Finite Group Databasebeta

← #14664666

Subgroups — #14664666

Order 2816.

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

normal subgroups only

This group has 382 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#13068693C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066640C212yesmaximal
4#13066616C212yesmaximal
5C11×#2611C211yesmaximal, characteristic
6C2×C11×#125C411yescharacteristic, complemented
7C2×C11×#117C2211yescharacteristic
8C11×#400C411yescharacteristic, complemented
9C11×#399C2211yescharacteristic
10C11×#398C411yescharacteristic, complemented
11C11×#397C2211yescharacteristic
12C11×#389—21no—
13C11×#388—21no—
14C11×#387—21no—
15C11×#385—21no—
16C11×#376C411yescharacteristic, complemented
17#10622824—21no—
18#10622538—21no—
19#10622166—21no—
20#10622164—21no—
21#10622164C2212yes—
22#10622163C2212yes—
23C23×C4×C11D411yescharacteristic
24C11×#125—41no—
25C11×#125—41no—
26C11×#117—41no—
27C11×#117—41no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4C2311yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2×C411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C22⋊Dic11—22no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51C11⋊#95—41no—
52C11⋊#95—41no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—41no—
55C4×C11⋊C8—41no—
56#11846—111nomaximal, Sylow
57C24×C11C2×D411yescharacteristic
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—42no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—42no—
91C22⋊Dic11—42no—
92C22⋊Dic11—42no—
93C2×C11⋊C8—42no—
94#2611D1111yescharacteristic
95#1820—111no—
96#1458—111no—
97#1352—112no—
98#1344—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11C2×C22⋊C411yescharacteristic
104C23×C11#13512yes—
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—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#9911yescharacteristic
134C2×Dic11—82no—
135C2×Dic11—82no—
136C2×Dic11—82no—
137C11⋊C8—82no—
138C2×#125Dic1111yescharacteristic, complemented
139C2×#117C2×D1111yescharacteristic
140#431—221no—
141#400Dic1111yescharacteristic, complemented
142#399C2×D1111yescharacteristic
143#398Dic1111yescharacteristic, complemented
144#397C2×D1111yescharacteristic
145#389—21no—
146#388—21no—
147#387—21no—
148#385—21no—
149#381—221no—
150#376Dic1111yescharacteristic, complemented
151#342—112no—
152#342—221no—
153#324—221no—
154#323—112no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—22no—
158C22×C11—42no—
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—42no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—81no—
174C4×C11—81no—
175C4×C11—81no—
176Dic11—162no—
177C23×C4C22⋊D1111yescharacteristic
178#125—41no—
179#125—41no—
180#117—41no—
181#117—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×Dic1111yescharacteristic
187C2×C4⋊C4C2×Dic1111yescharacteristic
188C2×C4⋊C4C2×Dic1111yescharacteristic
189C2×C4⋊C4C22⋊D1111yescharacteristic
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—222no—
193C2×C22⋊C4C22⋊D1111yescharacteristic
194C2×C22⋊C4C22×D1111yescharacteristic
195C2×C42—21no—
196C2×C42C2×Dic1111yescharacteristic
197C2×C42C22⋊D1111yescharacteristic
198C4⋊C8—441no—
199C22⋊C8—222no—
200C4×C8—441no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—441no—
207#95—441no—
208#95C2×Dic1111yescharacteristic
209#95C2×Dic1111yescharacteristic
210C2×C11—21no—
211C2×C11—21no—
212C2×C11—42no—
213C2×C11#151611yescharacteristic
214C2×C11#212311yescharacteristic
215C2×C11#212611yescharacteristic
216C24C2×C22⋊D1111yescharacteristic
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—442no—
226C22×C4C22⋊Dic1111yescharacteristic
227C22×C4C22⋊Dic1111yescharacteristic
228C22×C4C22⋊Dic1111yescharacteristic
229C22×C4C22⋊Dic1111yescharacteristic
230C22×C4C22×Dic1111yescharacteristic
231C22×C4C2×C22⋊D1111yescharacteristic
232C2×C8—442no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—442no—
247C22⋊C4—442no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—42no—
253C11#1184611yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#6700312yes—
259C23C2×C22⋊Dic1111yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—882no—
288C2×C4—882no—
289C2×C4—882no—
290C2×C4#6689811yescharacteristic
291C2×C4#6689811yescharacteristic
292C8—882no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#6689811yescharacteristic
301C22#1062284611yescharacteristic
302C22#1062284911yescharacteristic
303C4—21no—
304C4—21no—
305C4—42no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—1762no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1306717211yescharacteristic
319C2#1307027011yescharacteristic
320C2#1307028111yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2611C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#2611D11
hypocenterC11#11846
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2611

Complements

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

NH ≅ G/Ntype
6. C2×C11×#125C4semidirect
8. C11×#400C4semidirect
10. C11×#398C4semidirect
16. C11×#376C4semidirect
138. C2×#125Dic11semidirect
141. #400Dic11semidirect
143. #398Dic11semidirect
150. #376Dic11semidirect
253. C11#11846semidirect

Maximal subgroups

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

subgroupindex
#130686932
#130669302
#130666402
#130666162
C11×#26112
#1184611