Finite Group Databasebeta

← #14665237

Subgroups — #14665237

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#13079183C211yesmaximal, characteristic
2#13070370C211yesmaximal, characteristic, complemented
3#13067376C211yesmaximal, characteristic, complemented
4#13066669C211yesmaximal, characteristic, complemented
5#13066667C211yesmaximal, characteristic, complemented
6#13066659C211yesmaximal, characteristic, complemented
7C11×#1360C211yesmaximal, characteristic, complemented
8#10623211—21no—
9C11×#495C2211yescharacteristic
10#10622801C411yescharacteristic
11Q16×Dic11C411yescharacteristic
12#10622784—21no—
13SD16×Dic11—21no—
14#10622770C411yescharacteristic
15D8×Dic11C411yescharacteristic
16#10622669—21no—
17C2×#66862—21no—
18#10622448—21no—
19C4×C8×D11C2211yescharacteristic
20#10622296C2211yescharacteristic
21C11×C4⋊C16C2211yescharacteristic
22C11×#334C2211yescharacteristic
23Dic11⋊C16—21no—
24#10622117—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622095C2211yescharacteristic
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×SD16—21no—
29C2×C11×D8C2×C411yescharacteristic
30C11×#124—21no—
31#66999—21no—
32Q8×Dic11—21no—
33#66991—21no—
34D4×Dic11—21no—
35C2×C8×D11C2×C411yescharacteristic
36C2×C8×D11D411yescharacteristic
37#66936—41no—
38(C22⋊D11)⋊C4—41no—
39#66932—41no—
40#66930—41no—
41C42×D11D411yescharacteristic
42#66923—21no—
43C2×C11×C16—21no—
44C11×C4⋊C8—21no—
45C4×C8×C11C2311yescharacteristic
46#66899—21no—
47#66899—21no—
48#66896—21no—
49#66896—21no—
50(C2×D11)⋊C8—41no—
51#66882C2×C411yescharacteristic
52#66882C2×C411yescharacteristic
53#66881—21no—
54#66879—41no—
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58C4⋊(C11⋊C8)—21no—
59C4×C11⋊C8D411yescharacteristic
60#66862—42no—
61#11979—111nomaximal, Sylow
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×C22⋊D11—41no—
65C22×Dic11—41no—
66C2×C4×D11C22⋊C411yescharacteristic
67C2×C4×D11D811yescharacteristic
68C2×C4×D11SD1611yescharacteristic
69C11×Q16—41no—
70C11×SD16—41no—
71C11×SD16—41no—
72C11×D8—41no—
73C2×C8×C11—41no—
74C2×C8×C11C22×C411yescharacteristic
75C2×C8×C11C2×D411yescharacteristic
76C11×C22⋊C4—41no—
77C11×C22⋊C4—41no—
78C42×C11C2×D411yescharacteristic
79C22⋊Dic11—41no—
80C22⋊Dic11—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88C4×Dic11—41no—
89C4×Dic11C22⋊C411yescharacteristic
90C4×Dic11D811yescharacteristic
91C4×Dic11SD1611yescharacteristic
92C2×C11⋊C8—41no—
93C2×C11⋊C8C22⋊C411yescharacteristic
94C2×C11⋊C8C22⋊C411yescharacteristic
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#1363—111no—
105#1360—111no—
106#1360D1111yescharacteristic, complemented
107C23×C11—41no—
108C22×D11#10211yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111D4×C11—41no—
112D4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11C2×D811yescharacteristic
116C2×C4×C11C2×SD1611yescharacteristic
117C22⋊D11—82no—
118C2×Dic11—41no—
119C2×Dic11—41no—
120C2×Dic11—82no—
121C2×Dic11#10211yescharacteristic
122C2×Dic11#10211yescharacteristic
123C2×Dic11#10211yescharacteristic
124C4×D11—21no—
125C4×D11—21no—
126C4×D11—41no—
127C4×D11—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#499—111no—
138#495C2×D1111yescharacteristic
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×C11—81no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11C2×#10211yescharacteristic
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—81no—
164C4×C11#41311yescharacteristic
165C4×C11#41711yescharacteristic
166Dic11—21no—
167Dic11—21no—
168Dic11—21no—
169Dic11—81no—
170Dic11—81no—
171C2×Q16C4×D1111yescharacteristic
172C2×SD16—21no—
173C2×D8C4×D1111yescharacteristic
174C22×C8—111no—
175C22×C8—111no—
176#126—441no—
177#125—221no—
178#124—21no—
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#107—111no—
191#107—111no—
192#106—221no—
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—161no—
206C2×C11#154711yescharacteristic
207C2×C11#214311yescharacteristic
208C2×C11#214511yescharacteristic
209D11—41no—
210C2×Q8—21no—
211C2×D4—21no—
212C2×D4—441no—
213C22×C4—111no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—441no—
217Q16—41no—
218SD16—41no—
219SD16—41no—
220D8—41no—
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—221no—
231C4⋊C4—221no—
232C4⋊C4—441no—
233C4⋊C4—441no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C22⋊C4—41no—
237C22⋊C4—41no—
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—41no—
250C23—111no—
251Q8—41no—
252Q8—41no—
253D4—41no—
254D4—41no—
255D4—882no—
256C2×C4—41no—
257C2×C4—111no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—441no—
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#6696411yescharacteristic
276C8#6696811yescharacteristic
277C22—81no—
278C22—81no—
279C22—81no—
280C22—221no—
281C22—221no—
282C22—221no—
283C22D11×#10211yescharacteristic
284C4—21no—
285C4—21no—
286C4—81no—
287C4—221no—
288C4—221no—
289C4—221no—
290C4—881no—
291C4—881no—
292C4#1062235811yescharacteristic
293C4#1062238411yescharacteristic
294C2—161no—
295C2—441no—
296C2#1306729011yescharacteristic
297C2#1307034211yescharacteristic
298C2#1307035011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1360C2
socleC22×C11C2×#102
prime radical#10622770C4
cosocleC4×C8×C11C23
hypercenter#1360D11
hypocenterC11#11979
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1360

Complements

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

NH ≅ G/Ntype
2. #13070370C2semidirect
3. #13067376C2semidirect
4. #13066669C2semidirect
5. #13066667C2semidirect
6. #13066659C2semidirect
7. C11×#1360C2semidirect
106. #1360D11semidirect
248. C11#11979semidirect

Maximal subgroups

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

subgroupindex
#130791832
#130703702
#130673762
#130666692
#130666672
#130666592
C11×#13602
#1197911