Finite Group Databasebeta

← #14810460

Subgroups — #14810460

Order 2816.

1078 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 219 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
1C22×#66923C211yesmaximal, characteristic
2C2×#10622316C212yesmaximal, complemented
3#13076968C211yesmaximal, characteristic
4#13069768C214yesmaximal, complemented
5#13069585C212yesmaximal, complemented
6#13068921C214yesmaximal
7C11×#1749C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C22×C4⋊Dic11C2212yes—
10C2×#66977C2212yes—
11C22×Dic11⋊C4—22no—
12C2×#66923—22no—
13C2×#66923—28no—
14C2×#66923C2212yes—
15C2×#66923C2212yes—
16C2×#66922C2211yescharacteristic
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
29C23×Dic11—22no—
30C22×Dic22C2312yes—
31C22×C8×C11C2314yes—
32C2×C42×C11—24no—
33C2×C42×C11D412yes—
34C2×C42×C11C2311yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11—28no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11C2312yes—
42C2×C4⋊Dic11C2314yes—
43#66977—28no—
44C2×Dic11⋊C4—216no—
45C2×Dic11⋊C4—24no—
46C2×Dic11⋊C4—24no—
47C2×Dic11⋊C4—22no—
48#66923—216no—
49#66923—24no—
50#66923—28no—
51#66923D418yes—
52#66922—24no—
53C11×C22⋊C8—24no—
54C11×#97—24no—
55C11⋊#95—24no—
56#66880—216no—
57#25912—111nomaximal, Sylow
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—24no—
62C22×C4×C11—24no—
63C22×C4×C11—42no—
64C22×C4×C11C2×D412yes—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4114yes—
68C22×C4×C11C2411yescharacteristic
69C22×Dic11—28no—
70C22×Dic11—24no—
71C22×Dic11—22no—
72C22×Dic11—22no—
73C22×Dic11—44no—
74C22×Dic11—44no—
75C2×Dic22—24no—
76C2×Dic22—24no—
77C2×Dic22—24no—
78C2×C8×C11—24no—
79C2×C8×C11—24no—
80C2×C8×C11—24no—
81C42×C11—24no—
82C42×C11—22no—
83C42×C11C2×D414yes—
84C22⋊Dic11—44no—
85C4⋊Dic11—28no—
86C4⋊Dic11—24no—
87C4⋊Dic11—24no—
88C4⋊Dic11—44no—
89C4⋊Dic11—44no—
90C4⋊Dic11C2×D418yes—
91Dic11⋊C4—216no—
92Dic11⋊C4—216no—
93Dic11⋊C4—44no—
94C22×#125—111no—
95C2×#491—112no—
96#2857—111no—
97#2026—114no—
98#1992—112no—
99#1872—114no—
100#1749D1111yescharacteristic
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—22no—
104C23×C11#12412yes—
105C23×C11#13714yes—
106C23×C11C22×D411yescharacteristic
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—28no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—48no—
116C2×C4×C11#12014yes—
117C2×C4×C11#12412yes—
118C2×C4×C11C22×D412yes—
119C2×C4×C11C2×#4112yes—
120C2×C4×C112−1+412yes—
121C2×Dic11—28no—
122C2×Dic11—416no—
123C2×Dic11—44no—
124C2×Dic11—44no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—44no—
130Dic22—48no—
131C8×C11—44no—
132C2×C4⋊Q8—111no—
133C2×#125—112no—
134C2×#125—112no—
135C2×#125—228no—
136C2×#125—222no—
137C2×C22⋊Q8—112no—
138C22×C4⋊C4—112no—
139C22×C4⋊C4—222no—
140C22×C42C2×D1111yescharacteristic
141#491—228no—
142C2×#103—118no—
143C2×C22⋊C8C2×D1112yes—
144C2×#97C2×D1112yes—
145#391—112no—
146#389—222no—
147#384—111no—
148#380—222no—
149#340—118no—
150#336C2×D1112yes—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—24no—
154C22×C11—24no—
155C22×C11#49114yescomplemented
156C22×C11C2×#12011yescharacteristic
157C22×C11C2×#12411yescharacteristic
158C22×C11#53611yescharacteristic
159C22×C11C2×#13712yes—
160C22×C11#57512yes—
161C4×C11—22no—
162C4×C11—24no—
163C4×C11—42no—
164C4×C11#54814yes—
165Dic11—48no—
166Dic11—82no—
167Dic11—82no—
168C22×Q8—112no—
169C23×C4—222no—
170C23×C4D4412yes—
171C23×C4C22×D1111yescharacteristic
172C22×C8C22×D1114yes—
173C4⋊Q8—224no—
174#125—118no—
175#125—228no—
176#125—2216no—
177#125—224no—
178C22⋊Q8—228no—
179C2×C4⋊C4—114no—
180C2×C4⋊C4—112no—
181C2×C4⋊C4—228no—
182C2×C4⋊C4—2216no—
183C2×C4⋊C4—222no—
184C2×C4⋊C4—224no—
185C2×C4⋊C4—224no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—222no—
188C2×C4⋊C4—222no—
189C2×C22⋊C4—222no—
190C2×C42—24no—
191C2×C42D4412yes—
192C2×C42C22×D1111yescharacteristic
193C2×C42C22×D1111yescharacteristic
194#103—2216no—
195C22⋊C8—24no—
196#97—24no—
197#95—224no—
198C2×C11—24no—
199C2×C11#243611yescharacteristic
200C2×C11#300712yes—
201C2×C11C2×#49111yescharacteristic
202C2×C11#314211yescharacteristic
203C2×C11#323612yes—
204C24C2×D4411yescharacteristic
205C2×Q8—224no—
206C2×Q8—224no—
207C2×Q8—224no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—42no—
213C22×C4—228no—
214C22×C4—224no—
215C22×C4—222no—
216C22×C4—222no—
217C22×C4—444no—
218C22×C4—444no—
219C22×C4C2×D4412yes—
220C22×C4C2×D4411yescharacteristic
221C22×C4C2×D4412yes—
222C22×C4#433914yes—
223C22×C4C23×D1111yescharacteristic
224C2×C8—24no—
225C2×C8—24no—
226C2×C8—24no—
227C4⋊C4—118no—
228C4⋊C4—2216no—
229C4⋊C4—228no—
230C4⋊C4—2216no—
231C4⋊C4—224no—
232C4⋊C4—224no—
233C4⋊C4—444no—
234C4⋊C4—444no—
235C4⋊C4—444no—
236C22⋊C4—444no—
237C42—24no—
238C42—22no—
239C42D4×D1114yes—
240C11#2591211yescharacteristic, complemented, Sylow
241C23—21no—
242C23—22no—
243C23—21no—
244C23#6692812yes—
245C23#6696214yes—
246C23C22×D4411yescharacteristic
247Q8—448no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—28no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—48no—
257C2×C4—228no—
258C2×C4—4416no—
259C2×C4—444no—
260C2×C4—444no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—444no—
265C2×C4—442no—
266C2×C4#6692812yes—
267C2×C4#6693514yes—
268C2×C4C2×#433912yes—
269C2×C4C2×D4×D1112yes—
270C2×C4#6704312yes—
271C8—44no—
272C22—24no—
273C22—24no—
274C22—22no—
275C22—22no—
276C22#1062231614yescomplemented
277C22C2×#6692811yescharacteristic
278C22C2×#6693511yescharacteristic
279C22#1062305711yescharacteristic
280C22C2×#6696212yes—
281C22#1062327912yes—
282C4—24no—
283C4—22no—
284C4—42no—
285C4—448no—
286C4—882no—
287C4—882no—
288C4#1062308314yes—
289C2—24no—
290C2#1307227411yescharacteristic
291C2#1307787812yes—
292C2C2×#1062231611yescharacteristic
293C2#1307901711yescharacteristic
294C2#1307982412yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1749D11
hypocenterC11#25912
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. #13069768C2semidirect
5. #13069585C2semidirect
155. C22×C11#491semidirect
240. C11#25912semidirect
276. C22#10622316semidirect

Maximal subgroups

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

subgroupindex
C22×#669232
C2×#106223162
#130769682
#130697682
#130695852
#130689212
C11×#17492
#2591211