Finite Group Databasebeta

← #14719290

Subgroups — #14719290

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066881C213yesmaximal
2#13066881C211yesmaximal, characteristic
3#13066878C211yesmaximal, characteristic
4#13066877C213yesmaximal
5#13066873C213yesmaximal
6#13066868C213yesmaximal
7C11×#1443C211yesmaximal, characteristic
8C22×C4⋊Dic11C2213yes—
9C22×C4⋊Dic11C2213yes—
10C22×Dic11⋊C4C2211yescharacteristic
11C2×C11×#95C2213yes—
12C2×C11×#95C2213yes—
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95C2213yes—
15C2×C11⋊#95C2213yes—
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20C2×C11⋊#95C2213yes—
21C23×C4×C11C2311yescharacteristic
22C23×C4×C11C2313yes—
23C23×C4×C11C2313yes—
24C23×Dic11C2311yescharacteristic
25C23×Dic11C2313yes—
26C23×Dic11C2313yes—
27C23×Dic11C2311yescharacteristic
28C2×C4⋊Dic11—26no—
29C2×C4⋊Dic11—43no—
30C2×C4⋊Dic11—43no—
31C2×C4⋊Dic11—43no—
32C2×C4⋊Dic11—43no—
33C2×C4⋊Dic11—43no—
34C2×Dic11⋊C4—43no—
35C11×#95—26no—
36C11×#95—26no—
37C11×#95Q814yes—
38C11⋊#95—26no—
39C11⋊#95—43no—
40C11⋊#95—43no—
41C11⋊#95—43no—
42C11⋊#95—43no—
43C11⋊#95—43no—
44C11⋊#95—43no—
45#17302—111nomaximal, Sylow
46C24×C11C2411yescharacteristic
47C22×C4×C11—23no—
48C22×C4×C11—23no—
49C22×C4×C11—23no—
50C22×C4×C11—23no—
51C22×C4×C11—23no—
52C22×C4×C11—23no—
53C22×C4×C11—23no—
54C22×C4×C11—23no—
55C22×C4×C11—23no—
56C22×C4×C11—23no—
57C22×C4×C11—23no—
58C22×C4×C11—23no—
59C22×C4×C11—23no—
60C22×C4×C11—23no—
61C22×C4×C11—21no—
62C22×C4×C11C2×Q816yes—
63C22×C4×C11#4116yes—
64C22×Dic11—23no—
65C22×Dic11—23no—
66C22×Dic11—23no—
67C22×Dic11—23no—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11—23no—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—23no—
74C22×Dic11—23no—
75C22×Dic11—23no—
76C22×Dic11—23no—
77C22×Dic11—23no—
78C22×Dic11—23no—
79C22×Dic11—21no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11#4112yes—
84C4⋊Dic11—412no—
85C4⋊Dic11—412no—
86Dic11⋊C4—44no—
87#1444—113no—
88#1444—111no—
89#1443—113no—
90#1443—111no—
91#1443D1111yescharacteristic
92#1442—113no—
93#1441—113no—
94C23×C11C22×Q811yescharacteristic
95C23×C11C2×#4113yes—
96C23×C11C2×#4111yescharacteristic
97C23×C11H(5,𝔽2)13yes—
98C23×C11H(5,𝔽2)13yes—
99C23×C112−1+411yescharacteristic
100C23×C112−1+413yes—
101C2×C4×C11—26no—
102C2×C4×C11—26no—
103C2×C4×C11—26no—
104C2×C4×C11—26no—
105C2×C4×C11—26no—
106C2×C4×C11—26no—
107C2×C4×C11—43no—
108C2×C4×C11—43no—
109C2×C4×C11—43no—
110C2×C4×C11—43no—
111C2×C4×C11—43no—
112C2×C4×C11—43no—
113C2×C4×C11—43no—
114C2×C4×C11—43no—
115C2×C4×C11—43no—
116C2×C4×C11—43no—
117C2×C4×C11—41no—
118C2×Dic11—26no—
119C2×Dic11—41no—
120C2×Dic11—43no—
121C2×Dic11—43no—
122C2×Dic11—43no—
123C2×Dic11—43no—
124C2×Dic11—43no—
125C2×Dic11—43no—
126C2×Dic11—43no—
127C2×Dic11—43no—
128C2×Dic11—43no—
129C2×Dic11—41no—
130C2×Dic11—43no—
131C2×Dic11—43no—
132C2×Dic11—43no—
133C2×Dic11—43no—
134C2×Dic11—43no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—43no—
138C22×C4⋊C4—113no—
139C22×C4⋊C4—111no—
140C22×C4⋊C4—113no—
141C2×#95—113no—
142C2×#95—113no—
143C2×#95—113no—
144C2×#95—113no—
145C2×#95—113no—
146C2×#95—113no—
147C2×#95—113no—
148C2×#95C2×D1113yes—
149C2×#95C2×D1113yes—
150C2×#95C2×D1111yescharacteristic
151C22×C11#53813yes—
152C22×C11#53913yes—
153C22×C11#54213yes—
154C22×C11#54213yes—
155C22×C11#54413yes—
156C22×C11#55213yes—
157C22×C11#55313yes—
158C22×C11#55413yes—
159C22×C11#55711yescharacteristic
160C22×C11#56013yes—
161C22×C11#56011yescharacteristic
162C22×C11#56313yes—
163C22×C11#56313yes—
164C4×C11—46no—
165C4×C11—46no—
166C4×C11—81no—
167Dic11—42no—
168Dic11—83no—
169Dic11—83no—
170Dic11—81no—
171C23×C4—111no—
172C23×C4—113no—
173C23×C4—111no—
174C23×C4—113no—
175C23×C4C22×D1111yescharacteristic
176C23×C4C22×D1113yes—
177C23×C4C22×D1113yes—
178C2×C4⋊C4—226no—
179C2×C4⋊C4—443no—
180C2×C4⋊C4—443no—
181C2×C4⋊C4—443no—
182C2×C4⋊C4—443no—
183C2×C4⋊C4—443no—
184C2×C4⋊C4—443no—
185#95—26no—
186#95—26no—
187#95—226no—
188#95—443no—
189#95—443no—
190#95—443no—
191#95—443no—
192#95—443no—
193#95—443no—
194#95Dic2214yes—
195C2×C11#277013yes—
196C2×C11#277413yes—
197C2×C11#279013yes—
198C2×C11#280111yescharacteristic
199C2×C11#282511yescharacteristic
200C2×C11#283813yes—
201C2×C11#284311yescharacteristic
202C24C23×D1111yescharacteristic
203C22×C4—23no—
204C22×C4—23no—
205C22×C4—23no—
206C22×C4—23no—
207C22×C4—23no—
208C22×C4—23no—
209C22×C4—23no—
210C22×C4—23no—
211C22×C4—23no—
212C22×C4—23no—
213C22×C4—23no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—21no—
217C22×C4—23no—
218C22×C4—112no—
219C22×C4—223no—
220C22×C4—223no—
221C22×C4—223no—
222C22×C4—223no—
223C22×C4—221no—
224C22×C4—223no—
225C22×C4—223no—
226C22×C4—223no—
227C22×C4—223no—
228C22×C4—223no—
229C22×C4—223no—
230C22×C4—223no—
231C22×C4—223no—
232C22×C4—223no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—223no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4C2×Dic2216yes—
239C22×C4#434116yes—
240C4⋊C4—4412no—
241C4⋊C4—444no—
242C4⋊C4—4412no—
243C11#1730211yescharacteristic, complemented, Sylow
244C23C22×Dic2211yescharacteristic
245C23C2×#434113yes—
246C23#6704011yescharacteristic
247C23#41×D1111yescharacteristic
248C23#6704213yes—
249C23#6704213yes—
250C23#6704313yes—
251C2×C4—26no—
252C2×C4—26no—
253C2×C4—26no—
254C2×C4—26no—
255C2×C4—26no—
256C2×C4—26no—
257C2×C4—43no—
258C2×C4—43no—
259C2×C4—43no—
260C2×C4—43no—
261C2×C4—43no—
262C2×C4—43no—
263C2×C4—43no—
264C2×C4—43no—
265C2×C4—41no—
266C2×C4—43no—
267C2×C4—43no—
268C2×C4—226no—
269C2×C4—441no—
270C2×C4—443no—
271C2×C4—443no—
272C2×C4—443no—
273C2×C4—443no—
274C2×C4—441no—
275C2×C4—443no—
276C2×C4—443no—
277C2×C4—443no—
278C2×C4—443no—
279C2×C4—443no—
280C2×C4—443no—
281C2×C4—443no—
282C2×C4—443no—
283C2×C4—443no—
284C2×C4—443no—
285C2×C4—443no—
286C2×C4—443no—
287C2×C4—443no—
288C22#1062305013yes—
289C22#1062307413yes—
290C22#1062310011yescharacteristic
291C22#1062314913yes—
292C22#1062317413yes—
293C22#1062318113yes—
294C22#1062319613yes—
295C22#1062321313yes—
296C22#1062323013yes—
297C22#1062323513yes—
298C22#1062324211yescharacteristic
299C22#1062324213yes—
300C22#1062324313yes—
301C4—46no—
302C4—46no—
303C4—81no—
304C4—442no—
305C4—881no—
306C4—883no—
307C4—883no—
308C2#1307612213yes—
309C2#1307617813yes—
310C2#1307638613yes—
311C2#1307652511yescharacteristic
312C2#1307670311yescharacteristic
313C2#1307684513yes—
314C2#1307688311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1443C2
hypercenter#1443D11
hypocenterC11#17302
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
243. C11#17302semidirect

Maximal subgroups

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

subgroupindex
#130668812
#130668782
#130668772
#130668732
#130668682
C11×#14432
#1730211