Finite Group Databasebeta

← #14651638

Subgroups — #14651638

Order 2816.

454 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 119 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#13068612C211yesmaximal, characteristic
3#13067045C212yesmaximal
4#13066474C212yesmaximal
5C11×#2581C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#400C412yes—
9C11×#395C412yes—
10C11×#391—21no—
11C11×#389—21no—
12C11×#387—22no—
13C11×#382C2211yescharacteristic
14C2×#66900—21no—
15#10622637—24no—
16#10622539—22no—
17#10622538C2212yes—
18#10622537C2212yes—
19Q8⋊(C11⋊C8)—24no—
20#10622168—21no—
21C22×Q8×C11C2×C411yescharacteristic
22C22×Q8×C11D411yescharacteristic
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11D412yes—
35C2×C42×C11C2311yescharacteristic
36C2×#4318—22no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95—22no—
40C11×#95—21no—
41C11×#95C2×C412yes—
42#66900—42no—
43C22⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—24no—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
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—
55C2×Q8×C11—22no—
56C2×Q8×C11—42no—
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×C4⋊C4—24no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—44no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—42no—
76C42×C11C2×D412yes—
77C42×C11#4112yes—
78#4318—42no—
79#4318—42no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—42no—
82#2983—111no—
83#2581D1111yescharacteristic
84#1801—111no—
85#1487—112no—
86#1286—112no—
87C23×C11C2×C22⋊C411yescharacteristic
88Q8×C11—24no—
89Q8×C11—42no—
90Q8×C11—42no—
91Q8×C11—42no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—41no—
106C2×C4×C11—42no—
107C2×C4×C11C4×D412yes—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12311yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C11#13712yes—
113C2×C4×C11#13711yescharacteristic
114C11⋊C8—44no—
115C11⋊C8—82no—
116C2×C4×Q8C2×D1111yescharacteristic
117C2×C4×Q8C2×D1111yescharacteristic
118#446—224no—
119#432—222no—
120#431—112no—
121#423—112no—
122C2×#101—221no—
123#400Dic1112yes—
124#395Dic1112yes—
125#391—21no—
126#389—21no—
127#387—22no—
128#382C2×D1111yescharacteristic
129#343—221no—
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—42no—
142C4×C11—82no—
143C4×C11—81no—
144C4×C11#46812yes—
145C4×C11#47012yes—
146C22×Q8C2×Dic1111yescharacteristic
147C22×Q8C22⋊D1111yescharacteristic
148C2×M16—222no—
149C4×Q8—22no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×Dic1111yescharacteristic
157C2×C4⋊C4C2×Dic1112yes—
158C2×C4⋊C4C22⋊D1111yescharacteristic
159C2×C42—21no—
160C2×C42C22⋊D1112yes—
161C2×C42C22×D1111yescharacteristic
162C4⋊C8—224no—
163C4⋊C8—222no—
164C4⋊C8—222no—
165C4⋊C8—222no—
166#101—442no—
167C22⋊C8—222no—
168#97—224no—
169C4×C8—114no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—21no—
174#95C2×Dic1112yes—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#189111yescharacteristic
178C2×C11#189411yescharacteristic
179C2×C11#191211yescharacteristic
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—42no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4C22⋊Dic1112yes—
190C22×C4C22⋊Dic1112yes—
191C22×C4C22×Dic1111yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193C22×C4C2×C22⋊D1111yescharacteristic
194M16—442no—
195M16—442no—
196C2×C8—224no—
197C2×C8—442no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—44no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C42—22no—
207C42—22no—
208C42—42no—
209C42D4×D1112yes—
210C42#434112yes—
211C11#948811yescharacteristic, complemented, Sylow
212C23C2×C22⋊Dic1111yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4D4×Dic1112yes—
233C2×C4#6698811yescharacteristic
234C2×C4#6699011yescharacteristic
235C2×C4#6699212yes—
236C2×C4#6699512yes—
237C2×C4#6700211yescharacteristic
238C2×C4#6700411yescharacteristic
239C8—444no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22#1062283311yescharacteristic
244C22#1062283811yescharacteristic
245C22#1062284511yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#1062266212yes—
255C4#1062266512yes—
256C2—21no—
257C2—21no—
258C2#1306903511yescharacteristic
259C2#1306905011yescharacteristic
260C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2581C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2581D11
hypocenterC11#9488
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

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
#130686122
#130670452
#130664742
C11×#25812
#948811