Finite Group Databasebeta

← #14664329

Subgroups — #14664329

Order 2816.

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

normal subgroups only

This group has 482 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#13066957C211yesmaximal, characteristic
3#13066616C214yesmaximal, complemented
4C11×#2486C211yesmaximal, characteristic
5C2×C11×#123—21no—
6C2×C4×D4×C11C2211yescharacteristic
7C22×C11×C4⋊C4C411yescharacteristic, complemented
8C11×#398C412yescomplemented
9C11×#397C2212yes—
10C11×#389—21no—
11C11×#381—21no—
12C11×#380—21no—
13C11×#380C411yescharacteristic, complemented
14C2×#66898—21no—
15C4×C22⋊Dic11—21no—
16#10622539—21no—
17#10622164C2212yes—
18#10622163—21no—
19#10622163C2212yes—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C11×#123—44no—
25C4×D4×C11—41no—
26C4×D4×C11—41no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4—41no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—22no—
40C2×C4×Dic11—41no—
41C11×#95—22no—
42C11×#95—22no—
43C11×#95C2×C412yes—
44#66898—24no—
45C11⋊#95—41no—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—41no—
48#66867—41no—
49#11773—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C24×C11C2×D411yescharacteristic
52C2×D4×C11—22no—
53C2×D4×C11—22no—
54C2×D4×C11—41no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
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—44no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—44no—
82C42×C11—21no—
83C42×C11—21no—
84C22⋊Dic11—24no—
85C22⋊Dic11—42no—
86C4×Dic11—82no—
87C2×C11⋊C8—42no—
88#2486D1111yescharacteristic
89C4×#99—111no—
90#1466—111no—
91#1344—114no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—41no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11—41no—
100C23×C11#10412yes—
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11AGL(1,ℤ/8)12yes—
103D4×C11—44no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
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—84no—
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11#9911yescharacteristic
127C2×Dic11—44no—
128C2×Dic11—82no—
129C2×Dic11—82no—
130C11⋊C8—82no—
131C2×#123—21no—
132C2×C4×D4C2×D1111yescharacteristic
133C22×C4⋊C4Dic1111yescharacteristic, complemented
134#432—221no—
135C2×#99—221no—
136#398Dic1112yescomplemented
137#397C2×D1112yes—
138#389—21no—
139#381—21no—
140#380—21no—
141#380Dic1111yescharacteristic, complemented
142C4×C22⋊C4—221no—
143#342—112no—
144#323—112no—
145#323—221no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—42no—
151C22×C11—42no—
152C22×C11—42no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—81no—
158C22×C11C2×#9911yescharacteristic
159C22×C11#41811yescharacteristic
160C22×C11C2×#10411yescharacteristic
161C4×C11—21no—
162C4×C11—41no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11—82no—
167C4×C11—82no—
168C4×C11#35212yes—
169Dic11—84no—
170C22×D4C22⋊D1111yescharacteristic
171C23×C4—21no—
172C23×C4C2×Dic1111yescharacteristic
173C23×C4C22⋊D1111yescharacteristic
174#123—44no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4C2×Dic1112yes—
183C2×C4⋊C4C2×Dic1111yescharacteristic
184C2×C22⋊C4—21no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—222no—
187C2×C22⋊C4C22⋊D1111yescharacteristic
188C2×C22⋊C4C22×D1111yescharacteristic
189C2×C42—441no—
190C2×C42C22⋊D1111yescharacteristic
191C4⋊C8—441no—
192#99—224no—
193C22⋊C8—222no—
194#97—441no—
195#95—22no—
196#95—22no—
197#95—441no—
198#95C2×Dic1112yes—
199C2×C11—21no—
200C2×C11—21no—
201C2×C11—42no—
202C2×C11—42no—
203C2×C11#150711yescharacteristic
204C2×C11C2×#35211yescharacteristic
205C2×C11#212911yescharacteristic
206C24C22⋊Dic1111yescharacteristic
207C24C2×C22⋊D1111yescharacteristic
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—442no—
223C22×C4C22⋊Dic1111yescharacteristic
224C22×C4C22⋊Dic1111yescharacteristic
225C22×C4C22⋊Dic1111yescharacteristic
226C22×C4C22×Dic1111yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228C2×C8—442no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—44no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—42no—
238C22⋊C4—44no—
239C22⋊C4—224no—
240C22⋊C4—442no—
241C42—21no—
242C42—21no—
243C42—882no—
244C11#1177311yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#6690112yes—
254C23#6698512yes—
255C23C2×C22⋊Dic1111yescharacteristic
256D4—44no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—81no—
277C2×C4—84no—
278C2×C4—444no—
279C2×C4—882no—
280C2×C4—882no—
281C2×C4#6689811yescharacteristic
282C2×C4#6689811yescharacteristic
283C8—882no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22#1062282811yescharacteristic
297C22C2×#6689811yescharacteristic
298C22C2×#6690111yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—82no—
305C4—82no—
306C4—884no—
307C4#1062217712yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1306713211yescharacteristic
313C2C2×#1062217711yescharacteristic
314C2#1307029111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2486C2
socleC22×C11C2×#99
prime radicalC22×D4×C11D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2486D11
hypocenterC11#11773
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
3. #13066616C2semidirect
7. C22×C11×C4⋊C4C4semidirect
8. C11×#398C4semidirect
13. C11×#380C4semidirect
133. C22×C4⋊C4Dic11semidirect
136. #398Dic11semidirect
141. #380Dic11semidirect
244. C11#11773semidirect

Maximal subgroups

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

subgroupindex
C4×#668982
#130669572
#130666162
C11×#24862
#1177311