Finite Group Databasebeta

← #14771479

Subgroups — #14771479

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071493C212yesmaximal
2#13069355C212yesmaximal, complemented
3#13069189C214yesmaximal, complemented
4#13068706C212yesmaximal
5#13068641C211yesmaximal, characteristic
6#13068515C212yesmaximal, complemented
7#13068392C211yesmaximal, characteristic
8C22×C11×#107C211yesmaximal, characteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C2×C11×#107C418yescomplemented
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2212yes—
14C2×C11×#107C2211yescharacteristic
15#10622825—22no—
16#10622825C2212yes—
17C4×C22⋊Dic11—22no—
18C4×C22⋊Dic11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×#66881C2212yes—
21C2×#66879C2212yes—
22#10622598C2214yes—
23#10622594—24no—
24C4⋊C4×Dic11C2214yes—
25#10622189C2212yes—
26#10622188C2212yes—
27#10622167C2214yes—
28#10622167C2214yes—
29C23×C4×C11—22no—
30C23×C4×C11C2311yescharacteristic
31C22×C8×C11—24no—
32C22×C8×C11C2×C414yes—
33C22×C8×C11C2311yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4C2×C418yes—
38C2×C11×C4⋊C4C2312yes—
39C2×C11×C4⋊C4C2312yes—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11D412yes—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11C2314yes—
44C2×C4×Dic11—24no—
45C2×C4×Dic11C2312yes—
46C22×C11⋊C8C2312yes—
47C11×#107C2×C418yes—
48C11×#107C2×C414yes—
49C11×#107C2×C414yes—
50C11⋊#95—22no—
51C11⋊#95—24no—
52C11⋊#95—24no—
53C11⋊#95D412yes—
54C22⋊(C11⋊C8)—22no—
55#66881—24no—
56#66879—24no—
57#22618—111nomaximal, Sylow
58C24×C11C2×D411yescharacteristic
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—28no—
64C22×C4×C11—84no—
65C22×C4×C11C22×C412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11#4112yes—
68C22×C4×C11C2411yescharacteristic
69C22×Dic11—24no—
70C22×Dic11C2×D414yes—
71C2×C8×C11—28no—
72C2×C8×C11—22no—
73C2×C8×C11C22×C412yes—
74C2×C8×C11C22×C412yes—
75C2×C8×C11#4114yes—
76C11×C4⋊C4—28no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4C22×C414yes—
80C11×C4⋊C4C22×C414yes—
81C22⋊Dic11—24no—
82C22⋊Dic11—44no—
83C4⋊Dic11—24no—
84C4⋊Dic11—24no—
85C4⋊Dic11—84no—
86C4×Dic11—22no—
87C4×Dic11—22no—
88C4×Dic11—84no—
89C2×C11⋊C8—22no—
90C2×C11⋊C8—22no—
91C2×C11⋊C8—22no—
92C22×#107D1111yescharacteristic
93#2345—112no—
94#1943—112no—
95#1918—114no—
96#1824—112no—
97#1807—111no—
98#1776—112no—
99#1752—111no—
100C23×C11—22no—
101C23×C11—22no—
102C23×C11C4×D412yes—
103C23×C11#13714yes—
104C23×C11C22×D411yescharacteristic
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—24no—
109C2×C4×C11—24no—
110C2×C4×C11—24no—
111C2×C4×C11—44no—
112C2×C4×C11—44no—
113C2×C4×C11—88no—
114C2×C4×C11C4×D412yes—
115C2×C4×C11C23×C411yescharacteristic
116C2×C4×C11C2×#4112yes—
117C2×C4×C11C2×#4111yescharacteristic
118C2×C4×C112−1+412yes—
119C2×Dic11—24no—
120C2×Dic11—24no—
121C2×Dic11—24no—
122C2×Dic11—44no—
123C2×Dic11—44no—
124C2×Dic11—44no—
125C8×C11—22no—
126C8×C11#11714yes—
127C11⋊C8—42no—
128C23×C8C2×D1111yescharacteristic
129C22×C4⋊C4C2×D1112yes—
130C2×#107Dic1118yescomplemented
131C2×#107C2×D1112yes—
132C2×#107C2×D1111yescharacteristic
133C2×#107C2×D1111yescharacteristic
134C2×#106—112no—
135C2×C22⋊C8—111no—
136C2×#97—112no—
137#389—114no—
138#387—224no—
139#380—112no—
140#380—222no—
141C4×C4⋊C4—114no—
142C4×C22⋊C4—111no—
143C4×C22⋊C4—222no—
144#340—112no—
145#340—114no—
146#340—114no—
147#336—112no—
148C22×C11—28no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11#44114yes—
152C22×C11C2×C4×D411yescharacteristic
153C22×C11#54712yes—
154C22×C11C2×#13712yes—
155C22×C11#57612yes—
156C4×C11—22no—
157C4×C11—44no—
158C4×C11—44no—
159C4×C11C2×#11711yescharacteristic
160C4×C11#51911yescharacteristic
161C4×C11#55212yes—
162Dic11—44no—
163Dic11—84no—
164C23×C4—22no—
165C23×C4C22×D1111yescharacteristic
166C22×C8—24no—
167C22×C8—112no—
168C22×C8C2×Dic1114yes—
169C22×C8C22×D1111yescharacteristic
170C22×C8C22×D1111yescharacteristic
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—114no—
174C2×C4⋊C4—224no—
175C2×C4⋊C4C2×Dic1118yes—
176C2×C4⋊C4C22×D1112yes—
177C2×C4⋊C4C22×D1112yes—
178C2×C22⋊C4—112no—
179C2×C22⋊C4—222no—
180C2×C42—112no—
181C2×C42—224no—
182#107C2×Dic1118yes—
183#107C2×Dic1114yes—
184#107C2×Dic1114yes—
185#106—224no—
186C22⋊C8—222no—
187#97—224no—
188#95—112no—
189#95—224no—
190#95—224no—
191#95—222no—
192C2×C11—24no—
193C2×C11#234411yescharacteristic
194C2×C11C2×#44111yescharacteristic
195C2×C11#294811yescharacteristic
196C2×C11#334614yes—
197C24D4×D1111yescharacteristic
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—28no—
203C22×C4—84no—
204C22×C4—114no—
205C22×C4—224no—
206C22×C4D4×D1111yescharacteristic
207C22×C4#434112yes—
208C22×C4C22×Dic1112yes—
209C22×C4C23×D1111yescharacteristic
210C2×C8—22no—
211C2×C8—28no—
212C2×C8—222no—
213C2×C8—222no—
214C2×C8—222no—
215C2×C8#433914yes—
216C2×C8C22×Dic1112yes—
217C2×C8C22×Dic1112yes—
218C4⋊C4—28no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—224no—
222C4⋊C4—224no—
223C4⋊C4—884no—
224C4⋊C4C22×Dic1114yes—
225C4⋊C4C22×Dic1114yes—
226C22⋊C4—224no—
227C22⋊C4—444no—
228C42—222no—
229C42—222no—
230C42—884no—
231C11#2261811yescharacteristic, complemented, Sylow
232C23—22no—
233C23—22no—
234C23#6697114yes—
235C23D4×Dic1112yes—
236C23C2×D4×D1111yescharacteristic
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—24no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—88no—
246C2×C4—224no—
247C2×C4—224no—
248C2×C4—224no—
249C2×C4—444no—
250C2×C4—444no—
251C2×C4—444no—
252C2×C4D4×Dic1112yes—
253C2×C4C2×#433912yes—
254C2×C4C2×#434111yescharacteristic
255C2×C4#6704012yes—
256C2×C4C23×Dic1111yescharacteristic
257C8—22no—
258C8—442no—
259C8#6697914yes—
260C22—28no—
261C22—22no—
262C22—22no—
263C22#1062279714yes—
264C22#1062303812yes—
265C22#1062328812yes—
266C22C2×#6697112yes—
267C22C2×D4×Dic1111yescharacteristic
268C4—22no—
269C4—44no—
270C4—44no—
271C4—444no—
272C4—884no—
273C4#1062304412yes—
274C4C2×#6697911yescharacteristic
275C4#1062334311yescharacteristic
276C2—24no—
277C2#1307148511yescharacteristic
278C2C2×#1062279711yescharacteristic
279C2#1307746811yescharacteristic
280C2#1308109714yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#107C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×#107D11
hypocenterC11#22618
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. #13069355C2semidirect
3. #13069189C2semidirect
6. #13068515C2semidirect
11. C2×C11×#107C4semidirect
130. C2×#107Dic11semidirect
231. C11#22618semidirect

Maximal subgroups

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

subgroupindex
#130714932
#130693552
#130691892
#130687062
#130686412
#130685152
#130683922
C22×C11×#1072
#2261811