Finite Group Databasebeta

← C11×#10289 #14587482

Subgroups — C11×#10289 #14587482

Order 2816.

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

normal subgroups only

This group has 614 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×#3226C212yesmaximal
2C11×#2868C211yesmaximal, characteristic, complemented
3C11×#1962C211yesmaximal, characteristic
4C11×#1546C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6C11×#532C2211yescharacteristic
7C2×C11×C4⋊Q8—22no—
8C2×C11×C4⋊Q8C2212yes—
9C11×#500—22no—
10C11×#486—22no—
11C11×#480—24no—
12C11×#474—24no—
13C11×#431C2212yes—
14C11×#423C2211yescharacteristic
15C2×C11×#104—22no—
16C11×#384—24no—
17C43×C11C2211yescharacteristic
18C11×#332—24no—
19C2×C11×#41—21no—
20C22×Q8×C11—22no—
21C2×C11×M16—21no—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8—44no—
27C11×C4⋊Q8—44no—
28C11×C4⋊Q8D411yescharacteristic
29C11×#127D411yescharacteristic
30C11×#124—21no—
31C11×#121—22no—
32C4×D4×C11—22no—
33C2×C11×C4⋊C4—28no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4D414yes—
36C2×C42×C11—22no—
37C2×C42×C11D412yes—
38C2×C42×C11C2311yescharacteristic
39C11×#107—28no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8D414yes—
42C11×#104—44no—
43C11×#102—28no—
44C11×C22⋊C8—22no—
45C4×C8×C11—22no—
46#10289C1111yesmaximal, characteristic, direct product factor, Sylow
47C11×#41—42no—
48C11×#41—42no—
49C2×Q8×C11—21no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—44no—
53C2×Q8×C11—44no—
54C2×D4×C11—22no—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C22×C4×C11—22no—
58C22×C4×C11—24no—
59C22×C4×C11—41no—
60C22×C4×C11C2×D412yes—
61C22×C4×C11C2×D411yescharacteristic
62C11×M16—42no—
63C2×C8×C11—24no—
64C2×C8×C11—41no—
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—24no—
68C11×C4⋊C4—416no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C22⋊C4—42no—
72C42×C11—28no—
73C42×C11—22no—
74C42×C11D814yes—
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D412yes—
77C42×C11#4111yescharacteristic
78#3226C2×C1112yes—
79#2868C2×C1111yescharacteristic, complemented
80#1962C2×C1111yescharacteristic
81#1546C2×C1112yescomplemented
82#1276C2×C1111yescharacteristic, complemented
83C23×C11—41no—
84C23×C11#12011yescharacteristic
85Q8×C11—42no—
86Q8×C11—84no—
87Q8×C11—82no—
88Q8×C11—82no—
89D4×C11—44no—
90D4×C11—42no—
91D4×C11—82no—
92C2×C4×C11—28no—
93C2×C4×C11—24no—
94C2×C4×C11—24no—
95C2×C4×C11—41no—
96C2×C4×C11—44no—
97C2×C4×C11—48no—
98C2×C4×C11—81no—
99C2×C4×C11—81no—
100C2×C4×C11#12012yes—
101C2×C4×C11#12112yes—
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12711yescharacteristic
104C2×C4×C11C2×D812yes—
105C2×C4×C11AGL(1,ℤ/8)12yes—
106C8×C11—44no—
107C8×C11—81no—
108#532C22×C1111yescharacteristic
109C2×C4⋊Q8—22no—
110C2×C4⋊Q8C22×C1112yes—
111#500—22no—
112#486—22no—
113#480—24no—
114#474—24no—
115#431C22×C1112yes—
116#423C22×C1111yescharacteristic
117C2×#104—22no—
118#384—24no—
119C43C22×C1111yescharacteristic
120#332—24no—
121C22×C11—22no—
122C22×C11—82no—
123C22×C11—81no—
124C22×C11#39211yescharacteristic
125C22×C11#44712yes—
126C4×C11—28no—
127C4×C11—22no—
128C4×C11—84no—
129C4×C11—81no—
130C4×C11#45614yes—
131C4×C11#45912yes—
132C4×C11#49311yescharacteristic
133C4×C11#49611yescharacteristic
134C2×#41—21no—
135C22×Q8—22no—
136C2×M16—21no—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8—22no—
141C4⋊Q8—44no—
142C4⋊Q8—44no—
143C4⋊Q8D4×C1111yescharacteristic
144#127D4×C1111yescharacteristic
145#124—21no—
146#121—22no—
147C4×D4—22no—
148C2×C4⋊C4—28no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4D4×C1114yes—
151C2×C42—22no—
152C2×C42D4×C1112yes—
153C2×C42C23×C1111yescharacteristic
154#107—28no—
155C4⋊C8—22no—
156C4⋊C8D4×C1114yes—
157#104—44no—
158#102—28no—
159C22⋊C8—22no—
160C4×C8—22no—
161C2×C11—22no—
162C2×C11—161no—
163C2×C11#200512yes—
164C2×C11#201111yescharacteristic
165#41—42no—
166#41—42no—
167C2×Q8—21no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8—44no—
171C2×Q8—44no—
172C2×D4—22no—
173C2×D4—21no—
174C2×D4—41no—
175C22×C4—22no—
176C22×C4—24no—
177C22×C4—41no—
178C22×C4C2×D4×C1112yes—
179C22×C4C2×D4×C1111yescharacteristic
180M16—42no—
181C2×C8—24no—
182C2×C8—41no—
183C4⋊C4—24no—
184C4⋊C4—22no—
185C4⋊C4—24no—
186C4⋊C4—416no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—42no—
190C42—28no—
191C42—22no—
192C42C11×D814yes—
193C42C2×D4×C1111yescharacteristic
194C42C2×D4×C1112yes—
195C42C11×#4111yescharacteristic
196C11#1028911yescharacteristic, direct product factor, Sylow
197C23—41no—
198C23C11×#12011yescharacteristic
199Q8—42no—
200Q8—82no—
201Q8—82no—
202Q8—84no—
203D4—44no—
204D4—42no—
205D4—82no—
206C2×C4—28no—
207C2×C4—24no—
208C2×C4—24no—
209C2×C4—41no—
210C2×C4—44no—
211C2×C4—48no—
212C2×C4—81no—
213C2×C4—81no—
214C2×C4C11×#12012yes—
215C2×C4C11×#12112yes—
216C2×C4C11×#12111yescharacteristic
217C2×C4C11×#12711yescharacteristic
218C2×C4C2×C11×D812yes—
219C2×C4C11×AGL(1,ℤ/8)12yes—
220C8—44no—
221C8—81no—
222C22—22no—
223C22—82no—
224C22—81no—
225C22C11×#39211yescharacteristic
226C22C11×#44712yes—
227C4—28no—
228C4—22no—
229C4—84no—
230C4—81no—
231C4C11×#45614yes—
232C4C11×#45912yes—
233C4C11×#49311yescharacteristic
234C4C11×#49611yescharacteristic
235C2—22no—
236C2—161no—
237C2C11×#200512yes—
238C2C11×#201111yescharacteristic
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×#2868C2semidirect
4. C11×#1546C2semidirect
5. C11×#1276C2semidirect
46. #10289C11direct (N × H)
79. #2868C2×C11semidirect
81. #1546C2×C11semidirect
82. #1276C2×C11semidirect
196. C11#10289direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#28682
C11×#19622
C11×#15462
C11×#12762
#1028911