Finite Group Databasebeta

← C11×#11506 #14588699

Subgroups — C11×#11506 #14588699

Order 2816.

598 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C2×C11×#391C211yesmaximal, characteristic
2C11×#1463C212yesmaximal
3C11×#1319C214yesmaximal, complemented
4C23×Q8×C11C411yescharacteristic
5C22×C11×C4⋊C4C2211yescharacteristic
6C22×C42×C11C411yescharacteristic
7C11×#407—22no—
8C11×#391—22no—
9C11×#391C412yes—
10C11×#391C2212yes—
11C2×C11×#95—22no—
12C11×#324—22no—
13C11×#324C2214yes—
14C22×Q8×C11—24no—
15C22×Q8×C11—21no—
16C22×Q8×C11—42no—
17C22×Q8×C11—41no—
18C22×Q8×C11—41no—
19C22×Q8×C11C2×C412yes—
20C23×C4×C11—21no—
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D412yes—
24C2×C11×M16—42no—
25C2×C11×C4⋊C4—41no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11—42no—
32C2×C42×C11C2×C412yes—
33C11×C22⋊C8—24no—
34C11×C22⋊C8—42no—
35C11×#95—24no—
36C11×#95—24no—
37#11506C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11C22⋊C411yescharacteristic
39C2×Q8×C11—24no—
40C2×Q8×C11—22no—
41C2×Q8×C11—48no—
42C2×Q8×C11—48no—
43C2×Q8×C11—42no—
44C2×Q8×C11—42no—
45C2×Q8×C11—42no—
46C2×Q8×C11—42no—
47C2×Q8×C11M1614yescomplemented
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—24no—
53C22×C4×C11—24no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—42no—
59C22×C4×C11—42no—
60C22×C4×C11—42no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—44no—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D412yes—
68C11×M16—84no—
69C2×C8×C11—44no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C42×C11—42no—
74C42×C11—42no—
75C2×#391C2×C1111yescharacteristic
76#1463C2×C1112yes—
77#1319C2×C1114yescomplemented
78C23×C11—22no—
79C23×C11—22no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11#9911yescharacteristic
83C23×C11#9911yescharacteristic
84C23×C11C2×C22⋊C411yescharacteristic
85Q8×C11—44no—
86Q8×C11—48no—
87Q8×C11—44no—
88C2×C4×C11—24no—
89C2×C4×C11—24no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—24no—
95C2×C4×C11—24no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—48no—
99C2×C4×C11—42no—
100C2×C4×C11—44no—
101C2×C4×C11—44no—
102C2×C4×C11—44no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11—82no—
109C2×C4×C11#10012yes—
110C2×C4×C11C2×M1612yes—
111C8×C11—84no—
112C23×Q8C4×C1111yescharacteristic
113C22×C4⋊C4C22×C1111yescharacteristic
114C22×C42C4×C1111yescharacteristic
115#407—22no—
116#391—22no—
117#391C4×C1112yes—
118#391C22×C1112yes—
119C2×#95—22no—
120#324—22no—
121#324C22×C1114yes—
122C22×C11—24no—
123C22×C11—24no—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#35412yes—
131C22×C11#35612yes—
132C22×C11#40711yescharacteristic
133C22×C11C2×#9911yescharacteristic
134C22×C11C2×#10011yescharacteristic
135C4×C11—22no—
136C4×C11—22no—
137C4×C11—44no—
138C4×C11—42no—
139C4×C11—42no—
140C4×C11—44no—
141C22×Q8—24no—
142C22×Q8—21no—
143C22×Q8—42no—
144C22×Q8—41no—
145C22×Q8—41no—
146C22×Q8C2×C4×C1112yes—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4C2×C4×C1111yescharacteristic
150C23×C4D4×C1112yes—
151C2×M16—42no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4C2×C4×C1111yescharacteristic
155C2×C4⋊C4D4×C1112yes—
156C2×C4⋊C4C23×C1111yescharacteristic
157C2×C42—21no—
158C2×C42—42no—
159C2×C42C2×C4×C1112yes—
160C22⋊C8—24no—
161C22⋊C8—42no—
162#95—24no—
163#95—24no—
164C2×C11—21no—
165C2×C11—22no—
166C2×C11—22no—
167C2×C11—21no—
168C2×C11#146211yescharacteristic
169C2×C11C2×#35411yescharacteristic
170C2×C11C2×#35611yescharacteristic
171C24C11×C22⋊C411yescharacteristic
172C2×Q8—24no—
173C2×Q8—22no—
174C2×Q8—48no—
175C2×Q8—48no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8C11×M1614yescomplemented
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—44no—
197C22×C4C11×C22⋊C411yescharacteristic
198C22×C4C11×C22⋊C412yes—
199C22×C4C22×C4×C1111yescharacteristic
200C22×C4C2×D4×C1112yes—
201M16—84no—
202C2×C8—44no—
203C4⋊C4—41no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C42—42no—
207C42—42no—
208C11#1150611yescharacteristic, direct product factor, Sylow
209C23—22no—
210C23—22no—
211C23—21no—
212C23—21no—
213C23C11×#9911yescharacteristic
214C23C11×#9911yescharacteristic
215C23C2×C11×C22⋊C411yescharacteristic
216Q8—44no—
217Q8—48no—
218Q8—44no—
219C2×C4—24no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—48no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—82no—
240C2×C4C11×#10012yes—
241C2×C4C2×C11×M1612yes—
242C8—84no—
243C22—24no—
244C22—24no—
245C22—21no—
246C22—21no—
247C22—21no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22C11×#35412yes—
252C22C11×#35612yes—
253C22C11×#40711yescharacteristic
254C22C2×C11×#9911yescharacteristic
255C22C2×C11×#10011yescharacteristic
256C4—22no—
257C4—22no—
258C4—44no—
259C4—42no—
260C4—42no—
261C4—44no—
262C2—21no—
263C2—22no—
264C2—22no—
265C2—21no—
266C2C11×#146211yescharacteristic
267C2C2×C11×#35411yescharacteristic
268C2C2×C11×#35611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC24×C11C22⋊C4
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
3. C11×#1319C2semidirect
37. #11506C11direct (N × H)
47. C2×Q8×C11M16semidirect
77. #1319C2×C11semidirect
180. C2×Q8C11×M16semidirect
208. C11#11506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3912
C11×#14632
C11×#13192
#1150611