Finite Group Databasebeta

← #14763065

Subgroups — #14763065

Order 2816.

1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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×#10623336C211yesmaximal, characteristic
2#13077251C212yesmaximal, complemented
3#13069462C214yesmaximal, complemented
4#13069454C214yesmaximal, complemented
5#13068542C212yesmaximal, complemented
6#13068537C211yesmaximal, characteristic, complemented
7C11×#1783C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C2×#67006C414yes—
11#10623336—28no—
12C2×#66993C2212yes—
13C2×#66991C414yes—
14C2×#66989C2212yes—
15C2×#66979C2211yescharacteristic
16C2×C11×#100C2214yes—
17C11×#407C2212yes—
18C2×#66897C2214yes—
19#10622820C2212yes—
20C2×#66888C2214yescomplemented
21C2×#66887C2214yescomplemented
22#10622731C2214yescomplemented
23M16×Dic11C2214yescomplemented
24#10622333—28no—
25C25×C11C2×C412yes—
26C22×D4×C11—24no—
27C22×D4×C11—44no—
28C22×D4×C11C2×C412yes—
29C22×D4×C11C2312yes—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11C2×C412yes—
32C22×C22⋊D11C2×C418yes—
33C2×#4339—24no—
34C2×#4339—44no—
35C22×D44C2311yescharacteristic
36C22×C4×D11C2×C412yes—
37C22×Dic22C2311yescharacteristic
38C2×C11×M16C2314yes—
39#67006—216no—
40C2×C22⋊Dic11C2×C418yes—
41C2×C22⋊Dic11C2×C412yes—
42#66993—24no—
43#66993—24no—
44#66991—216no—
45#66989—24no—
46#66989—24no—
47#66979D418yes—
48C2×C4⋊Dic11C2×C412yes—
49C2×C4×Dic11C2312yes—
50C2×#4318C2314yes—
51C11×#100—44no—
52C11×C22⋊C8—24no—
53#66897—44no—
54C22⋊(C11⋊C8)—24no—
55#66888—44no—
56#66887—44no—
57#66879—24no—
58Dic11⋊C8—28no—
59C8×Dic11—24no—
60#21801—111nomaximal, Sylow
61C24×C11—24no—
62C24×C11—44no—
63C24×C11—84no—
64C24×C11C22×C414yes—
65C24×C11C22×C411yescharacteristic
66C23×D11C22×C412yes—
67C2×D4×C11—24no—
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—24no—
71C2×D4×C11—24no—
72C2×D4×C11—44no—
73C2×D4×C11—416no—
74C22×C4×C11—24no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D414yes—
77C22×C4×C11C2411yescharacteristic
78C2×C22⋊D11—216no—
79C2×C22⋊D11—24no—
80C2×C22⋊D11—44no—
81C2×C22⋊D11—88no—
82C22×Dic11C22×C412yes—
83C22×Dic11C22×C414yes—
84#4339—416no—
85C2×D44—22no—
86C2×D44—24no—
87C2×C4×D11—24no—
88C2×C4×D11—44no—
89C2×Dic22—22no—
90C2×Dic22—24no—
91C11×M16—24no—
92C11×M16—24no—
93C2×C8×C11—24no—
94C22⋊Dic11—216no—
95C22⋊Dic11C22⋊C418yes—
96C4⋊Dic11C22⋊C418yes—
97C4×Dic11C2×D414yes—
98C4×Dic11C2×D414yes—
99#4318—24no—
100#4318—24no—
101C2×C11⋊C8—24no—
102C2×#535—111no—
103#2921—112no—
104#1967—114no—
105#1965—114no—
106#1785—112no—
107#1783—111no—
108#1783D1111yescharacteristic, complemented
109C23×C11—22no—
110C23×C11—24no—
111C23×C11—24no—
112C23×C11—24no—
113C23×C11—42no—
114C23×C11—48no—
115C23×C11—48no—
116C23×C11—88no—
117C23×C11—816no—
118C23×C11C2×C22⋊C412yes—
119C23×C11C23×C411yescharacteristic
120C22×D11—22no—
121C22×D11—24no—
122C22×D11—44no—
123D4×C11—48no—
124D4×C11—44no—
125D4×C11—44no—
126C2×C4×C11—22no—
127C2×C4×C11—28no—
128C2×C4×C11C2×C22⋊C412yes—
129C2×C4×C11C22×D412yes—
130C2×C4×C11H(5,𝔽2)14yes—
131C22⋊D11—48no—
132C22⋊D11—816no—
133C2×Dic11—22no—
134C2×Dic11—24no—
135C2×Dic11—44no—
136C2×Dic11C2×C22⋊C418yes—
137D44—44no—
138C4×D11—48no—
139Dic22—44no—
140C8×C11—44no—
141C11⋊C8—44no—
142C22×#41—111no—
143C23×D4C2×D1111yescharacteristic
144#535—228no—
145C2×#127—112no—
146C2×#124—112no—
147C2×#121—114no—
148C2×#120—114no—
149C2×#117—111no—
150#433—228no—
151#423—114no—
152C2×#101—114no—
153C2×#100—114no—
154C2×#100—114no—
155C2×#100C2×D1114yes—
156#407—112no—
157#407C2×D1112yes—
158C4×M16—114no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11—24no—
162C22×C11—44no—
163C22×C11—44no—
164C22×C11—48no—
165C22×C11—84no—
166C22×C11—84no—
167C22×C11—816no—
168C22×C11C22×C22⋊C411yescharacteristic
169C22×C11#51812yes—
170C2×D11—42no—
171C2×D11—44no—
172C2×D11—84no—
173C4×C11—22no—
174C4×C11#53514yes—
175Dic11—28no—
176Dic11—42no—
177C25C4×D1112yes—
178C2×#41—224no—
179C2×#41—444no—
180C22×Q8—111no—
181C22×D4—24no—
182C22×D4—44no—
183C22×D4—112no—
184C22×D4—118no—
185C22×D4—111no—
186C22×D4C4×D1112yes—
187C22×D4C22×D1112yes—
188C23×C4—112no—
189C23×C4C22×D1111yescharacteristic
190C2×M16—114no—
191C2×M16C22×D1114yes—
192#127—224no—
193#127—224no—
194#124—224no—
195#124—224no—
196#121—2216no—
197#120—2216no—
198#117—118no—
199C2×C4⋊C4—112no—
200C2×C22⋊C4—112no—
201C2×C22⋊C4—118no—
202C2×C42—112no—
203C4⋊C8—228no—
204#101—444no—
205#100—44no—
206#100—444no—
207#100—444no—
208C22⋊C8—24no—
209C22⋊C8—224no—
210#97—224no—
211C4×C8—224no—
212C2×C11—22no—
213C2×C11—42no—
214C2×C11—84no—
215C2×C11#230911yescharacteristic
216C2×C11#288812yes—
217D11—82no—
218C24—24no—
219C24—44no—
220C24—84no—
221C24—112no—
222C24C2×C4×D1114yes—
223C24C2×C4×D1111yescharacteristic
224#41—4416no—
225C2×Q8—222no—
226C2×Q8—224no—
227C2×D4—24no—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—24no—
231C2×D4—24no—
232C2×D4—44no—
233C2×D4—416no—
234C2×D4—2216no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—224no—
238C2×D4—444no—
239C2×D4—888no—
240C22×C4—24no—
241C22×C4—114no—
242C22×C4—112no—
243C22×C4—224no—
244C22×C4—444no—
245C22×C4C2×C4×D1111yescharacteristic
246C22×C4D4×D1114yes—
247C22×C4C23×D1111yescharacteristic
248M16—24no—
249M16—24no—
250M16—224no—
251M16—224no—
252C2×C8—24no—
253C2×C8—224no—
254C4⋊C4—118no—
255C22⋊C4—118no—
256C22⋊C4—2216no—
257C42—114no—
258C42—114no—
259C11#2180111yescharacteristic, complemented, Sylow
260C23—22no—
261C23—24no—
262C23—24no—
263C23—24no—
264C23—42no—
265C23—48no—
266C23—48no—
267C23—88no—
268C23—816no—
269C23—222no—
270C23—224no—
271C23—444no—
272C23C22⋊C4×D1112yes—
273C23C22×C4×D1111yescharacteristic
274Q8—444no—
275D4—48no—
276D4—44no—
277D4—44no—
278D4—448no—
279D4—444no—
280D4—8816no—
281C2×C4—22no—
282C2×C4—28no—
283C2×C4—118no—
284C2×C4—222no—
285C2×C4—224no—
286C2×C4—448no—
287C2×C4—444no—
288C2×C4C22⋊C4×D1112yes—
289C2×C4C2×D4×D1112yes—
290C2×C4#6703714yes—
291C8—44no—
292C8—444no—
293C22—22no—
294C22—22no—
295C22—24no—
296C22—44no—
297C22—44no—
298C22—48no—
299C22—84no—
300C22—84no—
301C22—816no—
302C22—442no—
303C22—444no—
304C22—884no—
305C22C2×C22⋊C4×D1111yescharacteristic
306C22#1062301712yes—
307C4—22no—
308C4—228no—
309C4—442no—
310C4#1062312314yes—
311C2—22no—
312C2—42no—
313C2—84no—
314C2—882no—
315C2#1307119711yescharacteristic
316C2#1307709212yes—
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1783C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623336C2
cosocleC22×C4×C11C24
hypercenter#1783D11
hypocenterC11#21801
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1783

Complements

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

NH ≅ G/Ntype
2. #13077251C2semidirect
3. #13069462C2semidirect
4. #13069454C2semidirect
5. #13068542C2semidirect
6. #13068537C2semidirect
7. C11×#1783C2semidirect
20. C2×#66888C22semidirect
21. C2×#66887C22semidirect
22. #10622731C22semidirect
23. M16×Dic11C22semidirect
108. #1783D11semidirect
259. C11#21801semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
#130772512
#130694622
#130694542
#130685422
#130685372
C11×#17832
#2180111