Finite Group Databasebeta

← #14810406

Subgroups — #14810406

Order 2816.

1104 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622681C212yesmaximal, complemented
2#13076917C211yesmaximal, characteristic
3#13069754C212yesmaximal, complemented
4#13069749C212yesmaximal, complemented
5#13069582C212yesmaximal, complemented
6#13068938C212yesmaximal
7#13068928C212yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C2×C11×#533C211yesmaximal, characteristic, complemented
10C11×#533—28no—
11C2×C11×C4⋊Q8C2212yes—
12C2×C11×#125C2212yes—
13C2×C11×C22⋊Q8—22no—
14C2×C4×Q8×C11—22no—
15C2×C11×#117C2212yes—
16C22×C42×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C2×#66928C2211yescharacteristic
20#10622826—22no—
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622681—28no—
23C2×#66874C2214yes—
24C2×#66873C2214yes—
25#10622553—22no—
26#10622552C2211yescharacteristic
27#10622549C2211yescharacteristic
28#10622542C2211yescharacteristic
29C2×C4×C11⋊C8C2212yes—
30#10622167C2214yes—
31#10622167C2214yes—
32#10622162C2212yes—
33C22×Q8×C11—22no—
34C23×C4×C11D412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C22×D44C2311yescharacteristic
38C22×Dic22C2311yescharacteristic
39C11×C4⋊Q8—28no—
40C11×#125—24no—
41C11×#125D418yescomplemented
42C11×C22⋊Q8—216no—
43C4×Q8×C11—216no—
44C11×#117—28no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2314yes—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—22no—
50C2×C42×C11—24no—
51C2×C42×C11D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—21no—
55#66983—24no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61#66977—24no—
62C2×Dic11⋊C4—21no—
63C22×C11⋊C8C2314yes—
64#66928—24no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C22⋊(C11⋊C8)—24no—
68#66874—28no—
69#66873—28no—
70C4×C11⋊C8—24no—
71#25906—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C23×D11—21no—
74C2×Q8×C11—28no—
75C2×Q8×C11—44no—
76C2×Q8×C11—44no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—42no—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11#4114yes—
87C22×C4×C11C2411yescharacteristic
88C2×C22⋊D11—44no—
89C2×C22⋊D11—42no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C2×Dic22—22no—
99C11×C4⋊C4—28no—
100C11×C4⋊C4—216no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4C2×D418yes—
103C11×C22⋊C4—28no—
104C42×C11—28no—
105C42×C11—24no—
106C42×C11—22no—
107C42×C11C2×D414yes—
108C22⋊Dic11—42no—
109(C2×D11)⋊C4—44no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114Dic11⋊C4—42no—
115C2×C11⋊C8—24no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—24no—
118C2×#533D1111yescharacteristic, complemented
119C2×#488—112no—
120#2850—111no—
121#2024—112no—
122#2023—112no—
123#1991—112no—
124#1875—112no—
125#1873—112no—
126C4×C22⋊C8—111no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11#12412yes—
132C23×C11C22×D411yescharacteristic
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—42no—
138Q8×C11—416no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—28no—
146C2×C4×C11—28no—
147C2×C4×C11—48no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11#12014yes—
151C2×C4×C11#12412yes—
152C2×C4×C11#13514yes—
153C2×C4×C11C22×D412yes—
154C2×C4×C11C2×#4112yes—
155C2×C4×C112−1+412yes—
156C22⋊D11—84no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164D44—44no—
165Dic22—44no—
166C11⋊C8—44no—
167#533—28no—
168C2×C4⋊Q8C2×D1112yes—
169C2×#125C2×D1112yes—
170C2×#124—111no—
171C2×C22⋊Q8—22no—
172C2×C22⋊Q8—111no—
173C2×#121—111no—
174C2×C4×Q8—22no—
175C2×#117C2×D1112yes—
176C22×C42C2×D1111yescharacteristic
177#488—228no—
178C2×#103—114no—
179C2×#102—114no—
180C2×C22⋊C8—112no—
181C2×C4×C8—112no—
182#391—111no—
183#390—111no—
184#388—222no—
185#386—222no—
186#382—111no—
187#340—114no—
188#340—114no—
189#336—112no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—42no—
194C22×C11—42no—
195C22×C11C2×#12011yescharacteristic
196C22×C11C2×#12411yescharacteristic
197C22×C11#53611yescharacteristic
198C22×C11C2×#13512yes—
199C22×C11#57512yes—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—22no—
206C4×C11—24no—
207C4×C11—24no—
208C4×C11—48no—
209C4×C11#54814yes—
210Dic11—81no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8—22no—
214C22×Q8—111no—
215C22×D4—111no—
216C22×D4—221no—
217C23×C4C22⋊D1112yes—
218C23×C4C22×D1111yescharacteristic
219C22×C8—114no—
220C4⋊Q8—28no—
221#125—24no—
222#125C22⋊D1118yescomplemented
223#124—224no—
224C22⋊Q8—216no—
225C22⋊Q8—224no—
226#121—224no—
227C4×Q8—216no—
228#117—28no—
229C2×C4⋊C4—24no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4C22×D1114yes—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C42—22no—
241C2×C42—24no—
242C2×C42C22⋊D1112yes—
243C2×C42C22×D1111yescharacteristic
244C2×C42C22×D1111yescharacteristic
245#103—228no—
246#102—228no—
247C22⋊C8—224no—
248C4×C8—224no—
249#95—222no—
250#95—222no—
251C2×C11—42no—
252C2×C11#243611yescharacteristic
253C2×C11#300212yes—
254C2×C11#313111yescharacteristic
255C2×C11#314011yescharacteristic
256C2×C11#323312yes—
257D11—161no—
258C24—221no—
259C24C2×C22⋊D1111yescharacteristic
260C2×Q8—28no—
261C2×Q8—44no—
262C2×Q8—44no—
263C2×Q8—222no—
264C2×Q8—222no—
265C2×Q8—222no—
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—444no—
270C2×D4—442no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—42no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4#434314yes—
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1112yes—
283C22×C4C2×C22⋊D1112yes—
284C22×C4C23×D1111yescharacteristic
285C2×C8—224no—
286C2×C8—224no—
287C2×C8—224no—
288C4⋊C4—28no—
289C4⋊C4—216no—
290C4⋊C4—24no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—442no—
294C4⋊C4C2×C22⋊D1118yes—
295C22⋊C4—28no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C22⋊C4—444no—
299C22⋊C4—444no—
300C42—28no—
301C42—24no—
302C42—22no—
303C42C2×C22⋊D1114yes—
304C11#2590611yescharacteristic, complemented, Sylow
305C23—21no—
306C23—22no—
307C23—22no—
308C23—21no—
309C23—441no—
310C23—441no—
311C23—442no—
312C23—442no—
313C23—441no—
314C23#6700012yes—
315C23C22×C22⋊D1111yescharacteristic
316Q8—416no—
317Q8—444no—
318D4—444no—
319D4—884no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—48no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—441no—
338C2×C4#6700012yes—
339C2×C4#6700314yes—
340C2×C4#6700614yes—
341C2×C4C2×#434312yes—
342C2×C4#6704012yes—
343C2×C4C22×C22⋊D1112yes—
344C8—444no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—882no—
351C22—881no—
352C22—881no—
353C22—881no—
354C22—882no—
355C22C2×#6700011yescharacteristic
356C22#1062334711yescharacteristic
357C22C2×#6700312yes—
358C22#1062335312yes—
359C22C2×#6700611yescharacteristic
360C4—24no—
361C4—24no—
362C4—22no—
363C4—48no—
364C4—881no—
365C4—881no—
366C4—881no—
367C4#1062334814yes—
368C2—42no—
369C2—1761no—
370C2#1307227011yescharacteristic
371C2#1307783412yes—
372C2#1307894111yescharacteristic
373C2#1307900511yescharacteristic
374C2#1307979512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#533D11
hypocenterC11#25906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#10622681C2semidirect
3. #13069754C2semidirect
4. #13069749C2semidirect
5. #13069582C2semidirect
7. #13068928C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
9. C2×C11×#533C2semidirect
41. C11×#125D4semidirect
118. C2×#533D11semidirect
222. #125C22⋊D11semidirect
304. C11#25906semidirect

Maximal subgroups

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

subgroupindex
C2×#106226812
#130769172
#130697542
#130697492
#130695822
#130689382
#130689282
C4×C22⋊(C11⋊C8)2
C2×C11×#5332
#2590611