Finite Group Databasebeta

← #14763224

Subgroups — #14763224

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic
2#13071214C211yesmaximal, characteristic
3#13069601C214yesmaximal, complemented
4#13069600C214yesmaximal, complemented
5#13068688C214yesmaximal
6C11×#2312C211yesmaximal, characteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic11C2212yes—
9C2×#66977C2212yes—
10C2×#66977C2212yes—
11#10623014—24no—
12#10623014—24no—
13C2×#66931C414yescomplemented
14C2×#66931C414yescomplemented
15C11×#388—24no—
16C11×#380C2212yes—
17C11×#379C2212yes—
18C4×C11×C22⋊C4C2212yes—
19#10622860C2212yes—
20#10622825C2212yes—
21C4×C22⋊Dic11C2212yes—
22#10622564—24no—
23#10622165C22116yes—
24C25×C11C2311yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2×C412yes—
28C23×Dic11C2×C412yes—
29C22×Dic22C2×C412yes—
30C22×Dic22C2×C412yes—
31C2×C11×C4⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4C2×C414yes—
35C2×C11×C22⋊C4D414yes—
36C2×C11×C22⋊C4D414yes—
37C2×C11×C22⋊C4C2314yes—
38C2×C42×C11—22no—
39C2×C22⋊Dic11—24no—
40C2×C22⋊Dic11—24no—
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—22no—
43C2×C22⋊Dic11C2×C414yes—
44C2×C22⋊Dic11C2314yes—
45C2×C22⋊Dic11C2314yes—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11C2×C412yes—
48C2×C4⋊Dic11C2×C412yes—
49#66977—24no—
50#66977—24no—
51#66977—24no—
52#66977—24no—
53C2×Dic11⋊C4C2×C414yes—
54C2×Dic11⋊C4C2×C414yes—
55C2×C4×Dic11—22no—
56#66931—216no—
57#66931—216no—
58C11×#95—22no—
59C11×#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62#21827—111nomaximal, Sylow
63C24×C11—24no—
64C24×C11—81no—
65C24×C11—81no—
66C24×C11C22×C412yes—
67C24×C11C2×D412yes—
68C24×C11C2×D412yes—
69C24×C11C2411yescharacteristic
70C22×C4×C11—24no—
71C22×C4×C11—81no—
72C22×C4×C11—81no—
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C2×D412yes—
76C22×C4×C11C2×D412yes—
77C22×C4×C11C2×D412yes—
78C22×C4×C11C2×D412yes—
79C22×Dic11—24no—
80C22×Dic11—24no—
81C22×Dic11—24no—
82C22×Dic11—82no—
83C22×Dic11—82no—
84C22×Dic11C22×C414yes—
85C22×Dic11C22×C414yes—
86C2×Dic22—24no—
87C2×Dic22—24no—
88C2×Dic22—82no—
89C2×Dic22—82no—
90C11×C4⋊C4—82no—
91C11×C22⋊C4—28no—
92C11×C22⋊C4—82no—
93C11×C22⋊C4—82no—
94C11×C22⋊C4C22⋊C4116yes—
95C42×C11—82no—
96C22⋊Dic11—28no—
97C22⋊Dic11—24no—
98C22⋊Dic11—24no—
99C22⋊Dic11—28no—
100C22⋊Dic11—82no—
101C22⋊Dic11—82no—
102C4⋊Dic11—24no—
103C4⋊Dic11—24no—
104C4⋊Dic11—82no—
105Dic11⋊C4—28no—
106Dic11⋊C4—28no—
107C4×Dic11—82no—
108C2×#543—111no—
109#2312—111no—
110#2312D1111yescharacteristic
111#1996—114no—
112#1996—114no—
113#1819—114no—
114C23×C11—24no—
115C23×C11—24no—
116C23×C11—24no—
117C23×C11—42no—
118C23×C11—42no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—88no—
126C23×C11C2×C22⋊C414yes—
127C23×C11C23×C411yescharacteristic
128C23×C11C22×D411yescharacteristic
129C23×C11C22×D411yescharacteristic
130C23×C112−1+414yes—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—44no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11C2×C22⋊C414yes—
141C2×C4×C11C2×C22⋊C414yes—
142C2×Dic11—24no—
143C2×Dic11—24no—
144C2×Dic11—44no—
145C2×Dic11—44no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C2×Dic11—84no—
150C2×Dic11—84no—
151Dic22—84no—
152Dic22—84no—
153#543—224no—
154#543—224no—
155C2×C22⋊Q8—112no—
156C2×C22⋊Q8—112no—
157C2×C22⋊Q8—114no—
158C2×C22⋊Q8—114no—
159C22×C22⋊C4—112no—
160C22×C22⋊C4C2×D1111yescharacteristic
161#388—24no—
162#388—224no—
163#380—112no—
164#380C2×D1112yes—
165#379—112no—
166#379C2×D1112yes—
167C4×C22⋊C4—112no—
168C4×C22⋊C4C2×D1112yes—
169#342—1116no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—24no—
177C22×C11—24no—
178C22×C11—24no—
179C22×C11—44no—
180C22×C11—48no—
181C22×C11—84no—
182C22×C11—84no—
183C22×C11C22×C22⋊C411yescharacteristic
184C22×C11#51912yes—
185C22×C11#53612yes—
186C22×C11#53612yes—
187C4×C11—24no—
188C4×C11—24no—
189C4×C11—84no—
190Dic11—44no—
191Dic11—44no—
192Dic11—84no—
193C25C22×D1111yescharacteristic
194C22×Q8—112no—
195C22×Q8—112no—
196C23×C4—112no—
197C23×C4—112no—
198C23×C4C22×D1111yescharacteristic
199C23×C4C22×D1111yescharacteristic
200C22⋊Q8—224no—
201C22⋊Q8—224no—
202C22⋊Q8—224no—
203C22⋊Q8—224no—
204C22⋊Q8—2216no—
205C22⋊Q8—2216no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—114no—
208C2×C4⋊C4—114no—
209C2×C4⋊C4—112no—
210C2×C4⋊C4—112no—
211C2×C4⋊C4—222no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—114no—
215C2×C22⋊C4—114no—
216C2×C22⋊C4—114no—
217C2×C22⋊C4—224no—
218C2×C22⋊C4—224no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4—222no—
221C2×C22⋊C4C4×D1114yes—
222C2×C22⋊C4D4414yes—
223C2×C22⋊C4C22⋊D1114yes—
224C2×C22⋊C4C22×D1114yes—
225C2×C42—22no—
226C2×C42—222no—
227#95—22no—
228#95—22no—
229#95—222no—
230#95—222no—
231C2×C11—22no—
232C2×C11—22no—
233C2×C11—22no—
234C2×C11—44no—
235C2×C11#231011yescharacteristic
236C2×C11#288311yescharacteristic
237C2×C11#288311yescharacteristic
238C24—24no—
239C24—81no—
240C24—81no—
241C24C2×C4×D1112yes—
242C24C2×D4412yes—
243C24C2×C22⋊D1112yes—
244C24C23×D1111yescharacteristic
245C2×Q8—224no—
246C2×Q8—224no—
247C2×Q8—882no—
248C2×Q8—882no—
249C22×C4—24no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—114no—
253C22×C4—114no—
254C22×C4—224no—
255C22×C4—224no—
256C22×C4—224no—
257C22×C4—882no—
258C22×C4—882no—
259C22×C4C2×C4×D1112yes—
260C22×C4C2×C4×D1112yes—
261C22×C4C2×D4412yes—
262C22×C4C2×D4412yes—
263C22×C4C2×C22⋊D1112yes—
264C22×C4C2×C22⋊D1112yes—
265C4⋊C4—82no—
266C4⋊C4—228no—
267C4⋊C4—228no—
268C4⋊C4—224no—
269C4⋊C4—224no—
270C4⋊C4—882no—
271C22⋊C4—28no—
272C22⋊C4—82no—
273C22⋊C4—82no—
274C22⋊C4—228no—
275C22⋊C4—224no—
276C22⋊C4—224no—
277C22⋊C4—228no—
278C22⋊C4—882no—
279C22⋊C4—882no—
280C22⋊C4(C2×D11)⋊C4116yes—
281C42—82no—
282C42—882no—
283C11#2182711yescharacteristic, complemented, Sylow
284C23—24no—
285C23—24no—
286C23—24no—
287C23—41no—
288C23—41no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—88no—
296C23C2×(C2×D11)⋊C414yes—
297C23C22×C4×D1111yescharacteristic
298C23C22×D4411yescharacteristic
299C23#6704314yes—
300C23C22×C22⋊D1111yescharacteristic
301Q8—884no—
302Q8—884no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—224no—
313C2×C4—224no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4—444no—
317C2×C4—444no—
318C2×C4—444no—
319C2×C4—884no—
320C2×C4—884no—
321C2×C4C2×(C2×D11)⋊C414yes—
322C2×C4C2×(C2×D11)⋊C414yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—24no—
330C22—24no—
331C22—24no—
332C22—44no—
333C22—48no—
334C22—84no—
335C22—84no—
336C22#1062304712yes—
337C22#1062305712yes—
338C22C22×(C2×D11)⋊C411yescharacteristic
339C22#1062335612yes—
340C4—24no—
341C4—24no—
342C4—84no—
343C4—444no—
344C4—444no—
345C4—884no—
346C2—22no—
347C2—22no—
348C2—22no—
349C2—44no—
350C2#1307120011yescharacteristic
351C2#1307707611yescharacteristic
352C2#1307707611yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#2312C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C23
cosocleC24×C11C24
hypercenter#2312D11
hypocenterC11#21827
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
3. #13069601C2semidirect
4. #13069600C2semidirect
13. C2×#66931C4semidirect
14. C2×#66931C4semidirect
283. C11#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130712142
#130696012
#130696002
#130686882
C11×#23122
#2182711