Finite Group Databasebeta

← C11×#7264 #14584457

Subgroups — C11×#7264 #14584457

Order 2816.

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

normal subgroups only

This group has 374 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×#2112C211yesmaximal, characteristic
2C11×#1810C211yesmaximal, characteristic
3C2×C11×#340C211yesmaximal, characteristic
4C23×C8×C11C2211yescharacteristic
5C22×C11×C4⋊C4—21no—
6C2×C11×M32—21no—
7C2×C11×#108C412yescomplemented
8C11×#407—21no—
9C11×C22⋊C16—21no—
10C11×C22⋊C16C412yescomplemented
11C11×#341—21no—
12C11×#340—21no—
13C11×#340C412yes—
14C23×C4×C11—41no—
15C23×C4×C11D411yescharacteristic
16C2×C11×M16—22no—
17C22×C8×C11—42no—
18C22×C8×C11C2×C411yescharacteristic
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2×C411yescharacteristic
21C22×C8×C11D411yescharacteristic
22C22×C8×C11D411yescharacteristic
23C22×C8×C11Q811yescharacteristic
24C2×C11×C4⋊C4—24no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—42no—
27C2×C11×C4⋊C4—41no—
28C11×M32—42no—
29C2×C11×C16—22no—
30C11×#108—42no—
31C11×C22⋊C8—41no—
32C11×C22⋊C8—41no—
33#7264C1111yesmaximal, characteristic, direct product factor, Sylow
34C24×C11SD1611yescharacteristic
35C22×C4×C11—22no—
36C22×C4×C11—22no—
37C22×C4×C11—44no—
38C22×C4×C11—42no—
39C22×C4×C11—82no—
40C22×C4×C11—82no—
41C22×C4×C11C22⋊C411yescharacteristic
42C22×C4×C11C22⋊C411yescharacteristic
43C22×C4×C11C4⋊C411yescharacteristic
44C22×C4×C11D811yescharacteristic
45C22×C4×C11SD1611yescharacteristic
46C22×C4×C11Q1611yescharacteristic
47C11×M16—42no—
48C11×M16—42no—
49C2×C8×C11—22no—
50C2×C8×C11—22no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11—42no—
56C2×C8×C11C4211yescharacteristic
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C4⋊C411yescharacteristic
59C2×C8×C11C4⋊C411yescharacteristic
60C11×C4⋊C4—24no—
61C11×C4⋊C4—44no—
62C11×C4⋊C4—42no—
63C11×C16—42no—
64#2112C2×C1111yescharacteristic
65#1810C2×C1111yescharacteristic
66C2×#340C2×C1111yescharacteristic
67C23×C11—22no—
68C23×C11—21no—
69C23×C11—21no—
70C23×C11—22no—
71C23×C11#10211yescharacteristic
72C23×C11#10311yescharacteristic
73C23×C11#10611yescharacteristic
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—44no—
82C2×C4×C11—88no—
83C2×C4×C11—82no—
84C2×C4×C11—82no—
85C2×C4×C11#9511yescharacteristic
86C2×C4×C11#9912yes—
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10311yescharacteristic
89C2×C4×C11#10412yes—
90C2×C4×C11#10711yescharacteristic
91C8×C11—21no—
92C8×C11—21no—
93C8×C11—21no—
94C8×C11—21no—
95C8×C11—82no—
96C23×C8C22×C1111yescharacteristic
97C22×C4⋊C4—21no—
98C2×M32—21no—
99C2×#108C4×C1112yescomplemented
100#407—21no—
101C22⋊C16—21no—
102C22⋊C16C4×C1112yescomplemented
103#341—21no—
104#340—21no—
105#340C4×C1112yes—
106C22×C11—24no—
107C22×C11—24no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—21no—
112C22×C11—21no—
113C22×C11—21no—
114C22×C11#32812yes—
115C22×C11#34011yescharacteristic
116C22×C11#36111yescharacteristic
117C22×C11#36211yescharacteristic
118C22×C11#36512yes—
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—84no—
122C4×C11#32712yes—
123C4×C11#33911yescharacteristic
124C4×C11#34211yescharacteristic
125C23×C4—41no—
126C23×C4D4×C1111yescharacteristic
127C2×M16—22no—
128C22×C8—42no—
129C22×C8C2×C4×C1111yescharacteristic
130C22×C8C2×C4×C1111yescharacteristic
131C22×C8C2×C4×C1111yescharacteristic
132C22×C8D4×C1111yescharacteristic
133C22×C8D4×C1111yescharacteristic
134C22×C8Q8×C1111yescharacteristic
135C2×C4⋊C4—24no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4—41no—
139M32—42no—
140C2×C16—22no—
141#108—42no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C2×C11—21no—
145C2×C11—22no—
146C2×C11—21no—
147C2×C11—22no—
148C2×C11#129411yescharacteristic
149C2×C11#138311yescharacteristic
150C2×C11#138711yescharacteristic
151C24C11×SD1611yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—44no—
155C22×C4—42no—
156C22×C4—82no—
157C22×C4—82no—
158C22×C4C11×C22⋊C411yescharacteristic
159C22×C4C11×C22⋊C411yescharacteristic
160C22×C4C11×C4⋊C411yescharacteristic
161C22×C4C11×D811yescharacteristic
162C22×C4C11×SD1611yescharacteristic
163C22×C4C11×Q1611yescharacteristic
164M16—42no—
165M16—42no—
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8C42×C1111yescharacteristic
174C2×C8C11×C22⋊C411yescharacteristic
175C2×C8C11×C4⋊C411yescharacteristic
176C2×C8C11×C4⋊C411yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—44no—
179C4⋊C4—42no—
180C16—42no—
181C11#726411yescharacteristic, direct product factor, Sylow
182C23—22no—
183C23—21no—
184C23—21no—
185C23—22no—
186C23C11×#10211yescharacteristic
187C23C11×#10311yescharacteristic
188C23C11×#10611yescharacteristic
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—44no—
197C2×C4—88no—
198C2×C4—82no—
199C2×C4—82no—
200C2×C4C11×#9511yescharacteristic
201C2×C4C11×#9912yes—
202C2×C4C11×#10211yescharacteristic
203C2×C4C11×#10311yescharacteristic
204C2×C4C11×#10412yes—
205C2×C4C11×#10711yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—21no—
210C8—82no—
211C22—24no—
212C22—24no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—21no—
218C22—21no—
219C22C11×#32812yes—
220C22C11×#34011yescharacteristic
221C22C11×#36111yescharacteristic
222C22C11×#36211yescharacteristic
223C22C11×#36512yes—
224C4—21no—
225C4—21no—
226C4—84no—
227C4C11×#32712yes—
228C4C11×#33911yescharacteristic
229C4C11×#34211yescharacteristic
230C2—21no—
231C2—22no—
232C2—21no—
233C2—22no—
234C2C11×#129411yescharacteristic
235C2C11×#138311yescharacteristic
236C2C11×#138711yescharacteristic
subgroupG/H
center, socleC22×C11#340
commutatorC2×C8C42×C11
Frattini, cosocleC23×C8C22×C11
prime radicalC24×C11SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C11×#108C4semidirect
10. C11×C22⋊C16C4semidirect
33. #7264C11direct (N × H)
99. C2×#108C4×C11semidirect
102. C22⋊C16C4×C11semidirect
181. C11#7264direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21122
C11×#18102
C2×C11×#3402
#726411