Finite Group Databasebeta

← C11×#10287 #14587480

Subgroups — C11×#10287 #14587480

Order 2816.

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

normal subgroups only

This group has 566 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×#3206C212yesmaximal
2C11×#2862C211yesmaximal, characteristic, complemented
3C11×#1962C211yesmaximal, characteristic
4C11×#1548C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6C11×#532C2211yescharacteristic
7C2×C11×C4⋊Q8C2212yes—
8C11×#492—22no—
9C11×#487—22no—
10C11×#461—24no—
11C11×#448—24no—
12C11×#431C2212yes—
13C11×#423C2211yescharacteristic
14C2×C11×#104—22no—
15C11×#391—24no—
16C11×#382—22no—
17C43×C11C2211yescharacteristic
18C11×#333—24no—
19C2×C11×#41—21no—
20C22×Q8×C11D414yes—
21C2×C11×SD16—28no—
22C2×C11×M16—21no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8D411yescharacteristic
28C11×#127D411yescharacteristic
29C11×#124—21no—
30C11×#121—22no—
31C4×D4×C11—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C42×C11—22no—
35C2×C42×C11D412yes—
36C2×C42×C11C2311yescharacteristic
37C11×C4⋊C8—22no—
38C11×C4⋊C8D414yes—
39C11×#104—44no—
40C11×#103—28no—
41C11×C22⋊C8—22no—
42C4×C8×C11—22no—
43C11×#95—28no—
44#10287C1111yesmaximal, characteristic, direct product factor, Sylow
45C11×#41—42no—
46C11×#41—42no—
47C2×Q8×C11—24no—
48C2×Q8×C11—21no—
49C2×Q8×C11—24no—
50C2×Q8×C11—48no—
51C2×D4×C11—22no—
52C2×D4×C11—21no—
53C2×D4×C11—41no—
54C22×C4×C11—22no—
55C22×C4×C11—24no—
56C22×C4×C11—41no—
57C22×C4×C11C2×D412yes—
58C22×C4×C11C2×D411yescharacteristic
59C11×SD16—88no—
60C11×M16—42no—
61C2×C8×C11—24no—
62C2×C8×C11—41no—
63C11×C4⋊C4—22no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C11×C22⋊C4—42no—
69C42×C11—22no—
70C42×C11—44no—
71C42×C11SD1614yescomplemented
72C42×C11C2×D411yescharacteristic
73C42×C11C2×D412yes—
74C42×C11#4111yescharacteristic
75#3206C2×C1112yes—
76#2862C2×C1111yescharacteristic, complemented
77#1962C2×C1111yescharacteristic
78#1548C2×C1112yescomplemented
79#1276C2×C1111yescharacteristic, complemented
80C23×C11—41no—
81C23×C11#12011yescharacteristic
82Q8×C11—48no—
83Q8×C11—42no—
84Q8×C11—84no—
85D4×C11—44no—
86D4×C11—42no—
87D4×C11—82no—
88C2×C4×C11—24no—
89C2×C4×C11—24no—
90C2×C4×C11—44no—
91C2×C4×C11—48no—
92C2×C4×C11—41no—
93C2×C4×C11—44no—
94C2×C4×C11—81no—
95C2×C4×C11—81no—
96C2×C4×C11#12012yes—
97C2×C4×C11#12112yes—
98C2×C4×C11#12111yescharacteristic
99C2×C4×C11#12711yescharacteristic
100C2×C4×C11C2×SD1612yes—
101C2×C4×C11#13712yes—
102C8×C11—44no—
103C8×C11—81no—
104#532C22×C1111yescharacteristic
105C2×C4⋊Q8C22×C1112yes—
106#492—22no—
107#487—22no—
108#461—24no—
109#448—24no—
110#431C22×C1112yes—
111#423C22×C1111yescharacteristic
112C2×#104—22no—
113#391—24no—
114#382—22no—
115C43C22×C1111yescharacteristic
116#333—24no—
117C22×C11—22no—
118C22×C11—82no—
119C22×C11—81no—
120C22×C11#39211yescharacteristic
121C22×C11#44812yes—
122C4×C11—22no—
123C4×C11—44no—
124C4×C11—84no—
125C4×C11—81no—
126C4×C11#45514yes—
127C4×C11#46112yes—
128C4×C11#49211yescharacteristic
129C4×C11#49711yescharacteristic
130C2×#41—21no—
131C22×Q8D4×C1114yes—
132C2×SD16—28no—
133C2×M16—21no—
134C4⋊Q8—22no—
135C4⋊Q8—22no—
136C4⋊Q8—22no—
137C4⋊Q8—22no—
138C4⋊Q8D4×C1111yescharacteristic
139#127D4×C1111yescharacteristic
140#124—21no—
141#121—22no—
142C4×D4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C42—22no—
146C2×C42D4×C1112yes—
147C2×C42C23×C1111yescharacteristic
148C4⋊C8—22no—
149C4⋊C8D4×C1114yes—
150#104—44no—
151#103—28no—
152C22⋊C8—22no—
153C4×C8—22no—
154#95—28no—
155C2×C11—22no—
156C2×C11—161no—
157C2×C11#200412yes—
158C2×C11#201311yescharacteristic
159#41—42no—
160#41—42no—
161C2×Q8—24no—
162C2×Q8—21no—
163C2×Q8—24no—
164C2×Q8—48no—
165C2×D4—22no—
166C2×D4—21no—
167C2×D4—41no—
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—41no—
171C22×C4C2×D4×C1112yes—
172C22×C4C2×D4×C1111yescharacteristic
173SD16—88no—
174M16—42no—
175C2×C8—24no—
176C2×C8—41no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—22no—
184C42—44no—
185C42C11×SD1614yescomplemented
186C42C2×D4×C1111yescharacteristic
187C42C2×D4×C1112yes—
188C42C11×#4111yescharacteristic
189C11#1028711yescharacteristic, direct product factor, Sylow
190C23—41no—
191C23C11×#12011yescharacteristic
192Q8—48no—
193Q8—42no—
194Q8—84no—
195D4—44no—
196D4—42no—
197D4—82no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—44no—
201C2×C4—48no—
202C2×C4—41no—
203C2×C4—44no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4C11×#12012yes—
207C2×C4C11×#12112yes—
208C2×C4C11×#12111yescharacteristic
209C2×C4C11×#12711yescharacteristic
210C2×C4C2×C11×SD1612yes—
211C2×C4C11×#13712yes—
212C8—44no—
213C8—81no—
214C22—22no—
215C22—82no—
216C22—81no—
217C22C11×#39211yescharacteristic
218C22C11×#44812yes—
219C4—22no—
220C4—44no—
221C4—84no—
222C4—81no—
223C4C11×#45514yes—
224C4C11×#46112yes—
225C4C11×#49211yescharacteristic
226C4C11×#49711yescharacteristic
227C2—22no—
228C2—161no—
229C2C11×#200412yes—
230C2C11×#201311yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
2. C11×#2862C2semidirect
4. C11×#1548C2semidirect
5. C11×#1276C2semidirect
44. #10287C11direct (N × H)
71. C42×C11SD16semidirect
76. #2862C2×C11semidirect
78. #1548C2×C11semidirect
79. #1276C2×C11semidirect
185. C42C11×SD16semidirect
189. C11#10287direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32062
C11×#28622
C11×#19622
C11×#15482
C11×#12762
#1028711