Finite Group Databasebeta

← #14642339

Subgroups — #14642339

Order 2816.

500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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#13076968C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3#13066440C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66977—21no—
7C2×#66922C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9C2×C11×#97—21no—
10#10622825—21no—
11#10622825C412yes—
12C2×C22⋊(C11⋊C8)—21no—
13#10622548C411yescharacteristic
14#10622542—21no—
15#10622541—21no—
16#10622541C2212yes—
17C11×#336C2212yes—
18#10622162—21no—
19#10622162C2212yes—
20C23×C4×C11C2×C411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C22×Dic22—21no—
24C22×C8×C11—22no—
25C2×C42×C11—42no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C412yes—
35C2×C4⋊Dic11C2×C412yes—
36#66977—44no—
37C2×Dic11⋊C4—22no—
38C22×C11⋊C8—22no—
39#66922—42no—
40C11×C22⋊C8—24no—
41C11×#97—42no—
42C11⋊#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—42no—
45#7705—111nomaximal, Sylow
46C24×C11C22⋊C411yescharacteristic
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—41no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—42no—
66C2×Dic22—42no—
67C2×C8×C11—24no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C42×C11—22no—
71C42×C11—22no—
72C42×C11—41no—
73C42×C11—41no—
74C22⋊Dic11—44no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—42no—
78C4⋊Dic11—42no—
79C4⋊Dic11—42no—
80Dic11⋊C4—44no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2857—111no—
85#1817—111no—
86#1749D1111yescharacteristic
87#1271—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11#10112yes—
95C23×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—44no—
110C2×C4×C11—44no—
111C2×C4×C11—44no—
112C2×C4×C11#9912yes—
113C2×C4×C11#10412yes—
114C2×C4×C11#13112yes—
115C2×C4×C11AGL(1,ℤ/8)12yes—
116C2×C4×C11#13712yes—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123Dic22—84no—
124C8×C11—44no—
125C11⋊C8—82no—
126C2×C4⋊Q8—111no—
127C2×C22⋊Q8—221no—
128C22×C42C2×D1111yescharacteristic
129C2×C22⋊C8—21no—
130C2×C22⋊C8—221no—
131C2×#97—21no—
132#391—221no—
133#389—112no—
134#389—221no—
135#384—111no—
136#380—112no—
137#380—221no—
138#336—112no—
139#336—221no—
140#336C2×D1112yes—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11#40811yescharacteristic
149C22×C11C2×#9911yescharacteristic
150C22×C11C2×#10111yescharacteristic
151C22×C11#41811yescharacteristic
152C22×C11#41911yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C22×C11#42111yescharacteristic
155C4×C11—22no—
156C4×C11—22no—
157C4×C11—22no—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—41no—
161Dic11—82no—
162Dic11—82no—
163C22×Q8—221no—
164C23×C4C4×D1111yescharacteristic
165C23×C4D4411yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C22×C8—22no—
168C22×C8—222no—
169C4⋊Q8—442no—
170C22⋊Q8—444no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4—112no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—222no—
177C2×C22⋊C4—222no—
178C2×C42—42no—
179C2×C42C4×D1111yescharacteristic
180C2×C42D4411yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C2×C42C22×D1111yescharacteristic
183C22⋊C8—24no—
184C22⋊C8—442no—
185#97—42no—
186#95—222no—
187#95—222no—
188C2×C11—42no—
189C2×C11#147211yescharacteristic
190C2×C11#148511yescharacteristic
191C2×C11#149611yescharacteristic
192C2×C11#150711yescharacteristic
193C2×C11#151111yescharacteristic
194C2×C11#153111yescharacteristic
195C2×C11#155611yescharacteristic
196C24(C2×D11)⋊C411yescharacteristic
197C2×Q8—442no—
198C2×Q8—442no—
199C2×Q8—442no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—222no—
210C22×C4—222no—
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4(C2×D11)⋊C411yescharacteristic
214C22×C4C2×C4×D1111yescharacteristic
215C22×C4C2×D4411yescharacteristic
216C22×C4C2×C22⋊D1111yescharacteristic
217C2×C8—24no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—442no—
221C2×C8—442no—
222C2×C8—442no—
223C4⋊C4—224no—
224C4⋊C4—442no—
225C4⋊C4—442no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—444no—
229C22⋊C4—444no—
230C42—22no—
231C42—22no—
232C42—41no—
233C42—41no—
234C11#770511yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#6688812yes—
242C23C2×(C2×D11)⋊C411yescharacteristic
243Q8—884no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—442no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4#6686912yes—
267C2×C4#6687012yes—
268C2×C4#6696012yes—
269C2×C4#6696212yes—
270C2×C4#6700212yes—
271C8—44no—
272C8—882no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22C2×#6686911yescharacteristic
281C22C2×#6687011yescharacteristic
282C22#1062261411yescharacteristic
283C22#1062273311yescharacteristic
284C22#1062274211yescharacteristic
285C22C2×#6688811yescharacteristic
286C22#1062275211yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—882no—
294C4—882no—
295C2—42no—
296C2#1306698111yescharacteristic
297C2#1306703811yescharacteristic
298C2#1306708411yescharacteristic
299C2#1306713111yescharacteristic
300C2#1306715011yescharacteristic
301C2#1306723011yescharacteristic
302C2#1306733411yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#7705
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13066440C2semidirect
234. C11#7705semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130686842
#130664402
C11×#17492
#770511