Finite Group Databasebeta

← C11×#11503 #14588696

Subgroups — C11×#11503 #14588696

Order 2816.

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

normal subgroups only

This group has 670 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×#2309C211yesmaximal, characteristic
2C11×#1464C212yesmaximal, complemented
3C11×#1316C214yesmaximal, complemented
4C23×D4×C11C411yescharacteristic
5C2×C11×#117C411yescharacteristic
6C2×C11×#117C2211yescharacteristic
7C11×#432—22no—
8C11×#390—22no—
9C11×#390—22no—
10C11×#379C412yes—
11C11×#379C2212yes—
12C11×#324—22no—
13C11×#323C2214yes—
14C25×C11C2×C412yes—
15C22×D4×C11—24no—
16C22×D4×C11—21no—
17C22×D4×C11—21no—
18C22×D4×C11—41no—
19C22×D4×C11—41no—
20C22×D4×C11—42no—
21C23×C4×C11C2×C411yescharacteristic
22C11×#117—41no—
23C11×#117—41no—
24C11×#117—42no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D412yes—
27C2×C11×C22⋊C4—24no—
28C2×C11×C22⋊C4—24no—
29C2×C11×C22⋊C4C2×C412yes—
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11D412yes—
34C11×C4⋊C8—42no—
35C11×C22⋊C8—24no—
36C11×#97—42no—
37#11503C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11—22no—
39C24×C11—22no—
40C24×C11—42no—
41C24×C11—42no—
42C24×C11—84no—
43C24×C11M1614yes—
44C24×C11C22×C411yescharacteristic
45C2×D4×C11—24no—
46C2×D4×C11—24no—
47C2×D4×C11—48no—
48C2×D4×C11—48no—
49C2×D4×C11—42no—
50C2×D4×C11—42no—
51C2×D4×C11—41no—
52C2×D4×C11—41no—
53C2×D4×C11—42no—
54C22×C4×C11—22no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C2×D412yes—
63C2×C8×C11—44no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C22⋊C4—41no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—42no—
69C11×C22⋊C4—84no—
70C11×C22⋊C4—84no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11—42no—
74#2309C2×C1111yescharacteristic
75#1464C2×C1112yescomplemented
76#1316C2×C1114yescomplemented
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—24no—
80C23×C11—42no—
81C23×C11—44no—
82C23×C11—44no—
83C23×C11—44no—
84C23×C11—44no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11—84no—
88C23×C11—84no—
89C23×C11—88no—
90C23×C11—88no—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11C2×M1612yes—
93D4×C11—44no—
94D4×C11—44no—
95D4×C11—48no—
96C2×C4×C11—24no—
97C2×C4×C11—24no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—44no—
107C2×C4×C11—42no—
108C2×C4×C11#9911yescharacteristic
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11#10012yes—
111C8×C11—84no—
112C23×D4C4×C1111yescharacteristic
113C2×#117C4×C1111yescharacteristic
114C2×#117C22×C1111yescharacteristic
115#432—22no—
116#390—22no—
117#390—22no—
118#379C4×C1112yes—
119#379C22×C1112yes—
120#324—22no—
121#323C22×C1114yes—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—44no—
127C22×C11—44no—
128C22×C11—42no—
129C22×C11—44no—
130C22×C11—84no—
131C22×C11—88no—
132C22×C11—88no—
133C22×C11—84no—
134C22×C11#40711yescharacteristic
135C22×C11C2×#9911yescharacteristic
136C22×C11C2×#10011yescharacteristic
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—22no—
140C4×C11—42no—
141C4×C11—42no—
142C4×C11—82no—
143C25C2×C4×C1112yes—
144C22×D4—24no—
145C22×D4—21no—
146C22×D4—21no—
147C22×D4—41no—
148C22×D4—41no—
149C22×D4—42no—
150C23×C4C2×C4×C1111yescharacteristic
151#117—41no—
152#117—41no—
153#117—42no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4D4×C1112yes—
156C2×C22⋊C4—24no—
157C2×C22⋊C4—24no—
158C2×C22⋊C4C2×C4×C1112yes—
159C2×C22⋊C4C2×C4×C1111yescharacteristic
160C2×C22⋊C4C23×C1111yescharacteristic
161C2×C42—21no—
162C2×C42D4×C1112yes—
163C4⋊C8—42no—
164C22⋊C8—24no—
165#97—42no—
166C2×C11—21no—
167C2×C11—21no—
168C2×C11—42no—
169C2×C11—84no—
170C2×C11#146211yescharacteristic
171C2×C11#212212yes—
172C24—22no—
173C24—22no—
174C24—42no—
175C24—42no—
176C24—84no—
177C24C11×M1614yes—
178C24C22×C4×C1111yescharacteristic
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—48no—
182C2×D4—48no—
183C2×D4—42no—
184C2×D4—42no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4—42no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4C11×C22⋊C411yescharacteristic
194C22×C4C11×C22⋊C411yescharacteristic
195C22×C4C11×C22⋊C412yes—
196C22×C4C2×D4×C1112yes—
197C2×C8—44no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—41no—
202C22⋊C4—42no—
203C22⋊C4—84no—
204C22⋊C4—84no—
205C42—22no—
206C42—22no—
207C42—42no—
208C11#1150311yescharacteristic, direct product factor, Sylow
209C23—21no—
210C23—21no—
211C23—24no—
212C23—42no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—42no—
218C23—42no—
219C23—84no—
220C23—84no—
221C23—88no—
222C23—88no—
223C23C2×C11×C22⋊C411yescharacteristic
224C23C2×C11×M1612yes—
225D4—44no—
226D4—44no—
227D4—48no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—42no—
240C2×C4C11×#9911yescharacteristic
241C2×C4C11×#9911yescharacteristic
242C2×C4C11×#10012yes—
243C8—84no—
244C22—22no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—44no—
249C22—44no—
250C22—42no—
251C22—44no—
252C22—84no—
253C22—88no—
254C22—88no—
255C22—84no—
256C22C11×#40711yescharacteristic
257C22C2×C11×#9911yescharacteristic
258C22C2×C11×#10011yescharacteristic
259C4—21no—
260C4—21no—
261C4—22no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—84no—
269C2C11×#146211yescharacteristic
270C2C11×#212212yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC23×D4×C11C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1464C2semidirect
3. C11×#1316C2semidirect
37. #11503C11direct (N × H)
75. #1464C2×C11semidirect
76. #1316C2×C11semidirect
208. C11#11503direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23092
C11×#14642
C11×#13162
#1150311