—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4C2×C4×C1111yescharacteristic
183C2×C4⋊C4D4×C1112yes—
184C2×C4⋊C4C23×C1111yescharacteristic
185C2×C22⋊C4—21no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C42C2×C4×C1111yescharacteristic
189C2×C42C2×C4×C1111yescharacteristic
190C22⋊C8—24no—
191C22⋊C8—42no—
192#95—22no—
193#95—22no—
194C2×C11—21no—
195C2×C11—21no—
196C2×C11—42no—
197C2×C11—82no—
198C2×C11#146211yescharacteristic
199C2×C11#212711yescharacteristic
200C2×C11#213311yescharacteristic
201C24—21no—
202C24C11×C22⋊C411yescharacteristic
203#41—48no—
204#41—48no—
205C2×Q8—21no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8C11×M1612yescomplemented
209C2×D4—24no—
210C2×D4—21no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4C11×M1612yescomplemented
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—82no—
229C22×C4C11×C22⋊C411yescharacteristic
230C22×C4C11×C22⋊C412yes—
231C22×C4C22×C4×C1111yescharacteristic
232C22×C4C2×D4×C1112yes—
233M16—84no—
234C2×C8—44no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—82no—
241C22⋊C4—82no—
242C42—41no—
243C42—41no—
244C11#1150811yescharacteristic, direct product factor, Sylow
245C23—21no—
246C23—21no—
247C23—22no—
248C23—41no—
249C23—41no—
250C23—42no—
251C23—42no—
252C23—41no—
253C23—41no—
254C23C11×#9912yes—
255C23C2×C11×C22⋊C411yescharacteristic
256Q8—42no—
257Q8—42no—
258D4—42no—
259D4—42no—
260D4—48no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—82no—
283C2×C4C11×#10012yes—
284C2×C4C2×C11×M1611yescharacteristic
285C2×C4C2×C11×M1611yescharacteristic
286C8—84no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—44no—
295C22—42no—
296C22—82no—
297C22—81no—
298C22—81no—
299C22C11×#40711yescharacteristic
300C22C2×C11×#9911yescharacteristic
301C22C2×C11×#10011yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—42no—
306C4—42no—
307C4—42no—
308C4—81no—
309C4—81no—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—82no—
314C2C11×#146211yescharacteristic
315C2C11×#212711yescharacteristic
316C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×C11×#41C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1463C2semidirect
3. C11×#1319C2semidirect
4. C11×#1318C2semidirect
43. #11508C11direct (N × H)
51. C2×Q8×C11M16semidirect
58. C2×D4×C11M16semidirect
88. #1463C2×C11semidirect
89. #1319C2×C11semidirect
90. #1318C2×C11semidirect
208. C2×Q8C11×M16semidirect
215. C2×D4C11×M16semidirect
244. C11#11508direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23112
C11×#14632
C11×#13192
C11×#13182
#1150811