Finite Group Databasebeta

← #14671227

Subgroups — #14671227

Order 2816.

458 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 127 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#13078271C211yesmaximal, characteristic
2#13070337C212yesmaximal, complemented
3#13068662C211yesmaximal, characteristic
4#13066718C212yesmaximal, complemented
5C11×#3407C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7#10623356—21no—
8C22×Dic44C2211yescharacteristic
9C11×#504—24no—
10C2×C11×M32—22no—
11C2×C11×M32C2212yes—
12#10622853—21no—
13#10622750C414yescomplemented
14#10622733—21no—
15#10622729—22no—
16#10622719C2212yes—
17#10622719C2211yescharacteristic
18#10622195—21no—
19#10622141—24no—
20C2×C11×#41D411yescharacteristic
21C22×Dic22—21no—
22C11×#131—22no—
23C11×#131—22no—
24C2×C11×M16C2×C412yes—
25C2×C11×M16D411yescharacteristic
26C22×C8×C11D412yes—
27C22×C8×C11C2311yescharacteristic
28#66997—41no—
29#66989—41no—
30#66988—42no—
31#66979—21no—
32#66979—22no—
33#66977—24no—
34C2×Dic44—22no—
35C2×Dic44—22no—
36C2×Dic44—21no—
37C2×Dic44C2×C412yes—
38C11×M32—24no—
39C11×M32—22no—
40C11×M32—22no—
41C2×C11×C16—24no—
42C2×C11×C16D414yes—
43#66898—42no—
44#66882—21no—
45#66882—22no—
46#66881—22no—
47#66881C2×C412yes—
48#66880—24no—
49#13075—111nomaximal, Sylow
50C11×#41—22no—
51C11×#41—22no—
52C2×Q8×C11SD1611yescharacteristic
53C2×D4×C11D812yes—
54C2×D4×C11SD1611yescharacteristic
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—41no—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C2×Dic22—41no—
61C2×Dic22—42no—
62C11×M16—24no—
63C11×M16—22no—
64C2×C8×C11—22no—
65C2×C8×C11—22no—
66C2×C8×C11C22⋊C412yes—
67C2×C8×C11C22×C411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D412yes—
70C2×C8×C11#4112yes—
71C22⋊Dic11—44no—
72C22⋊Dic11—41no—
73C22⋊Dic11—42no—
74C4⋊Dic11—22no—
75C4⋊Dic11—42no—
76Dic11⋊C4—44no—
77C4×Dic11—41no—
78C4×Dic11—42no—
79Dic44—24no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—24no—
83#3407D1111yescharacteristic
84#3059—111no—
85#2141—112no—
86#1812—111no—
87#1384—112no—
88C23×C11#10212yes—
89C23×C11C2×D811yescharacteristic
90Q8×C11—22no—
91D4×C11—24no—
92D4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11#10212yes—
96C2×C4×C11C2×C22⋊C411yescharacteristic
97C2×C4×C11#12112yes—
98C2×C4×C11C2×SD1611yescharacteristic
99C2×C4×C11#13512yes—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—82no—
103C2×Dic11—82no—
104Dic22—42no—
105Dic22—42no—
106Dic22—82no—
107C8×C11—22no—
108C8×C11C4×D412yes—
109C8×C11#12011yescharacteristic
110C8×C11#12311yescharacteristic
111C22×Q16—111no—
112C2×#131C2×D1111yescharacteristic
113#536—221no—
114#504—24no—
115C2×M32—22no—
116C2×M32C2×D1112yes—
117#470—114no—
118#467—222no—
119#427—111no—
120#427—112no—
121#419—221no—
122#410—221no—
123#358—224no—
124H(3,ℤ/4)—221no—
125C22×C11—22no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11C2×#10211yescharacteristic
129C22×C11#46612yes—
130C4×C11—22no—
131C4×C11#38611yescharacteristic
132C4×C11#41611yescharacteristic
133C4×C11#46512yes—
134Dic11—82no—
135Dic11—82no—
136Dic11—162no—
137C2×#41D4411yescharacteristic
138C22×Q8—221no—
139C2×Q16—112no—
140C2×Q16—222no—
141C2×Q16—222no—
142C2×Q16—221no—
143#131—22no—
144#131—22no—
145C2×M16C4×D1112yes—
146C2×M16D4411yescharacteristic
147C22×C8C22⋊D1112yes—
148C22×C8C22×D1111yescharacteristic
149C4⋊Q8—441no—
150#124—441no—
151#123—442no—
152C22⋊Q8—224no—
153#117—221no—
154#117—222no—
155M32—24no—
156M32—22no—
157M32—22no—
158C2×C16—24no—
159C2×C16C22⋊D1114yes—
160#107—221no—
161#107—222no—
162#106—112no—
163#106—222no—
164#103—224no—
165#99—442no—
166C2×C11—21no—
167C2×C11—22no—
168C2×C11—42no—
169C2×C11#189311yescharacteristic
170#41—22no—
171#41—22no—
172C2×Q8—222no—
173C2×Q8—441no—
174C2×Q8—442no—
175C2×Q8—442no—
176C2×Q8#431411yescharacteristic
177C2×D4#431411yescharacteristic
178C2×D4D8812yes—
179C22×C4—441no—
180C22×C4(C2×D11)⋊C412yes—
181C22×C4C2×D4411yescharacteristic
182Q16—224no—
183Q16—441no—
184Q16—441no—
185M16—22no—
186M16—24no—
187C2×C8—22no—
188C2×C8—22no—
189C2×C8(C2×D11)⋊C412yes—
190C2×C8C2×C4×D1111yescharacteristic
191C2×C8#433912yes—
192C2×C8C2×C22⋊D1112yes—
193C2×C8C2×C22⋊D1111yescharacteristic
194C4⋊C4—222no—
195C4⋊C4—444no—
196C4⋊C4—442no—
197C22⋊C4—444no—
198C22⋊C4—441no—
199C22⋊C4—442no—
200C42—441no—
201C42—442no—
202C16—24no—
203C11#1307511yescharacteristic, complemented, Sylow
204C23#6688512yes—
205C23C2×D8811yescharacteristic
206Q8—22no—
207Q8—442no—
208Q8—442no—
209Q8—882no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4—882no—
217C2×C4—882no—
218C2×C4#6688512yes—
219C2×C4C2×#431411yescharacteristic
220C2×C4#6695712yes—
221C2×C4C2×(C2×D11)⋊C411yescharacteristic
222C2×C4#6698312yes—
223C8—22no—
224C8C4×C22⋊D1112yes—
225C8#6698211yescharacteristic
226C8#6700611yescharacteristic
227C22—22no—
228C22—41no—
229C22—42no—
230C22C2×#6688511yescharacteristic
231C22#1062272812yes—
232C4—22no—
233C4—882no—
234C4—882no—
235C4—1762no—
236C4#1062272611yescharacteristic
237C4#1062272712yes—
238C4#1062282611yescharacteristic
239C2—21no—
240C2—22no—
241C2—42no—
242C2#1306904411yescharacteristic
subgroupG/H
centerC2#13069044
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#3407C2
socleC2×C11#1893
prime radicalC2×C11×#41D4
cosocleC22×C8×C11C23
hypercenter#3407D11
hypocenterC11#13075
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #13070337C2semidirect
4. #13066718C2semidirect
13. #10622750C4semidirect
203. C11#13075semidirect

Maximal subgroups

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

subgroupindex
#130782712
#130703372
#130686622
#130667182
C11×#34072
#1307511