Finite Group Databasebeta

← #14644144

Subgroups — #14644144

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C212yesmaximal
2#13066524C214yesmaximal, complemented
3C2×C11×#381C211yesmaximal, characteristic
4C24×C4×C11C2211yescharacteristic
5C22×C11×C22⋊C4C412yes—
6C22×#4318—22no—
7C11×#381—22no—
8C11×#381C412yes—
9C11×#381C2212yes—
10C2×C11×#95—22no—
11#10622820—22no—
12#10622820—22no—
13#10622820C414yescomplemented
14#10622820C2214yes—
15C2×C22⋊(C11⋊C8)—22no—
16C2×C22⋊(C11⋊C8)C414yescomplemented
17C25×C11C2×C411yescharacteristic
18C23×C4×C11—22no—
19C23×C4×C11—44no—
20C23×C4×C11C2×C412yes—
21C23×C4×C11C2×C412yes—
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D412yes—
24C23×C4×C11D412yes—
25C23×C4×C11D412yes—
26C23×C4×C11Q812yes—
27C23×C4×C11C2311yescharacteristic
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—44no—
30C2×C11×C22⋊C4C2×C414yes—
31C2×#4318—24no—
32C2×#4318—24no—
33C2×#4318—48no—
34C22×C11⋊C8—24no—
35C11×#95—24no—
36C11×#95—24no—
37C22⋊(C11⋊C8)—24no—
38C22⋊(C11⋊C8)—24no—
39C22⋊(C11⋊C8)—24no—
40C22⋊(C11⋊C8)C2×C418yescomplemented
41#8114—111nomaximal, Sylow
42C24×C11—24no—
43C24×C11—44no—
44C24×C11C4212yes—
45C24×C11C22⋊C411yescharacteristic
46C24×C11C22⋊C411yescharacteristic
47C24×C11C4⋊C412yes—
48C24×C11C22×C411yescharacteristic
49C22×C4×C11—28no—
50C22×C4×C11—24no—
51C22×C4×C11—44no—
52C22×C4×C11—44no—
53C22×C4×C11—42no—
54C22×C4×C11—44no—
55C22×C4×C11—44no—
56C22×C4×C11—44no—
57C22×C4×C11—42no—
58C22×C4×C11—44no—
59C22×C4×C11—48no—
60C22×C4×C11C4211yescharacteristic
61C22×C4×C11C4211yescharacteristic
62C22×C4×C11C22⋊C412yes—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C4⋊C412yes—
68C22×C4×C11C4⋊C412yes—
69C22×C4×C11C4⋊C412yes—
70C22×C4×C11C4⋊C412yes—
71C22×C4×C11C4⋊C412yes—
72C22×C4×C11C22×C412yes—
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q811yescharacteristic
76C11×C22⋊C4—44no—
77C11×C22⋊C4—44no—
78#4318—48no—
79#4318—48no—
80C2×C11⋊C8—28no—
81C2×C11⋊C8—48no—
82C2×#407—112no—
83C2×#381D1111yescharacteristic
84#1306—114no—
85C23×C11—24no—
86C23×C11—22no—
87C23×C11—24no—
88C23×C11—24no—
89C23×C11—24no—
90C23×C11—24no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—42no—
96C23×C11—416no—
97C23×C11#9512yes—
98C23×C11#9512yes—
99C23×C11#9914yes—
100C23×C11C2×C4211yescharacteristic
101C23×C11C2×C22⋊C411yescharacteristic
102C23×C11C2×C4⋊C411yescharacteristic
103C2×C4×C11—24no—
104C2×C4×C11—24no—
105C2×C4×C11—24no—
106C2×C4×C11—24no—
107C2×C4×C11—24no—
108C2×C4×C11—24no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—42no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—48no—
120C2×C4×C11—44no—
121C2×C4×C11—88no—
122C2×C4×C11#9512yes—
123C2×C4×C11#9512yes—
124C2×C4×C11C2×C22⋊C412yes—
125C2×C4×C11C2×C4⋊C412yes—
126C11⋊C8—48no—
127C24×C4C2×D1111yescharacteristic
128C22×M16—222no—
129C22×C22⋊C4Dic1112yes—
130#407—114no—
131#407—114no—
132#407—222no—
133#407—222no—
134C2×C22⋊C8—114no—
135C2×C22⋊C8—222no—
136#381—22no—
137#381Dic1112yes—
138#381C2×D1112yes—
139C2×#95—22no—
140C22×C11—28no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—22no—
144C22×C11—22no—
145C22×C11—22no—
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—44no—
151C22×C11—48no—
152C22×C11—48no—
153C22×C11—44no—
154C22×C11#34214yes—
155C22×C11#34414yes—
156C22×C11C2×#9511yescharacteristic
157C22×C11C2×#9912yes—
158C4×C11—22no—
159C4×C11—22no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—84no—
163C25C2×Dic1111yescharacteristic
164C23×C4—22no—
165C23×C4—44no—
166C23×C4Dic2212yes—
167C23×C4C4×D1112yes—
168C23×C4C4×D1112yes—
169C23×C4D4412yes—
170C23×C4C2×Dic1111yescharacteristic
171C23×C4C22⋊D1112yes—
172C23×C4C22⋊D1112yes—
173C23×C4C22×D1111yescharacteristic
174C2×M16—224no—
175C2×M16—224no—
176C2×M16—448no—
177C22×C8—224no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—44no—
180C2×C22⋊C4C2×Dic1114yes—
181C22⋊C8—118no—
182C22⋊C8—224no—
183C22⋊C8—224no—
184C22⋊C8—224no—
185#95—24no—
186#95—24no—
187C2×C11—22no—
188C2×C11—24no—
189C2×C11—24no—
190C2×C11—41no—
191C2×C11—41no—
192C2×C11C2×#34211yescharacteristic
193C2×C11C2×#34412yes—
194C24—24no—
195C24—44no—
196C24C4×Dic1112yes—
197C24C4⋊Dic1112yes—
198C24C22⋊Dic1111yescharacteristic
199C24C22⋊Dic1111yescharacteristic
200C24C22×Dic1111yescharacteristic
201C22×C4—28no—
202C22×C4—24no—
203C22×C4—42no—
204C22×C4—44no—
205C22×C4—44no—
206C22×C4—44no—
207C22×C4—44no—
208C22×C4—42no—
209C22×C4—44no—
210C22×C4—44no—
211C22×C4—48no—
212C22×C4C4×Dic1111yescharacteristic
213C22×C4C4×Dic1111yescharacteristic
214C22×C4Dic11⋊C412yes—
215C22×C4Dic11⋊C412yes—
216C22×C4Dic11⋊C412yes—
217C22×C4Dic11⋊C412yes—
218C22×C4C4⋊Dic1112yes—
219C22×C4(C2×D11)⋊C412yes—
220C22×C4(C2×D11)⋊C412yes—
221C22×C4(C2×D11)⋊C412yes—
222C22×C4(C2×D11)⋊C412yes—
223C22×C4C22⋊Dic1112yes—
224C22×C4C2×Dic2211yescharacteristic
225C22×C4C2×C4×D1112yes—
226C22×C4C2×D4411yescharacteristic
227C22×C4C2×C22⋊D1112yes—
228M16—448no—
229M16—448no—
230C2×C8—228no—
231C2×C8—448no—
232C22⋊C4—44no—
233C22⋊C4—44no—
234C11#811411yescharacteristic, complemented, Sylow
235C23—22no—
236C23—24no—
237C23—22no—
238C23—24no—
239C23—24no—
240C23—24no—
241C23—24no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—42no—
246C23—416no—
247C23C11⋊#9512yes—
248C23C11⋊#9512yes—
249C23#6689814yes—
250C23C2×C4×Dic1111yescharacteristic
251C23C2×C4⋊Dic1111yescharacteristic
252C23C2×C22⋊Dic1111yescharacteristic
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—48no—
270C2×C4—44no—
271C2×C4—88no—
272C2×C4C11⋊#9512yes—
273C2×C4C11⋊#9512yes—
274C2×C4C2×Dic11⋊C412yes—
275C2×C4C2×(C2×D11)⋊C412yes—
276C8—448no—
277C22—28no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—44no—
288C22—48no—
289C22—48no—
290C22—44no—
291C22#1062216414yes—
292C22#1062217114yes—
293C22C2×C11⋊#9511yescharacteristic
294C22C2×#6689812yes—
295C4—22no—
296C4—22no—
297C4—22no—
298C4—22no—
299C4—84no—
300C2—22no—
301C2—24no—
302C2—24no—
303C2—41no—
304C2—41no—
305C2C2×#1062216411yescharacteristic
306C2C2×#1062217112yes—
subgroupG/H
centerC22C2×C11⋊#95
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#381C2
socleC22×C11C2×#95
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#381D11
hypocenterC11#8114
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
2. #13066524C2semidirect
13. #10622820C4semidirect
16. C2×C22⋊(C11⋊C8)C4semidirect
40. C22⋊(C11⋊C8)C2×C4semidirect
234. C11#8114semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130665242
C2×C11×#3812
#811411