Finite Group Databasebeta

← #14670763

Subgroups — #14670763

Order 2816.

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

normal subgroups only

This group has 512 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#13077206C211yesmaximal, characteristic
2#13070336C212yesmaximal, complemented
3C2×#10622191C211yesmaximal, characteristic
4#13066723C212yesmaximal, complemented
5C2×C11×#470C211yesmaximal, characteristic
6C22×C11×Q16C2211yescharacteristic
7C22×C11×M16C2211yescharacteristic
8C2×C11×C22⋊Q8—21no—
9C2×#66979—21no—
10C11×#470—22no—
11C11×#470C414yescomplemented
12C2×C11×#106C2211yescharacteristic
13C2×C11×#103—21no—
14#10622734—24no—
15#10622719—21no—
16#10622719C2212yes—
17C2×#66876C2212yes—
18#10622202—24no—
19#10622191—22no—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—22no—
23C2×C11×Q16—21no—
24C2×C11×Q16—22no—
25C2×C11×Q16C2×C412yescomplemented
26C2×C11×M16—22no—
27C2×C11×M16—22no—
28C2×C11×M16C2×C412yes—
29C2×C11×M16D412yes—
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—24no—
33C11×C22⋊Q8—42no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—41no—
36C2×C11×C22⋊C4—41no—
37C2×C22⋊Dic11—41no—
38#66979—22no—
39#66979—22no—
40#66979—41no—
41#66979—41no—
42C2×C4⋊Dic11—22no—
43C2×C4×Dic11—41no—
44C11×#106—21no—
45C11×#106C2×C412yescomplemented
46C11×#103—24no—
47#66882—22no—
48#66882D414yes—
49#66881—22no—
50#66881—22no—
51#66876—22no—
52#66876—22no—
53C2×C11⋊C16—22no—
54#13000—111nomaximal, Sylow
55C24×C11D811yescharacteristic
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11D811yescharacteristic
70C22×C4×C11SD1612yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—42no—
73C11×Q16—24no—
74C11×Q16—42no—
75C11×M16—24no—
76C11×M16—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—22no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—44no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C4⋊Dic11—24no—
91C4⋊Dic11—42no—
92C4×Dic11—42no—
93C4×Dic11—42no—
94C11⋊C16—42no—
95C2×#470D1111yescharacteristic
96#2911—111no—
97#2141—112no—
98C2×#349—111no—
99#1386—112no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—42no—
103C23×C11#10212yes—
104C23×C11C2×D811yescharacteristic
105Q8×C11—42no—
106Q8×C11—42no—
107Q8×C11—81no—
108Q8×C11—81no—
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—42no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11#10212yes—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11C2×SD1611yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×Dic11—44no—
128C2×Dic11—84no—
129C8×C11—22no—
130C8×C11C4×D412yes—
131C8×C11#12112yes—
132C22×Q16C2×D1111yescharacteristic
133C22×M16C2×D1111yescharacteristic
134C2×C22⋊Q8—21no—
135C2×#117—221no—
136C2×M32—112no—
137#470—22no—
138#470Dic1114yescomplemented
139#428—224no—
140#427—112no—
141#427—221no—
142C2×#106C2×D1111yescharacteristic
143C2×#103—21no—
144#358—224no—
145#349—222no—
146C22×C11—22no—
147C22×C11—22no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—81no—
151C22×C11C2×#10211yescharacteristic
152C22×C11#44711yescharacteristic
153C22×C11#48011yescharacteristic
154C4×C11—22no—
155C4×C11—82no—
156C4×C11—82no—
157C4×C11#38611yescharacteristic
158C4×C11#41711yescharacteristic
159C4×C11#44811yescharacteristic
160C4×C11#48111yescharacteristic
161Dic11—84no—
162C22×Q8—21no—
163C23×C4C22⋊D1111yescharacteristic
164C2×Q16—22no—
165C2×Q16—22no—
166C2×Q16—21no—
167C2×Q16C2×Dic1112yescomplemented
168C2×M16—22no—
169C2×M16—22no—
170C2×M16C2×Dic1112yes—
171C2×M16C22⋊D1112yes—
172C22×C8C22⋊D1111yescharacteristic
173C22×C8C22×D1111yescharacteristic
174C22⋊Q8—24no—
175C22⋊Q8—42no—
176#117—222no—
177#117—222no—
178#117—441no—
179#117—441no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—222no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—441no—
185C2×C42—441no—
186M32—222no—
187M32—222no—
188C2×C16—222no—
189#107—114no—
190#107—222no—
191#106—21no—
192#106—222no—
193#106—222no—
194#106C2×Dic1112yescomplemented
195#103—24no—
196C2×C11—21no—
197C2×C11—21no—
198C2×C11—42no—
199C2×C11#187411yescharacteristic
200C2×C11#219112yes—
201C24#432311yescharacteristic
202C2×Q8—22no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—41no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—442no—
215C22×C4#432311yescharacteristic
216C22×C4#432412yes—
217C22×C4C22⋊Dic1112yes—
218C22×C4C2×C22⋊D1111yescharacteristic
219Q16—24no—
220Q16—42no—
221M16—24no—
222M16—24no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8C22⋊Dic1112yes—
226C2×C8D4×D1112yes—
227C2×C8#434112yes—
228C2×C8C22×Dic1111yescharacteristic
229C2×C8C2×C22⋊D1111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—44no—
232C4⋊C4—41no—
233C4⋊C4—224no—
234C4⋊C4—442no—
235C22⋊C4—44no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C42—442no—
239C42—442no—
240C16—442no—
241C11#1300011yescharacteristic, complemented, Sylow
242C23—21no—
243C23—21no—
244C23—42no—
245C23#6689612yes—
246C23C2×#432311yescharacteristic
247Q8—42no—
248Q8—42no—
249Q8—81no—
250Q8—81no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—82no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—444no—
263C2×C4—884no—
264C2×C4#6689612yes—
265C2×C4C2×#432411yescharacteristic
266C2×C4#6698811yescharacteristic
267C2×C4#6699011yescharacteristic
268C2×C4#6700211yescharacteristic
269C2×C4#6700411yescharacteristic
270C2×C4C2×C22⋊Dic1111yescharacteristic
271C8—22no—
272C8D4×Dic1112yes—
273C8#6699212yes—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—81no—
279C22#1062264611yescharacteristic
280C22#1062264911yescharacteristic
281C22C2×#6689611yescharacteristic
282C4—22no—
283C4—82no—
284C4—82no—
285C4—884no—
286C4#1062264711yescharacteristic
287C4#1062265311yescharacteristic
288C4#1062283311yescharacteristic
289C4#1062284511yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2#1306893411yescharacteristic
294C2#1307056612yes—
subgroupG/H
centerC22#10622649
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#470C2
socleC22×C11#447
prime radicalC24×C11D8
cosocleC22×C8×C11C23
hypercenterC2×#470D11
hypocenterC11#13000
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. #13070336C2semidirect
4. #13066723C2semidirect
11. C11×#470C4semidirect
25. C2×C11×Q16C2×C4semidirect
45. C11×#106C2×C4semidirect
138. #470Dic11semidirect
167. C2×Q16C2×Dic11semidirect
194. #106C2×Dic11semidirect
241. C11#13000semidirect

Maximal subgroups

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

subgroupindex
#130772062
#130703362
C2×#106221912
#130667232
C2×C11×#4702
#1300011