Finite Group Databasebeta

← C11×#33755 #14610948

Subgroups — C11×#33755 #14610948

Order 2816.

590 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 214 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×#2236C214yesmaximal, complemented
3C11×#2216C214yesmaximal, complemented
4C11×#2188C214yesmaximal, complemented
5C2×C11×C22⋊C16C211yesmaximal, characteristic
6C22×C11×Q16C2212yes—
7C23×C8×C11C2211yescharacteristic
8C2×C11×C22⋊Q8—22no—
9C2×C11×Q32C2214yescomplemented
10C22×C11×C16C2212yes—
11C11×#467—22no—
12C11×#467—22no—
13C11×#467C2214yes—
14C11×#467C2214yes—
15C2×C11×#107C2212yes—
16C2×C11×#103—22no—
17C11×#366C2214yescomplemented
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—
38C2×C11×C16—42no—
39C2×C11×C16C2314yes—
40C11×#107—22no—
41C11×#107C2314yes—
42C11×#103—24no—
43C11×#103—24no—
44#33755C1111yesmaximal, 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#2236C2×C1114yescomplemented
76#2216C2×C1114yescomplemented
77#2188C2×C1114yescomplemented
78C2×C22⋊C16C2×C1111yescharacteristic
79C23×C11—41no—
80C23×C11—41no—
81C23×C11Q3214yescomplemented
82C23×C11C2×D811yescharacteristic
83C23×C11C2×D812yes—
84Q8×C11—44no—
85Q8×C11—44no—
86Q8×C11—84no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11—44no—
94C2×C4×C11—44no—
95C2×C4×C11—84no—
96C2×C4×C11—84no—
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11C2×D812yes—
99C2×C4×C11C22×D411yescharacteristic
100C8×C11—21no—
101C8×C11—22no—
102C8×C11H(5,𝔽2)12yes—
103C22×Q16C22×C1112yes—
104C23×C8C22×C1111yescharacteristic
105C2×C22⋊Q8—22no—
106C2×Q32C22×C1114yescomplemented
107C22×C16C22×C1112yes—
108#467—22no—
109#467—22no—
110#467C22×C1114yes—
111#467C22×C1114yes—
112C2×#107C22×C1112yes—
113C2×#103—22no—
114#366C22×C1114yescomplemented
115#358C22×C1118yescomplemented
116C22⋊C16C22×C1114yes—
117C22×C11—22no—
118C22×C11—21no—
119C22×C11—22no—
120C22×C11—21no—
121C22×C11—44no—
122C22×C11C2×Q3212yes—
123C22×C11C2×Q3214yes—
124C22×C11C22×D811yescharacteristic
125C4×C11—21no—
126C4×C11—22no—
127C4×C11—84no—
128C4×C11—84no—
129C4×C11#53411yescharacteristic
130C4×C11#57511yescharacteristic
131C22×Q8—22no—
132C23×C4D4×C1111yescharacteristic
133C2×Q16—22no—
134C2×Q16—44no—
135C2×Q16C23×C1114yes—
136C22×C8—42no—
137C22×C8D4×C1112yes—
138C22×C8D4×C1111yescharacteristic
139C22×C8C23×C1112yes—
140C22×C8C23×C1111yescharacteristic
141C22⋊Q8—24no—
142C22⋊Q8—24no—
143C22⋊Q8—42no—
144C22⋊Q8—42no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—42no—
147C2×C22⋊C4—42no—
148Q32—44no—
149C2×C16—42no—
150C2×C16C23×C1114yes—
151#107—22no—
152#107C23×C1114yes—
153#103—24no—
154#103—24no—
155C2×C11—24no—
156C2×C11—22no—
157C2×C11#318611yescharacteristic
158C2×C11C22×Q3211yescharacteristic
159C2×C11#341411yescharacteristic
160C24C11×D811yescharacteristic
161C2×Q8—24no—
162C2×Q8—44no—
163C2×Q8—44no—
164C2×Q8—42no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4C11×D812yes—
170C22×C4C11×D811yescharacteristic
171C22×C4C2×D4×C1112yes—
172C22×C4C2×D4×C1111yescharacteristic
173Q16—28no—
174Q16—44no—
175C2×C8—22no—
176C2×C8—24no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8C2×D4×C1111yescharacteristic
180C2×C8C2×D4×C1112yes—
181C2×C8C24×C1111yescharacteristic
182C4⋊C4—24no—
183C4⋊C4—42no—
184C4⋊C4—44no—
185C4⋊C4—44no—
186C22⋊C4—44no—
187C22⋊C4—44no—
188C16—24no—
189C11#3375511yescharacteristic, direct product factor, Sylow
190C23—41no—
191C23—41no—
192C23C11×Q3214yescomplemented
193C23C2×C11×D811yescharacteristic
194C23C2×C11×D812yes—
195Q8—44no—
196Q8—44no—
197Q8—84no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—84no—
207C2×C4—84no—
208C2×C4C2×C11×D811yescharacteristic
209C2×C4C2×C11×D812yes—
210C2×C4C22×D4×C1111yescharacteristic
211C8—22no—
212C8—21no—
213C8C11×H(5,𝔽2)12yes—
214C22—22no—
215C22—21no—
216C22—22no—
217C22—21no—
218C22—44no—
219C22C2×C11×Q3212yes—
220C22C2×C11×Q3214yes—
221C22C22×C11×D811yescharacteristic
222C4—22no—
223C4—21no—
224C4—84no—
225C4—84no—
226C4C11×#53411yescharacteristic
227C4C11×#57511yescharacteristic
228C2—24no—
229C2—22no—
230C2C11×#318611yescharacteristic
231C2C22×C11×Q3211yescharacteristic
232C2C11×#341411yescharacteristic
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×#2236C2semidirect
3. C11×#2216C2semidirect
4. C11×#2188C2semidirect
9. C2×C11×Q32C22semidirect
17. C11×#366C22semidirect
18. C11×#358C22semidirect
44. #33755C11direct (N × H)
75. #2236C2×C11semidirect
76. #2216C2×C11semidirect
77. #2188C2×C11semidirect
81. C23×C11Q32semidirect
106. C2×Q32C22×C11semidirect
114. #366C22×C11semidirect
115. #358C22×C11semidirect
189. C11#33755direct (N × H)
192. C23C11×Q32semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C11×#22362
C11×#22162
C11×#21882
C2×C11×C22⋊C162
#3375511