Finite Group Databasebeta

← C11×#10280 #14587473

Subgroups — C11×#10280 #14587473

Order 2816.

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

normal subgroups only

This group has 950 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×#3205C212yesmaximal, complemented
2C11×#2867C211yesmaximal, characteristic, complemented
3C11×#1962C211yesmaximal, characteristic, complemented
4C11×#1545C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6C11×#532C2211yescharacteristic
7C2×C11×#127—24no—
8C2×C11×#127—22no—
9C2×C11×#127C2212yes—
10C11×#493—22no—
11C11×#486—22no—
12C11×#459—24no—
13C11×#447—24no—
14C11×#431C2212yes—
15C11×#423C2211yescharacteristic
16C2×C11×#104—22no—
17C43×C11C2211yescharacteristic
18C11×#331—24no—
19C2×C11×#41—21no—
20C22×D4×C11—28no—
21C22×D4×C11—22no—
22C22×D4×C11—22no—
23C22×D4×C11D414yes—
24C2×C11×D8—28no—
25C2×C11×M16—21no—
26C11×C4⋊Q8D411yescharacteristic, complemented
27C11×#127—22no—
28C11×#127—22no—
29C11×#127—22no—
30C11×#127—22no—
31C11×#127—416no—
32C11×#127—44no—
33C11×#127—44no—
34C11×#127D411yescharacteristic, complemented
35C11×#124—21no—
36C11×#121—22no—
37C4×D4×C11—22no—
38C2×C42×C11—22no—
39C2×C42×C11D412yes—
40C2×C42×C11C2311yescharacteristic
41C11×C4⋊C8—22no—
42C11×C4⋊C8D414yescomplemented
43C11×#104—44no—
44C11×#102—28no—
45C11×C22⋊C8—22no—
46C4×C8×C11—22no—
47#10280C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11—24no—
49C11×#41—42no—
50C11×#41—42no—
51C2×Q8×C11—21no—
52C2×D4×C11—24no—
53C2×D4×C11—22no—
54C2×D4×C11—21no—
55C2×D4×C11—24no—
56C2×D4×C11—48no—
57C2×D4×C11—432no—
58C2×D4×C11—416no—
59C2×D4×C11—48no—
60C2×D4×C11—41no—
61C2×D4×C11—42no—
62C2×D4×C11—42no—
63C2×D4×C11—42no—
64C2×D4×C11—42no—
65C2×D4×C11—44no—
66C2×D4×C11—44no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C11×D8—88no—
72C11×M16—42no—
73C2×C8×C11—24no—
74C2×C8×C11—41no—
75C11×C4⋊C4—22no—
76C11×C22⋊C4—42no—
77C42×C11—28no—
78C42×C11—22no—
79C42×C11D814yescomplemented
80C42×C11C2×D411yescharacteristic
81C42×C11C2×D412yes—
82C42×C11#4111yescharacteristic
83#3205C2×C1112yescomplemented
84#2867C2×C1111yescharacteristic, complemented
85#1962C2×C1111yescharacteristic, complemented
86#1545C2×C1112yescomplemented
87#1276C2×C1111yescharacteristic, complemented
88C23×C11—48no—
89C23×C11—48no—
90C23×C11—41no—
91C23×C11—44no—
92C23×C11—48no—
93C23×C11#12011yescharacteristic
94Q8×C11—42no—
95D4×C11—44no—
96D4×C11—48no—
97D4×C11—42no—
98D4×C11—84no—
99D4×C11—832no—
100D4×C11—84no—
101D4×C11—82no—
102D4×C11—84no—
103D4×C11—84no—
104D4×C11—82no—
105D4×C11—82no—
106C2×C4×C11—28no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—41no—
110C2×C4×C11—81no—
111C2×C4×C11—81no—
112C2×C4×C11#12012yes—
113C2×C4×C11#12112yes—
114C2×C4×C11#12111yescharacteristic
115C2×C4×C11#12711yescharacteristic
116C2×C4×C11C2×D812yes—
117C2×C4×C11AGL(1,ℤ/8)12yes—
118C8×C11—44no—
119C8×C11—81no—
120#532C22×C1111yescharacteristic
121C2×#127—24no—
122C2×#127—22no—
123C2×#127C22×C1112yes—
124#493—22no—
125#486—22no—
126#459—24no—
127#447—24no—
128#431C22×C1112yes—
129#423C22×C1111yescharacteristic
130C2×#104—22no—
131C43C22×C1111yescharacteristic
132#331—24no—
133C22×C11—22no—
134C22×C11—816no—
135C22×C11—84no—
136C22×C11—82no—
137C22×C11—84no—
138C22×C11—81no—
139C22×C11—84no—
140C22×C11#39211yescharacteristic
141C22×C11#44712yes—
142C4×C11—28no—
143C4×C11—22no—
144C4×C11—81no—
145C4×C11#45314yes—
146C4×C11#45912yes—
147C4×C11#49311yescharacteristic
148C4×C11#49611yescharacteristic
149C2×#41—21no—
150C22×D4—28no—
151C22×D4—22no—
152C22×D4—22no—
153C22×D4D4×C1114yes—
154C2×D8—28no—
155C2×M16—21no—
156C4⋊Q8D4×C1111yescharacteristic, complemented
157#127—22no—
158#127—22no—
159#127—22no—
160#127—22no—
161#127—416no—
162#127—44no—
163#127—44no—
164#127D4×C1111yescharacteristic, complemented
165#124—21no—
166#121—22no—
167C4×D4—22no—
168C2×C42—22no—
169C2×C42D4×C1112yes—
170C2×C42C23×C1111yescharacteristic
171C4⋊C8—22no—
172C4⋊C8D4×C1114yescomplemented
173#104—44no—
174#102—28no—
175C22⋊C8—22no—
176C4×C8—22no—
177C2×C11—22no—
178C2×C11—161no—
179C2×C11—164no—
180C2×C11#200212yes—
181C2×C11#201111yescharacteristic
182C24—24no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×D4—24no—
187C2×D4—22no—
188C2×D4—21no—
189C2×D4—24no—
190C2×D4—48no—
191C2×D4—432no—
192C2×D4—416no—
193C2×D4—48no—
194C2×D4—41no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—44no—
200C2×D4—44no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4C2×D4×C1112yes—
204C22×C4C2×D4×C1111yescharacteristic
205D8—88no—
206M16—42no—
207C2×C8—24no—
208C2×C8—41no—
209C4⋊C4—22no—
210C22⋊C4—42no—
211C42—28no—
212C42—22no—
213C42C11×D814yescomplemented
214C42C2×D4×C1111yescharacteristic
215C42C2×D4×C1112yes—
216C42C11×#4111yescharacteristic
217C11#1028011yescharacteristic, direct product factor, Sylow
218C23—48no—
219C23—48no—
220C23—41no—
221C23—44no—
222C23—48no—
223C23C11×#12011yescharacteristic
224Q8—42no—
225D4—44no—
226D4—48no—
227D4—42no—
228D4—84no—
229D4—832no—
230D4—84no—
231D4—82no—
232D4—82no—
233D4—82no—
234D4—84no—
235D4—84no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—24no—
239C2×C4—41no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4C11×#12012yes—
243C2×C4C11×#12112yes—
244C2×C4C11×#12111yescharacteristic
245C2×C4C11×#12711yescharacteristic
246C2×C4C2×C11×D812yes—
247C2×C4C11×AGL(1,ℤ/8)12yes—
248C8—44no—
249C8—81no—
250C22—22no—
251C22—816no—
252C22—84no—
253C22—82no—
254C22—84no—
255C22—81no—
256C22—84no—
257C22C11×#39211yescharacteristic
258C22C11×#44712yes—
259C4—28no—
260C4—22no—
261C4—81no—
262C4C11×#45314yes—
263C4C11×#45912yes—
264C4C11×#49311yescharacteristic
265C4C11×#49611yescharacteristic
266C2—22no—
267C2—164no—
268C2—161no—
269C2C11×#200212yes—
270C2C11×#201111yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3205C2semidirect
2. C11×#2867C2semidirect
3. C11×#1962C2semidirect
4. C11×#1545C2semidirect
5. C11×#1276C2semidirect
26. C11×C4⋊Q8D4semidirect
34. C11×#127D4semidirect
42. C11×C4⋊C8D4semidirect
47. #10280C11direct (N × H)
79. C42×C11D8semidirect
83. #3205C2×C11semidirect
84. #2867C2×C11semidirect
85. #1962C2×C11semidirect
86. #1545C2×C11semidirect
87. #1276C2×C11semidirect
156. C4⋊Q8D4×C11semidirect
164. #127D4×C11semidirect
172. C4⋊C8D4×C11semidirect
213. C42C11×D8semidirect
217. C11#10280direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#28672
C11×#19622
C11×#15452
C11×#12762
#1028011