Finite Group Databasebeta

← #14665242

Subgroups — #14665242

Order 2816.

314 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 81 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#13067370C211yesmaximal, 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#10622450—21no—
19C4×C8×D11C2211yescharacteristic
20#10622296C2211yescharacteristic
21C11×C4⋊C16C2211yescharacteristic
22C11×#334C2211yescharacteristic
23Dic11⋊C16—21no—
24#10622118—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×#4313—41no—
36C2×C8×D11C2×C411yescharacteristic
37C2×C8×D11D411yescharacteristic
38#66936—41no—
39(C22⋊D11)⋊C4—41no—
40#66932—41no—
41#66930—41no—
42C42×D11D411yescharacteristic
43#66923—21no—
44C2×C11×C16—21no—
45C11×C4⋊C8—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—21no—
48#66899—21no—
49#66896—21no—
50#66896—21no—
51#66882C2×C411yescharacteristic
52#66882C2×C411yescharacteristic
53#66881—21no—
54Dic11⋊C8—41no—
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58C4⋊(C11⋊C8)—21no—
59C4×C11⋊C8D411yescharacteristic
60#66862—42no—
61#11980—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
95#4313—82no—
96C8×D11—21no—
97C8×D11—21no—
98C8×D11—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3168—111no—
102#2150—111no—
103#1566—111no—
104#1363—111no—
105#1363—111no—
106#1360—111no—
107#1360D1111yescharacteristic, complemented
108C23×C11—41no—
109C22×D11#10211yescharacteristic
110Q8×C11—41no—
111Q8×C11—41no—
112D4×C11—41no—
113D4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C2×C4×C11C2×SD1611yescharacteristic
118C22⋊D11—82no—
119C2×Dic11—41no—
120C2×Dic11—41no—
121C2×Dic11—82no—
122C2×Dic11#10211yescharacteristic
123C2×Dic11#10211yescharacteristic
124C2×Dic11#10211yescharacteristic
125C4×D11—21no—
126C4×D11—21no—
127C4×D11—22no—
128C4×D11—41no—
129C8×C11—21no—
130C8×C11—81no—
131C8×C11AGL(1,ℤ/8)11yescharacteristic
132C8×C11#13711yescharacteristic
133C11⋊C8—21no—
134C11⋊C8—21no—
135C11⋊C8—81no—
136#529—221no—
137C2×M32—221no—
138#499—111no—
139#495C2×D1111yescharacteristic
140#488—221no—
141#467—111no—
142#466—111no—
143#465—221no—
144C4×Q16—111no—
145C4×SD16—221no—
146C4×D8—111no—
147#423—221no—
148C2×C4×C8—111no—
149C4⋊C16—111no—
150C4⋊C16—221no—
151C4⋊C16C2×D1111yescharacteristic
152#334—111no—
153#334—221no—
154#334C2×D1111yescharacteristic
155C22×C11—81no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11C2×#10211yescharacteristic
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—21no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—81no—
165C4×C11#41311yescharacteristic
166C4×C11#41711yescharacteristic
167Dic11—21no—
168Dic11—21no—
169Dic11—81no—
170Dic11—81no—
171Dic11#36012yes—
172C2×Q16C4×D1111yescharacteristic
173C2×SD16—21no—
174C2×D8C4×D1111yescharacteristic
175C2×M16—441no—
176C22×C8—111no—
177C22×C8—111no—
178#126—441no—
179#125—221no—
180#124—21no—
181#123—441no—
182C22⋊Q8—221no—
183#121—221no—
184C4×Q8—221no—
185C4×D4—221no—
186C4×D4—441no—
187#117—441no—
188C2×C42—111no—
189M32—442no—
190C2×C16—21no—
191C2×C16—221no—
192#107—111no—
193#107—111no—
194#106—221no—
195C4⋊C8—21no—
196C4⋊C8—221no—
197C4⋊C8—441no—
198#103—221no—
199#103—221no—
200#102—221no—
201#102—221no—
202C4×C8—111no—
203C4×C8—111no—
204C4×C8—111no—
205C4×C8C22×D1111yescharacteristic
206C2×C11—161no—
207C2×C11#154711yescharacteristic
208C2×C11#214311yescharacteristic
209C2×C11C2×#36011yescharacteristic
210D11—41no—
211C2×Q8—21no—
212C2×D4—21no—
213C2×D4—441no—
214C22×C4—111no—
215C22×C4—111no—
216C22×C4—111no—
217C22×C4—441no—
218Q16—41no—
219SD16—41no—
220SD16—41no—
221D8—41no—
222M16—882no—
223C2×C8—41no—
224C2×C8—111no—
225C2×C8—111no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—441no—
229C2×C8—441no—
230C2×C8C2×C4×D1111yescharacteristic
231C2×C8D4×D1111yescharacteristic
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4—441no—
235C4⋊C4—441no—
236C4⋊C4—441no—
237C4⋊C4—441no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C22⋊C4—441no—
241C22⋊C4—441no—
242C22⋊C4—441no—
243C42—111no—
244C42—111no—
245C42—111no—
246C42—441no—
247C42D4×D1111yescharacteristic
248C16—41no—
249C16—441no—
250C11#1198011yescharacteristic, complemented, Sylow
251C23—41no—
252C23—111no—
253Q8—41no—
254Q8—41no—
255D4—41no—
256D4—41no—
257D4—882no—
258C2×C4—41no—
259C2×C4—111no—
260C2×C4—111no—
261C2×C4—111no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—221no—
265C2×C4—441no—
266C2×C4—441no—
267C2×C4—441no—
268C2×C4—882no—
269C2×C4C22⋊C4×D1111yescharacteristic
270C2×C4D8×D1111yescharacteristic
271C2×C4SD16×D1111yescharacteristic
272C8—21no—
273C8—81no—
274C8—221no—
275C8—221no—
276C8—881no—
277C8#6696411yescharacteristic
278C8#6696811yescharacteristic
279C22—81no—
280C22—81no—
281C22—81no—
282C22—221no—
283C22—221no—
284C22—221no—
285C22D11×#10211yescharacteristic
286C4—21no—
287C4—21no—
288C4—81no—
289C4—112no—
290C4—221no—
291C4—221no—
292C4—881no—
293C4—881no—
294C4#1062235811yescharacteristic
295C4#1062238411yescharacteristic
296C2—161no—
297C2—441no—
298C2#1306729011yescharacteristic
299C2#1307034211yescharacteristic
300C2D11×#36011yescharacteristic
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#11980
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. #13067370C2semidirect
4. #13066669C2semidirect
5. #13066667C2semidirect
6. #13066659C2semidirect
7. C11×#1360C2semidirect
107. #1360D11semidirect
250. C11#11980semidirect

Maximal subgroups

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

subgroupindex
#130791832
#130703702
#130673702
#130666692
#130666672
#130666592
C11×#13602
#1198011