Finite Group Databasebeta

← #14919946

Subgroups — #14919946

Order 2816.

1800 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071802C213yesmaximal
2#13071722C216yesmaximal
3#13071716C216yesmaximal
4#13071422C216yesmaximal
5#13071358C216yesmaximal
6#125×Dic11C213yesmaximal
7C2×C11×#564C211yesmaximal, characteristic
8C11×#564C4116yescomplemented
9C2×C11×#125C2216yes—
10C2×C11×#125C2213yes—
11C2×C11×#125C2216yes—
12#10622598C2213yes—
13#10622598C2216yes—
14#10622598C2213yes—
15#10622598C2216yes—
16#10622598C2216yes—
17#10622598C2216yes—
18#10622594C2216yes—
19#10622594C2216yes—
20#10622594C2216yes—
21#10622594C2216yes—
22#10622594C2216yes—
23#10622594C2216yes—
24#10622594C2216yes—
25#10622594C2216yes—
26#10622594C2216yes—
27#10622594C2216yes—
28C4⋊C4×Dic11C2216yes—
29C4⋊C4×Dic11C2216yes—
30C4⋊C4×Dic11C2213yes—
31C4⋊C4×Dic11C2216yes—
32C4⋊C4×Dic11C2213yes—
33C4⋊C4×Dic11C2216yes—
34#10622550C2212yes—
35#10622549C2213yes—
36#10622548C2212yes—
37C4×C4⋊Dic11C2216yes—
38#10622545C2216yes—
39C42×Dic11C2211yescharacteristic
40C11×#125C2×C4148yes—
41C11×#125C2×C4124yes—
42C11×#125C2×C4148yes—
43C2×C11×C4⋊C4C2316yes—
44C2×C11×C4⋊C4C2316yes—
45C2×C11×C4⋊C4C2313yes—
46C2×C11×C4⋊C4C2316yes—
47C2×C11×C4⋊C4C2313yes—
48C2×C11×C4⋊C4C2316yes—
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2312yes—
51C2×C42×C11C2312yes—
52C2×C4⋊Dic11C2316yes—
53C2×C4⋊Dic11C2316yes—
54C2×C4⋊Dic11C2316yes—
55C2×C4⋊Dic11C2316yes—
56C2×C4⋊Dic11C2313yes—
57C2×C4⋊Dic11C2313yes—
58C2×C4×Dic11C2313yes—
59C2×C4×Dic11C2316yes—
60C2×C4×Dic11C2313yes—
61C2×C4×Dic11C2316yes—
62C2×C4×Dic11C2316yes—
63C2×C4×Dic11C2316yes—
64C11⋊#95C2316yes—
65C11⋊#95C2316yes—
66C11⋊#95C2316yes—
67C11⋊#95C2316yes—
68C11⋊#95C2316yes—
69C11⋊#95C2316yes—
70C11⋊#95C2316yes—
71C11⋊#95C2316yes—
72C11⋊#95C2316yes—
73C11⋊#95C2316yes—
74#34530—111nomaximal, Sylow
75C22×C4×C11C2416yes—
76C22×C4×C11C2413yes—
77C22×C4×C11C2416yes—
78C22×Dic11C2416yes—
79C22×Dic11C2416yes—
80C22×Dic11C2411yescharacteristic
81C22×Dic11C2413yes—
82C11×C4⋊C4C22×C4124yes—
83C11×C4⋊C4C22×C4124yes—
84C11×C4⋊C4C22×C4112yes—
85C11×C4⋊C4C22×C4124yes—
86C11×C4⋊C4C22×C4112yes—
87C11×C4⋊C4C22×C4124yes—
88C42×C11C22×C414yes—
89C42×C11C22×C418yes—
90C42×C11C22×C418yes—
91C4⋊Dic11—212no—
92C4⋊Dic11—46no—
93C4⋊Dic11—43no—
94C4⋊Dic11—46no—
95C4⋊Dic11—46no—
96C4⋊Dic11—43no—
97C4×Dic11—26no—
98C4×Dic11—212no—
99C4×Dic11—46no—
100C4×Dic11—46no—
101C4×Dic11—43no—
102C4×Dic11—46no—
103C2×#564D1111yescharacteristic
104#2382—113no—
105#2371—116no—
106#2370—116no—
107#2336—116no—
108#2330—116no—
109C4×#125—113no—
110C23×C11C2511yescharacteristic
111C2×C4×C11—23no—
112C2×C4×C11—26no—
113C2×C4×C11—26no—
114C2×C4×C11—26no—
115C2×C4×C11—23no—
116C2×C4×C11—26no—
117C2×C4×C11C23×C416yes—
118C2×C4×C11C23×C4112yes—
119C2×C4×C11C23×C4112yes—
120C2×Dic11—23no—
121C2×Dic11—23no—
122C2×Dic11—26no—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—26no—
126C2×Dic11—26no—
127C2×Dic11—23no—
128C2×Dic11—26no—
129C2×Dic112−1+416yes—
130#564Dic11116yescomplemented
131C2×#125C2×D1113yes—
132C2×#125C2×D1116yes—
133C2×#125C2×D1116yes—
134#389—113no—
135#389—113no—
136#389—116no—
137#389—116no—
138#389—116no—
139#389—116no—
140#387—116no—
141#387—116no—
142#387—116no—
143#387—116no—
144#387—116no—
145#387—116no—
146#387—116no—
147#387—116no—
148#387—116no—
149#387—116no—
150#384—112no—
151#383—112no—
152#382—113no—
153C4×C4⋊C4—116no—
154C4×C4⋊C4—113no—
155C4×C4⋊C4—116no—
156C4×C4⋊C4—113no—
157C4×C4⋊C4—116no—
158C4×C4⋊C4—116no—
159C4×C4⋊C4—116no—
160#376—116no—
161C43—111no—
162C22×C11C24×C411yescharacteristic
163C22×C11C2×2−1+413yes—
164C22×C11#58513yes—
165C4×C11—26no—
166C4×C11—212no—
167C4×C11—212no—
168Dic11—26no—
169Dic11—46no—
170Dic11—46no—
171Dic11—41no—
172#125C2×Dic11124yes—
173#125C2×Dic11148yes—
174#125C2×Dic11148yes—
175C2×C4⋊C4—116no—
176C2×C4⋊C4—113no—
177C2×C4⋊C4—113no—
178C2×C4⋊C4—116no—
179C2×C4⋊C4—116no—
180C2×C4⋊C4—116no—
181C2×C4⋊C4C22×D1113yes—
182C2×C4⋊C4C22×D1116yes—
183C2×C4⋊C4C22×D1116yes—
184C2×C4⋊C4C22×D1113yes—
185C2×C4⋊C4C22×D1116yes—
186C2×C4⋊C4C22×D1116yes—
187C2×C42—113no—
188C2×C42—116no—
189C2×C42—113no—
190C2×C42—116no—
191C2×C42—116no—
192C2×C42—116no—
193C2×C42C22×D1111yescharacteristic
194C2×C42C22×D1112yes—
195C2×C42C22×D1112yes—
196#95—116no—
197#95—116no—
198#95—116no—
199#95—116no—
200#95—116no—
201#95—116no—
202#95—116no—
203#95—116no—
204#95—116no—
205#95—116no—
206C2×C11C4×2−1+413yes—
207C2×C11#356313yes—
208C2×C11#356711yescharacteristic
209C22×C4—113no—
210C22×C4—116no—
211C22×C4—116no—
212C22×C4—111no—
213C22×C4C23×D1116yes—
214C22×C4C23×D1113yes—
215C22×C4C23×D1116yes—
216C4⋊C4—2212no—
217C4⋊C4—446no—
218C4⋊C4—443no—
219C4⋊C4—446no—
220C4⋊C4—446no—
221C4⋊C4—443no—
222C4⋊C4C22×Dic11112yes—
223C4⋊C4C22×Dic11124yes—
224C4⋊C4C22×Dic11124yes—
225C4⋊C4C22×Dic11112yes—
226C4⋊C4C22×Dic11124yes—
227C4⋊C4C22×Dic11124yes—
228C42—226no—
229C42—2212no—
230C42—446no—
231C42—446no—
232C42—443no—
233C42—446no—
234C42C22×Dic1114yes—
235C42C22×Dic1118yes—
236C42C22×Dic1118yes—
237C11#3453011yescharacteristic, complemented, Sylow
238C23C24×D1111yescharacteristic
239C2×C4—23no—
240C2×C4—26no—
241C2×C4—26no—
242C2×C4—26no—
243C2×C4—23no—
244C2×C4—26no—
245C2×C4—116no—
246C2×C4—223no—
247C2×C4—223no—
248C2×C4—226no—
249C2×C4—226no—
250C2×C4—226no—
251C2×C4—226no—
252C2×C4—226no—
253C2×C4—223no—
254C2×C4—226no—
255C2×C4C23×Dic1116yes—
256C2×C4C23×Dic11112yes—
257C2×C4C23×Dic11112yes—
258C22D11×2−1+413yes—
259C22#1062345713yes—
260C22C24×Dic1111yescharacteristic
261C4—26no—
262C4—212no—
263C4—212no—
264C4—226no—
265C4—446no—
266C4—446no—
267C4—441no—
268C22−1+4×Dic1113yes—
269C2#1308322513yes—
270C2#1308330611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#564C2
socle, prime radical, cosocleC23×C11C25
hypercenterC2×#564D11
hypocenterC11#34530
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#564

Complements

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

NH ≅ G/Ntype
8. C11×#564C4semidirect
130. #564Dic11semidirect
237. C11#34530semidirect

Maximal subgroups

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

subgroupindex
#130718022
#130717222
#130717162
#130714222
#130713582
#125×Dic112
C2×C11×#5642
#3453011