Finite Group Databasebeta

← #14664682

Subgroups — #14664682

Order 2816.

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

normal subgroups only

This group has 376 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#13074193C211yesmaximal, characteristic
2#13068699C211yesmaximal, characteristic
3#13066647C212yesmaximal, complemented
4#13066623C212yesmaximal, complemented
5C11×#1458C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×C4×Dic22C411yescharacteristic
8C11×#431—21no—
9#10622823—21no—
10#10622820—21no—
11#10622596C2211yescharacteristic
12#10622592C2211yescharacteristic
13#10622591—21no—
14#10622566C411yescharacteristic
15#10622560C411yescharacteristic
16#10622557—21no—
17#10622550C411yescharacteristic
18#10622546—21no—
19C11×#324C2212yes—
20C11×#323—21no—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
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×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×#4318—22no—
41C4×Dic22—41no—
42C4×Dic22—41no—
43C11×C4⋊C8—41no—
44C11×C22⋊C8—22no—
45C4×C8×C11—41no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—41no—
55C22⋊(C11⋊C8)—41no—
56#11849—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—41no—
73C2×Dic22—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—
86Dic11⋊C4—42no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—42no—
90C4×Dic11—42no—
91#4318—42no—
92#4318—42no—
93C2×C11⋊C8—42no—
94#2599—111no—
95#1822—111no—
96#1458D1111yescharacteristic
97#1354—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—
134Dic22—42no—
135Dic22—42no—
136C8×C11—82no—
137C11⋊C8—82no—
138C2×C4×Q8—111no—
139C2×#117C2×D1111yescharacteristic
140#431—21no—
141#407—221no—
142#398—111no—
143#397—111no—
144#395—111no—
145#393—111no—
146#388—221no—
147#387—221no—
148#387—221no—
149#385—221no—
150#383—111no—
151#343—112no—
152#343—221no—
153#324C2×D1112yes—
154#323—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—42no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—81no—
162C22×C11C2×#9911yescharacteristic
163C22×C11#41611yescharacteristic
164C22×C11#42111yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172Dic11—42no—
173Dic11—81no—
174Dic11—81no—
175Dic11—81no—
176C22×Q8—111no—
177C23×C4D4411yescharacteristic
178C2×M16—222no—
179C4×Q8—441no—
180C4×Q8—441no—
181#117—41no—
182#117—41no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4D4411yescharacteristic
188C2×C4⋊C4C22×D1111yescharacteristic
189C2×C22⋊C4—221no—
190C2×C22⋊C4—221no—
191C2×C22⋊C4C4×D1111yescharacteristic
192C2×C22⋊C4C22⋊D1111yescharacteristic
193C2×C42—221no—
194C2×C42C4×D1111yescharacteristic
195C2×C42C22⋊D1111yescharacteristic
196C4⋊C8—41no—
197C22⋊C8—22no—
198C22⋊C8—441no—
199C22⋊C8—441no—
200C4×C8—41no—
201#95—111no—
202#95—111no—
203#95—221no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11—81no—
212C2×C11#151611yescharacteristic
213C2×C11#212011yescharacteristic
214C2×C11#213511yescharacteristic
215C24(C2×D11)⋊C411yescharacteristic
216C2×Q8—441no—
217C2×Q8—442no—
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
232M16—442no—
233M16—442no—
234C2×C8—42no—
235C2×C8—442no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—441no—
239C4⋊C4—442no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—442no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—442no—
252C11#1184911yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×(C2×D11)⋊C411yescharacteristic
259Q8—442no—
260Q8—442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—222no—
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—441no—
286C2×C4—441no—
287C2×C4#6687011yescharacteristic
288C2×C4#6687011yescharacteristic
289C2×C4#6695712yes—
290C8—82no—
291C8—882no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C2×#6687011yescharacteristic
300C22#1062272611yescharacteristic
301C22#1062275211yescharacteristic
302C4—22no—
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—442no—
310C4—881no—
311C4—881no—
312C4—881no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#1306717311yescharacteristic
317C2#1307025511yescharacteristic
318C2#1307031011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1458D11
hypocenterC11#11849
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13066647C2semidirect
4. #13066623C2semidirect
252. C11#11849semidirect

Maximal subgroups

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

subgroupindex
#130741932
#130686992
#130666472
#130666232
C11×#14582
#1184911