Finite Group Databasebeta

← #14763228

Subgroups — #14763228

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623031C211yesmaximal, characteristic
2#13071219C211yesmaximal, characteristic
3#13069601C214yesmaximal
4#13069600C214yesmaximal
5#13068691C214yesmaximal
6C11×#2313C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66979C2212yes—
9C2×#66977C2212yes—
10C2×#66977C2212yes—
11#10623031—24no—
12#10623031—24no—
13C2×#66943C414yescomplemented
14C2×#66941C414yescomplemented
15C11×#387—24no—
16C11×#381C2212yes—
17C11×#380C2212yes—
18C4×C11×C22⋊C4C2212yes—
19#10622825C2212yes—
20#10622824C2212yes—
21C4×C22⋊Dic11C2212yes—
22#10622594—24no—
23#10622165C22116yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C22×Dic22C2×C412yes—
28C22×Dic22C2×C412yes—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C414yes—
31C2×C11×C4⋊C4D414yes—
32C2×C11×C4⋊C4D414yes—
33C2×C11×C22⋊C4C2314yes—
34C2×C42×C11—22no—
35C2×C22⋊Dic11C2314yes—
36C2×C22⋊Dic11C2314yes—
37#66979—24no—
38#66979—24no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11C2×C412yes—
41C2×C4⋊Dic11C2×C412yes—
42C2×C4⋊Dic11C2×C412yes—
43C2×C4⋊Dic11C2×C412yes—
44#66977—24no—
45#66977—24no—
46#66977—24no—
47#66977—24no—
48C2×Dic11⋊C4C2×C414yes—
49C2×Dic11⋊C4C2×C414yes—
50C2×C4×Dic11—22no—
51C2×C4×Dic11C2×C414yes—
52#66943—216no—
53#66941—216no—
54C11×#95—22no—
55C11×#95—22no—
56C11×#95—24no—
57C11⋊#95—22no—
58C11⋊#95—24no—
59C11⋊#95—22no—
60#21828—111nomaximal, Sylow
61C24×C11C2411yescharacteristic
62C22×C4×C11—24no—
63C22×C4×C11—24no—
64C22×C4×C11—81no—
65C22×C4×C11—81no—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C22×C412yes—
68C22×C4×C11C22×C412yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D412yes—
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D412yes—
75C22×Dic11—24no—
76C22×Dic11C22×C414yes—
77C22×Dic11C22×C414yes—
78C2×Dic22—24no—
79C2×Dic22—24no—
80C2×Dic22—82no—
81C2×Dic22—82no—
82C11×C4⋊C4—82no—
83C11×C4⋊C4C22⋊C4116yes—
84C11×C22⋊C4—28no—
85C42×C11—82no—
86C22⋊Dic11—24no—
87C22⋊Dic11—24no—
88C22⋊Dic11—28no—
89C4⋊Dic11—24no—
90C4⋊Dic11—24no—
91C4⋊Dic11—24no—
92C4⋊Dic11—24no—
93C4⋊Dic11—82no—
94Dic11⋊C4—28no—
95Dic11⋊C4—28no—
96C4×Dic11—28no—
97C4×Dic11—82no—
98C2×#544—111no—
99#2313—111no—
100#2313D1111yescharacteristic
101#1996—114no—
102#1996—114no—
103#1820—114no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11C23×C411yescharacteristic
107C23×C11C22×D411yescharacteristic
108C23×C11C22×D411yescharacteristic
109C23×C112−1+414yes—
110C2×C4×C11—24no—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—44no—
120C2×C4×C11—44no—
121C2×C4×C11—44no—
122C2×C4×C11C2×C22⋊C414yes—
123C2×C4×C11C2×C22⋊C414yes—
124C2×C4×C11C2×C22⋊C414yes—
125C2×Dic11—24no—
126C2×Dic11—24no—
127C2×Dic11—44no—
128C2×Dic11—44no—
129C2×Dic11—44no—
130C2×Dic11—44no—
131C2×Dic11—44no—
132Dic22—84no—
133Dic22—84no—
134#544—224no—
135#544—224no—
136C2×C4⋊Q8—114no—
137C2×#125—114no—
138C2×C22⋊Q8—112no—
139C2×C22⋊Q8—112no—
140C2×#117—112no—
141C22×C4⋊C4C2×D1111yescharacteristic
142#387—24no—
143#387—224no—
144#381—112no—
145#381C2×D1112yes—
146#380—112no—
147#380C2×D1112yes—
148C4×C22⋊C4—112no—
149C4×C22⋊C4C2×D1112yes—
150#342—1116no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—44no—
158C22×C11C22×C22⋊C411yescharacteristic
159C22×C11#51912yes—
160C22×C11#53612yes—
161C22×C11#53612yes—
162C4×C11—24no—
163C4×C11—24no—
164C4×C11—24no—
165C4×C11—84no—
166Dic11—44no—
167Dic11—44no—
168Dic11—84no—
169C22×Q8—112no—
170C22×Q8—112no—
171C23×C4C22×D1111yescharacteristic
172C23×C4C22×D1111yescharacteristic
173C23×C4C22×D1111yescharacteristic
174C4⋊Q8—2216no—
175#125—2216no—
176C22⋊Q8—224no—
177C22⋊Q8—224no—
178C22⋊Q8—224no—
179C22⋊Q8—224no—
180#117—224no—
181#117—224no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—112no—
184C2×C4⋊C4—112no—
185C2×C4⋊C4—112no—
186C2×C4⋊C4—112no—
187C2×C4⋊C4—114no—
188C2×C4⋊C4—114no—
189C2×C4⋊C4—222no—
190C2×C4⋊C4C4×D1114yes—
191C2×C4⋊C4D4414yes—
192C2×C4⋊C4C22⋊D1114yes—
193C2×C22⋊C4—114no—
194C2×C22⋊C4—114no—
195C2×C22⋊C4C22×D1114yes—
196C2×C42—22no—
197C2×C42—114no—
198C2×C42—222no—
199#95—22no—
200#95—22no—
201#95—24no—
202#95—222no—
203#95—222no—
204#95—224no—
205C2×C11—22no—
206C2×C11—22no—
207C2×C11—22no—
208C2×C11#231011yescharacteristic
209C2×C11#288311yescharacteristic
210C2×C11#288411yescharacteristic
211C24C23×D1111yescharacteristic
212C2×Q8—224no—
213C2×Q8—224no—
214C2×Q8—882no—
215C2×Q8—882no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—114no—
221C22×C4—114no—
222C22×C4—224no—
223C22×C4C2×C4×D1112yes—
224C22×C4C2×C4×D1112yes—
225C22×C4C2×C4×D1112yes—
226C22×C4C2×D4412yes—
227C22×C4C2×D4412yes—
228C22×C4C2×D4412yes—
229C22×C4C2×C22⋊D1112yes—
230C22×C4C2×C22⋊D1112yes—
231C22×C4C2×C22⋊D1112yes—
232C4⋊C4—82no—
233C4⋊C4—224no—
234C4⋊C4—224no—
235C4⋊C4—224no—
236C4⋊C4—224no—
237C4⋊C4—228no—
238C4⋊C4—228no—
239C4⋊C4—882no—
240C4⋊C4(C2×D11)⋊C4116yes—
241C22⋊C4—28no—
242C22⋊C4—224no—
243C22⋊C4—224no—
244C22⋊C4—228no—
245C42—82no—
246C42—228no—
247C42—882no—
248C11#2182811yescharacteristic, complemented, Sylow
249C23—41no—
250C23—41no—
251C23C22×C4×D1111yescharacteristic
252C23C22×D4411yescharacteristic
253C23#6704314yes—
254C23C22×C22⋊D1111yescharacteristic
255Q8—884no—
256Q8—884no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—224no—
270C2×C4—224no—
271C2×C4—444no—
272C2×C4—444no—
273C2×C4—444no—
274C2×C4—444no—
275C2×C4—444no—
276C2×C4C2×(C2×D11)⋊C414yes—
277C2×C4C2×(C2×D11)⋊C414yes—
278C2×C4C2×(C2×D11)⋊C414yes—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—44no—
286C22#1062304712yes—
287C22#1062305712yes—
288C22C22×(C2×D11)⋊C411yescharacteristic
289C22#1062335612yes—
290C4—24no—
291C4—24no—
292C4—24no—
293C4—84no—
294C4—444no—
295C4—444no—
296C4—884no—
297C2—22no—
298C2—22no—
299C2—22no—
300C2#1307120011yescharacteristic
301C2#1307707611yescharacteristic
302C2#1307707911yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2313C2
socleC22×C11C22×C22⋊C4
prime radical, cosocleC24×C11C24
hypercenter#2313D11
hypocenterC11#21828
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
13. C2×#66943C4semidirect
14. C2×#66941C4semidirect
248. C11#21828semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130712192
#130696012
#130696002
#130686912
C11×#23132
#2182811