Finite Group Databasebeta

← C11×#11480 #14588673

Subgroups — C11×#11480 #14588673

Order 2816.

440 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2326C211yesmaximal, characteristic
2C11×#1461C212yesmaximal, complemented
3C11×#1325C212yesmaximal, complemented
4C11×#1318C212yesmaximal
5C2×C11×#124C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×D4×C11C411yescharacteristic
8C11×#431—22no—
9C11×#391C411yescharacteristic
10C11×#390C2211yescharacteristic
11C11×#388—22no—
12C11×#385—22no—
13C11×#384C2211yescharacteristic
14C11×#376C411yescharacteristic
15C11×#324—22no—
16C11×#324C2214yes—
17C22×Q8×C11C2×C411yescharacteristic
18C22×D4×C11C2×C411yescharacteristic
19C23×C4×C11—21no—
20C11×#124—22no—
21C11×#124C814yescomplemented
22C4×Q8×C11—42no—
23C4×D4×C11—42no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4C2×C411yescharacteristic
26C2×C11×C4⋊C4D412yes—
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—22no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D412yes—
35C11×C4⋊C8—42no—
36C11×C22⋊C8—24no—
37C4×C8×C11—42no—
38C11×#95—21no—
39C11×#95—22no—
40C11×#95—21no—
41#11480C1111yesmaximal, characteristic, direct product factor, Sylow
42C24×C11—21no—
43C2×Q8×C11—41no—
44C2×Q8×C11—41no—
45C2×Q8×C11C2×C812yes—
46C2×Q8×C11M1612yes—
47C2×D4×C11—21no—
48C2×D4×C11—41no—
49C2×D4×C11—41no—
50C2×D4×C11C2×C812yes—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—42no—
55C22×C4×C11—82no—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D412yes—
61C2×C8×C11—44no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—82no—
66C11×C22⋊C4—28no—
67C11×C22⋊C4—42no—
68C11×C22⋊C4—82no—
69C42×C11—22no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—21no—
73C42×C11—41no—
74C42×C11C2×C812yes—
75#2326C2×C1111yescharacteristic
76#1461C2×C1112yescomplemented
77#1325C2×C1112yescomplemented
78#1318C2×C1112yes—
79C23×C11—22no—
80C23×C11—42no—
81C23×C11—42no—
82C23×C11—41no—
83C23×C11—41no—
84C23×C11C2×C22⋊C411yescharacteristic
85Q8×C11—42no—
86Q8×C11—42no—
87D4×C11—42no—
88D4×C11—42no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—84no—
107C2×C4×C11C22⋊C814yes—
108C2×C4×C11#9912yes—
109C2×C4×C11C22×C811yescharacteristic
110C2×C4×C11C2×M1611yescharacteristic
111C8×C11—84no—
112C2×#124C4×C1111yescharacteristic
113C2×C4×Q8C22×C1111yescharacteristic
114C2×C4×D4C4×C1111yescharacteristic
115#431—22no—
116#391C4×C1111yescharacteristic
117#390C22×C1111yescharacteristic
118#388—22no—
119#385—22no—
120#384C22×C1111yescharacteristic
121#376C4×C1111yescharacteristic
122#324—22no—
123#324C22×C1114yes—
124C22×C11—21no—
125C22×C11—21no—
126C22×C11—44no—
127C22×C11—42no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11C2×C22⋊C811yescharacteristic
132C22×C11C2×#9911yescharacteristic
133C22×C11#41311yescharacteristic
134C4×C11—22no—
135C4×C11—24no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—42no—
139C4×C11—41no—
140C4×C11—42no—
141C4×C11—81no—
142C4×C11—81no—
143C22×Q8C2×C4×C1111yescharacteristic
144C22×D4C2×C4×C1111yescharacteristic
145C23×C4—21no—
146#124—22no—
147#124C8×C1114yescomplemented
148C4×Q8—42no—
149C4×D4—42no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C2×C4×C1111yescharacteristic
152C2×C4⋊C4D4×C1112yes—
153C2×C4⋊C4C23×C1111yescharacteristic
154C2×C22⋊C4—22no—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—22no—
157C2×C42C2×C4×C1111yescharacteristic
158C2×C42C2×C4×C1111yescharacteristic
159C2×C42C2×C4×C1111yescharacteristic
160C2×C42D4×C1112yes—
161C4⋊C8—42no—
162C22⋊C8—24no—
163C4×C8—42no—
164#95—21no—
165#95—21no—
166#95—22no—
167C2×C11—21no—
168C2×C11—21no—
169C2×C11—82no—
170C2×C11#145911yescharacteristic
171C2×C11#212811yescharacteristic
172C2×C11#213311yescharacteristic
173C24—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C2×C8×C1112yes—
177C2×Q8C11×M1612yes—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4C2×C8×C1112yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—42no—
186C22×C4—82no—
187C22×C4C11×C22⋊C412yes—
188C22×C4C11×C22⋊C411yescharacteristic
189C22×C4C11×C22⋊C411yescharacteristic
190C22×C4C22×C4×C1111yescharacteristic
191C22×C4C2×D4×C1112yes—
192C2×C8—44no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—82no—
197C22⋊C4—28no—
198C22⋊C4—42no—
199C22⋊C4—82no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—21no—
204C42—41no—
205C42C2×C8×C1112yes—
206C11#1148011yescharacteristic, direct product factor, Sylow
207C23—22no—
208C23—42no—
209C23—42no—
210C23—41no—
211C23—41no—
212C23C2×C11×C22⋊C411yescharacteristic
213Q8—42no—
214Q8—42no—
215D4—42no—
216D4—42no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—84no—
235C2×C4C11×C22⋊C814yes—
236C2×C4C11×#9912yes—
237C2×C4C22×C8×C1111yescharacteristic
238C2×C4C2×C11×M1611yescharacteristic
239C8—84no—
240C22—21no—
241C22—21no—
242C22—44no—
243C22—42no—
244C22—82no—
245C22—81no—
246C22—81no—
247C22C2×C11×C22⋊C811yescharacteristic
248C22C2×C11×#9911yescharacteristic
249C22C11×#41311yescharacteristic
250C4—22no—
251C4—24no—
252C4—21no—
253C4—21no—
254C4—42no—
255C4—42no—
256C4—41no—
257C4—81no—
258C4—81no—
259C2—21no—
260C2—21no—
261C2—82no—
262C2C11×#145911yescharacteristic
263C2C11×#212811yescharacteristic
264C2C11×#213311yescharacteristic
subgroupG/H
center, socleC22×C11C2×#99
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11C2×C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#1461C2semidirect
3. C11×#1325C2semidirect
21. C11×#124C8semidirect
41. #11480C11direct (N × H)
76. #1461C2×C11semidirect
77. #1325C2×C11semidirect
147. #124C8×C11semidirect
206. C11#11480direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#23262
C11×#14612
C11×#13252
C11×#13182
#1148011