Finite Group Databasebeta

← #14664347

Subgroups — #14664347

Order 2816.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#66898C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066616C214yesmaximal, complemented
4C11×#2547C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×#124—21no—
7C2×C4×D4×C11C2211yescharacteristic
8C11×#397C412yescomplemented
9C11×#397C2212yes—
10C11×#391—21no—
11C11×#380—21no—
12C11×#380—21no—
13C4×C11×C4⋊C4C411yescharacteristic, complemented
14C2×#66898—21no—
15C4×C22⋊Dic11—21no—
16#10622820—21no—
17#10622166—21no—
18#10622164C2212yes—
19#10622163C2212yes—
20C22×Q8×C11—21no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×C4⋊Q8—41no—
25C11×C4⋊Q8—41no—
26C11×#124—44no—
27C4×D4×C11—41no—
28C4×D4×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C42×C11—21no—
38C2×C42×C11C2×C411yescharacteristic
39C2×C22⋊Dic11—22no—
40C2×C4×Dic11—41no—
41C2×#4318—41no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95C2×C412yes—
45#66898—24no—
46C11⋊#95—41no—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—41no—
49#11777—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C24×C11C2×D411yescharacteristic
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—41no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—42no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—44no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—42no—
84C22⋊Dic11—24no—
85C22⋊Dic11—42no—
86C4×Dic11—82no—
87#4318—82no—
88C2×C11⋊C8—42no—
89#2547D1111yescharacteristic
90C4×#99—111no—
91#1465—111no—
92#1344—114no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11C2×C22⋊C411yescharacteristic
103C23×C11AGL(1,ℤ/8)12yes—
104Q8×C11—84no—
105D4×C11—44no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11#10412yes—
128C2×Dic11—44no—
129C2×Dic11—82no—
130C2×Dic11—82no—
131C11⋊C8—82no—
132C2×C4⋊Q8Dic1111yescharacteristic, complemented
133C2×#124—21no—
134C2×C4×D4C2×D1111yescharacteristic
135C2×#99—221no—
136#407—221no—
137#397Dic1112yescomplemented
138#397C2×D1112yes—
139#391—21no—
140#380—21no—
141#380—21no—
142C4×C4⋊C4Dic1111yescharacteristic, complemented
143C4×C22⋊C4—221no—
144#342—112no—
145#324—221no—
146#323—112no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11—22no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—81no—
158C22×C11—81no—
159C22×C11C2×#9911yescharacteristic
160C22×C11#41811yescharacteristic
161C22×C11C2×#10411yescharacteristic
162C4×C11—21no—
163C4×C11—22no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—82no—
168C4×C11—82no—
169C4×C11#35412yes—
170Dic11—84no—
171C22×Q8—21no—
172C22×D4C22⋊D1111yescharacteristic
173C23×C4C22⋊D1111yescharacteristic
174C23×C4C22⋊D1111yescharacteristic
175C2×M16—441no—
176C4⋊Q8—41no—
177C4⋊Q8—41no—
178#124—44no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1112yes—
184C2×C4⋊C4C22⋊D1111yescharacteristic
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—222no—
188C2×C22⋊C4C2×Dic1111yescharacteristic
189C2×C22⋊C4C22×D1111yescharacteristic
190C2×C42—21no—
191C2×C42—441no—
192C2×C42C2×Dic1111yescharacteristic
193#99—224no—
194C22⋊C8—222no—
195C22⋊C8—441no—
196#95—22no—
197#95—22no—
198#95—441no—
199#95C2×Dic1112yes—
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—42no—
203C2×C11—81no—
204C2×C11#150711yescharacteristic
205C2×C11#212311yescharacteristic
206C2×C11C2×#35411yescharacteristic
207C24C22⋊Dic1111yescharacteristic
208C24C2×C22⋊D1111yescharacteristic
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—442no—
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22×Dic1111yescharacteristic
228C22×C4C2×C22⋊D1111yescharacteristic
229M16—882no—
230C2×C8—442no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—44no—
239C22⋊C4—44no—
240C22⋊C4—224no—
241C22⋊C4—442no—
242C42—21no—
243C42—21no—
244C42—42no—
245C42—882no—
246C11#1177711yescharacteristic, complemented, Sylow
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#6698512yes—
257C23C2×C22⋊Dic1111yescharacteristic
258Q8—84no—
259D4—44no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—444no—
280C2×C4—882no—
281C2×C4—882no—
282C2×C4#6689811yescharacteristic
283C2×C4#6689811yescharacteristic
284C2×C4#6690112yes—
285C8—882no—
286C22—21no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22#1062282811yescharacteristic
299C22C2×#6689811yescharacteristic
300C22C2×#6690111yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—82no—
307C4—82no—
308C4—884no—
309C4#1062217912yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—81no—
314C2#1306713211yescharacteristic
315C2#1307027011yescharacteristic
316C2C2×#1062217911yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2547C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2547D11
hypocenterC11#11777
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
3. #13066616C2semidirect
5. C2×C11×C4⋊Q8C4semidirect
8. C11×#397C4semidirect
13. C4×C11×C4⋊C4C4semidirect
132. C2×C4⋊Q8Dic11semidirect
137. #397Dic11semidirect
142. C4×C4⋊C4Dic11semidirect
246. C11#11777semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669542
#130666162
C11×#25472
#1177711