Finite Group Databasebeta

← #14651617

Subgroups — #14651617

Order 2816.

474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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#13073978C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13067046C212yesmaximal
4#13066475C212yesmaximal
5C11×#2982C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C2211yescharacteristic
8C8×Q8×C11—24no—
9C11×#431—22no—
10C11×#431C2212yes—
11#10622843—21no—
12C2×#66900—21no—
13#10622599C412yes—
14#10622592C412yes—
15#10622586—21no—
16#10622549C2211yescharacteristic
17#10622546—22no—
18#10622537C2212yes—
19#10622168—21no—
20#10622094—24no—
21C22×Q8×C11D411yescharacteristic
22C22×Dic22C2×C411yescharacteristic
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4C2×C412yes—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11D412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11C2×C411yescharacteristic
31C2×Dic11⋊C4—22no—
32C2×Dic11⋊C4—21no—
33C2×C4×Dic11—21no—
34C2×#4318—22no—
35C4×Dic22—22no—
36C4×Dic22—22no—
37C11×C4⋊C8—24no—
38C11×C4⋊C8—22no—
39C11×C22⋊C8—22no—
40C4×C8×C11—24no—
41C4×C8×C11D414yes—
42#66900—42no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95C2×C412yes—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)—22no—
50#9484—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C2×Q8×C11SD1612yes—
54C2×Q8×C11Q1612yes—
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—
65C2×C8×C11—24no—
66C11×C4⋊C4—24no—
67C11×C4⋊C4—22no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11C2×D412yes—
71C42×C11#4112yes—
72C4⋊Dic11—22no—
73C4⋊Dic11—42no—
74Dic11⋊C4—44no—
75Dic11⋊C4—41no—
76Dic11⋊C4—41no—
77C4×Dic11—42no—
78#4318—42no—
79#4318—42no—
80C2×C11⋊C8—42no—
81#2982D1111yescharacteristic
82#2581—111no—
83#1801—111no—
84#1487—112no—
85#1286—112no—
86C23×C11C2×C22⋊C411yescharacteristic
87Q8×C11—24no—
88Q8×C11—24no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11#10314yes—
96C2×C4×C11C4×D412yes—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11#12112yes—
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11C2×SD1611yescharacteristic
101C2×C4×C11C2×Q1611yescharacteristic
102C2×C4×C11#13512yes—
103C2×Dic11—22no—
104C2×Dic11—41no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—41no—
110C2×Dic11—42no—
111Dic22—24no—
112Dic22—42no—
113C8×C11—44no—
114C11⋊C8—82no—
115C2×C4×Q8—111no—
116C2×C4×Q8C2×D1111yescharacteristic
117C8×Q8—24no—
118#431—22no—
119#431C2×D1112yes—
120#423—112no—
121C2×#101—221no—
122#400—112no—
123#395—112no—
124#391—221no—
125#389—221no—
126#387—222no—
127#382—111no—
128#343—221no—
129Q8⋊C8—224no—
130C22×C11—21no—
131C22×C11—21no—
132C22×C11#38611yescharacteristic
133C22×C11C2×#10311yescharacteristic
134C22×C11#41611yescharacteristic
135C4×C11—22no—
136C4×C11—24no—
137C4×C11—21no—
138C4×C11—21no—
139C4×C11—42no—
140C4×C11#46512yes—
141C4×C11#46712yes—
142Dic11—42no—
143Dic11—82no—
144Dic11—81no—
145C22×Q8—111no—
146C22×Q8D4411yescharacteristic
147C2×M16—222no—
148C4×Q8—22no—
149C4×Q8—22no—
150C4×Q8—222no—
151C4×Q8—222no—
152C2×C4⋊C4—111no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4C4×D1112yes—
157C2×C4⋊C4D4411yescharacteristic
158C2×C42—221no—
159C2×C42C22⋊D1112yes—
160C2×C42C22×D1111yescharacteristic
161C4⋊C8—24no—
162C4⋊C8—22no—
163C4⋊C8—222no—
164C4⋊C8—222no—
165#101—442no—
166C22⋊C8—22no—
167C4×C8—24no—
168C4×C8C22⋊D1114yes—
169#95—112no—
170#95—222no—
171#95—222no—
172#95—222no—
173#95—221no—
174C2×C11—21no—
175C2×C11—21no—
176C2×C11#189111yescharacteristic
177C2×C11#189211yescharacteristic
178C2×C11#191211yescharacteristic
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—222no—
182C2×Q8—442no—
183C2×Q8#431412yes—
184C2×Q8Dic4412yes—
185C22×C4—221no—
186C22×C4—222no—
187C22×C4—221no—
188C22×C4(C2×D11)⋊C412yes—
189C22×C4(C2×D11)⋊C412yes—
190C22×C4C2×C4×D1111yescharacteristic
191C22×C4C2×D4411yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193M16—442no—
194M16—442no—
195C2×C8—24no—
196C2×C8—442no—
197C4⋊C4—24no—
198C4⋊C4—22no—
199C4⋊C4—222no—
200C4⋊C4—444no—
201C4⋊C4—442no—
202C4⋊C4—441no—
203C4⋊C4—441no—
204C42—22no—
205C42—22no—
206C42—442no—
207C42#433912yes—
208C42C2×C22⋊D1112yes—
209C11#948411yescharacteristic, complemented, Sylow
210C23C2×(C2×D11)⋊C411yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—224no—
214Q8—442no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—222no—
222C2×C4—441no—
223C2×C4—441no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4#6688014yes—
230C2×C4C2×#431411yescharacteristic
231C2×C4#6695712yes—
232C2×C4C2×Dic4411yescharacteristic
233C2×C4C4×C22⋊D1112yes—
234C2×C4#6698211yescharacteristic
235C2×C4#6698312yes—
236C2×C4#6700611yescharacteristic
237C8—44no—
238C8—882no—
239C22—21no—
240C22—21no—
241C22C2×#6688011yescharacteristic
242C22#1062272611yescharacteristic
243C22#1062282611yescharacteristic
244C4—21no—
245C4—21no—
246C4—22no—
247C4—24no—
248C4—42no—
249C4—442no—
250C4—882no—
251C4—881no—
252C4#1062272712yes—
253C4#1062272912yes—
254C2—21no—
255C2—21no—
256C2#1306903411yescharacteristic
257C2#1306903911yescharacteristic
258C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2982C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#2982D11
hypocenterC11#9484
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
209. C11#9484semidirect

Maximal subgroups

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

subgroupindex
#130739782
#130686122
#130670462
#130664752
C11×#29822
#948411