Finite Group Databasebeta

← #14681034

Subgroups — #14681034

Order 2816.

1550 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622589C213yesmaximal
2C2×#10622263C213yesmaximal
3C2×#10622261C211yesmaximal, characteristic
4#13066881C211yesmaximal, characteristic
5#13066880C213yesmaximal
6#13066879C213yesmaximal
7C11×#1444C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2213yes—
9C22×C4⋊Dic11C2213yes—
10C22×Dic11⋊C4C2211yescharacteristic
11C22×Dic11⋊C4C2213yes—
12C22×Dic11⋊C4C2216yes—
13C22×C4×Dic11C2213yes—
14C2×C11×#95C2213yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11⋊#95C2213yes—
17C2×C11⋊#95C2213yes—
18C2×C11⋊#95C2213yes—
19C2×C11⋊#95C2213yes—
20#10622589—212no—
21#10622263—212no—
22#10622261C418yescomplemented
23C23×C4×C11C2313yes—
24C23×C4×C11C2311yescharacteristic
25C23×C4×C11C2313yes—
26C23×Dic11C2313yes—
27C23×Dic11C2311yescharacteristic
28C23×Dic11C2313yes—
29C23×Dic11C2311yescharacteristic
30C2×C11×C4⋊C4—26no—
31C2×C11×C4⋊C4—46no—
32C2×C4⋊Dic11—26no—
33C2×C4⋊Dic11—46no—
34C2×Dic11⋊C4—26no—
35C2×Dic11⋊C4—26no—
36C2×Dic11⋊C4—212no—
37C2×Dic11⋊C4—212no—
38C2×Dic11⋊C4—46no—
39C2×Dic11⋊C4—46no—
40C2×C4×Dic11C2×C4112yes—
41C2×C4×Dic11D4112yes—
42C2×C4×Dic11Q8112yes—
43C11×#95—26no—
44C11×#95C2×C414yes—
45C11⋊#95—26no—
46C11⋊#95—26no—
47C11⋊#95—26no—
48C11⋊#95C2×C4112yes—
49#14354—111nomaximal, Sylow
50C24×C11C2411yescharacteristic
51C22×C4×C11—26no—
52C22×C4×C11—26no—
53C22×C4×C11—23no—
54C22×C4×C11—23no—
55C22×C4×C11—26no—
56C22×C4×C11—23no—
57C22×C4×C11—26no—
58C22×C4×C11—23no—
59C22×C4×C11—21no—
60C22×C4×C11—23no—
61C22×C4×C11C22×C416yes—
62C22×C4×C11C2×D416yes—
63C22×C4×C11C2×Q816yes—
64C22×Dic11—23no—
65C22×Dic11—23no—
66C22×Dic11—26no—
67C22×Dic11—23no—
68C22×Dic11—23no—
69C22×Dic11—23no—
70C22×Dic11—26no—
71C22×Dic11—23no—
72C22×Dic11—23no—
73C22×Dic11—23no—
74C22×Dic11—21no—
75C22×Dic11—23no—
76C22×Dic11C22×C416yes—
77C22×Dic11C22×C412yes—
78C22×Dic11C2×D416yes—
79C22×Dic11C2×D416yes—
80C22×Dic11C2×Q816yes—
81C22×Dic11C2×Q816yes—
82C11×C4⋊C4—412no—
83C4⋊Dic11—412no—
84Dic11⋊C4—424no—
85Dic11⋊C4—44no—
86Dic11⋊C4—412no—
87C4×Dic11C4⋊C4148yescomplemented
88C2×#384—113no—
89C2×#382—113no—
90C2×#376—111no—
91#1444—113no—
92#1444—111no—
93#1444—113no—
94#1444D1111yescharacteristic
95C23×C11C23×C411yescharacteristic
96C23×C11C22×D413yes—
97C23×C11C22×Q813yes—
98C23×C11H(5,𝔽2)13yes—
99C23×C11H(5,𝔽2)11yescharacteristic
100C23×C112−1+411yescharacteristic
101C23×C112−1+413yes—
102C2×C4×C11—212no—
103C2×C4×C11—26no—
104C2×C4×C11—26no—
105C2×C4×C11—212no—
106C2×C4×C11—43no—
107C2×C4×C11—41no—
108C2×C4×C11—46no—
109C2×C4×C11—46no—
110C2×C4×C11—43no—
111C2×C4×C11—43no—
112C2×C4×C11—43no—
113C2×C4×C11—43no—
114C2×C4×C11C2×C4⋊C4112yes—
115C2×Dic11—26no—
116C2×Dic11—26no—
117C2×Dic11—26no—
118C2×Dic11—26no—
119C2×Dic11—26no—
120C2×Dic11—26no—
121C2×Dic11—43no—
122C2×Dic11—41no—
123C2×Dic11—46no—
124C2×Dic11—46no—
125C2×Dic11—43no—
126C2×Dic11—43no—
127C2×Dic11—43no—
128C2×Dic11—43no—
129C2×Dic11C2×C4⋊C4112yes—
130C2×Dic11C2×C4⋊C4112yes—
131C2×Dic11#12714yes—
132C2×Dic11C4⋊Q8112yes—
133C22×C4⋊C4—111no—
134C22×C4⋊C4—113no—
135C22×C4⋊C4—116no—
136C22×C4⋊C4—113no—
137C22×C4⋊C4C2×D1113yes—
138C22×C42—113no—
139#384—2212no—
140#382—2212no—
141#376—118no—
142C2×#95—113no—
143C2×#95—113no—
144C2×#95—113no—
145C2×#95—113no—
146C2×#95C2×D1113yes—
147C2×#95C2×D1111yescharacteristic
148C22×C11C22×C4⋊C413yes—
149C22×C11#52013yes—
150C22×C11#52011yescharacteristic
151C22×C11C2×#12711yescharacteristic
152C22×C11C2×C4⋊Q813yes—
153C22×C11#53513yes—
154C22×C11#53513yes—
155C22×C11#53613yes—
156C22×C11#53613yes—
157C22×C11#54413yes—
158C22×C11#54416yes—
159C22×C11#54413yes—
160C4×C11—212no—
161C4×C11—83no—
162C4×C11—81no—
163Dic11—212no—
164Dic11—83no—
165Dic11—81no—
166Dic11#38418yes—
167C23×C4—111no—
168C23×C4—113no—
169C23×C4—113no—
170C23×C4—111no—
171C23×C4C22×D1113yes—
172C23×C4C22×D1111yescharacteristic
173C23×C4C22×D1113yes—
174C2×C4⋊C4—26no—
175C2×C4⋊C4—46no—
176C2×C4⋊C4—226no—
177C2×C4⋊C4—226no—
178C2×C4⋊C4—2212no—
179C2×C4⋊C4—2212no—
180C2×C4⋊C4—226no—
181C2×C4⋊C4—446no—
182C2×C4⋊C4—446no—
183C2×C4⋊C4—446no—
184C2×C42—1112no—
185C2×C42—1112no—
186C2×C42—1112no—
187#95—26no—
188#95—1112no—
189#95—226no—
190#95—226no—
191#95—226no—
192#95C4×D1114yes—
193C2×C11C2×#38411yescharacteristic
194C2×C11#231713yes—
195C2×C11#231713yes—
196C2×C11#265711yescharacteristic
197C2×C11#265811yescharacteristic
198C2×C11#266013yes—
199C2×C11#266013yes—
200C24C23×D1111yescharacteristic
201C22×C4—26no—
202C22×C4—26no—
203C22×C4—23no—
204C22×C4—23no—
205C22×C4—26no—
206C22×C4—23no—
207C22×C4—26no—
208C22×C4—21no—
209C22×C4—23no—
210C22×C4—23no—
211C22×C4—112no—
212C22×C4—116no—
213C22×C4—116no—
214C22×C4—116no—
215C22×C4—116no—
216C22×C4—116no—
217C22×C4—223no—
218C22×C4—223no—
219C22×C4—223no—
220C22×C4—223no—
221C22×C4—223no—
222C22×C4—223no—
223C22×C4—226no—
224C22×C4—223no—
225C22×C4—226no—
226C22×C4—221no—
227C22×C4—223no—
228C22×C4—223no—
229C22×C4C2×C4×D1116yes—
230C22×C4D4×D1116yes—
231C22×C4Q8×D1116yes—
232C4⋊C4—412no—
233C4⋊C4—4412no—
234C4⋊C4—444no—
235C4⋊C4—4412no—
236C4⋊C4—4424no—
237C42—1148no—
238C11#1435411yescharacteristic, complemented, Sylow
239C23C22×C4×D1111yescharacteristic
240C23C2×D4×D1113yes—
241C23#6703713yes—
242C23C2×Q8×D1113yes—
243C23#6704011yescharacteristic
244C23#6704211yescharacteristic
245C23#6704313yes—
246C2×C4—212no—
247C2×C4—26no—
248C2×C4—212no—
249C2×C4—26no—
250C2×C4—43no—
251C2×C4—41no—
252C2×C4—46no—
253C2×C4—43no—
254C2×C4—46no—
255C2×C4—43no—
256C2×C4—43no—
257C2×C4—43no—
258C2×C4—114no—
259C2×C4—1112no—
260C2×C4—1112no—
261C2×C4—1112no—
262C2×C4—226no—
263C2×C4—226no—
264C2×C4—226no—
265C2×C4—226no—
266C2×C4—226no—
267C2×C4—226no—
268C2×C4—443no—
269C2×C4—441no—
270C2×C4—446no—
271C2×C4—443no—
272C2×C4—446no—
273C2×C4—443no—
274C2×C4—443no—
275C2×C4—443no—
276C2×C4C4⋊C4×D11112yes—
277C22C2×C4⋊C4×D1113yes—
278C22#1062307713yes—
279C22#1062310511yescharacteristic
280C22#1062312313yes—
281C22#1062313813yes—
282C22#1062315416yes—
283C22#1062315913yes—
284C22#1062317913yes—
285C22#1062322013yes—
286C22D11×#12711yescharacteristic
287C22D11×C4⋊Q813yes—
288C22#1062326013yes—
289C4—212no—
290C4—83no—
291C4—81no—
292C4—118no—
293C4—2212no—
294C4—883no—
295C4—881no—
296C2D11×#38411yescharacteristic
297C2#1307123513yes—
298C2#1307123813yes—
299C2#1307472111yescharacteristic
300C2#1307472511yescharacteristic
301C2#1307473413yes—
302C2#1307473913yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11#14354
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
22. #10622261C4semidirect
87. C4×Dic11C4⋊C4semidirect
238. C11#14354semidirect

Maximal subgroups

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

subgroupindex
C2×#106225892
C2×#106222632
C2×#106222612
#130668812
#130668802
#130668792
C11×#14442
#1435411