Finite Group Databasebeta

← #14651635

Subgroups — #14651635

Order 2816.

454 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#13077701C211yesmaximal, characteristic
2#13073978C211yesmaximal, characteristic
3#13067044C212yesmaximal
4#13066476C212yesmaximal
5C11×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C2211yescharacteristic
8C11×#423C2212yes—
9C2×C11×#101—21no—
10#10622843—21no—
11#10622637—24no—
12#10622599C412yes—
13#10622592C412yes—
14#10622586—21no—
15#10622549C2211yescharacteristic
16#10622546—22no—
17#10622539—22no—
18#10622538C2212yes—
19C11×#343—21no—
20#10622122—24no—
21C22×Q8×C11D411yescharacteristic
22C22×Dic22C2×C411yescharacteristic
23C2×C11×M16—22no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4C2×C412yes—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11C2×C411yescharacteristic
32C2×Dic11⋊C4—22no—
33C2×Dic11⋊C4—21no—
34C2×C4×Dic11—21no—
35C4×Dic22—22no—
36C4×Dic22—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11×#101—42no—
40C11⋊#95—22no—
41C11⋊#95—22no—
42C11⋊#95—22no—
43C11⋊#95—21no—
44C11⋊#95C2×C412yes—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—24no—
47C4⋊(C11⋊C8)—22no—
48#66867—24no—
49C4×C11⋊C8D414yes—
50#9488—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—21no—
53C2×Q8×C11—21no—
54C2×Q8×C11—22no—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C22×C411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—21no—
61C22×Dic11—22no—
62C22×Dic11—21no—
63C2×Dic22—22no—
64C2×Dic22—42no—
65C11×M16—42no—
66C11×M16—42no—
67C2×C8×C11—42no—
68C11×C4⋊C4—24no—
69C11×C4⋊C4—22no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11C2×D412yes—
73C42×C11#4112yes—
74C4⋊Dic11—22no—
75C4⋊Dic11—41no—
76C4⋊Dic11—41no—
77Dic11⋊C4—44no—
78Dic11⋊C4—41no—
79Dic11⋊C4—41no—
80C4×Dic11—42no—
81C2×C11⋊C8—24no—
82#2983—111no—
83#2581—111no—
84#1801D1111yescharacteristic
85#1487—112no—
86#1286—112no—
87C23×C11C2×C22⋊C411yescharacteristic
88Q8×C11—42no—
89Q8×C11—42no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11C4×D412yes—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11#12112yes—
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C2×C4×C11#13712yes—
104C2×Dic11—22no—
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—41no—
111C2×Dic11—42no—
112Dic22—24no—
113Dic22—42no—
114C8×C11—82no—
115C11⋊C8—44no—
116C2×C4×Q8—111no—
117C2×C4×Q8C2×D1111yescharacteristic
118#446—224no—
119#432—222no—
120#431—112no—
121#423C2×D1112yes—
122C2×#101—21no—
123#400—112no—
124#395—112no—
125#391—221no—
126#389—221no—
127#387—222no—
128#382—111no—
129#343—21no—
130Q8⋊C8—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11#38611yescharacteristic
134C22×C11#41711yescharacteristic
135C22×C11#41911yescharacteristic
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—42no—
140C4×C11—42no—
141C4×C11#46812yes—
142C4×C11#47012yes—
143Dic11—42no—
144Dic11—82no—
145Dic11—81no—
146C22×Q8—111no—
147C22×Q8C22⋊D1111yescharacteristic
148C2×M16—22no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—222no—
152C4×Q8—222no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—222no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4C4×D1112yes—
158C2×C4⋊C4C22⋊D1111yescharacteristic
159C2×C42—221no—
160C2×C42D4412yes—
161C2×C42C22×D1111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—224no—
165C4⋊C8—222no—
166#101—42no—
167C22⋊C8—222no—
168#97—224no—
169C4×C8—114no—
170#95—112no—
171#95—222no—
172#95—222no—
173#95—222no—
174#95—221no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#189111yescharacteristic
178C2×C11#189411yescharacteristic
179C2×C11#191211yescharacteristic
180C2×Q8—21no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—22no—
184C2×Q8—222no—
185C2×Q8—442no—
186C22×C4—221no—
187C22×C4—222no—
188C22×C4—221no—
189C22×C4(C2×D11)⋊C412yes—
190C22×C4(C2×D11)⋊C412yes—
191C22×C4C2×C4×D1111yescharacteristic
192C22×C4C2×D4411yescharacteristic
193C22×C4C2×C22⋊D1111yescharacteristic
194M16—42no—
195M16—42no—
196C2×C8—42no—
197C2×C8—224no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—222no—
201C4⋊C4—444no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C42—22no—
207C42—22no—
208C42—442no—
209C42D4×D1112yes—
210C42#434112yes—
211C11#948811yescharacteristic, complemented, Sylow
212C23C2×(C2×D11)⋊C411yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—224no—
216Q8—442no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—222no—
225C2×C4—441no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—441no—
231C2×C4—442no—
232C2×C4(C22⋊D11)⋊C412yes—
233C2×C4#6693511yescharacteristic
234C2×C4#6693911yescharacteristic
235C2×C4#6698511yescharacteristic
236C2×C4#6699212yes—
237C2×C4#6699511yescharacteristic
238C2×C4#6700412yes—
239C8—82no—
240C8—444no—
241C22—21no—
242C22—21no—
243C22#1062257111yescharacteristic
244C22#1062257911yescharacteristic
245C22#1062261711yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—442no—
252C4—882no—
253C4—881no—
254C4#1062265512yes—
255C4#1062266512yes—
256C2—21no—
257C2—21no—
258C2#1306903211yescharacteristic
259C2#1306904711yescharacteristic
260C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1801D11
hypocenterC11#9488
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
211. C11#9488semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130739782
#130670442
#130664762
C11×#18012
#948811