Finite Group Databasebeta

← #14663248

Subgroups — #14663248

Order 2816.

460 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 77 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#13071155C211yesmaximal, characteristic
2#13066953C212yesmaximal
3#13066560C211yesmaximal, characteristic, complemented
4#13066549C212yesmaximal, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6C2×#66946C2211yescharacteristic
7C2×#66940C411yescharacteristic
8C2×#66928C411yescharacteristic
9C11×#382C2211yescharacteristic
10#10622601C411yescharacteristic
11#10622587C2211yescharacteristic
12C42×Dic11C411yescharacteristic
13#10622339—22no—
14#10622282—22no—
15#10622279—22no—
16C11×#324C2212yes—
17#10622166C2212yes—
18#10622106—22no—
19C22×D44C2×C411yescharacteristic
20C22×C4×D11D412yes—
21C22×Dic22C2×C411yescharacteristic
22C2×C11×C4⋊C4C2×C411yescharacteristic
23C2×C11×C4⋊C4C2311yescharacteristic
24C2×C42×C11C2×C411yescharacteristic
25C2×(C2×D11)⋊C4—22no—
26C2×(C2×D11)⋊C4—22no—
27C2×(C2×D11)⋊C4D412yes—
28C2×Dic11⋊C4—21no—
29C2×C4×Dic11—21no—
30C2×C4×Dic11—21no—
31C2×C4×Dic11—21no—
32C2×C4×Dic11C2×C411yescharacteristic
33C2×C4×Dic11C2×C411yescharacteristic
34C2×#4313—42no—
35#66946—41no—
36#66946—41no—
37#66940—41no—
38#66940—41no—
39#66928—22no—
40#66928—22no—
41C11×C22⋊C8—22no—
42C11×#95—22no—
43C11⋊#95—22no—
44C22⋊(C11⋊C8)—22no—
45(C2×D11)⋊C8—42no—
46#11531—111nomaximal, Sylow
47C23×D11C22⋊C412yes—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—21no—
53C22×Dic11—21no—
54C22×Dic11C22⋊C411yescharacteristic
55C22×Dic11C22⋊C411yescharacteristic
56C2×D44—21no—
57C2×D44—21no—
58C2×D44—41no—
59C2×D44—41no—
60C2×C4×D11—22no—
61C2×C4×D11—22no—
62C2×C4×D11—44no—
63C2×Dic22—21no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22M1612yescomplemented
67C2×C8×C11—42no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C42×C11—21no—
71C42×C11M1612yescomplemented
72(C2×D11)⋊C4—28no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—44no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11—41no—
79C4×Dic11—42no—
80C4×Dic11—42no—
81C4×Dic11—41no—
82C4×Dic11—41no—
83C2×C11⋊C8—42no—
84#4313—84no—
85C4×#124—111no—
86#1465—112no—
87#1324—111no—
88#1324D1111yescharacteristic, complemented
89#1319—112no—
90C23×C11C2×C22⋊C411yescharacteristic
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—42no—
95C22×D11—42no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11C2×M1611yescharacteristic
106C2×C4×C11C2×M1611yescharacteristic
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—21no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11#9911yescharacteristic
117C2×Dic11#9911yescharacteristic
118D44—42no—
119D44—42no—
120C4×D11—44no—
121C4×D11—82no—
122Dic22—42no—
123Dic22—42no—
124C8×C11—82no—
125C11⋊C8—82no—
126C2×#124—111no—
127C2×C4×Q8—111no—
128C2×C4×D4—111no—
129#407—222no—
130#391—111no—
131#390—111no—
132#388—222no—
133#382C2×D1111yescharacteristic
134C4×C22⋊C4—222no—
135C43—111no—
136#324—112no—
137#324C2×D1112yes—
138#323—222no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#40711yescharacteristic
142C22×C11C2×#9911yescharacteristic
143C22×C11#41311yescharacteristic
144C2×D11—44no—
145C2×D11—42no—
146C2×D11—42no—
147C2×D11—42no—
148C2×D11—82no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—81no—
154Dic11—21no—
155Dic11—42no—
156Dic11—41no—
157Dic11—42no—
158Dic11#35412yes—
159C22×Q8—111no—
160C22×D4—111no—
161C23×C4—112no—
162C2×M16—442no—
163#124—222no—
164#124—222no—
165C4×Q8—441no—
166C4×Q8—441no—
167C4×D4—441no—
168C4×D4—441no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4C4×D1111yescharacteristic
171C2×C4⋊C4C22×D1111yescharacteristic
172C2×C22⋊C4—112no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4—222no—
175C2×C42—111no—
176C2×C42—111no—
177C2×C42—221no—
178C2×C42—221no—
179C2×C42—221no—
180C2×C42C4×D1111yescharacteristic
181C22⋊C8—22no—
182C22⋊C8—222no—
183C22⋊C8—442no—
184#95—22no—
185#95—222no—
186C2×C11—21no—
187C2×C11—21no—
188C2×C11#146511yescharacteristic
189C2×C11C2×#35411yescharacteristic
190C2×C11#213211yescharacteristic
191D11—82no—
192C24—112no—
193C2×Q8—112no—
194C2×Q8—221no—
195C2×Q8—441no—
196C2×Q8—441no—
197C2×D4—221no—
198C2×D4—221no—
199C2×D4—441no—
200C2×D4—441no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—222no—
206C22×C4—222no—
207C22×C4—221no—
208C22×C4—221no—
209C22×C4—444no—
210C22×C4C2×C4×D1111yescharacteristic
211C22×C4D4×D1112yes—
212M16—884no—
213C2×C8—42no—
214C2×C8—442no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—442no—
218C22⋊C4—228no—
219C22⋊C4—442no—
220C22⋊C4—444no—
221C42—21no—
222C42—221no—
223C42—221no—
224C42—441no—
225C42—441no—
226C42—441no—
227C42—442no—
228C42—442no—
229C42#431312yescomplemented
230C11#1153111yescharacteristic, complemented, Sylow
231C23—222no—
232C23—222no—
233C23—222no—
234C23—442no—
235C23—442no—
236C23C22⋊C4×D1111yescharacteristic
237Q8—442no—
238Q8—442no—
239D4—442no—
240D4—442no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—111no—
251C2×C4—111no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—221no—
256C2×C4—444no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—441no—
262C2×C4—882no—
263C2×C4C2×#431311yescharacteristic
264C2×C4M16×D1111yescharacteristic
265C8—82no—
266C8—882no—
267C22—21no—
268C22—21no—
269C22—444no—
270C22—442no—
271C22—442no—
272C22—442no—
273C22—882no—
274C22#1062233911yescharacteristic
275C22D11×#9911yescharacteristic
276C22#1062236411yescharacteristic
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—81no—
282C4—112no—
283C4—221no—
284C4—442no—
285C4—442no—
286C4—441no—
287C2—21no—
288C2—21no—
289C2—882no—
290C2#1306695311yescharacteristic
291C2D11×#35411yescharacteristic
292C2#1307029811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1324D11
hypocenterC11#11531
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
3. #13066560C2semidirect
4. #13066549C2semidirect
5. C11×#1324C2semidirect
66. C2×Dic22M16semidirect
71. C42×C11M16semidirect
88. #1324D11semidirect
229. C42#4313semidirect
230. C11#11531semidirect

Maximal subgroups

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

subgroupindex
#130711552
#130669532
#130665602
#130665492
C11×#13242
#1153111