Finite Group Databasebeta

← C11×#33761 #14610954

Subgroups — C11×#33761 #14610954

Order 2816.

584 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 202 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
1C2×C11×#467C212yesmaximal
2C11×#2235C214yesmaximal, complemented
3C11×#2219C214yesmaximal, complemented
4C11×#2188C214yesmaximal, complemented
5C11×#2112C211yesmaximal, characteristic
6C22×C11×Q16C2212yes—
7C23×C8×C11C2211yescharacteristic
8C2×C11×C22⋊Q8—22no—
9C2×C11×Q32C2214yescomplemented
10C2×C11×M32C2212yes—
11C11×#467—22no—
12C11×#467—22no—
13C11×#467C2214yes—
14C11×#467C2214yes—
15C2×C11×#107C2212yes—
16C2×C11×#103—22no—
17C11×#367C2214yescomplemented
18C11×#358C2218yescomplemented
19C11×C22⋊C16C2214yes—
20C22×Q8×C11—22no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—22no—
23C2×C11×Q16—44no—
24C2×C11×Q16C2314yes—
25C22×C8×C11—42no—
26C22×C8×C11D412yes—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C22×C8×C11C2312yes—
30C11×C22⋊Q8—24no—
31C11×C22⋊Q8—24no—
32C11×C22⋊Q8—42no—
33C11×C22⋊Q8—42no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—42no—
36C2×C11×C22⋊C4—42no—
37C11×Q32—44no—
38C11×M32—42no—
39C2×C11×C16C2314yes—
40C11×#107—22no—
41C11×#107C2314yes—
42C11×#103—24no—
43C11×#103—24no—
44#33761C1111yesmaximal, characteristic, direct product factor, Sylow
45C24×C11D811yescharacteristic
46C2×Q8×C11—24no—
47C2×Q8×C11—44no—
48C2×Q8×C11—44no—
49C2×Q8×C11—42no—
50C22×C4×C11—41no—
51C22×C4×C11—41no—
52C22×C4×C11—42no—
53C22×C4×C11—42no—
54C22×C4×C11D812yes—
55C22×C4×C11D811yescharacteristic
56C22×C4×C11C2×D412yes—
57C22×C4×C11C2×D411yescharacteristic
58C11×Q16—28no—
59C11×Q16—44no—
60C2×C8×C11—22no—
61C2×C8×C11—24no—
62C2×C8×C11—41no—
63C2×C8×C11—42no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D412yes—
66C2×C8×C11C2411yescharacteristic
67C11×C4⋊C4—24no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—44no—
70C11×C4⋊C4—44no—
71C11×C22⋊C4—44no—
72C11×C22⋊C4—44no—
73C11×C16—24no—
74C2×#467C2×C1112yes—
75#2235C2×C1114yescomplemented
76#2219C2×C1114yescomplemented
77#2188C2×C1114yescomplemented
78#2112C2×C1111yescharacteristic
79C23×C11—24no—
80C23×C11—41no—
81C23×C11C2×D811yescharacteristic
82C23×C11C2×D812yes—
83Q8×C11—44no—
84Q8×C11—44no—
85Q8×C11—84no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—44no—
93C2×C4×C11—44no—
94C2×C4×C11—84no—
95C2×C4×C11—84no—
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11C2×D812yes—
98C2×C4×C11C22×D411yescharacteristic
99C8×C11—21no—
100C8×C11—22no—
101C8×C11H(5,𝔽2)12yes—
102C22×Q16C22×C1112yes—
103C23×C8C22×C1111yescharacteristic
104C2×C22⋊Q8—22no—
105C2×Q32C22×C1114yescomplemented
106C2×M32C22×C1112yes—
107#467—22no—
108#467—22no—
109#467C22×C1114yes—
110#467C22×C1114yes—
111C2×#107C22×C1112yes—
112C2×#103—22no—
113#367C22×C1114yescomplemented
114#358C22×C1118yescomplemented
115C22⋊C16C22×C1114yes—
116C22×C11—22no—
117C22×C11—22no—
118C22×C11—22no—
119C22×C11—21no—
120C22×C11—44no—
121C22×C11#51014yes—
122C22×C11C22×D811yescharacteristic
123C4×C11—21no—
124C4×C11—22no—
125C4×C11—84no—
126C4×C11—84no—
127C4×C11#53411yescharacteristic
128C4×C11#57511yescharacteristic
129C22×Q8—22no—
130C23×C4D4×C1111yescharacteristic
131C2×Q16—22no—
132C2×Q16—44no—
133C2×Q16C23×C1114yes—
134C22×C8—42no—
135C22×C8D4×C1112yes—
136C22×C8D4×C1111yescharacteristic
137C22×C8C23×C1112yes—
138C22×C8C23×C1111yescharacteristic
139C22⋊Q8—24no—
140C22⋊Q8—24no—
141C22⋊Q8—42no—
142C22⋊Q8—42no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—42no—
145C2×C22⋊C4—42no—
146Q32—44no—
147M32—42no—
148C2×C16C23×C1114yes—
149#107—22no—
150#107C23×C1114yes—
151#103—24no—
152#103—24no—
153C2×C11—24no—
154C2×C11—41no—
155C2×C11#318611yescharacteristic
156C2×C11C2×#51012yes—
157C24C11×D811yescharacteristic
158C2×Q8—24no—
159C2×Q8—44no—
160C2×Q8—44no—
161C2×Q8—42no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4C11×D812yes—
167C22×C4C11×D811yescharacteristic
168C22×C4C2×D4×C1112yes—
169C22×C4C2×D4×C1111yescharacteristic
170Q16—28no—
171Q16—44no—
172C2×C8—22no—
173C2×C8—24no—
174C2×C8—41no—
175C2×C8—42no—
176C2×C8C2×D4×C1111yescharacteristic
177C2×C8C2×D4×C1112yes—
178C2×C8C24×C1111yescharacteristic
179C4⋊C4—24no—
180C4⋊C4—42no—
181C4⋊C4—44no—
182C4⋊C4—44no—
183C22⋊C4—44no—
184C22⋊C4—44no—
185C16—24no—
186C11#3376111yescharacteristic, direct product factor, Sylow
187C23—24no—
188C23—41no—
189C23C2×C11×D811yescharacteristic
190C23C2×C11×D812yes—
191Q8—44no—
192Q8—44no—
193Q8—84no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—44no—
202C2×C4—84no—
203C2×C4—84no—
204C2×C4C2×C11×D811yescharacteristic
205C2×C4C2×C11×D812yes—
206C2×C4C22×D4×C1111yescharacteristic
207C8—22no—
208C8—21no—
209C8C11×H(5,𝔽2)12yes—
210C22—22no—
211C22—22no—
212C22—22no—
213C22—21no—
214C22—44no—
215C22C11×#51014yes—
216C22C22×C11×D811yescharacteristic
217C4—22no—
218C4—21no—
219C4—84no—
220C4—84no—
221C4C11×#53411yescharacteristic
222C4C11×#57511yescharacteristic
223C2—24no—
224C2—41no—
225C2C11×#318611yescharacteristic
226C2C2×C11×#51012yes—
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC24×C11D8
LCSG ▷ C2×C8 ▷ 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
2. C11×#2235C2semidirect
3. C11×#2219C2semidirect
4. C11×#2188C2semidirect
9. C2×C11×Q32C22semidirect
17. C11×#367C22semidirect
18. C11×#358C22semidirect
44. #33761C11direct (N × H)
75. #2235C2×C11semidirect
76. #2219C2×C11semidirect
77. #2188C2×C11semidirect
105. C2×Q32C22×C11semidirect
113. #367C22×C11semidirect
114. #358C22×C11semidirect
186. C11#33761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C11×#22352
C11×#22192
C11×#21882
C11×#21122
#3376111