Finite Group Databasebeta

← #14663088

Subgroups — #14663088

Order 2816.

430 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic
2#13070412C212yesmaximal, complemented
3#13066540C211yesmaximal, characteristic, complemented
4#13066539C212yesmaximal, complemented
5C11×#1314C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊D11C411yescharacteristic
7C23×C11⋊C8C411yescharacteristic
8C22×C8×D11C411yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C2×(C2×D11)⋊C8C2211yescharacteristic
11C2×Dic11⋊C8C411yescharacteristic
12C2×C8×Dic11C2211yescharacteristic
13(C22⋊D11)⋊C8—22no—
14(C22⋊D11)⋊C8—22no—
15C11×C22⋊C16C2212yes—
16C22⋊(C11⋊C16)C2212yes—
17Dic11⋊C16—22no—
18C16×Dic11—22no—
19C23×C4×C11C2×C411yescharacteristic
20C22×C22⋊D11C811yescharacteristic
21C22×C4×D11C2×C411yescharacteristic
22C22×C8×C11C2×C411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C2×C22⋊Dic11C811yescharacteristic
25C4×C22⋊D11—22no—
26C4×C22⋊D11—22no—
27C2×(C2×D11)⋊C4C811yescharacteristic
28C2×Dic11⋊C4C811yescharacteristic
29C2×C4×Dic11C2×C411yescharacteristic
30C22×C11⋊C8—21no—
31C22×C11⋊C8—21no—
32C22×C11⋊C8—42no—
33C22×C11⋊C8C2×C411yescharacteristic
34C22×C11⋊C8C2×C411yescharacteristic
35C2×C8×D11—21no—
36C2×C8×D11—21no—
37C2×C8×D11—42no—
38C2×C11×C16—22no—
39C11×C22⋊C8—22no—
40(C2×D11)⋊C8—22no—
41Dic11⋊C8—22no—
42C8×Dic11D412yes—
43C8×Dic11D412yes—
44C2×C11⋊C16—22no—
45#11487—111nomaximal, Sylow
46C24×C11C2×C811yescharacteristic
47C23×D11C2×C811yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—41no—
51C22×C4×C11—41no—
52C22×C4×C11C2×C811yescharacteristic
53C22×C4×C11C22×C411yescharacteristic
54C2×C22⋊D11—22no—
55C2×C22⋊D11—22no—
56C2×C22⋊D11C1614yescomplemented
57C22×Dic11C2×C811yescharacteristic
58C22×Dic11C2×C811yescharacteristic
59C22×Dic11C2×C811yescharacteristic
60C2×C4×D11—21no—
61C2×C4×D11—21no—
62C2×C4×D11—41no—
63C2×C4×D11—41no—
64C2×C8×C11—21no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11C2×D412yes—
68C22⋊Dic11—22no—
69(C2×D11)⋊C4—22no—
70Dic11⋊C4—22no—
71C4×Dic11C22⋊C412yes—
72C4×Dic11M1612yes—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—21no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8C22⋊C411yescharacteristic
79C2×C11⋊C8C22⋊C411yescharacteristic
80C8×D11—42no—
81C8×D11—42no—
82C11×C16—42no—
83C11⋊C16—42no—
84C2×C8×D4—111no—
85#2162—112no—
86#1314—111no—
87#1314—112no—
88#1314D1111yescharacteristic, complemented
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—41no—
92C23×C11—41no—
93C23×C11C2×C1612yes—
94C23×C11C22×C811yescharacteristic
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—41no—
98C22×D11—41no—
99C22×D11C2×C1612yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11C2×C22⋊C411yescharacteristic
108C2×C4×C11C2×M1611yescharacteristic
109C22⋊D11—28no—
110C2×Dic11—21no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11C22⋊C812yes—
114C2×Dic11C22⋊C812yes—
115C2×Dic11C2×C1612yes—
116C2×Dic11M3212yes—
117C4×D11—42no—
118C4×D11—41no—
119C4×D11—41no—
120C8×C11—22no—
121C8×C11—41no—
122C11⋊C8—21no—
123C11⋊C8—41no—
124C11⋊C8#10012yes—
125C23×C8—111no—
126C23×C8—111no—
127C2×C4×D4—111no—
128C8×D4—222no—
129C8×D4—222no—
130C2×C4⋊C8—111no—
131C2×C22⋊C8—111no—
132C2×C22⋊C8C2×D1111yescharacteristic
133C2×C4×C8—111no—
134C4⋊C16—222no—
135C22⋊C16—112no—
136C22⋊C16C2×D1112yes—
137C4×C16—222no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—22no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11C2×C22⋊C811yescharacteristic
146C22×C11C22×C1611yescharacteristic
147C22×C11C2×M3211yescharacteristic
148C2×D11—22no—
149C2×D11—42no—
150C2×D11—41no—
151C2×D11—41no—
152C2×D11—42no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11#41011yescharacteristic
156C4×C11C2×#10011yescharacteristic
157Dic11—22no—
158Dic11—41no—
159Dic11C22⋊C1614yes—
160C22×D4—111no—
161C23×C4—111no—
162C23×C4C4×D1111yescharacteristic
163C22×C8—111no—
164C22×C8—111no—
165C22×C8—221no—
166C22×C8—221no—
167C22×C8—221no—
168C22×C8—221no—
169C22×C8—442no—
170C22×C8—442no—
171C22×C8C4×D1111yescharacteristic
172C22×C8C22×D1111yescharacteristic
173C4×D4—222no—
174C4×D4—222no—
175C2×C4⋊C4—111no—
176C2×C22⋊C4—111no—
177C2×C22⋊C4—111no—
178C2×C42—111no—
179C2×C16—22no—
180C2×C16—222no—
181C4⋊C8—222no—
182C22⋊C8—22no—
183C22⋊C8—222no—
184C4×C8—112no—
185C4×C8—112no—
186C2×C11—21no—
187C2×C11—21no—
188C2×C11—42no—
189C2×C11#146011yescharacteristic
190C2×C11C2×C22⋊C1611yescharacteristic
191C2×C11#211511yescharacteristic
192D11—42no—
193C24—111no—
194C24C8×D1111yescharacteristic
195C2×D4—114no—
196C2×D4—222no—
197C2×D4—222no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—111no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—221no—
206C22×C4—221no—
207C22×C4—441no—
208C22×C4—441no—
209C22×C4C8×D1111yescharacteristic
210C22×C4C2×C4×D1111yescharacteristic
211C2×C8—21no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—111no—
215C2×C8—111no—
216C2×C8—222no—
217C2×C8—221no—
218C2×C8—442no—
219C2×C8—442no—
220C2×C8—442no—
221C2×C8—442no—
222C2×C8—441no—
223C2×C8D4×D1112yes—
224C4⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—222no—
227C42—112no—
228C42—112no—
229C16—42no—
230C16—442no—
231C11#1148711yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—112no—
237C23—221no—
238C23—221no—
239C23—441no—
240C23—441no—
241C23C16×D1112yes—
242C23C2×C8×D1111yescharacteristic
243D4—228no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—112no—
252C2×C4—112no—
253C2×C4—112no—
254C2×C4—112no—
255C2×C4—221no—
256C2×C4—442no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4C22⋊C4×D1111yescharacteristic
262C2×C4M16×D1111yescharacteristic
263C8—22no—
264C8—41no—
265C8—112no—
266C8—221no—
267C8—441no—
268C22—21no—
269C22—21no—
270C22—22no—
271C22—42no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—222no—
276C22—442no—
277C22—442no—
278C22—441no—
279C22—441no—
280C22D11×C22⋊C811yescharacteristic
281C22C2×C16×D1111yescharacteristic
282C22D11×M3211yescharacteristic
283C4—21no—
284C4—41no—
285C4—114no—
286C4—222no—
287C4—441no—
288C4#1062235311yescharacteristic
289C4D11×#10011yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2—442no—
294C2#1306693511yescharacteristic
295C2D11×C22⋊C1611yescharacteristic
296C2#1307023511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC22×C11C22×C16
FrattiniC22×C8C22×D11
FittingC11×#1314C2
socleC22×C11C2×C22⋊C8
prime radicalC22×C22⋊D11C8
cosocleC22×C8×C11C23
hypercenter#1314D11
hypocenterC11#11487
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #13070412C2semidirect
3. #13066540C2semidirect
4. #13066539C2semidirect
5. C11×#1314C2semidirect
56. C2×C22⋊D11C16semidirect
88. #1314D11semidirect
231. C11#11487semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D11)⋊C82
#130704122
#130665402
#130665392
C11×#13142
#1148711