Finite Group Databasebeta

← #14671242

Subgroups — #14671242

Order 2816.

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

normal subgroups only

This group has 454 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
2C2×#10622155C212yesmaximal, complemented
3#13068666C211yesmaximal, characteristic
4#13066731C212yesmaximal, complemented
5C11×#3407C211yesmaximal, characteristic
6C2×C11×#131C2211yescharacteristic
7#10623356—21no—
8C22×Dic44C2211yescharacteristic
9C11×#504—24no—
10C2×C11×M32—22no—
11C2×C11×M32C2212yes—
12#10622850—21no—
13#10622750C414yes—
14#10622733—21no—
15#10622729—22no—
16C2×#66883C2212yes—
17#10622719C2211yescharacteristic
18C11⋊#338—21no—
19#10622155—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#66977—24no—
33C2×#4318—22no—
34C2×Dic44—22no—
35C2×Dic44—22no—
36C2×Dic44—21no—
37C2×Dic44C2×C412yes—
38C11×M32—24no—
39C11×M32—22no—
40C11×M32D414yes—
41C2×C11×C16—24no—
42C2×C11×C16—22no—
43#66900—41no—
44#66897—41no—
45#66883—22no—
46#66883—22no—
47#66882—21no—
48#66881C2×C412yes—
49#66880—24no—
50#13078—111nomaximal, Sylow
51C11×#41—22no—
52C11×#41—22no—
53C2×Q8×C11D811yescharacteristic
54C2×D4×C11D811yescharacteristic
55C2×D4×C11SD1612yes—
56C22×C4×C11C22⋊C412yes—
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—41no—
59C2×Dic22—22no—
60C2×Dic22—42no—
61C2×Dic22—41no—
62C2×Dic22—42no—
63C11×M16—24no—
64C11×M16—22no—
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11C22⋊C412yes—
68C2×C8×C11C22×C411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D412yes—
71C2×C8×C11#4112yes—
72C22⋊Dic11—44no—
73C22⋊Dic11—41no—
74C4⋊Dic11—22no—
75Dic11⋊C4—44no—
76C4×Dic11—41no—
77#4318—42no—
78#4318—42no—
79C2×C11⋊C8—42no—
80Dic44—24no—
81Dic44—41no—
82Dic44—41no—
83C11×C16—24no—
84#3407D1111yescharacteristic
85#3059—111no—
86C2×#362—112no—
87#1813—111no—
88#1389—112no—
89C23×C11#10212yes—
90C23×C11C2×SD1611yescharacteristic
91Q8×C11—22no—
92D4×C11—24no—
93D4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11#10212yes—
97C2×C4×C11C2×C22⋊C411yescharacteristic
98C2×C4×C11#12112yes—
99C2×C4×C11C2×D811yescharacteristic
100C2×C4×C11#13512yes—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—82no—
104Dic22—42no—
105Dic22—42no—
106Dic22—82no—
107C8×C11—22no—
108C8×C11C4×D412yes—
109C8×C11#12011yescharacteristic
110C8×C11#12311yescharacteristic
111C11⋊C8—82no—
112C22×Q16—111no—
113C2×#131C2×D1111yescharacteristic
114#536—221no—
115#504—24no—
116C2×M32—22no—
117C2×M32C2×D1112yes—
118#470—114no—
119#467—222no—
120C2×#108—112no—
121#427—111no—
122#419—221no—
123#413—221no—
124#362—224no—
125#338—221no—
126C22×C11—22no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11C2×#10211yescharacteristic
130C22×C11#46512yes—
131C4×C11—22no—
132C4×C11#38611yescharacteristic
133C4×C11#41611yescharacteristic
134C4×C11#46612yes—
135Dic11—82no—
136Dic11—82no—
137C2×#41D4411yescharacteristic
138C22×Q8—221no—
139C2×Q16—112no—
140C2×Q16—222no—
141C2×Q16—222no—
142C2×Q16—221no—
143#131—22no—
144#131—22no—
145C2×M16—222no—
146C2×M16C4×D1112yes—
147C2×M16D4411yescharacteristic
148C22×C8C22⋊D1112yes—
149C22×C8C22×D1111yescharacteristic
150C4⋊Q8—441no—
151#124—441no—
152#123—442no—
153C22⋊Q8—224no—
154#117—221no—
155M32—24no—
156M32—22no—
157M32C22⋊D1114yes—
158C2×C16—24no—
159C2×C16—22no—
160#108—222no—
161#108—222no—
162#107—221no—
163#106—112no—
164#103—224no—
165#101—441no—
166#100—441no—
167C2×C11—21no—
168C2×C11—22no—
169C2×C11—42no—
170C2×C11#189311yescharacteristic
171#41—22no—
172#41—22no—
173C2×Q8—222no—
174C2×Q8—441no—
175C2×Q8—442no—
176C2×Q8—442no—
177C2×Q8D8811yescharacteristic
178C2×D4#431412yes—
179C2×D4D8811yescharacteristic
180C22×C4—441no—
181C22×C4(C2×D11)⋊C412yes—
182C22×C4C2×D4411yescharacteristic
183Q16—224no—
184Q16—441no—
185Q16—441no—
186M16—22no—
187M16—24no—
188M16—442no—
189M16—442no—
190C2×C8—22no—
191C2×C8—22no—
192C2×C8—442no—
193C2×C8(C2×D11)⋊C412yes—
194C2×C8C2×C4×D1111yescharacteristic
195C2×C8#433912yes—
196C2×C8C2×C22⋊D1112yes—
197C2×C8C2×C22⋊D1111yescharacteristic
198C4⋊C4—222no—
199C4⋊C4—444no—
200C22⋊C4—444no—
201C22⋊C4—441no—
202C42—441no—
203C16—24no—
204C11#1307811yescharacteristic, complemented, Sylow
205C23#6688512yes—
206C23C2×#431411yescharacteristic
207Q8—22no—
208Q8—442no—
209Q8—442no—
210Q8—882no—
211D4—24no—
212D4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4—882no—
218C2×C4#6688512yes—
219C2×C4C2×D8811yescharacteristic
220C2×C4#6695712yes—
221C2×C4C2×(C2×D11)⋊C411yescharacteristic
222C2×C4#6698312yes—
223C8—22no—
224C8—882no—
225C8C4×C22⋊D1112yes—
226C8#6698211yescharacteristic
227C8#6700611yescharacteristic
228C22—22no—
229C22—41no—
230C22—42no—
231C22C2×#6688511yescharacteristic
232C22#1062272712yes—
233C4—22no—
234C4—882no—
235C4—882no—
236C4#1062272611yescharacteristic
237C4#1062272812yes—
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#13078
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. C2×#10622155C2semidirect
4. #13066731C2semidirect
204. C11#13078semidirect

Maximal subgroups

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

subgroupindex
#130782712
C2×#106221552
#130686662
#130667312
C11×#34072
#1307811