Finite Group Databasebeta

← #14640331

Subgroups — #14640331

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2C4×C11⋊#95C211yesmaximal, characteristic
3C11×#1797C211yesmaximal, characteristic
4C22×C42×C11C2211yescharacteristic
5C22×C4×Dic11—21no—
6C2×C11×C4⋊C8C412yescomplemented
7C2×C11×C22⋊C8—21no—
8C2×C11⋊#95—21no—
9C2×C11⋊#95C412yes—
10C2×C22⋊(C11⋊C8)—21no—
11C2×C4×C11⋊C8—21no—
12C11×#336—21no—
13#10622162C412yescomplemented
14C23×C4×C11C2×C411yescharacteristic
15C23×C4×C11D411yescharacteristic
16C23×C4×C11D411yescharacteristic
17C23×Dic11—22no—
18C22×C8×C11—22no—
19C2×C42×C11—42no—
20C2×C42×C11C2×C411yescharacteristic
21C2×C42×C11C2×C411yescharacteristic
22C2×C42×C11D411yescharacteristic
23C2×C42×C11Q811yescharacteristic
24C2×C4×Dic11—24no—
25C2×C4×Dic11—42no—
26C2×C4×Dic11—41no—
27C2×C4×Dic11—41no—
28C22×C11⋊C8—22no—
29C11×C4⋊C8—42no—
30C11×C22⋊C8—41no—
31C11×C22⋊C8—41no—
32C11⋊#95—24no—
33C11⋊#95—22no—
34C11⋊#95C814yescomplemented
35C22⋊(C11⋊C8)—24no—
36C4×C11⋊C8—42no—
37#7028—111nomaximal, Sylow
38C24×C11C22⋊C411yescharacteristic
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—41no—
44C22×C4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11C4211yescharacteristic
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11C22⋊C411yescharacteristic
49C22×C4×C11C4⋊C411yescharacteristic
50C22×C4×C11C4⋊C411yescharacteristic
51C22×C4×C11C4⋊C411yescharacteristic
52C22×C4×C11C2×C812yes—
53C22×C4×C11M1612yes—
54C22×C4×C11D811yescharacteristic
55C22×C4×C11SD1611yescharacteristic
56C22×C4×C11SD1611yescharacteristic
57C22×C4×C11Q1611yescharacteristic
58C22×Dic11—24no—
59C22×Dic11—24no—
60C22×Dic11—24no—
61C22×Dic11—42no—
62C22×Dic11—42no—
63C22×Dic11—42no—
64C22×Dic11—42no—
65C2×C8×C11—42no—
66C2×C8×C11—42no—
67C2×C8×C11—42no—
68C42×C11—22no—
69C42×C11—22no—
70C42×C11—41no—
71C42×C11—41no—
72C4×Dic11—44no—
73C4×Dic11—44no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—42no—
77#1797D1111yescharacteristic
78C4×C22⋊C8—111no—
79C4×#95—111no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11#9511yescharacteristic
85C23×C11C22⋊C812yes—
86C23×C11#10211yescharacteristic
87C23×C11#10311yescharacteristic
88C23×C11#10412yes—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—44no—
107C2×C4×C11C4×C811yescharacteristic
108C2×C4×C11#9711yescharacteristic
109C2×C4×C11#9912yes—
110C2×C4×C11#10211yescharacteristic
111C2×C4×C11#10311yescharacteristic
112C2×C4×C11#10412yes—
113C2×C4×C11#10412yes—
114C2×C4×C11C4⋊C812yes—
115C2×C4×C11#10611yescharacteristic
116C2×C4×C11#10711yescharacteristic
117C2×Dic11—28no—
118C2×Dic11—44no—
119C2×Dic11—44no—
120C2×Dic11—44no—
121C2×Dic11—44no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C8×C11—82no—
125C11⋊C8—44no—
126C22×C42—221no—
127C22×C42C2×D1111yescharacteristic
128C2×C4⋊C8Dic1112yescomplemented
129C2×C22⋊C8—21no—
130C2×C22⋊C8—221no—
131C2×C4×C8—221no—
132C2×#95—112no—
133C2×#95—221no—
134#336—21no—
135#336—112no—
136C22×C11—22no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—22no—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—22no—
144C22×C11D4⋊C812yes—
145C22×C11Q8⋊C812yes—
146C22×C11#33611yescharacteristic
147C22×C11#33911yescharacteristic
148C22×C11#33911yescharacteristic
149C22×C11#33911yescharacteristic
150C22×C11#34011yescharacteristic
151C22×C11#34211yescharacteristic
152C22×C11#34411yescharacteristic
153C4×C11—21no—
154C4×C11—21no—
155C4×C11—22no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—22no—
159C4×C11—41no—
160C4×C11#32712yes—
161C4×C11#32812yes—
162Dic11—48no—
163C23×C4—222no—
164C23×C4C4×D1111yescharacteristic
165C23×C4D4411yescharacteristic
166C23×C4C22⋊D1111yescharacteristic
167C22×C8—22no—
168C22×C8—222no—
169C2×C42—42no—
170C2×C42—224no—
171C2×C42—442no—
172C2×C42—441no—
173C2×C42—441no—
174C2×C42Dic2211yescharacteristic
175C2×C42C4×D1111yescharacteristic
176C2×C42C2×Dic1111yescharacteristic
177C2×C42C22⋊D1111yescharacteristic
178C4⋊C8—42no—
179C22⋊C8—41no—
180C22⋊C8—41no—
181C22⋊C8—224no—
182C4×C8—442no—
183#95—114no—
184#95—224no—
185#95—222no—
186C2×C11—22no—
187C2×C11—22no—
188C2×C11#127611yescharacteristic
189C2×C11#127911yescharacteristic
190C2×C11#128211yescharacteristic
191C2×C11#129411yescharacteristic
192C2×C11#129711yescharacteristic
193C2×C11#130011yescharacteristic
194C2×C11#130311yescharacteristic
195C24(C2×D11)⋊C411yescharacteristic
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—224no—
204C22×C4—224no—
205C22×C4—224no—
206C22×C4—442no—
207C22×C4—442no—
208C22×C4—442no—
209C22×C4—442no—
210C22×C4C8×D1112yes—
211C22×C4#431312yes—
212C22×C4C4×Dic1111yescharacteristic
213C22×C4Dic11⋊C411yescharacteristic
214C22×C4Dic11⋊C411yescharacteristic
215C22×C4C4⋊Dic1111yescharacteristic
216C22×C4(C2×D11)⋊C411yescharacteristic
217C22×C4#432311yescharacteristic
218C22×C4#432411yescharacteristic
219C22×C4#432511yescharacteristic
220C22×C4#432611yescharacteristic
221C22×C4C22⋊Dic1111yescharacteristic
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—224no—
226C2×C8—442no—
227C2×C8—442no—
228C42—22no—
229C42—22no—
230C42—41no—
231C42—41no—
232C42—444no—
233C42—444no—
234C11#702811yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23#6687311yescharacteristic
240C23#6687411yescharacteristic
241C23(C2×D11)⋊C812yes—
242C23#6688912yes—
243C23C11⋊#9511yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—228no—
263C2×C4—444no—
264C2×C4—444no—
265C2×C4—444no—
266C2×C4—444no—
267C2×C4—444no—
268C2×C4—444no—
269C2×C4#6687111yescharacteristic
270C2×C4#6687211yescharacteristic
271C2×C4C8×Dic1111yescharacteristic
272C2×C4Dic11⋊C812yes—
273C2×C4#6687911yescharacteristic
274C2×C4#6688912yes—
275C2×C4#6689611yescharacteristic
276C2×C4#6689812yes—
277C2×C4#6689911yescharacteristic
278C2×C4#6690112yes—
279C8—82no—
280C8—444no—
281C22—22no—
282C22—22no—
283C22—21no—
284C22—21no—
285C22—22no—
286C22—22no—
287C22—21no—
288C22—21no—
289C22#1062212112yes—
290C22#1062212212yes—
291C22#1062216411yescharacteristic
292C22#1062216711yescharacteristic
293C22#1062217011yescharacteristic
294C22#1062218811yescharacteristic
295C22#1062219311yescharacteristic
296C22#1062219311yescharacteristic
297C22#1062219411yescharacteristic
298C4—22no—
299C4—21no—
300C4—22no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—448no—
306C4#1062217512yes—
307C4#1062217612yes—
308C2—22no—
309C2—22no—
310C2#1306644811yescharacteristic
311C2#1306645511yescharacteristic
312C2#1306646311yescharacteristic
313C2#1306649411yescharacteristic
314C2#1306650111yescharacteristic
315C2#1306650811yescharacteristic
316C2#1306651711yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic11
commutatorC2×C4×C11C4×C8
FrattiniC22×C42C2×D11
FittingC11×#1797C2
socleC23×C11#95
prime radicalC24×C11C22⋊C4
cosocleC22×C42×C11C22
hypercenter#1797D11
hypocenterC11#7028
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
6. C2×C11×C4⋊C8C4semidirect
13. #10622162C4semidirect
34. C11⋊#95C8semidirect
128. C2×C4⋊C8Dic11semidirect
234. C11#7028semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C11⋊C8)2
C4×C11⋊#952
C11×#17972
#702811