Finite Group Databasebeta

← #14680947

Subgroups — #14680947

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622824C212yesmaximal
2C2×#10622825C212yesmaximal
3#13066869C218yesmaximal, complemented
4#13066839C212yesmaximal
5C23×C11×C4⋊C4C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C24×C4×C11C2211yescharacteristic
8C24×C4×C11C2211yescharacteristic
9C22×C11×C4⋊C4—28no—
10C22×C11×C4⋊C4C418yescomplemented
11C22×C11×C4⋊C4C2214yes—
12C22×C22⋊Dic11C2214yes—
13C22×C4⋊Dic11C2214yes—
14#10622825—28no—
15#10622824—28no—
16C2×C11⋊#95C2214yes—
17C2×C11⋊#95C2218yes—
18C2×C11⋊#95C2218yes—
19C25×C11C2311yescharacteristic
20C23×C4×C11—24no—
21C23×C4×C11—24no—
22C23×C4×C11—24no—
23C23×C4×C11—44no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C414yes—
26C23×C4×C11C2×C414yes—
27C23×C4×C11C2×C414yes—
28C23×C4×C11D414yes—
29C23×C4×C11D418yes—
30C23×C4×C11Q814yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×Dic11C2318yes—
35C2×C11×C4⋊C4—232no—
36C2×C11×C4⋊C4—28no—
37C2×C11×C4⋊C4—28no—
38C2×C11×C4⋊C4C2×C4116yes—
39C2×C22⋊Dic11—28no—
40C2×C22⋊Dic11—28no—
41C2×C22⋊Dic11—28no—
42C2×C4⋊Dic11—28no—
43C2×C4⋊Dic11—48no—
44C11⋊#95—216no—
45C11⋊#95—28no—
46C11⋊#95—48no—
47#14339—111nomaximal, Sylow
48C24×C11—24no—
49C24×C11—24no—
50C24×C11C22×C412yes—
51C24×C11C2×D414yes—
52C24×C11C2×D412yes—
53C24×C11C2×Q812yes—
54C24×C11#4114yes—
55C24×C11C2411yescharacteristic
56C22×C4×C11—28no—
57C22×C4×C11—28no—
58C22×C4×C11—216no—
59C22×C4×C11—216no—
60C22×C4×C11—24no—
61C22×C4×C11—24no—
62C22×C4×C11—28no—
63C22×C4×C11—28no—
64C22×C4×C11—24no—
65C22×C4×C11—28no—
66C22×C4×C11—48no—
67C22×C4×C11—48no—
68C22×C4×C11—416no—
69C22×C4×C11—416no—
70C22×C4×C11C22⋊C4116yes—
71C22×C4×C11C4⋊C4116yescomplemented
72C22×C4×C11C22×C414yes—
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C414yes—
75C22×C4×C11C2×D414yes—
76C22×C4×C11C2×D414yes—
77C22×C4×C11C2×D414yes—
78C22×C4×C11C2×Q814yes—
79C22×Dic11—28no—
80C22×Dic11—28no—
81C22×Dic11—28no—
82C22×Dic11—216no—
83C22×Dic11—216no—
84C11×C4⋊C4—232no—
85C22⋊Dic11—416no—
86C4⋊Dic11—416no—
87C23×C4⋊C4D1111yescharacteristic
88C2×#381—112no—
89C2×#380—112no—
90#1441—118no—
91C22⋊#95—112no—
92C23×C11—24no—
93C23×C11—24no—
94C23×C11—28no—
95C23×C11—28no—
96C23×C11—28no—
97C23×C11—216no—
98C23×C11—28no—
99C23×C11C2×C22⋊C414yes—
100C23×C11C2×C4⋊C414yes—
101C23×C11#11714yes—
102C23×C11#12118yes—
103C23×C11C22⋊Q818yes—
104C23×C11C23×C411yescharacteristic
105C23×C11C22×D411yescharacteristic
106C23×C11C22×D412yes—
107C23×C11C22×Q811yescharacteristic
108C23×C11C2×#4112yes—
109C23×C11H(5,𝔽2)14yes—
110C23×C112−1+414yes—
111C2×C4×C11—24no—
112C2×C4×C11—24no—
113C2×C4×C11—28no—
114C2×C4×C11—28no—
115C2×C4×C11—28no—
116C2×C4×C11—28no—
117C2×C4×C11—28no—
118C2×C4×C11—232no—
119C2×C4×C11—24no—
120C2×C4×C11—28no—
121C2×C4×C11—416no—
122C2×C4×C11—416no—
123C2×C4×C11—48no—
124C2×C4×C11C2×C22⋊C418yes—
125C2×C4×C11C2×C4⋊C418yes—
126C2×Dic11—48no—
127C2×Dic11—48no—
128C2×Dic11—48no—
129C2×Dic11—416no—
130C2×Dic11—416no—
131C24×C4C2×D1111yescharacteristic
132C24×C4C2×D1111yescharacteristic
133C24×C4C2×D1111yescharacteristic
134C22×C4⋊C4—28no—
135C22×C4⋊C4—114no—
136C22×C4⋊C4Dic1118yescomplemented
137C22×C4⋊C4C2×D1114yes—
138C22×C22⋊C4—114no—
139#381—228no—
140#380—228no—
141C2×#95—114no—
142C2×#95—118no—
143C2×#95—118no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—28no—
147C22×C11—28no—
148C22×C11—216no—
149C22×C11—216no—
150C22×C11#38018yes—
151C22×C11C22×C22⋊C411yescharacteristic
152C22×C11C22×C4⋊C411yescharacteristic
153C22×C11C2×#11711yescharacteristic
154C22×C11#51812yes—
155C22×C11#51912yes—
156C22×C11C2×#12112yes—
157C22×C11C2×C22⋊Q812yes—
158C22×C11#53414yes—
159C22×C11#53614yes—
160C22×C11#53714yes—
161C22×C11#53918yes—
162C22×C11#54414yes—
163C4×C11—28no—
164C4×C11—28no—
165C4×C11—44no—
166Dic11—88no—
167C25C22×D1111yescharacteristic
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—44no—
172C23×C4—44no—
173C23×C4—118no—
174C23×C4Dic2214yes—
175C23×C4D4414yes—
176C23×C4C2×Dic1114yes—
177C23×C4C2×Dic1114yes—
178C23×C4C2×Dic1114yes—
179C23×C4C22⋊D1118yes—
180C23×C4C22×D1112yes—
181C23×C4C22×D1112yes—
182C23×C4C22×D1112yes—
183C2×C4⋊C4—232no—
184C2×C4⋊C4—28no—
185C2×C4⋊C4—28no—
186C2×C4⋊C4—228no—
187C2×C4⋊C4—448no—
188C2×C4⋊C4C2×Dic11116yes—
189C2×C22⋊C4—228no—
190C2×C22⋊C4—228no—
191C2×C22⋊C4—228no—
192#95—2216no—
193#95—228no—
194#95—448no—
195C2×C11—28no—
196C2×C11C2×#38011yescharacteristic
197C2×C11#230811yescharacteristic
198C2×C11#231011yescharacteristic
199C2×C11#231312yes—
200C2×C11#231612yes—
201C2×C11#261814yes—
202C2×C11#262714yes—
203C24—24no—
204C24—24no—
205C24C2×Dic2212yes—
206C24C2×D4412yes—
207C24#433914yes—
208C24C22×Dic1112yes—
209C24C2×C22⋊D1114yes—
210C24C23×D1111yescharacteristic
211C22×C4—216no—
212C22×C4—28no—
213C22×C4—216no—
214C22×C4—28no—
215C22×C4—24no—
216C22×C4—28no—
217C22×C4—24no—
218C22×C4—28no—
219C22×C4—28no—
220C22×C4—24no—
221C22×C4—48no—
222C22×C4—48no—
223C22×C4—416no—
224C22×C4—416no—
225C22×C4—228no—
226C22×C4—228no—
227C22×C4—2216no—
228C22×C4—2216no—
229C22×C4—228no—
230C22×C4C4⋊Dic11116yescomplemented
231C22×C4C22⋊Dic11116yes—
232C22×C4C2×Dic2214yes—
233C22×C4C2×D4414yes—
234C22×C4C22×Dic1114yes—
235C22×C4C22×Dic1114yes—
236C22×C4C22×Dic1114yes—
237C22×C4C2×C22⋊D1114yes—
238C22×C4C2×C22⋊D1114yes—
239C4⋊C4—232no—
240C4⋊C4—4416no—
241C22⋊C4—4416no—
242C11#1433911yescharacteristic, complemented, Sylow
243C23—28no—
244C23—28no—
245C23—216no—
246C23—24no—
247C23—28no—
248C23—24no—
249C23—28no—
250C23#6697718yes—
251C23C2×C4⋊Dic1114yes—
252C23#6697914yes—
253C23#6698318yes—
254C23C2×C22⋊Dic1114yes—
255C23C22×Dic2211yescharacteristic
256C23C22×D4411yescharacteristic
257C23C2×#433912yes—
258C23#6703714yes—
259C23#6704014yes—
260C23C23×Dic1111yescharacteristic
261C23C22×C22⋊D1112yes—
262C2×C4—28no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—28no—
268C2×C4—232no—
269C2×C4—24no—
270C2×C4—28no—
271C2×C4—24no—
272C2×C4—416no—
273C2×C4—416no—
274C2×C4—48no—
275C2×C4—4416no—
276C2×C4—4416no—
277C2×C4—448no—
278C2×C4—448no—
279C2×C4—448no—
280C2×C4C2×C4⋊Dic1118yes—
281C2×C4C2×C22⋊Dic1118yes—
282C22—24no—
283C22—24no—
284C22—28no—
285C22—28no—
286C22—216no—
287C22—216no—
288C22#1062282518yes—
289C22#1062303114yes—
290C22#1062304114yes—
291C22#1062304618yes—
292C22C2×#6697712yes—
293C22C22×C4⋊Dic1111yescharacteristic
294C22C2×#6697911yescharacteristic
295C22C2×#6698312yes—
296C22#1062332912yes—
297C22#1062333514yes—
298C22#1062334312yes—
299C22#1062334714yes—
300C22C22×C22⋊Dic1111yescharacteristic
301C4—28no—
302C4—28no—
303C4—44no—
304C4—888no—
305C2—28no—
306C2C2×#1062282511yescharacteristic
307C2#1307119411yescharacteristic
308C2#1307120211yescharacteristic
309C2#1307121912yes—
310C2#1307123412yes—
311C2#1307435814yes—
312C2#1307442914yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC23×C4⋊C4D11
hypocenterC11#14339
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13066869C2semidirect
10. C22×C11×C4⋊C4C4semidirect
71. C22×C4×C11C4⋊C4semidirect
136. C22×C4⋊C4Dic11semidirect
230. C22×C4C4⋊Dic11semidirect
242. C11#14339semidirect

Maximal subgroups

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

subgroupindex
C2×#106228242
C2×#106228252
#130668692
#130668392
C23×C11×C4⋊C42
#1433911