Finite Group Databasebeta

← C11×#11519 #14588712

Subgroups — C11×#11519 #14588712

Order 2816.

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

normal subgroups only

This group has 542 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×#2315C211yesmaximal, characteristic
2C11×#1462C212yesmaximal
3C11×#1326C214yesmaximal, complemented
4C22×C11×C22⋊C4C411yescharacteristic
5C22×C11×C22⋊C4C411yescharacteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C11×#407—22no—
8C11×#385—22no—
9C11×#385C412yes—
10C11×#385C2212yes—
11C11×#380—22no—
12C11×#323—22no—
13C11×#323C2214yes—
14C25×C11C2×C411yescharacteristic
15C23×C4×C11—21no—
16C23×C4×C11C2×C412yes—
17C23×C4×C11D412yes—
18C2×C11×M16—42no—
19C2×C11×C4⋊C4—22no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C22⋊C4—21no—
22C2×C11×C22⋊C4—24no—
23C2×C11×C22⋊C4—21no—
24C2×C11×C22⋊C4—21no—
25C2×C11×C22⋊C4—41no—
26C2×C11×C22⋊C4—41no—
27C2×C11×C22⋊C4—41no—
28C2×C11×C22⋊C4—41no—
29C2×C11×C22⋊C4C2×C412yes—
30C2×C11×C22⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4D412yes—
32C2×C11×C22⋊C4C2311yescharacteristic
33C11×C22⋊C8—24no—
34C11×C22⋊C8—42no—
35C11×#95—22no—
36C11×#95—22no—
37#11519C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11—21no—
39C24×C11—21no—
40C24×C11—22no—
41C24×C11—22no—
42C24×C11—82no—
43C24×C11C22⋊C411yescharacteristic
44C24×C11C22⋊C411yescharacteristic
45C24×C11C22×C411yescharacteristic
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—24no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—42no—
52C22×C4×C11—82no—
53C22×C4×C11—82no—
54C22×C4×C11—82no—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C2×D412yes—
57C11×M16—84no—
58C2×C8×C11—44no—
59C11×C4⋊C4—82no—
60C11×C4⋊C4—82no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—41no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—41no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—41no—
69C11×C22⋊C4M1614yescomplemented
70#2315C2×C1111yescharacteristic
71#1462C2×C1112yes—
72#1326C2×C1114yescomplemented
73C23×C11—24no—
74C23×C11—24no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—42no—
82C23×C11—42no—
83C23×C11—42no—
84C23×C11—82no—
85C23×C11—82no—
86C23×C11—84no—
87C23×C11—84no—
88C23×C11#9911yescharacteristic
89C23×C11#9911yescharacteristic
90C23×C11#10112yes—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11C2×M1612yes—
93C2×C4×C11—24no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—44no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—82no—
105C2×C4×C11—84no—
106C2×C4×C11—84no—
107C8×C11—84no—
108C22×C22⋊C4C4×C1111yescharacteristic
109C22×C22⋊C4C4×C1111yescharacteristic
110C22×C22⋊C4C22×C1111yescharacteristic
111#407—22no—
112#385—22no—
113#385C4×C1112yes—
114#385C22×C1112yes—
115#380—22no—
116#323—22no—
117#323C22×C1114yes—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—84no—
134C22×C11—84no—
135C22×C11#40711yescharacteristic
136C22×C11C2×#9911yescharacteristic
137C22×C11C2×#10111yescharacteristic
138C4×C11—44no—
139C4×C11—42no—
140C4×C11—42no—
141C4×C11—82no—
142C25C2×C4×C1111yescharacteristic
143C23×C4—21no—
144C23×C4C2×C4×C1112yes—
145C23×C4D4×C1112yes—
146C2×M16—42no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—24no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—21no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4C2×C4×C1112yes—
158C2×C22⋊C4C2×C4×C1111yescharacteristic
159C2×C22⋊C4D4×C1112yes—
160C2×C22⋊C4C23×C1111yescharacteristic
161C22⋊C8—24no—
162C22⋊C8—42no—
163#95—22no—
164#95—22no—
165C2×C11—21no—
166C2×C11—21no—
167C2×C11—41no—
168C2×C11—41no—
169C2×C11—42no—
170C2×C11—42no—
171C2×C11#146311yescharacteristic
172C2×C11#212112yes—
173C24—21no—
174C24—21no—
175C24—22no—
176C24—22no—
177C24—82no—
178C24C11×C22⋊C411yescharacteristic
179C24C11×C22⋊C411yescharacteristic
180C24C22×C4×C1111yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—82no—
188C22×C4—82no—
189C22×C4—82no—
190C22×C4C11×C22⋊C412yes—
191C22×C4C2×D4×C1112yes—
192M16—84no—
193C2×C8—44no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C22⋊C4—24no—
197C22⋊C4—22no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—41no—
201C22⋊C4—42no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4C11×M1614yescomplemented
205C11#1151911yescharacteristic, direct product factor, Sylow
206C23—24no—
207C23—24no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—42no—
215C23—42no—
216C23—42no—
217C23—82no—
218C23—82no—
219C23—84no—
220C23—84no—
221C23C11×#9911yescharacteristic
222C23C11×#9911yescharacteristic
223C23C11×#10112yes—
224C23C2×C11×C22⋊C411yescharacteristic
225C23C2×C11×M1612yes—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—82no—
238C2×C4—84no—
239C2×C4—84no—
240C8—84no—
241C22—22no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—84no—
257C22—84no—
258C22C11×#40711yescharacteristic
259C22C2×C11×#9911yescharacteristic
260C22C2×C11×#10111yescharacteristic
261C4—44no—
262C4—42no—
263C4—42no—
264C4—82no—
265C2—21no—
266C2—21no—
267C2—41no—
268C2—41no—
269C2—42no—
270C2—42no—
271C2C11×#146311yescharacteristic
272C2C11×#212112yes—
subgroupG/H
center, socleC22×C11C2×#99
commutatorC24C22×C4×C11
Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC25×C11C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C24×C11 ◁ C22×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1326C2semidirect
37. #11519C11direct (N × H)
69. C11×C22⋊C4M16semidirect
72. #1326C2×C11semidirect
204. C22⋊C4C11×M16semidirect
205. C11#11519direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23152
C11×#14622
C11×#13262
#1151911