Finite Group Databasebeta

← #14680435

Subgroups — #14680435

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622550C211yesmaximal, characteristic
2C2×C4×C4⋊Dic11C211yesmaximal, characteristic
3#13066884C212yesmaximal
4#13066884C212yesmaximal
5#13066869C214yesmaximal
6#13066848C214yesmaximal
7C22×C11×#125C211yesmaximal, characteristic
8C2×C11×#125—24no—
9C2×C11×#125—24no—
10C2×C11×#125C418yescomplemented
11C22×C11×C4⋊C4C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2218yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2218yes—
24#10622550—24no—
25C4×C4⋊Dic11—24no—
26C23×C4×C11C2312yes—
27C23×C4×C11C2312yes—
28C23×C4×C11C2311yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×Dic11C2314yes—
32C23×Dic11C2314yes—
33C11×#125—232no—
34C2×C11×C4⋊C4—24no—
35C2×C11×C4⋊C4—24no—
36C2×C11×C4⋊C4—22no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—24no—
41C2×C11×C4⋊C4—24no—
42C2×C11×C4⋊C4C2×C418yes—
43C2×C11×C4⋊C4C2×C418yes—
44C2×C11×C4⋊C4C2×C414yes—
45C2×C11×C4⋊C4C2×C414yes—
46C2×C42×C11C2×C414yes—
47C2×C42×C11D414yes—
48C2×C42×C11D414yes—
49C2×C4⋊Dic11—24no—
50C2×C4⋊Dic11—28no—
51C2×C4×Dic11—24no—
52C2×C4×Dic11—44no—
53C11⋊#95—24no—
54C11⋊#95—24no—
55C11⋊#95—24no—
56C11⋊#95—24no—
57C11⋊#95—216no—
58C11⋊#95—48no—
59#14289—111nomaximal, Sylow
60C24×C11C2411yescharacteristic
61C22×C4×C11—24no—
62C22×C4×C11—22no—
63C22×C4×C11—24no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—28no—
70C22×C4×C11—24no—
71C22×C4×C11—24no—
72C22×C4×C11C22×C414yes—
73C22×C4×C11C22×C414yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C412yes—
76C22×C4×C11C22×C412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D412yes—
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—24no—
86C22×Dic11—28no—
87C22×Dic11—28no—
88C22×Dic11—24no—
89C22×Dic11—28no—
90C22×Dic11—28no—
91C22×Dic11—24no—
92C22×Dic11#4118yes—
93C11×C4⋊C4—28no—
94C11×C4⋊C4—216no—
95C11×C4⋊C4—216no—
96C11×C4⋊C4—28no—
97C42×C11C22⋊C4116yes—
98C4⋊Dic11—216no—
99C4×Dic11—48no—
100C22×#125D1111yescharacteristic
101C2×#383—111no—
102C2×C4×C4⋊C4—111no—
103#1445—112no—
104#1445—112no—
105#1441—114no—
106#1436—114no—
107C23×C11C23×C411yescharacteristic
108C23×C11C22×D411yescharacteristic
109C23×C11C22×D411yescharacteristic
110C23×C11C2×#4114yes—
111C23×C11H(5,𝔽2)12yes—
112C23×C112−1+414yes—
113C23×C112−1+412yes—
114C2×C4×C11—24no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—28no—
127C2×C4×C11—28no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—44no—
133C2×C4×C11C2×C22⋊C414yes—
134C2×C4×C11C2×C22⋊C414yes—
135C2×C4×C11C2×C22⋊C414yes—
136C2×Dic11—28no—
137C2×Dic11—216no—
138C2×Dic11—44no—
139C2×Dic11—44no—
140C2×Dic11—48no—
141C2×Dic11—44no—
142C2×Dic11—44no—
143C2×Dic11—44no—
144C2×Dic11—48no—
145C2×Dic11—48no—
146C2×#125—24no—
147C2×#125—24no—
148C2×#125Dic1118yescomplemented
149C22×C4⋊C4—112no—
150C22×C4⋊C4C2×D1112yes—
151C22×C4⋊C4C2×D1112yes—
152C22×C4⋊C4C2×D1111yescharacteristic
153C22×C4⋊C4C2×D1111yescharacteristic
154C22×C42—112no—
155C22×C42C2×D1111yescharacteristic
156#383—224no—
157C4×C4⋊C4—224no—
158C2×#95—112no—
159C2×#95—118no—
160C2×#95—112no—
161C2×#95—112no—
162C2×#95—112no—
163C2×#95—118no—
164C22×C11C22×C22⋊C411yescharacteristic
165C22×C11C4×#4112yes—
166C22×C11#51912yes—
167C22×C11#52012yes—
168C22×C11#52512yes—
169C22×C11#53212yes—
170C22×C11#53511yescharacteristic
171C22×C11#53612yes—
172C22×C11#53612yes—
173C22×C11#53611yescharacteristic
174C22×C11#53712yes—
175C22×C11#53918yes—
176C22×C11#54118yes—
177C4×C11—24no—
178C4×C11—24no—
179C4×C11—24no—
180C4×C11—44no—
181C4×C11—44no—
182Dic11—48no—
183Dic11—84no—
184C23×C4—114no—
185C23×C4—114no—
186C23×C4C22×D1112yes—
187C23×C4C22×D1112yes—
188C23×C4C22×D1111yescharacteristic
189C23×C4C22×D1111yescharacteristic
190C23×C4C22×D1111yescharacteristic
191#125—232no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—228no—
201C2×C4⋊C4—224no—
202C2×C4⋊C4C2×Dic1118yes—
203C2×C4⋊C4C2×Dic1118yes—
204C2×C4⋊C4C2×Dic1114yes—
205C2×C4⋊C4C2×Dic1114yes—
206C2×C42—224no—
207C2×C42—444no—
208C2×C42C2×Dic1114yes—
209C2×C42C22⋊D1114yes—
210C2×C42C22⋊D1114yes—
211#95—2216no—
212#95—224no—
213#95—224no—
214#95—224no—
215#95—224no—
216#95—448no—
217C2×C11#229711yescharacteristic
218C2×C11#231011yescharacteristic
219C2×C11#231111yescharacteristic
220C2×C11#233614yes—
221C2×C11#263312yes—
222C2×C11#263412yes—
223C2×C11#266414yes—
224C24C23×D1111yescharacteristic
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—28no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—118no—
237C22×C4—228no—
238C22×C4—224no—
239C22×C4—228no—
240C22×C4—224no—
241C22×C4—228no—
242C22×C4—228no—
243C22×C4—224no—
244C22×C4—224no—
245C22×C4—224no—
246C22×C4C22×Dic1114yes—
247C22×C4C22×Dic1114yes—
248C22×C4C22×Dic1112yes—
249C22×C4C22×Dic1112yes—
250C22×C4C22×Dic1112yes—
251C22×C4C2×C22⋊D1112yes—
252C22×C4C2×C22⋊D1112yes—
253C22×C4C2×C22⋊D1112yes—
254C22×C4C2×C22⋊D1112yes—
255C22×C4C2×C22⋊D1112yes—
256C22×C4C2×C22⋊D1112yes—
257C4⋊C4—28no—
258C4⋊C4—216no—
259C4⋊C4—216no—
260C4⋊C4—28no—
261C4⋊C4—2216no—
262C42—448no—
263C42C22⋊Dic11116yes—
264C11#1428911yescharacteristic, complemented, Sylow
265C23#6704014yes—
266C23#41×D1114yes—
267C23#6704212yes—
268C23#6704312yes—
269C23C23×Dic1111yescharacteristic
270C23C22×C22⋊D1111yescharacteristic
271C23C22×C22⋊D1111yescharacteristic
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—24no—
282C2×C4—28no—
283C2×C4—28no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—228no—
292C2×C4—2216no—
293C2×C4—444no—
294C2×C4—444no—
295C2×C4—448no—
296C2×C4—444no—
297C2×C4—444no—
298C2×C4—444no—
299C2×C4—448no—
300C2×C4—448no—
301C2×C4C2×C22⋊Dic1114yes—
302C2×C4C2×C22⋊Dic1114yes—
303C2×C4C2×C22⋊Dic1114yes—
304C22#1062322318yes—
305C22#1062322718yes—
306C22#1062334312yes—
307C22#1062334712yes—
308C22#1062334712yes—
309C22#1062335611yescharacteristic
310C22#41×Dic1112yes—
311C22#1062335812yes—
312C22#1062335912yes—
313C22#1062336111yescharacteristic
314C22#1062336312yes—
315C22#1062336412yes—
316C22C22×C22⋊Dic1111yescharacteristic
317C4—24no—
318C4—24no—
319C4—24no—
320C4—44no—
321C4—44no—
322C4—448no—
323C4—884no—
324C2#1307110711yescharacteristic
325C2#1307120211yescharacteristic
326C2#1307120811yescharacteristic
327C2#1307142214yes—
328C2#1307448512yes—
329C2#1307449312yes—
330C2#1307477714yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#125C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×#125D11
hypocenterC11#14289
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
10. C2×C11×#125C4semidirect
148. C2×#125Dic11semidirect
264. C11#14289semidirect

Maximal subgroups

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

subgroupindex
C2×#106225502
C2×C4×C4⋊Dic112
#130668842
#130668692
#130668482
C22×C11×#1252
#1428911