Finite Group Databasebeta

← C11×#9399 #14586592

Subgroups — C11×#9399 #14586592

Order 2816.

514 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2975C211yesmaximal, characteristic
2C11×#2563C211yesmaximal, characteristic
3C11×#1800C211yesmaximal, characteristic
4C11×#1548C212yesmaximal, complemented
5C11×#1303C212yesmaximal, complemented
6C2×C11×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C11C2211yescharacteristic
8C11×#436—24no—
9C11×#431C2212yes—
10C11×#423C2212yes—
11C2×C11×#100—21no—
12C11×#407—22no—
13C11×#393C414yes—
14C11×#390—21no—
15C11×#382—21no—
16C11×#380—22no—
17C4×C11×C4⋊C4C2211yescharacteristic
18C11×#343—21no—
19C11×#333—24no—
20C22×Q8×C11C2×C412yes—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C2×C11×M16—24no—
24C2×C11×M16—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—24no—
34C2×C11×C22⋊C4C2×C412yes—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11×C4⋊C8D414yes—
40C11×#100—42no—
41C11×C22⋊C8—24no—
42C11×C22⋊C8—22no—
43C4×C8×C11—22no—
44C11×#95—24no—
45C11×#95C2×C412yes—
46#9399C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11C22⋊C412yes—
48C2×Q8×C11—24no—
49C2×Q8×C11—82no—
50C2×D4×C11—22no—
51C2×D4×C11—21no—
52C2×D4×C11—22no—
53C2×D4×C11—21no—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—44no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×M16—42no—
64C11×M16—42no—
65C11×M16—84no—
66C2×C8×C11—24no—
67C2×C8×C11—42no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4—84no—
75C42×C11—41no—
76C42×C11—41no—
77C42×C11C2×D412yes—
78C42×C11#4112yes—
79#2975C2×C1111yescharacteristic
80#2563C2×C1111yescharacteristic
81#1800C2×C1111yescharacteristic
82#1548C2×C1112yescomplemented
83#1303C2×C1112yescomplemented
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11C2×C22⋊C411yescharacteristic
90Q8×C11—84no—
91D4×C11—42no—
92D4×C11—42no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—41no—
96C2×C4×C11—44no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—44no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—82no—
104C2×C4×C11C4×D412yes—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11#12112yes—
107C2×C4×C11#12311yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C11#13712yes—
110C2×C4×C11#13711yescharacteristic
111C8×C11—44no—
112C8×C11—82no—
113C2×C4⋊Q8C22×C1111yescharacteristic
114C2×C4×D4C22×C1111yescharacteristic
115#436—24no—
116#431C22×C1112yes—
117#423C22×C1112yes—
118C2×#100—21no—
119#407—22no—
120#393C4×C1114yes—
121#390—21no—
122#382—21no—
123#380—22no—
124C4×C4⋊C4C22×C1111yescharacteristic
125#343—21no—
126#333—24no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—44no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—82no—
134C22×C11#38611yescharacteristic
135C22×C11#41711yescharacteristic
136C22×C11#41911yescharacteristic
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11—82no—
141C4×C11—82no—
142C4×C11#45512yes—
143C4×C11#46812yes—
144C4×C11#47012yes—
145C22×Q8C2×C4×C1112yes—
146C22×D4D4×C1111yescharacteristic
147C23×C4D4×C1112yes—
148C2×M16—24no—
149C2×M16—22no—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4×D4—22no—
153C4×D4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4D4×C1111yescharacteristic
158C2×C22⋊C4—24no—
159C2×C22⋊C4C2×C4×C1112yes—
160C2×C42—21no—
161C2×C42C23×C1111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8D4×C1114yes—
165#100—42no—
166C22⋊C8—24no—
167C22⋊C8—22no—
168C4×C8—22no—
169#95—24no—
170#95C2×C4×C1112yes—
171C2×C11—21no—
172C2×C11—21no—
173C2×C11—82no—
174C2×C11#188511yescharacteristic
175C2×C11#189411yescharacteristic
176C2×C11#191411yescharacteristic
177C24C11×C22⋊C412yes—
178C2×Q8—24no—
179C2×Q8—82no—
180C2×D4—22no—
181C2×D4—21no—
182C2×D4—22no—
183C2×D4—21no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—44no—
189C22×C4C11×C22⋊C412yes—
190C22×C4C22×C4×C1111yescharacteristic
191C22×C4C2×D4×C1111yescharacteristic
192C22×C4C2×D4×C1111yescharacteristic
193M16—42no—
194M16—42no—
195M16—84no—
196C2×C8—24no—
197C2×C8—42no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C22⋊C4—24no—
204C22⋊C4—84no—
205C42—41no—
206C42—41no—
207C42C2×D4×C1112yes—
208C42C11×#4112yes—
209C11#939911yescharacteristic, direct product factor, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×C11×C22⋊C411yescharacteristic
216Q8—84no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—44no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—82no—
230C2×C4C4×D4×C1112yes—
231C2×C4C11×#12011yescharacteristic
232C2×C4C11×#12112yes—
233C2×C4C11×#12311yescharacteristic
234C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
235C2×C4C11×#13712yes—
236C2×C4C11×#13711yescharacteristic
237C8—44no—
238C8—82no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22C11×#38611yescharacteristic
247C22C11×#41711yescharacteristic
248C22C11×#41911yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—82no—
253C4—82no—
254C4C11×#45512yes—
255C4C11×#46812yes—
256C4C11×#47012yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2C11×#188511yescharacteristic
261C2C11×#189411yescharacteristic
262C2C11×#191411yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC22×C4C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1548C2semidirect
5. C11×#1303C2semidirect
46. #9399C11direct (N × H)
82. #1548C2×C11semidirect
83. #1303C2×C11semidirect
209. C11#9399direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29752
C11×#25632
C11×#18002
C11×#15482
C11×#13032
#939911