Finite Group Databasebeta

← #14663423

Subgroups — #14663423

Order 2816.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#13073569C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066561C214yesmaximal, complemented
4C11×#1459C211yesmaximal, characteristic
5C2×C4×D4×C11C2211yescharacteristic
6C2×#66977—21no—
7C2×#66977—21no—
8C2×#66922C411yescharacteristic
9C2×C11×C22⋊C8—21no—
10#10622834C412yes—
11#10622820—21no—
12#10622589C2212yes—
13#10622562—21no—
14#10622562—21no—
15C4×C4⋊Dic11C411yescharacteristic
16C11×#324C2212yes—
17C11×#323—21no—
18#10622166C2212yes—
19#10622163—21no—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C22×C8×C11—41no—
25C4×D4×C11—41no—
26C4×D4×C11—41no—
27C2×C11×C4⋊C4C2311yescharacteristic
28C2×C11×C22⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C22⋊Dic11—22no—
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2×C412yes—
36#66977—44no—
37#66977—44no—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11C2×C412yes—
41C2×#4318—41no—
42#66922—41no—
43#66922—41no—
44C11×C22⋊C8—22no—
45C11×C22⋊C8—41no—
46C11⋊#95—21no—
47C22⋊(C11⋊C8)—22no—
48C22⋊(C11⋊C8)—41no—
49#11570—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C24×C11C22⋊C411yescharacteristic
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—42no—
60C22×C4×C11—42no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—22no—
67C22×Dic11—22no—
68C2×Dic22—42no—
69C2×Dic22—42no—
70C2×Dic22—41no—
71C2×Dic22—41no—
72C2×C8×C11—42no—
73C2×C8×C11—82no—
74C11×C4⋊C4—41no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—41no—
77C42×C11—21no—
78C42×C11—21no—
79C22⋊Dic11—44no—
80C22⋊Dic11—44no—
81C4⋊Dic11—24no—
82C4⋊Dic11—42no—
83C4⋊Dic11—42no—
84Dic11⋊C4—44no—
85Dic11⋊C4—44no—
86C4×Dic11—24no—
87#4318—82no—
88C2×C11⋊C8—42no—
89#2542—111no—
90#1465—111no—
91#1459D1111yescharacteristic
92#1325—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×C11#10112yes—
103C23×C11C2×C22⋊C411yescharacteristic
104D4×C11—44no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#9911yescharacteristic
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#13112yes—
121C2×Dic11—24no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127Dic22—82no—
128Dic22—82no—
129C8×C11—82no—
130C11⋊C8—82no—
131C2×C4⋊Q8—111no—
132C2×C22⋊Q8—221no—
133C2×C22⋊Q8—221no—
134C2×C4×D4C2×D1111yescharacteristic
135#407—221no—
136C2×C22⋊C8—21no—
137#399—221no—
138#399—221no—
139#390—112no—
140#384—112no—
141C4×C4⋊C4—111no—
142#324—112no—
143#324C2×D1112yes—
144#323—21no—
145#323—221no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—22no—
149C22×C11—42no—
150C22×C11—42no—
151C22×C11—41no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11#40811yescharacteristic
159C22×C11C2×#9911yescharacteristic
160C22×C11C2×#10111yescharacteristic
161C4×C11—21no—
162C4×C11—22no—
163C4×C11—41no—
164C4×C11—41no—
165C4×C11—41no—
166C4×C11#35312yes—
167Dic11—44no—
168Dic11—82no—
169C22×Q8—221no—
170C22×D4C4×D1111yescharacteristic
171C23×C4D4411yescharacteristic
172C23×C4C22⋊D1111yescharacteristic
173C2×M16—441no—
174C22×C8—41no—
175C4⋊Q8—441no—
176C4⋊Q8—441no—
177C22⋊Q8—444no—
178C22⋊Q8—444no—
179C4×D4—41no—
180C4×D4—41no—
181C2×C4⋊C4—112no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—222no—
185C2×C4⋊C4—222no—
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C22⋊C4—222no—
188C2×C22⋊C4—222no—
189C2×C22⋊C4D4411yescharacteristic
190C2×C22⋊C4C22⋊D1111yescharacteristic
191C2×C42—112no—
192C2×C42C4×D1111yescharacteristic
193C22⋊C8—22no—
194C22⋊C8—41no—
195C22⋊C8—222no—
196C22⋊C8—441no—
197#95—221no—
198C2×C11—21no—
199C2×C11—21no—
200C2×C11—42no—
201C2×C11—81no—
202C2×C11#147211yescharacteristic
203C2×C11C2×#35311yescharacteristic
204C2×C11#213511yescharacteristic
205C24(C2×D11)⋊C411yescharacteristic
206C24(C2×D11)⋊C411yescharacteristic
207C2×Q8—442no—
208C2×Q8—442no—
209C2×Q8—441no—
210C2×Q8—441no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—41no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4C2×C4×D1111yescharacteristic
225C22×C4C2×D4411yescharacteristic
226C22×C4C2×C22⋊D1111yescharacteristic
227M16—882no—
228C2×C8—42no—
229C2×C8—82no—
230C2×C8—442no—
231C4⋊C4—41no—
232C4⋊C4—224no—
233C4⋊C4—442no—
234C4⋊C4—442no—
235C4⋊C4—444no—
236C4⋊C4—444no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—444no—
240C22⋊C4—444no—
241C42—21no—
242C42—21no—
243C42—224no—
244C11#1157011yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23#6688812yes—
255C23C2×(C2×D11)⋊C411yescharacteristic
256Q8—882no—
257Q8—882no—
258D4—44no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—224no—
273C2×C4—442no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4—442no—
277C2×C4—442no—
278C2×C4#6687011yescharacteristic
279C2×C4#6687011yescharacteristic
280C2×C4#6695412yes—
281C8—82no—
282C8—882no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22C2×#6687011yescharacteristic
296C22#1062272311yescharacteristic
297C22C2×#6688811yescharacteristic
298C4—21no—
299C4—22no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—444no—
304C4—882no—
305C4#1062211212yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1306697911yescharacteristic
311C2C2×#1062211211yescharacteristic
312C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1459D11
hypocenterC11#11570
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066561C2semidirect
244. C11#11570semidirect

Maximal subgroups

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

subgroupindex
#130735692
#130669542
#130665612
C11×#14592
#1157011