Finite Group Databasebeta

← #14670657

Subgroups — #14670657

Order 2816.

488 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 135 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#13077308C211yesmaximal, characteristic
2#13070237C211yesmaximal, characteristic, complemented
3#13070226C212yesmaximal, complemented
4#13066701C212yesmaximal, complemented
5C11×#3407C211yesmaximal, characteristic, complemented
6C2×C11×#131C2211yescharacteristic
7#10623359C411yescharacteristic
8C22×C8×D11C2211yescharacteristic
9C11×#504—24no—
10C2×C11×M32—22no—
11C2×C11×M32C2212yes—
12#10622847C411yescharacteristic
13#10622740—22no—
14#10622739C411yescharacteristic
15#10622732C411yescharacteristic
16C8×C22⋊D11—22no—
17#10622714C2211yescharacteristic
18C2×#66876C2212yes—
19#10622191—22no—
20(C2×D11)⋊C16—24no—
21C2×C11×#41C2×C411yescharacteristic
22C22×C4×D11C2×C411yescharacteristic
23C11×#131—22no—
24C11×#131—22no—
25C2×C11×M16C2×C411yescharacteristic
26C2×C11×M16D412yes—
27C22×C8×C11D412yes—
28C22×C8×C11C2311yescharacteristic
29#66999—21no—
30#66991—21no—
31#66990C812yes—
32#66988C812yes—
33C4×C22⋊D11—22no—
34#66979C2×C411yescharacteristic
35C2×#4318C2×C411yescharacteristic
36C22×C11⋊C8C2×C411yescharacteristic
37C2×C8×D11—21no—
38C2×C8×D11—21no—
39C2×C8×D11—22no—
40C2×C8×D11—22no—
41C11×M32—24no—
42C11×M32—22no—
43C11×M32—22no—
44C2×C11×C16—24no—
45C2×C11×C16D414yescomplemented
46C22⋊(C11⋊C8)—22no—
47(C2×D11)⋊C8—22no—
48#66879—21no—
49Dic11⋊C8—22no—
50C8×Dic11—21no—
51#66876—22no—
52#66876—22no—
53C2×C11⋊C16—22no—
54#12981—111nomaximal, Sylow
55C23×D11C2×C811yescharacteristic
56C11×#41—22no—
57C11×#41—22no—
58C2×Q8×C11M1611yescharacteristic
59C2×D4×C11C2×C812yes—
60C2×D4×C11M1611yescharacteristic
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C2×C22⋊D11—22no—
64C22×Dic11C2×C811yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11—22no—
67C2×C4×D11—21no—
68C2×C4×D11—22no—
69C11×M16—24no—
70C11×M16—22no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11C22⋊C412yes—
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C2×C8×C11C2×D412yes—
77C2×C8×C11#4112yes—
78C22⋊Dic11—22no—
79C22⋊Dic11C2×C812yes—
80(C2×D11)⋊C4—22no—
81C4⋊Dic11—21no—
82Dic11⋊C4—22no—
83C4×Dic11—21no—
84#4318—22no—
85C2×C11⋊C8—21no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—22no—
88C8×D11—41no—
89C8×D11—42no—
90C8×D11—41no—
91C11×C16—24no—
92C11⋊C16—42no—
93#3407D1111yescharacteristic, complemented
94#2929—111no—
95#2115—111no—
96#2112—112no—
97#1378—112no—
98C23×C11C22⋊C812yes—
99C23×C11C22×C811yescharacteristic
100C22×D11—21no—
101C22×D11—22no—
102C22×D11—42no—
103Q8×C11—22no—
104D4×C11—24no—
105D4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11C22⋊C812yes—
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11C4×D412yes—
111C2×C4×C11C2×M1611yescharacteristic
112C2×C4×C11#13112yes—
113C22⋊D11—44no—
114C2×Dic11—22no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C4×D11—41no—
118C4×D11—41no—
119C4×D11—42no—
120C8×C11—22no—
121C8×C11#12011yescharacteristic
122C8×C11#12112yes—
123C8×C11#12311yescharacteristic
124C11⋊C8—41no—
125C11⋊C8—41no—
126C2×#131C2×D1111yescharacteristic
127C23×C8—111no—
128#525—111no—
129#504—24no—
130C2×M32—22no—
131C2×M32—112no—
132C2×M32C2×D1112yes—
133#435—222no—
134C8×D4—222no—
135#424—111no—
136#408—111no—
137#407—111no—
138#405—111no—
139#349—222no—
140C22⋊C16—224no—
141C22×C11—22no—
142C22×C11—41no—
143C22×C11—42no—
144C22×C11C2×C22⋊C811yescharacteristic
145C22×C11C8×D412yes—
146C2×D11—24no—
147C2×D11—22no—
148C2×D11—41no—
149C2×D11—42no—
150C2×D11—41no—
151C4×C11—22no—
152C4×C11#38611yescharacteristic
153C4×C11#40811yescharacteristic
154C4×C11#43512yes—
155Dic11—42no—
156Dic11—41no—
157C2×#41C4×D1111yescharacteristic
158C23×C4—111no—
159#131—22no—
160#131—22no—
161C2×M16—111no—
162C2×M16C4×D1111yescharacteristic
163C2×M16D4412yes—
164C22×C8—111no—
165C22×C8—221no—
166C22×C8—222no—
167C22×C8—222no—
168C22×C8—221no—
169C22×C8C22⋊D1112yes—
170C22×C8C22×D1111yescharacteristic
171#123—112no—
172C22⋊Q8—221no—
173#121—221no—
174#120—112no—
175C4×D4—222no—
176#117—111no—
177M32—24no—
178M32—22no—
179M32—22no—
180M32—222no—
181M32—222no—
182C2×C16—24no—
183C2×C16—222no—
184C2×C16C22⋊D1114yescomplemented
185C4⋊C8—222no—
186C22⋊C8—222no—
187C22⋊C8—222no—
188#97—221no—
189C4×C8—221no—
190C2×C11—21no—
191C2×C11—22no—
192C2×C11—42no—
193C2×C11#186911yescharacteristic
194D11—42no—
195C24—111no—
196#41—22no—
197#41—22no—
198C2×Q8#431311yescharacteristic
199C2×D4—222no—
200C2×D4C8×D1112yes—
201C2×D4#431311yescharacteristic
202C22×C4—111no—
203C22×C4—221no—
204C22×C4—222no—
205C22×C4—221no—
206C22×C4—222no—
207C22×C4(C2×D11)⋊C412yes—
208C22×C4C2×C4×D1111yescharacteristic
209M16—22no—
210M16—24no—
211M16—222no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—221no—
215C2×C8—221no—
216C2×C8—222no—
217C2×C8—441no—
218C2×C8—442no—
219C2×C8—441no—
220C2×C8(C2×D11)⋊C412yes—
221C2×C8C2×D4411yescharacteristic
222C2×C8#433912yes—
223C2×C8C2×C22⋊D1111yescharacteristic
224C2×C8C2×C22⋊D1112yes—
225C4⋊C4—222no—
226C4⋊C4—221no—
227C22⋊C4—112no—
228C22⋊C4—222no—
229C22⋊C4—222no—
230C42—221no—
231C16—24no—
232C16—442no—
233C11#1298111yescharacteristic, complemented, Sylow
234C23—221no—
235C23—222no—
236C23—442no—
237C23(C2×D11)⋊C812yes—
238C23C2×C8×D1111yescharacteristic
239Q8—22no—
240D4—24no—
241D4—22no—
242D4—444no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—222no—
246C2×C4—221no—
247C2×C4—222no—
248C2×C4—441no—
249C2×C4—442no—
250C2×C4—441no—
251C2×C4(C2×D11)⋊C812yes—
252C2×C4C2×#431311yescharacteristic
253C2×C4#6695412yes—
254C2×C4C2×(C2×D11)⋊C411yescharacteristic
255C2×C4C4×C22⋊D1112yes—
256C8—22no—
257C8—441no—
258C8—441no—
259C8#6698211yescharacteristic
260C8#6698312yes—
261C8#6700611yescharacteristic
262C22—22no—
263C22—41no—
264C22—42no—
265C22—222no—
266C22—224no—
267C22—441no—
268C22—442no—
269C22—441no—
270C22C2×(C2×D11)⋊C811yescharacteristic
271C22C8×C22⋊D1112yes—
272C4—22no—
273C4—442no—
274C4—441no—
275C4#1062272311yescharacteristic
276C4#1062272412yes—
277C4#1062282611yescharacteristic
278C2—21no—
279C2—22no—
280C2—42no—
281C2—442no—
282C2#1306890811yescharacteristic
subgroupG/H
centerC8#67006
commutatorC23×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#3407C2
socleC2×C11#1869
prime radical#10623359C4
cosocleC22×C8×C11C23
hypercenter#3407D11
hypocenterC11#12981
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #13070237C2semidirect
3. #13070226C2semidirect
4. #13066701C2semidirect
5. C11×#3407C2semidirect
45. C2×C11×C16D4semidirect
93. #3407D11semidirect
184. C2×C16C22⋊D11semidirect
233. C11#12981semidirect

Maximal subgroups

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

subgroupindex
#130773082
#130702372
#130702262
#130667012
C11×#34072
#1298111