Finite Group Databasebeta

← #14719216

Subgroups — #14719216

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066886C213yesmaximal
2#13066882C213yesmaximal
3#13066881C211yesmaximal, characteristic
4#13066878C211yesmaximal, characteristic
5#13066868C213yesmaximal
6#13066868C213yesmaximal
7C11×#1443C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C22×C4⋊Dic11C2213yes—
10C22×Dic11⋊C4C2213yes—
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×C11C2313yes—
22C23×C4×C11C2313yes—
23C23×C4×C11C2311yescharacteristic
24C23×Dic11C2313yes—
25C23×Dic11C2311yescharacteristic
26C23×Dic11C2311yescharacteristic
27C23×Dic11C2313yes—
28C22×Dic22—43no—
29C22×Dic22—43no—
30C22×Dic22Q814yes—
31C2×C4⋊Dic11—26no—
32C2×C4⋊Dic11—26no—
33C2×C4⋊Dic11—43no—
34C2×Dic11⋊C4—26no—
35C2×Dic11⋊C4—43no—
36C2×Dic11⋊C4—43no—
37C11×#95—43no—
38C11×#95—43no—
39C11×#95Q814yescomplemented
40C11⋊#95—43no—
41C11⋊#95—43no—
42C11⋊#95—43no—
43C11⋊#95—43no—
44C11⋊#95—43no—
45C11⋊#95—43no—
46C11⋊#95—43no—
47#17295—111nomaximal, Sylow
48C24×C11C2411yescharacteristic
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—23no—
62C22×C4×C11—23no—
63C22×C4×C11—23no—
64C22×C4×C11C2×Q816yes—
65C22×C4×C11C2×Q812yes—
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—23no—
80C22×Dic11—23no—
81C22×Dic11—23no—
82C22×Dic11—23no—
83C22×Dic11C2×Q812yes—
84C22×Dic11C2×Q812yes—
85C22×Dic11#4116yes—
86C2×Dic22—412no—
87C2×Dic22—44no—
88C2×Dic22—412no—
89C4⋊Dic11—412no—
90Dic11⋊C4—412no—
91#1446—113no—
92#1445—113no—
93#1444—111no—
94#1443—111no—
95#1443D1111yescharacteristic
96#1441—113no—
97#1441—113no—
98C23×C11C22×Q811yescharacteristic
99C23×C11C22×Q811yescharacteristic
100C23×C11C2×#4113yes—
101C23×C11H(5,𝔽2)13yes—
102C23×C11H(5,𝔽2)11yescharacteristic
103C23×C11H(5,𝔽2)13yes—
104C23×C112−1+413yes—
105C2×C4×C11—26no—
106C2×C4×C11—26no—
107C2×C4×C11—26no—
108C2×C4×C11—26no—
109C2×C4×C11—43no—
110C2×C4×C11—43no—
111C2×C4×C11—43no—
112C2×C4×C11—41no—
113C2×C4×C11—43no—
114C2×C4×C11—43no—
115C2×C4×C11—43no—
116C2×C4×C11—43no—
117C2×C4×C11—43no—
118C2×C4×C11—43no—
119C2×C4×C11—43no—
120C2×C4×C11—43no—
121C2×C4×C11—43no—
122C2×Dic11—26no—
123C2×Dic11—26no—
124C2×Dic11—26no—
125C2×Dic11—26no—
126C2×Dic11—26no—
127C2×Dic11—43no—
128C2×Dic11—43no—
129C2×Dic11—43no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—43no—
133C2×Dic11—43no—
134C2×Dic11—43no—
135C2×Dic11—43no—
136C2×Dic11—43no—
137C2×Dic11—43no—
138C2×Dic11—43no—
139C2×Dic11—43no—
140C2×Dic11—43no—
141C2×Dic11—43no—
142Dic22—416no—
143C23×Q8—111no—
144C22×C4⋊C4—113no—
145C22×C4⋊C4—113no—
146C2×#95—113no—
147C2×#95—113no—
148C2×#95—113no—
149C2×#95—113no—
150C2×#95—113no—
151C2×#95—113no—
152C2×#95—113no—
153C2×#95C2×D1113yes—
154C2×#95C2×D1113yes—
155C2×#95C2×D1111yescharacteristic
156C22×C11#53813yes—
157C22×C11#54213yes—
158C22×C11#54213yes—
159C22×C11#54313yes—
160C22×C11#54413yes—
161C22×C11#55113yes—
162C22×C11#55413yes—
163C22×C11#55713yes—
164C22×C11Q8211yescharacteristic
165C22×C11#56011yescharacteristic
166C22×C11#56013yes—
167C22×C11#56213yes—
168C22×C11#56313yes—
169C4×C11—42no—
170C4×C11—46no—
171C4×C11—83no—
172Dic11—42no—
173Dic11—42no—
174Dic11—46no—
175Dic11—83no—
176C22×Q8—114no—
177C22×Q8—443no—
178C22×Q8—443no—
179C23×C4—113no—
180C23×C4—111no—
181C23×C4—111no—
182C23×C4—113no—
183C23×C4C22×D1113yes—
184C23×C4C22×D1113yes—
185C23×C4C22×D1111yescharacteristic
186C2×C4⋊C4—226no—
187C2×C4⋊C4—226no—
188C2×C4⋊C4—226no—
189C2×C4⋊C4—443no—
190C2×C4⋊C4—443no—
191C2×C4⋊C4—443no—
192#95—43no—
193#95—43no—
194#95—443no—
195#95—443no—
196#95—443no—
197#95—443no—
198#95—443no—
199#95—443no—
200#95—443no—
201#95Dic2214yescomplemented
202C2×C11#274213yes—
203C2×C11#276011yescharacteristic
204C2×C11#279913yes—
205C2×C11#280613yes—
206C2×C11#283013yes—
207C2×C11#284211yescharacteristic
208C2×C11#284311yescharacteristic
209C24C23×D1111yescharacteristic
210C2×Q8—4412no—
211C2×Q8—444no—
212C2×Q8—4412no—
213C22×C4—23no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—23no—
221C22×C4—23no—
222C22×C4—23no—
223C22×C4—23no—
224C22×C4—23no—
225C22×C4—23no—
226C22×C4—23no—
227C22×C4—23no—
228C22×C4—112no—
229C22×C4—112no—
230C22×C4—116no—
231C22×C4—223no—
232C22×C4—223no—
233C22×C4—223no—
234C22×C4—223no—
235C22×C4—223no—
236C22×C4—223no—
237C22×C4—223no—
238C22×C4—223no—
239C22×C4—223no—
240C22×C4—223no—
241C22×C4—223no—
242C22×C4—223no—
243C22×C4—223no—
244C22×C4—223no—
245C22×C4—223no—
246C22×C4—223no—
247C22×C4—223no—
248C22×C4C2×Dic2216yes—
249C22×C4Q8×D1112yes—
250C4⋊C4—4412no—
251C4⋊C4—4412no—
252C11#1729511yescharacteristic, complemented, Sylow
253C23C22×Dic2211yescharacteristic
254C23#6703713yes—
255C23C2×Q8×D1111yescharacteristic
256C23#41×D1113yes—
257C23#6704211yescharacteristic
258C23#6704213yes—
259C23#6704313yes—
260Q8—4416no—
261C2×C4—26no—
262C2×C4—26no—
263C2×C4—26no—
264C2×C4—26no—
265C2×C4—43no—
266C2×C4—41no—
267C2×C4—43no—
268C2×C4—43no—
269C2×C4—43no—
270C2×C4—43no—
271C2×C4—43no—
272C2×C4—43no—
273C2×C4—43no—
274C2×C4—43no—
275C2×C4—43no—
276C2×C4—43no—
277C2×C4—43no—
278C2×C4—226no—
279C2×C4—226no—
280C2×C4—226no—
281C2×C4—226no—
282C2×C4—226no—
283C2×C4—443no—
284C2×C4—443no—
285C2×C4—443no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—443no—
289C2×C4—443no—
290C2×C4—443no—
291C2×C4—443no—
292C2×C4—443no—
293C2×C4—443no—
294C2×C4—443no—
295C2×C4—443no—
296C2×C4—443no—
297C2×C4—443no—
298C22#1062305013yes—
299C22#1062307013yes—
300C22Q8×Dic2211yescharacteristic
301C22#1062315113yes—
302C22#1062316513yes—
303C22#1062319313yes—
304C22#1062319813yes—
305C22#1062320013yes—
306C22#1062321613yes—
307C22#1062323513yes—
308C22#1062323613yes—
309C22#1062324211yescharacteristic
310C22#1062324313yes—
311C4—46no—
312C4—42no—
313C4—83no—
314C4—446no—
315C4—442no—
316C4—442no—
317C4—883no—
318C2#1307574213yes—
319C2#1307599411yescharacteristic
320C2#1307650113yes—
321C2#1307657413yes—
322C2#1307676113yes—
323C2#1307687911yescharacteristic
324C2#1307688311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1443C2
hypercenter#1443D11
hypocenterC11#17295
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1443

Complements

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

NH ≅ G/Ntype
39. C11×#95Q8semidirect
201. #95Dic22semidirect
252. C11#17295semidirect

Maximal subgroups

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

subgroupindex
#130668862
#130668822
#130668812
#130668782
#130668682
C11×#14432
#1729511