Finite Group Databasebeta

← #14644440

Subgroups — #14644440

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
2#13068362C211yesmaximal, characteristic, complemented
3C2×D4⋊(C11⋊C8)C212yesmaximal
4#13066457C212yesmaximal, complemented
5C11×#2293C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×C11×#117—21no—
8C11×#390C412yes—
9C11×#389C412yes—
10C11×#388—22no—
11C4×C11×C4⋊C4C2211yescharacteristic
12C4×C11×C22⋊C4—21no—
13C43×C11C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8—21no—
16C2×C4×C11⋊C8C2212yes—
17D4⋊(C11⋊C8)C418yescomplemented
18#10622162—22no—
19#10622162—21no—
20C22×D4×C11C2×C411yescharacteristic
21C23×C4×C11—21no—
22C4×D4×C11—22no—
23C4×D4×C11C2×C414yes—
24C11×#117—42no—
25C11×#117—42no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4C2×C412yes—
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11—21no—
33C2×C42×C11C2×C412yes—
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D412yes—
36C2×C42×C11D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8—22no—
39C22×C11⋊C8—22no—
40C11×#95—22no—
41C11×#95—21no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)C2×C414yes—
44C4×C11⋊C8—22no—
45C4×C11⋊C8—42no—
46C4×C11⋊C8C2×C414yes—
47#8183—111nomaximal, Sylow
48C24×C11—21no—
49C2×D4×C11—21no—
50C2×D4×C11—24no—
51C2×D4×C11C4212yes—
52C22×C4×C11—21no—
53C22×C4×C11—24no—
54C22×C4×C11—22no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—42no—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C11×C4⋊C4—21no—
64C11×C4⋊C4—24no—
65C11×C4⋊C4—44no—
66C11×C4⋊C4C4212yes—
67C11×C22⋊C4—24no—
68C11×C22⋊C4—44no—
69C11×C22⋊C4—44no—
70C42×C11—24no—
71C42×C11—22no—
72C42×C11—42no—
73C42×C11—41no—
74C42×C11—41no—
75C42×C11D812yes—
76C42×C11SD1612yes—
77C42×C11C22×C412yes—
78C42×C11#4112yes—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—24no—
81C2×C11⋊C8—44no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84#2293D1111yescharacteristic
85C4×C4⋊C8—111no—
86#1744—111no—
87C2×D4⋊C8—112no—
88#1279—112no—
89C23×C11—22no—
90C23×C11—42no—
91C23×C11—41no—
92C23×C11—41no—
93C23×C11—42no—
94C23×C11C2×C22⋊C411yescharacteristic
95D4×C11—24no—
96D4×C11—42no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—44no—
107C2×C4×C11—44no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11#10214yes—
112C2×C4×C11C2×C4211yescharacteristic
113C2×C4×C11#11711yescharacteristic
114C2×C4×C11C4×D412yes—
115C2×C4×C11C4×D412yes—
116C2×C4×C11#13114yes—
117C2×C4×C11C2×D811yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11#13512yes—
120C11⋊C8—44no—
121C11⋊C8—44no—
122C2×C4×D4C2×D1111yescharacteristic
123C2×#117—21no—
124C2×C4⋊C8—112no—
125C2×C4×C8—112no—
126C2×C4×C8—221no—
127#390Dic1112yes—
128#389Dic1112yes—
129#388—22no—
130C4×C4⋊C4C2×D1111yescharacteristic
131C4×C22⋊C4—21no—
132C43C2×D1111yescharacteristic
133#336—222no—
134#336—221no—
135D4⋊C8—118no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—82no—
140C22×C11—82no—
141C22×C11C4×C22⋊C411yescharacteristic
142C22×C11#40812yes—
143C22×C11C2×#10211yescharacteristic
144C22×C11#41611yescharacteristic
145C22×C11#42112yes—
146C4×C11—24no—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11—42no—
150C4×C11—82no—
151C4×C11#40512yes—
152C4×C11#43312yes—
153C4×C11C4×D812yes—
154C4×C11C4×SD1612yes—
155C22×D4C2×Dic1111yescharacteristic
156C23×C4—21no—
157C22×C8—222no—
158C22×C8—222no—
159C4×D4—22no—
160C4×D4C4×D1114yes—
161#117—42no—
162#117—42no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×Dic1112yes—
165C2×C4⋊C4C2×Dic1111yescharacteristic
166C2×C22⋊C4—21no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C42—21no—
170C2×C42C2×Dic1112yes—
171C2×C42C22⋊D1111yescharacteristic
172C2×C42C22⋊D1112yes—
173C2×C42C22⋊D1111yescharacteristic
174C2×C42C22×D1111yescharacteristic
175C4⋊C8—114no—
176C4⋊C8—222no—
177C4×C8—114no—
178C4×C8—222no—
179C4×C8—442no—
180#95—22no—
181#95—21no—
182C2×C11—82no—
183C2×C11#148012yes—
184C2×C11#148212yes—
185C2×C11#175011yescharacteristic
186C2×C11#175911yescharacteristic
187C2×C11C4×#10211yescharacteristic
188C24—21no—
189C2×D4—21no—
190C2×D4—24no—
191C2×D4C4×Dic1112yes—
192C22×C4—21no—
193C22×C4—24no—
194C22×C4—22no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—42no—
198C22×C4C22⋊Dic1112yes—
199C22×C4C22⋊Dic1112yes—
200C22×C4C22×Dic1111yescharacteristic
201C22×C4C2×C22⋊D1111yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203C2×C8—224no—
204C2×C8—224no—
205C2×C8—444no—
206C2×C8—442no—
207C2×C8—442no—
208C4⋊C4—21no—
209C4⋊C4—24no—
210C4⋊C4—44no—
211C4⋊C4C4×Dic1112yes—
212C22⋊C4—24no—
213C22⋊C4—44no—
214C22⋊C4—44no—
215C42—24no—
216C42—22no—
217C42—42no—
218C42—41no—
219C42—41no—
220C42#432312yes—
221C42#432412yes—
222C42C2×C4×D1112yes—
223C42#433912yes—
224C11#818311yescharacteristic, complemented, Sylow
225C23—22no—
226C23—41no—
227C23—41no—
228C23—42no—
229C23—42no—
230C23C2×C22⋊Dic1111yescharacteristic
231D4—24no—
232D4—42no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4#6689614yes—
248C2×C4C2×C4×Dic1111yescharacteristic
249C2×C4#6697911yescharacteristic
250C2×C4C4×C22⋊D1112yes—
251C2×C4C4×C22⋊D1112yes—
252C2×C4C2×#432311yescharacteristic
253C2×C4C2×#432411yescharacteristic
254C2×C4#6700114yes—
255C2×C4#6700312yes—
256C8—444no—
257C8—444no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—82no—
262C22—82no—
263C22C4×C22⋊Dic1111yescharacteristic
264C22C2×#6689611yescharacteristic
265C22#1062284611yescharacteristic
266C22#1062284712yes—
267C22#1062284912yes—
268C4—24no—
269C4—22no—
270C4—42no—
271C4—42no—
272C4—82no—
273C4#1062261012yes—
274C4#1062261312yes—
275C4C4×#432312yes—
276C4C4×#432412yes—
277C2—82no—
278C2#1306701512yes—
279C2#1306702412yes—
280C2#1306838211yescharacteristic
281C2#1306842611yescharacteristic
282C2C4×#6689611yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#2293C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#2293D11
hypocenterC11#8183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C11⋊C8)C2semidirect
2. #13068362C2semidirect
4. #13066457C2semidirect
17. D4⋊(C11⋊C8)C4semidirect
224. C11#8183semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C11⋊C8)2
#130683622
C2×D4⋊(C11⋊C8)2
#130664572
C11×#22932
#818311