Finite Group Databasebeta

← #14663345

Subgroups — #14663345

Order 2816.

366 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 79 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#13073065C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066561C212yesmaximal, complemented
4#13066549C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C11×#432—21no—
9C4×C22⋊Dic11C411yescharacteristic
10#10622590C411yescharacteristic
11#10622589C2211yescharacteristic
12#10622587C411yescharacteristic
13#10622587C2211yescharacteristic
14#10622565—21no—
15#10622565—21no—
16#10622546—21no—
17#10622546—21no—
18#10622538—21no—
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11C2×C411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36#66977—41no—
37#66977—41no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43C11×C4⋊C8—41no—
44C11×C22⋊C8—22no—
45C11×#97—41no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11552—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—22no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×C8×C11—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C22⋊Dic11—42no—
85C22⋊Dic11—42no—
86C4⋊Dic11—41no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91C4×Dic11—22no—
92C4×Dic11—41no—
93C2×C11⋊C8—42no—
94#2499—111no—
95#1464D1111yescharacteristic
96#1458—111no—
97#1325—112no—
98#1319—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11C2×C22⋊C411yescharacteristic
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—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11#9911yescharacteristic
121C2×C4×C11#13112yes—
122C2×Dic11—22no—
123C2×Dic11—41no—
124C2×Dic11—41no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134Dic22—82no—
135C8×C11—82no—
136C11⋊C8—82no—
137C2×C22⋊Q8—111no—
138C2×#117C2×D1111yescharacteristic
139#432—21no—
140#431—221no—
141#397—221no—
142#397—221no—
143#391—111no—
144#391—111no—
145#387—221no—
146#387—221no—
147#384—111no—
148#382—111no—
149C4×C22⋊C4—111no—
150#324—112no—
151#324C2×D1112yes—
152#323—21no—
153#323—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—81no—
160C22×C11—81no—
161C22×C11#40811yescharacteristic
162C22×C11C2×#9911yescharacteristic
163C22×C11#41311yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—22no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171Dic11—42no—
172Dic11—81no—
173Dic11—81no—
174Dic11—81no—
175C22×Q8—111no—
176C23×C4C4×D1111yescharacteristic
177C22⋊Q8—441no—
178C22⋊Q8—441no—
179#117—41no—
180#117—41no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4C4×D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C22⋊C4—221no—
188C2×C22⋊C4—221no—
189C2×C22⋊C4D4411yescharacteristic
190C2×C22⋊C4C22⋊D1111yescharacteristic
191C2×C42—111no—
192C2×C42—111no—
193C2×C42D4411yescharacteristic
194C2×C42C22⋊D1111yescharacteristic
195C4⋊C8—41no—
196C4⋊C8—441no—
197C22⋊C8—22no—
198C22⋊C8—222no—
199#97—41no—
200C4×C8—441no—
201#95—221no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—81no—
211C2×C11#146811yescharacteristic
212C2×C11#212611yescharacteristic
213C2×C11#213511yescharacteristic
214C24(C2×D11)⋊C411yescharacteristic
215C2×Q8—222no—
216C2×Q8—441no—
217C2×Q8—441no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4—221no—
225C22×C4—221no—
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4(C2×D11)⋊C411yescharacteristic
229C22×C4C2×C4×D1111yescharacteristic
230C22×C4C2×D4411yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—42no—
233C2×C8—442no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—441no—
237C4⋊C4—442no—
238C4⋊C4—442no—
239C4⋊C4—441no—
240C4⋊C4—441no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—222no—
250C42—441no—
251C11#1155211yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×(C2×D11)⋊C411yescharacteristic
258Q8—882no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—222no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4#6687011yescharacteristic
286C2×C4#6687011yescharacteristic
287C2×C4#6696012yes—
288C8—82no—
289C8—882no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—81no—
297C22C2×#6687011yescharacteristic
298C22#1062274211yescharacteristic
299C22#1062274511yescharacteristic
300C4—21no—
301C4—21no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—442no—
308C4—881no—
309C4—881no—
310C4—881no—
311C2—21no—
312C2—21no—
313C2—81no—
314C2#1306696511yescharacteristic
315C2#1307027911yescharacteristic
316C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1464D11
hypocenterC11#11552
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13066561C2semidirect
4. #13066549C2semidirect
251. C11#11552semidirect

Maximal subgroups

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

subgroupindex
#130730652
#130669302
#130665612
#130665492
C11×#14642
#1155211