Finite Group Databasebeta

← #14665239

Subgroups — #14665239

Order 2816.

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

normal subgroups only

This group has 306 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#13079188C211yesmaximal, characteristic
2#13070370C211yesmaximal, characteristic, complemented
3#13067376C211yesmaximal, characteristic, complemented
4#13066668C211yesmaximal, characteristic, complemented
5#13066660C211yesmaximal, characteristic, complemented
6#13066658C211yesmaximal, characteristic, complemented
7C11×#1363C211yesmaximal, characteristic, complemented
8#10623222—21no—
9C11×#499C2211yescharacteristic
10#10622681—21no—
11C2×#66862—21no—
12#10622500C411yescharacteristic
13#10622496C411yescharacteristic
14#10622486C411yescharacteristic
15#10622485C411yescharacteristic
16#10622477—21no—
17#10622465—21no—
18#10622448—21no—
19#10622309C2211yescharacteristic
20C4×C8×D11C2211yescharacteristic
21C11×C4⋊C16C2211yescharacteristic
22C11×#334C2211yescharacteristic
23Dic11⋊C16—21no—
24#10622117—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622095C2211yescharacteristic
27C11×#125—21no—
28C2×Dic44C2×C411yescharacteristic
29C2×D88C2×C411yescharacteristic
30C2×#4314—21no—
31C2×C8×D11C2×C411yescharacteristic
32C2×C8×D11D411yescharacteristic
33#66951—41no—
34#66950—21no—
35#66948—21no—
36#66947—41no—
37#66946—21no—
38#66946—41no—
39#66945—41no—
40#66940—21no—
41#66928—21no—
42C42×D11D411yescharacteristic
43C2×C11×C16—21no—
44C11×#107C2×C411yescharacteristic
45C11×#107C2×C411yescharacteristic
46C11×#106—21no—
47C11×C4⋊C8—21no—
48C4×C8×C11C2311yescharacteristic
49(C2×D11)⋊C8—41no—
50#66879—41no—
51C8×Dic11C2×C411yescharacteristic
52C8×Dic11D411yescharacteristic
53C2×C11⋊C16—21no—
54#66874—21no—
55#66874—21no—
56#66873—21no—
57#66873—21no—
58C4⋊(C11⋊C8)—21no—
59C4×C11⋊C8D411yescharacteristic
60#66862—42no—
61#11979—111nomaximal, Sylow
62C2×D44—21no—
63C2×D44—41no—
64C2×C4×D11—41no—
65C2×C4×D11C22⋊C411yescharacteristic
66C2×C4×D11D811yescharacteristic
67C2×C4×D11SD1611yescharacteristic
68C2×Dic22—21no—
69C2×C8×C11—41no—
70C2×C8×C11C22×C411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C42×C11C2×D411yescharacteristic
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84C4×Dic11—41no—
85C4×Dic11C22⋊C411yescharacteristic
86C4×Dic11D811yescharacteristic
87C4×Dic11SD1611yescharacteristic
88C2×C11⋊C8—41no—
89C2×C11⋊C8C22⋊C411yescharacteristic
90C2×C11⋊C8C22⋊C411yescharacteristic
91Dic44—41no—
92D88—41no—
93#4314—41no—
94#4314—41no—
95C8×D11—21no—
96C8×D11—21no—
97C8×D11—41no—
98C11×C16—41no—
99C11⋊C16—41no—
100#3168—111no—
101#2150—111no—
102#1568—111no—
103#1363—111no—
104#1363D1111yescharacteristic, complemented
105#1360—111no—
106#1360—111no—
107C22×D11—41no—
108C22×D11#10211yescharacteristic
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11C2×SD1611yescharacteristic
114C2×Dic11—41no—
115C2×Dic11#10211yescharacteristic
116C2×Dic11#10211yescharacteristic
117C2×Dic11#10211yescharacteristic
118D44—41no—
119D44—41no—
120D44—82no—
121C4×D11—21no—
122C4×D11—21no—
123C4×D11—41no—
124C4×D11—41no—
125C4×D11—82no—
126Dic22—41no—
127Dic22—41no—
128C8×C11—21no—
129C8×C11—81no—
130C8×C11AGL(1,ℤ/8)11yescharacteristic
131C8×C11#13711yescharacteristic
132C11⋊C8—21no—
133C11⋊C8—21no—
134C11⋊C8—81no—
135#529—221no—
136C2×M32—221no—
137#499C2×D1111yescharacteristic
138#495—111no—
139#488—221no—
140#467—111no—
141#466—111no—
142#465—221no—
143C4×Q16—111no—
144C4×SD16—221no—
145C4×D8—111no—
146#432—221no—
147C2×C4×C8—111no—
148C4⋊C16—111no—
149C4⋊C16—221no—
150C4⋊C16C2×D1111yescharacteristic
151#335—221no—
152#334—111no—
153#334C2×D1111yescharacteristic
154C22×C11C2×#10211yescharacteristic
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—81no—
159C2×D11—81no—
160C2×D11—81no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—81no—
164C4×C11—81no—
165C4×C11#41311yescharacteristic
166C4×C11#41711yescharacteristic
167Dic11—21no—
168Dic11—21no—
169Dic11—21no—
170Dic11—81no—
171C2×Q16—111no—
172C2×SD16—221no—
173C2×D8—111no—
174C22×C8—111no—
175C22×C8—111no—
176#126—441no—
177#125—21no—
178#124—221no—
179#123—441no—
180C22⋊Q8—221no—
181#121—221no—
182C4×Q8—221no—
183C4×D4—221no—
184C4×D4—441no—
185#117—441no—
186C2×C42—111no—
187M32—442no—
188C2×C16—21no—
189C2×C16—221no—
190#107C4×D1111yescharacteristic
191#107C4×D1111yescharacteristic
192#106—21no—
193C4⋊C8—21no—
194C4⋊C8—221no—
195#103—221no—
196#103—221no—
197#102—221no—
198#102—221no—
199C22⋊C8—441no—
200#97—441no—
201C4×C8—111no—
202C4×C8—111no—
203C4×C8—111no—
204C4×C8C22×D1111yescharacteristic
205C2×C11#154711yescharacteristic
206C2×C11#214311yescharacteristic
207C2×C11#214511yescharacteristic
208D11—41no—
209D11—161no—
210C2×Q8—221no—
211C2×D4—221no—
212C2×D4—441no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—441no—
217Q16—441no—
218SD16—441no—
219SD16—441no—
220D8—441no—
221C2×C8—41no—
222C2×C8—111no—
223C2×C8—111no—
224C2×C8—221no—
225C2×C8—221no—
226C2×C8—441no—
227C2×C8—441no—
228C2×C8C2×C4×D1111yescharacteristic
229C2×C8D4×D1111yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C22⋊C4—441no—
237C22⋊C4—441no—
238C22⋊C4—441no—
239C22⋊C4—441no—
240C22⋊C4—441no—
241C42—111no—
242C42—111no—
243C42—111no—
244C42—441no—
245C42D4×D1111yescharacteristic
246C16—41no—
247C16—441no—
248C11#1197911yescharacteristic, complemented, Sylow
249C23—111no—
250C23—441no—
251Q8—441no—
252Q8—441no—
253D4—441no—
254D4—441no—
255D4—882no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—111no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—441no—
264C2×C4—441no—
265C2×C4—441no—
266C2×C4—882no—
267C2×C4C22⋊C4×D1111yescharacteristic
268C2×C4D8×D1111yescharacteristic
269C2×C4SD16×D1111yescharacteristic
270C8—21no—
271C8—81no—
272C8—221no—
273C8—221no—
274C8—881no—
275C8#6696711yescharacteristic
276C8#6697111yescharacteristic
277C22—221no—
278C22—221no—
279C22—221no—
280C22—881no—
281C22—881no—
282C22—881no—
283C22D11×#10211yescharacteristic
284C4—21no—
285C4—21no—
286C4—81no—
287C4—81no—
288C4—221no—
289C4—221no—
290C4—221no—
291C4—881no—
292C4#1062236411yescharacteristic
293C4#1062241611yescharacteristic
294C2—441no—
295C2—1761no—
296C2#1306729211yescharacteristic
297C2#1307034211yescharacteristic
298C2#1307035011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1363C2
socleC22×C11C2×#102
prime radical#10622496C4
cosocleC4×C8×C11C23
hypercenter#1363D11
hypocenterC11#11979
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1363

Complements

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

NH ≅ G/Ntype
2. #13070370C2semidirect
3. #13067376C2semidirect
4. #13066668C2semidirect
5. #13066660C2semidirect
6. #13066658C2semidirect
7. C11×#1363C2semidirect
104. #1363D11semidirect
248. C11#11979semidirect

Maximal subgroups

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

subgroupindex
#130791882
#130703702
#130673762
#130666682
#130666602
#130666582
C11×#13632
#1197911