Finite Group Databasebeta

← #14810415

Subgroups — #14810415

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622681C212yesmaximal, complemented
2#13076917C211yesmaximal, characteristic
3#13069764C212yesmaximal, complemented
4#13069759C212yesmaximal, complemented
5#13069582C212yesmaximal, complemented
6#13068933C212yesmaximal
7#13068923C212yesmaximal, complemented
8C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9C22×C11×#125C211yesmaximal, characteristic, complemented
10C2×C11×#125—28no—
11C2×C11×#125—22no—
12C2×C11×#125C2212yes—
13C2×C11×#125C2212yes—
14C22×C11×C4⋊C4—22no—
15C22×C11×C4⋊C4C2212yes—
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—
33C23×C4×C11—22no—
34C23×C4×C11D412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C22×D44C2311yescharacteristic
38C22×Dic22C2311yescharacteristic
39C11×#125—216no—
40C11×#125—28no—
41C11×#125—24no—
42C11×#125D418yescomplemented
43C2×C11×C4⋊C4—216no—
44C2×C11×C4⋊C4—24no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—28no—
48C2×C11×C4⋊C4C2314yes—
49C2×C42×C11—24no—
50C2×C42×C11D412yes—
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—21no—
54#66983—24no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2311yescharacteristic
60#66977—24no—
61C2×Dic11⋊C4—21no—
62C22×C11⋊C8C2314yes—
63#66928—24no—
64C11⋊#95—22no—
65C11⋊#95—22no—
66C22⋊(C11⋊C8)—24no—
67#66874—28no—
68#66873—28no—
69C4×C11⋊C8—24no—
70#25907—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C23×D11—21no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—28no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—42no—
80C22×C4×C11—44no—
81C22×C4×C11—44no—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4114yes—
86C22×C4×C11C2411yescharacteristic
87C2×C22⋊D11—42no—
88C2×C22⋊D11—44no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—22no—
95C2×Dic22—22no—
96C2×Dic22—22no—
97C2×Dic22—22no—
98C11×C4⋊C4—28no—
99C11×C4⋊C4—216no—
100C11×C4⋊C4—216no—
101C11×C4⋊C4—24no—
102C11×C4⋊C4C2×D418yes—
103C42×C11—24no—
104C42×C11—22no—
105C42×C11C2×D414yes—
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—44no—
108(C2×D11)⋊C4—44no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112Dic11⋊C4—42no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—24no—
115C2×C11⋊C8—24no—
116C22×#125D1111yescharacteristic, complemented
117C2×#488—112no—
118#2850—111no—
119#2026—112no—
120#2025—112no—
121#1991—112no—
122#1874—112no—
123#1872—112no—
124C4×C22⋊C8—111no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—22no—
128C23×C11#12412yes—
129C23×C11#13514yes—
130C23×C11C22×D411yescharacteristic
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—42no—
135C22×D11—42no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—28no—
141C2×C4×C11—22no—
142C2×C4×C11—28no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—48no—
146C2×C4×C11—416no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11#12014yes—
150C2×C4×C11#12412yes—
151C2×C4×C11C22×D412yes—
152C2×C4×C11C2×#4112yes—
153C2×C4×C112−1+412yes—
154C22⋊D11—84no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—42no—
162D44—44no—
163Dic22—44no—
164C11⋊C8—44no—
165C2×#125—28no—
166C2×#125—22no—
167C2×#125C2×D1112yes—
168C2×#125C2×D1112yes—
169C2×#124—111no—
170C2×C22⋊Q8—111no—
171C2×#121—111no—
172C22×C4⋊C4—22no—
173C22×C4⋊C4C2×D1112yes—
174C22×C42C2×D1111yescharacteristic
175#488—228no—
176C2×#103—114no—
177C2×#102—114no—
178C2×C22⋊C8—112no—
179C2×C4×C8—112no—
180#391—111no—
181#390—111no—
182#388—222no—
183#386—222no—
184#382—111no—
185#340—114no—
186#340—114no—
187#336—112no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—24no—
191C22×C11—24no—
192C22×C11#48814yescomplemented
193C22×C11C2×#12011yescharacteristic
194C22×C11C2×#12411yescharacteristic
195C22×C11#53611yescharacteristic
196C22×C11C2×#13512yes—
197C22×C11#57512yes—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—82no—
202C2×D11—82no—
203C4×C11—22no—
204C4×C11—24no—
205C4×C11—42no—
206C4×C11—48no—
207C4×C11#54814yes—
208Dic11—81no—
209Dic11—81no—
210Dic11—81no—
211C22×Q8—111no—
212C22×D4—111no—
213C22×D4—221no—
214C23×C4—22no—
215C23×C4C22⋊D1112yes—
216C23×C4C22×D1111yescharacteristic
217C22×C8—114no—
218#125—216no—
219#125—28no—
220#125—24no—
221#125C22⋊D1118yescomplemented
222#124—224no—
223C22⋊Q8—224no—
224#121—224no—
225C2×C4⋊C4—216no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4C22×D1114yes—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C42—24no—
239C2×C42C22⋊D1112yes—
240C2×C42C22×D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242#103—228no—
243#102—228no—
244C22⋊C8—224no—
245C4×C8—224no—
246#95—222no—
247#95—222no—
248C2×C11—24no—
249C2×C11#243611yescharacteristic
250C2×C11#300212yes—
251C2×C11C2×#48811yescharacteristic
252C2×C11#314211yescharacteristic
253C2×C11#323212yes—
254D11—161no—
255C24—221no—
256C24C2×C22⋊D1111yescharacteristic
257C2×Q8—222no—
258C2×Q8—222no—
259C2×Q8—222no—
260C2×D4—222no—
261C2×D4—222no—
262C2×D4—222no—
263C2×D4—442no—
264C2×D4—444no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—28no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—42no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4#434314yes—
278C22×C4C2×C22⋊D1112yes—
279C22×C4C2×C22⋊D1111yescharacteristic
280C22×C4C2×C22⋊D1112yes—
281C22×C4C23×D1111yescharacteristic
282C2×C8—224no—
283C2×C8—224no—
284C2×C8—224no—
285C4⋊C4—28no—
286C4⋊C4—216no—
287C4⋊C4—216no—
288C4⋊C4—24no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—442no—
292C4⋊C4C2×C22⋊D1118yes—
293C22⋊C4—444no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—444no—
297C42—24no—
298C42—22no—
299C42C2×C22⋊D1114yes—
300C11#2590711yescharacteristic, complemented, Sylow
301C23—21no—
302C23—22no—
303C23—21no—
304C23—441no—
305C23—441no—
306C23—442no—
307C23—442no—
308C23—441no—
309C23#6700012yes—
310C23#6700314yes—
311C23C22×C22⋊D1111yescharacteristic
312Q8—444no—
313D4—444no—
314D4—884no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—28no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—28no—
324C2×C4—48no—
325C2×C4—416no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4—441no—
335C2×C4#6700012yes—
336C2×C4#6700614yes—
337C2×C4C2×#434312yes—
338C2×C4#6704012yes—
339C2×C4C22×C22⋊D1112yes—
340C8—444no—
341C22—24no—
342C22—22no—
343C22—24no—
344C22—22no—
345C22—882no—
346C22—881no—
347C22—881no—
348C22—882no—
349C22—881no—
350C22#1062268114yescomplemented
351C22C2×#6700011yescharacteristic
352C22#1062334711yescharacteristic
353C22C2×#6700312yes—
354C22#1062335312yes—
355C22C2×#6700611yescharacteristic
356C4—24no—
357C4—22no—
358C4—42no—
359C4—48no—
360C4—881no—
361C4—881no—
362C4—881no—
363C4#1062334814yes—
364C2—24no—
365C2—1761no—
366C2#1307227011yescharacteristic
367C2#1307783412yes—
368C2C2×#1062268111yescharacteristic
369C2#1307901911yescharacteristic
370C2#1307978412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#125C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC22×#125D11
hypocenterC11#25907
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. C2×#10622681C2semidirect
3. #13069764C2semidirect
4. #13069759C2semidirect
5. #13069582C2semidirect
7. #13068923C2semidirect
8. C4×C22⋊(C11⋊C8)C2semidirect
9. C22×C11×#125C2semidirect
42. C11×#125D4semidirect
116. C22×#125D11semidirect
192. C22×C11#488semidirect
221. #125C22⋊D11semidirect
300. C11#25907semidirect
350. C22#10622681semidirect

Maximal subgroups

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

subgroupindex
C2×#106226812
#130769172
#130697642
#130697592
#130695822
#130689332
#130689232
C4×C22⋊(C11⋊C8)2
C22×C11×#1252
#2590711