Finite Group Databasebeta

← #14664699

Subgroups — #14664699

Order 2816.

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

normal subgroups only

This group has 368 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#13074314C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066642C212yesmaximal, complemented
4#13066621C212yesmaximal, complemented
5C11×#1822C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66923C411yescharacteristic
8C11×#407—21no—
9#10622823—21no—
10#10622599C2211yescharacteristic
11#10622596C2211yescharacteristic
12#10622585—21no—
13#10622566C411yescharacteristic
14#10622562C411yescharacteristic
15#10622558—21no—
16#10622546—21no—
17#10622545C411yescharacteristic
18#10622538—21no—
19C11×#343—21no—
20C11×#343C2212yes—
21#10622166C2212yes—
22#10622163—21no—
23C23×C4×C11D411yescharacteristic
24C2×C11×M16—22no—
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C11×C22⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42#66923—41no—
43#66923—41no—
44C11×C22⋊C8—41no—
45C11×C22⋊C8—41no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11853—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—
72C11×M16—42no—
73C11×M16—42no—
74C2×C8×C11—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C11×C22⋊C4—41no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—21no—
82C42×C11—21no—
83C22⋊Dic11—42no—
84C22⋊Dic11—42no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—42no—
88Dic11⋊C4—42no—
89Dic11⋊C4—41no—
90Dic11⋊C4—41no—
91Dic11⋊C4—42no—
92C4×Dic11—42no—
93C2×C11⋊C8—42no—
94#2611—111no—
95#1822D1111yescharacteristic
96#1458—111no—
97#1353—112no—
98#1346—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#13512yes—
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—
134C8×C11—82no—
135C11⋊C8—82no—
136C2×#125—111no—
137C2×#117C2×D1111yescharacteristic
138#431—221no—
139#407—21no—
140#400—111no—
141#399—111no—
142#398—111no—
143#397—111no—
144#389—221no—
145#388—221no—
146#387—221no—
147#385—221no—
148#376—111no—
149#343—21no—
150#343C2×D1112yes—
151#324—112no—
152#323—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—42no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—81no—
160C22×C11C2×#9911yescharacteristic
161C22×C11#41611yescharacteristic
162C22×C11#42111yescharacteristic
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—22no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170Dic11—42no—
171Dic11—81no—
172Dic11—81no—
173Dic11—81no—
174C23×C4C22⋊D1111yescharacteristic
175C2×M16—22no—
176#125—441no—
177#125—441no—
178#117—41no—
179#117—41no—
180C2×C4⋊C4—111no—
181C2×C4⋊C4—111no—
182C2×C4⋊C4—221no—
183C2×C4⋊C4—221no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4C22⋊D1111yescharacteristic
187C2×C4⋊C4C22×D1111yescharacteristic
188C2×C22⋊C4—221no—
189C2×C22⋊C4—221no—
190C2×C22⋊C4C4×D1111yescharacteristic
191C2×C22⋊C4D4411yescharacteristic
192C2×C42—221no—
193C2×C42C4×D1111yescharacteristic
194C2×C42D4411yescharacteristic
195C4⋊C8—441no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198C22⋊C8—222no—
199C4×C8—441no—
200#95—111no—
201#95—111no—
202#95—221no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—81no—
210C2×C11#151611yescharacteristic
211C2×C11#212311yescharacteristic
212C2×C11#213211yescharacteristic
213C24(C2×D11)⋊C411yescharacteristic
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—221no—
219C22×C4—221no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4(C2×D11)⋊C411yescharacteristic
223C22×C4(C2×D11)⋊C411yescharacteristic
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4C2×C4×D1111yescharacteristic
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—42no—
229M16—42no—
230C2×C8—42no—
231C2×C8—442no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—442no—
237C4⋊C4—442no—
238C4⋊C4—441no—
239C4⋊C4—441no—
240C4⋊C4—442no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—442no—
250C11#1185311yescharacteristic, complemented, Sylow
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×(C2×D11)⋊C411yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
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—41no—
271C2×C4—222no—
272C2×C4—441no—
273C2×C4—441no—
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#6687011yescharacteristic
284C2×C4#6687011yescharacteristic
285C2×C4#6700312yes—
286C8—82no—
287C8—882no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×#6687011yescharacteristic
296C22#1062261511yescharacteristic
297C22#1062261811yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—442no—
306C4—881no—
307C4—881no—
308C4—881no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2#1306717011yescharacteristic
313C2#1307027111yescharacteristic
314C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1822C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1822D11
hypocenterC11#11853
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
3. #13066642C2semidirect
4. #13066621C2semidirect
250. C11#11853semidirect

Maximal subgroups

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

subgroupindex
#130743142
#130669302
#130666422
#130666212
C11×#18222
#1185311