Finite Group Databasebeta

← #14810446

Subgroups — #14810446

Order 2816.

1066 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 211 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×#10623001C211yesmaximal, characteristic
2C2×#10622316C212yesmaximal, complemented
3#13076968C211yesmaximal, characteristic
4#13069758C214yesmaximal, complemented
5#13069585C212yesmaximal, complemented
6#13068926C214yesmaximal
7C11×#1749C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C2×#66979C2212yes—
10C2×#66977—22no—
11C2×#66977C2212yes—
12#10623001—28no—
13C2×#66923C2212yes—
14C2×#66922C2211yescharacteristic
15C2×#66922C2212yes—
16C2×C4×Dic22—22no—
17C2×C11×C22⋊C8C2212yes—
18C2×C11×#97C2212yes—
19#10622825—22no—
20C2×#66880C2218yes—
21#10622548C2211yescharacteristic
22#10622542C2212yes—
23#10622541—22no—
24#10622316—28no—
25C11×#336C2212yes—
26#10622189C2218yes—
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C22×Dic22—22no—
30C22×Dic22C2312yes—
31C22×C8×C11C2314yes—
32C2×C42×C11—24no—
33C2×C42×C11D412yes—
34C2×C42×C11C2311yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38#66979—28no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11C2312yes—
43C2×C4⋊Dic11C2314yes—
44#66977—216no—
45#66977—28no—
46C2×Dic11⋊C4—24no—
47C2×Dic11⋊C4—22no—
48C2×C4×Dic11—22no—
49#66923—24no—
50#66923D418yes—
51#66922—28no—
52#66922—24no—
53C4×Dic22—216no—
54C11×C22⋊C8—24no—
55C11×#97—24no—
56C11⋊#95—24no—
57#66880—216no—
58#25910—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—42no—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D412yes—
68C22×C4×C11#4114yes—
69C22×C4×C11C2411yescharacteristic
70C22×Dic11—24no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C2×Dic22—28no—
74C2×Dic22—24no—
75C2×Dic22—24no—
76C2×Dic22—24no—
77C2×Dic22—44no—
78C2×Dic22—44no—
79C2×C8×C11—24no—
80C2×C8×C11—24no—
81C2×C8×C11—24no—
82C42×C11—24no—
83C42×C11—22no—
84C42×C11C2×D414yes—
85C22⋊Dic11—28no—
86C22⋊Dic11—44no—
87C4⋊Dic11—28no—
88C4⋊Dic11—24no—
89C4⋊Dic11—24no—
90C4⋊Dic11—44no—
91C4⋊Dic11—44no—
92C4⋊Dic11C2×D418yes—
93Dic11⋊C4—216no—
94Dic11⋊C4—44no—
95C4×Dic11—28no—
96C2×#533—111no—
97C2×#491—112no—
98#2857—111no—
99#2024—114no—
100#1992—112no—
101#1873—114no—
102#1749D1111yescharacteristic
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—22no—
106C23×C11—22no—
107C23×C11#12412yes—
108C23×C11C22×D411yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—28no—
116C2×C4×C11—48no—
117C2×C4×C11#12014yes—
118C2×C4×C11#12412yes—
119C2×C4×C11#13714yes—
120C2×C4×C11C22×D412yes—
121C2×C4×C11C2×#4112yes—
122C2×C4×C112−1+412yes—
123C2×Dic11—28no—
124C2×Dic11—44no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—44no—
131Dic22—416no—
132Dic22—48no—
133C8×C11—44no—
134#533—228no—
135C2×C4⋊Q8—112no—
136C2×C4⋊Q8—111no—
137C2×#125—112no—
138C2×C22⋊Q8—112no—
139C2×C22⋊Q8—222no—
140C2×C4×Q8—222no—
141C2×#117—112no—
142C22×C42C2×D1111yescharacteristic
143#491—228no—
144C2×#103—118no—
145C2×C22⋊C8C2×D1112yes—
146C2×#97C2×D1112yes—
147#391—112no—
148#389—222no—
149#384—111no—
150#380—222no—
151#340—118no—
152#336C2×D1112yes—
153C22×C11—22no—
154C22×C11—22no—
155C22×C11—22no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11C2×#12011yescharacteristic
159C22×C11C2×#12411yescharacteristic
160C22×C11#53611yescharacteristic
161C22×C11C2×#13712yes—
162C22×C11#57512yes—
163C4×C11—22no—
164C4×C11—24no—
165C4×C11—24no—
166C4×C11#54814yes—
167Dic11—48no—
168Dic11—82no—
169Dic11—82no—
170C22×Q8—112no—
171C22×Q8—222no—
172C23×C4D4412yes—
173C23×C4C22×D1111yescharacteristic
174C22×C8C22×D1114yes—
175C4⋊Q8—228no—
176C4⋊Q8—224no—
177#125—118no—
178#125—224no—
179C22⋊Q8—2216no—
180C22⋊Q8—228no—
181C4×Q8—2216no—
182#117—228no—
183C2×C4⋊C4—114no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—224no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4—222no—
189C2×C4⋊C4—222no—
190C2×C22⋊C4—222no—
191C2×C22⋊C4—222no—
192C2×C42—24no—
193C2×C42—222no—
194C2×C42D4412yes—
195C2×C42C22×D1111yescharacteristic
196C2×C42C22×D1111yescharacteristic
197#103—2216no—
198C22⋊C8—24no—
199#97—24no—
200#95—224no—
201C2×C11—42no—
202C2×C11#243611yescharacteristic
203C2×C11#300712yes—
204C2×C11#313511yescharacteristic
205C2×C11#313911yescharacteristic
206C2×C11#323712yes—
207C24C2×D4411yescharacteristic
208C2×Q8—228no—
209C2×Q8—224no—
210C2×Q8—224no—
211C2×Q8—224no—
212C2×Q8—444no—
213C2×Q8—444no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—42no—
219C22×C4—224no—
220C22×C4—222no—
221C22×C4—222no—
222C22×C4C2×D4411yescharacteristic
223C22×C4C2×D4412yes—
224C22×C4C2×D4412yes—
225C22×C4#433914yes—
226C22×C4C23×D1111yescharacteristic
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—24no—
230C4⋊C4—118no—
231C4⋊C4—228no—
232C4⋊C4—2216no—
233C4⋊C4—224no—
234C4⋊C4—224no—
235C4⋊C4—444no—
236C4⋊C4—444no—
237C4⋊C4—444no—
238C22⋊C4—228no—
239C22⋊C4—444no—
240C42—24no—
241C42—22no—
242C42—228no—
243C42D4×D1114yes—
244C11#2591011yescharacteristic, complemented, Sylow
245C23—21no—
246C23—22no—
247C23—22no—
248C23—21no—
249C23#6692812yes—
250C23C22×D4411yescharacteristic
251Q8—4416no—
252Q8—448no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—28no—
260C2×C4—48no—
261C2×C4—228no—
262C2×C4—444no—
263C2×C4—444no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—444no—
268C2×C4—442no—
269C2×C4#6692812yes—
270C2×C4#6693514yes—
271C2×C4#6696214yes—
272C2×C4C2×#433912yes—
273C2×C4C2×D4×D1112yes—
274C2×C4#6704312yes—
275C8—44no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22C2×#6692811yescharacteristic
282C22C2×#6693511yescharacteristic
283C22#1062305711yescharacteristic
284C22C2×#6696212yes—
285C22#1062327912yes—
286C4—24no—
287C4—24no—
288C4—22no—
289C4—448no—
290C4—882no—
291C4—882no—
292C4#1062308314yes—
293C2—42no—
294C2#1307227411yescharacteristic
295C2#1307787812yes—
296C2#1307896211yescharacteristic
297C2#1307899711yescharacteristic
298C2#1307983212yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1749D11
hypocenterC11#25910
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#10622316C2semidirect
4. #13069758C2semidirect
5. #13069585C2semidirect
244. C11#25910semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106223162
#130769682
#130697582
#130695852
#130689262
C11×#17492
#2591011