Finite Group Databasebeta

← #14663136

Subgroups — #14663136

Order 2816.

662 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 77 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#13070996C211yesmaximal, characteristic
2#13066947C212yesmaximal, complemented
3#13066546C211yesmaximal, characteristic, complemented
4#13066543C212yesmaximal
5C11×#1317C211yesmaximal, characteristic, complemented
6C23×C4×D11C411yescharacteristic
7C2×#66930C411yescharacteristic
8C2×#66930C2211yescharacteristic
9C11×#381C2211yescharacteristic
10#10622824C411yescharacteristic
11#10622568C411yescharacteristic
12#10622568C2211yescharacteristic
13#10622332—22no—
14#10622280—22no—
15#10622279—22no—
16C11×#323C2212yes—
17#10622163C2212yes—
18#10622107—22no—
19C24×D11C2×C411yescharacteristic
20C23×C4×C11C2×C411yescharacteristic
21C23×Dic11C2×C411yescharacteristic
22C22×C4×D11—22no—
23C22×C4×D11—22no—
24C22×C4×D11—21no—
25C22×C4×D11—21no—
26C22×C4×D11—42no—
27C22×C4×D11—42no—
28C2×C11×C22⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4C2311yescharacteristic
30C2×C22⋊Dic11C2×C411yescharacteristic
31C2×C22⋊Dic11C2×C411yescharacteristic
32C2×(C2×D11)⋊C4—22no—
33C2×(C2×D11)⋊C4—22no—
34C2×Dic11⋊C4—21no—
35C2×Dic11⋊C4D412yes—
36C2×C4×Dic11—21no—
37C2×C4×Dic11D412yes—
38#66930—42no—
39#66930—42no—
40C11×C22⋊C8—22no—
41C11×#95—22no—
42C11⋊#95—22no—
43C22⋊(C11⋊C8)—22no—
44#66879—42no—
45Dic11⋊C8—42no—
46#11501—111nomaximal, Sylow
47C24×C11C22×C411yescharacteristic
48C23×D11—21no—
49C23×D11—21no—
50C23×D11—44no—
51C23×D11—41no—
52C23×D11—41no—
53C23×D11M1612yes—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11M1612yes—
60C22×C4×C11C2×D412yes—
61C22×Dic11—22no—
62C22×Dic11—22no—
63C22×Dic11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C412yes—
69C2×C4×D11—24no—
70C2×C4×D11—24no—
71C2×C4×D11—48no—
72C2×C4×D11—42no—
73C2×C4×D11—42no—
74C2×C4×D11—48no—
75C2×C4×D11—42no—
76C2×C4×D11—42no—
77C2×C8×C11—42no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—44no—
84Dic11⋊C4—42no—
85Dic11⋊C4—42no—
86C4×Dic11—22no—
87C4×Dic11—22no—
88C4×Dic11—42no—
89C2×C11⋊C8—42no—
90#2280—111no—
91#1464—112no—
92#1317—111no—
93#1317D1111yescharacteristic, complemented
94#1316—112no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—42no—
98C23×C11C2×C22⋊C411yescharacteristic
99C23×C11C2×M1611yescharacteristic
100C23×C11C2×M1611yescharacteristic
101C22×D11—24no—
102C22×D11—22no—
103C22×D11—44no—
104C22×D11—44no—
105C22×D11—42no—
106C22×D11—42no—
107C22×D11—48no—
108C22×D11—44no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—42no—
112C22×D11—44no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×Dic11—24no—
123C2×Dic11—24no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—22no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—41no—
132C2×Dic11#9912yes—
133C2×Dic11#10012yes—
134C4×D11—48no—
135C4×D11—48no—
136C8×C11—82no—
137C11⋊C8—82no—
138C24×C4—111no—
139C2×#117—111no—
140C2×#117—111no—
141#432—222no—
142#381—111no—
143#381C2×D1111yescharacteristic
144#380—222no—
145#379—111no—
146#379—111no—
147C4×C22⋊C4—222no—
148#324—222no—
149#323—112no—
150#323C2×D1112yes—
151C22×C11—22no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11#40711yescharacteristic
159C22×C11C2×#9911yescharacteristic
160C22×C11C2×#10011yescharacteristic
161C2×D11—24no—
162C2×D11—44no—
163C2×D11—42no—
164C2×D11—48no—
165C2×D11—44no—
166C2×D11—44no—
167C2×D11—42no—
168C2×D11—44no—
169C4×C11—42no—
170C4×C11—42no—
171C4×C11—81no—
172Dic11—22no—
173Dic11—22no—
174Dic11—42no—
175Dic11—81no—
176C25—111no—
177C23×C4—111no—
178C23×C4—221no—
179C23×C4—221no—
180C23×C4—222no—
181C23×C4—222no—
182C23×C4—442no—
183C23×C4—442no—
184C23×C4C4×D1111yescharacteristic
185#117—442no—
186#117—442no—
187C2×C4⋊C4—112no—
188C2×C4⋊C4—221no—
189C2×C22⋊C4—111no—
190C2×C22⋊C4—111no—
191C2×C22⋊C4—222no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4C4×D1111yescharacteristic
194C2×C22⋊C4C22×D1111yescharacteristic
195C2×C42—112no—
196C2×C42—221no—
197C4⋊C8—442no—
198C22⋊C8—22no—
199C22⋊C8—222no—
200#97—442no—
201#95—22no—
202#95—222no—
203C2×C11—21no—
204C2×C11—21no—
205C2×C11—41no—
206C2×C11—41no—
207C2×C11#146211yescharacteristic
208C2×C11#212012yes—
209D11—44no—
210C24—112no—
211C24—221no—
212C24—221no—
213C24—441no—
214C24—441no—
215C24—444no—
216C24C2×C4×D1111yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—111no—
223C22×C4—111no—
224C22×C4—112no—
225C22×C4—224no—
226C22×C4—224no—
227C22×C4—222no—
228C22×C4—222no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—442no—
233C22×C4—442no—
234C22×C4—448no—
235C22×C4—442no—
236C22×C4—442no—
237C22×C4—448no—
238C22×C4#431312yes—
239C22×C4D4×D1112yes—
240C2×C8—42no—
241C2×C8—442no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—444no—
247C22⋊C4—444no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C42—222no—
251C42—222no—
252C42—442no—
253C11#1150111yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—42no—
257C23—224no—
258C23—222no—
259C23—442no—
260C23—442no—
261C23—442no—
262C23—444no—
263C23—444no—
264C23—444no—
265C23—448no—
266C23—444no—
267C23—441no—
268C23—441no—
269C23C22⋊C4×D1111yescharacteristic
270C23C2×#431311yescharacteristic
271C23M16×D1111yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—112no—
282C2×C4—112no—
283C2×C4—224no—
284C2×C4—224no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—222no—
290C2×C4—448no—
291C2×C4—448no—
292C2×C4—442no—
293C2×C4—442no—
294C2×C4—441no—
295C8—82no—
296C8—882no—
297C22—22no—
298C22—21no—
299C22—21no—
300C22—41no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—224no—
305C22—444no—
306C22—442no—
307C22—444no—
308C22—444no—
309C22—448no—
310C22—444no—
311C22—442no—
312C22#1062233911yescharacteristic
313C22D11×#9911yescharacteristic
314C22D11×#10011yescharacteristic
315C4—42no—
316C4—42no—
317C4—81no—
318C4—222no—
319C4—222no—
320C4—442no—
321C4—881no—
322C2—21no—
323C2—21no—
324C2—41no—
325C2—41no—
326C2—444no—
327C2#1306694111yescharacteristic
328C2#1307025612yes—
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1317C2
socleC22×C11C2×#99
prime radicalC24×D11C2×C4
cosocleC2×C11×C22⋊C4C23
hypercenter#1317D11
hypocenterC11#11501
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
2. #13066947C2semidirect
3. #13066546C2semidirect
5. C11×#1317C2semidirect
93. #1317D11semidirect
253. C11#11501semidirect

Maximal subgroups

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

subgroupindex
#130709962
#130669472
#130665462
#130665432
C11×#13172
#1150111