Finite Group Databasebeta

← #14670772

Subgroups — #14670772

Order 2816.

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

normal subgroups only

This group has 528 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#13078197C211yesmaximal, characteristic
2C2×#10622126C212yesmaximal, complemented
3#13070227C211yesmaximal, characteristic, complemented
4#13066723C212yesmaximal, complemented
5C2×C11×#427C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7C2×C11×#117—21no—
8#10623322—21no—
9C2×#66957C2211yescharacteristic
10C11×#427—24no—
11C2×C11×#107—21no—
12C2×C11×#106C2212yes—
13#10622729C412yescomplemented
14#10622728C412yescomplemented
15#10622727—22no—
16#10622726—21no—
17#10622719C2211yescharacteristic
18C2×#66876C2212yes—
19C22⋊(C11⋊C16)—22no—
20#10622126—24no—
21C23×C4×C11D411yescharacteristic
22C2×#4339—21no—
23C22×C8×C11—22no—
24C22×C8×C11—22no—
25C22×C8×C11C2×C412yes—
26C22×C8×C11D412yes—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C11×#117—24no—
30C11×#117—42no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C22⋊C4—41no—
33C2×C42×C11—41no—
34#67006—41no—
35#66983—22no—
36#66982—41no—
37C4×C22⋊D11—42no—
38#66979—21no—
39#66977—22no—
40C2×Dic44C2×C411yescharacteristic
41#66957—22no—
42#66957—22no—
43C2×D88C2×C411yescharacteristic
44C2×#4314—21no—
45C11×#107—24no—
46C11×#106—22no—
47C11×#106D414yescomplemented
48#66885—22no—
49#66882C2×C412yes—
50#66881—21no—
51#66880—22no—
52#66876—22no—
53#66876—22no—
54C2×C11⋊C16—22no—
55#13002—111nomaximal, Sylow
56C24×C11D811yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11D811yescharacteristic
64C22×C4×C11SD1612yes—
65C22×C4×C11C2×D411yescharacteristic
66C2×C22⋊D11—42no—
67C2×C22⋊D11—41no—
68#4339—41no—
69#4339—41no—
70#4339—41no—
71#4339—41no—
72C2×D44—21no—
73C2×C4×D11—41no—
74C2×Dic22—21no—
75C2×C8×C11—24no—
76C2×C8×C11—24no—
77C2×C8×C11—21no—
78C2×C8×C11—21no—
79C2×C8×C11C22⋊C412yes—
80C2×C8×C11C22×C411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D412yes—
83C2×C8×C11#4112yes—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—42no—
86C11×C22⋊C4—44no—
87C42×C11—44no—
88C22⋊Dic11—42no—
89C22⋊Dic11—41no—
90(C2×D11)⋊C4—42no—
91C4⋊Dic11—22no—
92Dic11⋊C4—42no—
93C4×Dic11—41no—
94Dic44—22no—
95D88—22no—
96#4314—42no—
97C11⋊C16—42no—
98#3050—111no—
99C2×#427D1111yescharacteristic, complemented
100C2×#360—112no—
101#2112—111no—
102#1386—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—42no—
106C23×C11#10212yes—
107C23×C11C2×D811yescharacteristic
108C22×D11—41no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—44no—
116C2×C4×C11—84no—
117C2×C4×C11#10212yes—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11C2×SD1611yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C22⋊D11—84no—
125C22⋊D11—81no—
126C22⋊D11—81no—
127C2×Dic11—42no—
128C2×Dic11—41no—
129D44—41no—
130D44—41no—
131C4×D11—81no—
132C4×D11—81no—
133Dic22—41no—
134Dic22—41no—
135C8×C11—22no—
136C8×C11C4×D412yes—
137C8×C11#12112yes—
138C2×#135—111no—
139C23×C8C2×D1111yescharacteristic
140#525—221no—
141C2×#117—21no—
142C2×M32—112no—
143#467—112no—
144#466—112no—
145#465—222no—
146#427—24no—
147#427—111no—
148C2×#107—21no—
149C2×#106C2×D1112yes—
150#416—221no—
151#360—224no—
152C22⋊C16—222no—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—42no—
158C22×C11—42no—
159C22×C11C2×#10211yescharacteristic
160C22×C11#44711yescharacteristic
161C22×C11#48011yescharacteristic
162C2×D11—81no—
163C2×D11—82no—
164C4×C11—22no—
165C4×C11—84no—
166C4×C11#38611yescharacteristic
167C4×C11#41711yescharacteristic
168C4×C11#44811yescharacteristic
169C4×C11#48111yescharacteristic
170Dic11—81no—
171Dic11—82no—
172C2×#41—221no—
173C23×C4C22⋊D1111yescharacteristic
174#135—222no—
175#135—222no—
176C2×Q16—111no—
177C2×SD16—221no—
178C2×D8—111no—
179C22×C8—22no—
180C22×C8—22no—
181C22×C8C4×D1112yes—
182C22×C8D4412yes—
183C22×C8C22⋊D1111yescharacteristic
184C22×C8C22×D1111yescharacteristic
185#123—441no—
186C22⋊Q8—222no—
187#121—222no—
188#120—441no—
189C4×D4—442no—
190#117—24no—
191#117—42no—
192#117—221no—
193C2×C4⋊C4—22no—
194C2×C22⋊C4—41no—
195C2×C42—41no—
196M32—222no—
197M32—222no—
198C2×C16—222no—
199#107—24no—
200#107—112no—
201#106—22no—
202#106—221no—
203#106C22⋊D1114yescomplemented
204#103—222no—
205#102—222no—
206C2×C11—21no—
207C2×C11—21no—
208C2×C11—42no—
209C2×C11#187411yescharacteristic
210C2×C11#214512yes—
211D11—161no—
212C24#432311yescharacteristic
213#41—441no—
214#41—441no—
215#41—441no—
216#41—441no—
217C2×Q8—221no—
218C2×D4—221no—
219C2×D4—442no—
220C2×D4—441no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—42no—
226C22×C4—441no—
227C22×C4(C2×D11)⋊C412yes—
228C22×C4#432311yescharacteristic
229C22×C4#432512yes—
230C22×C4C2×C22⋊D1111yescharacteristic
231Q16—222no—
232SD16—442no—
233D8—222no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8(C2×D11)⋊C412yes—
239C2×C8C2×C4×D1111yescharacteristic
240C2×C8C2×D4411yescharacteristic
241C2×C8#433912yes—
242C2×C8C2×C22⋊D1112yes—
243C4⋊C4—24no—
244C4⋊C4—42no—
245C4⋊C4—222no—
246C4⋊C4—442no—
247C22⋊C4—44no—
248C22⋊C4—442no—
249C22⋊C4—441no—
250C22⋊C4—442no—
251C42—44no—
252C42—441no—
253C16—442no—
254C11#1300211yescharacteristic, complemented, Sylow
255C23—21no—
256C23—21no—
257C23—42no—
258C23—441no—
259C23#6687312yes—
260C23C2×#432311yescharacteristic
261Q8—441no—
262Q8—441no—
263D4—441no—
264D4—441no—
265D4—884no—
266D4—881no—
267D4—881no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—44no—
275C2×C4—84no—
276C2×C4—442no—
277C2×C4—441no—
278C2×C4—881no—
279C2×C4—881no—
280C2×C4#6687312yes—
281C2×C4C2×(C2×D11)⋊C411yescharacteristic
282C2×C4#6698211yescharacteristic
283C2×C4#6698511yescharacteristic
284C2×C4C2×#432511yescharacteristic
285C2×C4#6699511yescharacteristic
286C2×C4#6700611yescharacteristic
287C8—22no—
288C8C4×C22⋊D1112yes—
289C8#6698312yes—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22—42no—
295C22—42no—
296C22—882no—
297C22—881no—
298C22C2×#6687311yescharacteristic
299C22#1062258011yescharacteristic
300C22#1062283011yescharacteristic
301C4—22no—
302C4—84no—
303C4—882no—
304C4—881no—
305C4#1062257911yescharacteristic
306C4#1062258111yescharacteristic
307C4#1062282611yescharacteristic
308C4#1062284011yescharacteristic
309C2—21no—
310C2—21no—
311C2—42no—
312C2—1761no—
313C2#1306893311yescharacteristic
314C2#1307035112yes—
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#427C2
socleC22×C11C2×#102
prime radical#13078197C2
cosocleC22×C8×C11C23
hypercenterC2×#427D11
hypocenterC11#13002
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#10622126C2semidirect
3. #13070227C2semidirect
4. #13066723C2semidirect
5. C2×C11×#427C2semidirect
13. #10622729C4semidirect
14. #10622728C4semidirect
47. C11×#106D4semidirect
99. C2×#427D11semidirect
203. #106C22⋊D11semidirect
254. C11#13002semidirect

Maximal subgroups

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

subgroupindex
#130781972
C2×#106221262
#130702272
#130667232
C2×C11×#4272
#1300211