Finite Group Databasebeta

← #14729876

Subgroups — #14729876

Order 2816.

1630 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623248C211yesmaximal, characteristic
2#13078711C212yesmaximal, complemented
3#13067792C218yesmaximal, complemented
4#13067330C211yesmaximal, characteristic, complemented
5#13067060C212yesmaximal, complemented
6C11×#3138C211yesmaximal, characteristic, complemented
7C22×D4×D11—22no—
8C11×#533C2211yescharacteristic, complemented
9C2×C11×#127C2211yescharacteristic
10C2×#66991—22no—
11C2×#66990—22no—
12#10623248—22no—
13#10623248—24no—
14#10623248C2214yes—
15C2×C4×D44C2212yes—
16C11×#490—22no—
17C11×#486C2214yescomplemented
18C11×#418—22no—
19C4×C11×M16C2211yescharacteristic, complemented
20#10622700C2214yescomplemented
21#10622696C2214yescomplemented
22#10622659—22no—
23#10622657—22no—
24#10622639—24no—
25#10622539C2212yescomplemented
26#10622182C2214yescomplemented
27#10622097C2218yescomplemented
28C24×D11—22no—
29C22×D4×C11—22no—
30C22×D4×C11D412yes—
31C22×C22⋊D11—24no—
32C2×D4×D11—28no—
33C2×D4×D11—28no—
34C2×D4×D11—416no—
35C22×D44D412yes—
36C22×C4×D11—22no—
37C2×C11×M16—21no—
38C11×C4⋊Q8C2312yescomplemented
39C11×#127—22no—
40C11×#127D412yes—
41C11×#127C2312yes—
42C11×#125—21no—
43C11×C22⋊Q8—22no—
44C4×Q8×C11—22no—
45C11×#117—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48C2×#4325—24no—
49#66991—28no—
50#66991—28no—
51#66990—28no—
52#66990—28no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11D412yes—
55C4×D44—22no—
56C4×D44—22no—
57C4×D44D414yes—
58C4×D44C2314yes—
59C11×#102—28no—
60C11×#97—21no—
61C4×C8×C11C2312yescomplemented
62#66899—24no—
63C22⋊(C11⋊C8)—22no—
64#66873—24no—
65#66871—24no—
66C4⋊(C11⋊C8)C2314yescomplemented
67#66867—22no—
68#18529—111nomaximal, Sylow
69C24×C11—22no—
70C23×D11—22no—
71C23×D11—28no—
72C23×D11—416no—
73C23×D11—84no—
74C2×Q8×C11—22no—
75C2×D4×C11—24no—
76C2×D4×C11—22no—
77C2×D4×C11—24no—
78C2×D4×C11—48no—
79C2×D4×C11—44no—
80C2×D4×C11C2×D414yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—216no—
84C2×C22⋊D11—416no—
85C22×Dic11—22no—
86D4×D11—432no—
87D4×D11—416no—
88D4×D11—416no—
89C2×D44—28no—
90C2×D44—22no—
91C2×D44C2×D414yes—
92C2×C4×D11—24no—
93C2×C4×D11—24no—
94C2×C4×D11—48no—
95C11×M16—42no—
96C2×C8×C11—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—42no—
100C11×C22⋊C4—41no—
101C42×C11—41no—
102C42×C11C2×D412yes—
103C42×C11C2×D411yescharacteristic
104C42×C11C2411yescharacteristic
105C22⋊Dic11—28no—
106#4325—48no—
107(C2×D11)⋊C4—24no—
108(C2×D11)⋊C4—24no—
109C4⋊Dic11—22no—
110C4⋊Dic11C2×D414yes—
111C2×C11⋊C8—24no—
112C2×D42—111no—
113#3138D1111yescharacteristic, complemented
114#3110—112no—
115#1639—118no—
116#1555—111no—
117#1490—112no—
118C23×C11—24no—
119C23×C11—48no—
120C23×C11—44no—
121C23×C11#12011yescharacteristic
122C22×D11—28no—
123C22×D11—24no—
124C22×D11—432no—
125C22×D11—44no—
126C22×D11—44no—
127C22×D11—88no—
128C22×D11—832no—
129Q8×C11—44no—
130D4×C11—44no—
131D4×C11—48no—
132D4×C11—48no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—42no—
137C2×C4×C11#12012yes—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11C22×D412yes—
140C2×C4×C11C22×D411yescharacteristic
141C22⋊D11—432no—
142C2×Dic11—24no—
143C2×Dic11—44no—
144D44—28no—
145D44—24no—
146D44AGL(1,ℤ/8)18yes—
147C4×D11—48no—
148C4×D11—48no—
149C8×C11—42no—
150C11⋊C8—44no—
151C23×D4—222no—
152D42—114no—
153D42—224no—
154D42—222no—
155#533C2×D1111yescharacteristic, complemented
156C2×#127C2×D1111yescharacteristic
157C2×#121—222no—
158C2×#120—222no—
159C2×C4×D4—112no—
160#490—22no—
161#486C2×D1114yescomplemented
162#484—222no—
163#474—114no—
164#461—114no—
165#450—222no—
166#440—224no—
167#432—112no—
168#418—22no—
169C4×M16C2×D1111yescharacteristic, complemented
170#331—114no—
171D4⋊C8—118no—
172C22×C11—22no—
173C22×C11—48no—
174C22×C11—44no—
175C22×C11—88no—
176C22×C11#45512yes—
177C22×C11C2×#12011yescharacteristic
178C2×D11—28no—
179C2×D11—416no—
180C2×D11—44no—
181C2×D11—44no—
182C2×D11—832no—
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—82no—
187C4×C11C2×AGL(1,ℤ/8)14yes—
188Dic11—44no—
189C25—222no—
190C22×D4—22no—
191C22×D4—112no—
192C22×D4—228no—
193C22×D4—228no—
194C22×D4—224no—
195C22×D4—4416no—
196C22×D4C22⋊D1112yes—
197C23×C4—222no—
198C2×SD16—224no—
199C2×M16—21no—
200C4⋊Q8C22×D1112yescomplemented
201#127—22no—
202#127C22⋊D1112yes—
203#127C22×D1112yes—
204#125—21no—
205C22⋊Q8—22no—
206#121—228no—
207#121—228no—
208#120—228no—
209#120—228no—
210C4×Q8—22no—
211C4×D4—114no—
212C4×D4—114no—
213C4×D4—222no—
214C4×D4—222no—
215#117—21no—
216C2×C4⋊C4—112no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4—222no—
219C2×C42C22×D1111yescharacteristic
220#107—224no—
221C4⋊C8—114no—
222#103—224no—
223#102—28no—
224#102—224no—
225C22⋊C8—222no—
226#97—21no—
227#97—222no—
228C4×C8C22×D1112yescomplemented
229C2×C11—22no—
230C2×C11—84no—
231C2×C11#300312yes—
232C2×C11C2×#45511yescharacteristic
233D11—48no—
234C24—22no—
235C24—228no—
236C24—222no—
237C24—4416no—
238C24—884no—
239C2×Q8—22no—
240C2×D4—24no—
241C2×D4—22no—
242C2×D4—24no—
243C2×D4—48no—
244C2×D4—44no—
245C2×D4—114no—
246C2×D4—228no—
247C2×D4—2216no—
248C2×D4—222no—
249C2×D4—4416no—
250C2×D4—4432no—
251C2×D4—4416no—
252C2×D4—4416no—
253C2×D4C2×C22⋊D1114yes—
254C22×C4—222no—
255C22×C4—224no—
256C22×C4—224no—
257C22×C4—448no—
258C22×C4D4×D1112yes—
259C22×C4C2×C22⋊D1111yescharacteristic
260SD16—448no—
261M16—42no—
262C2×C8—22no—
263C2×C8—224no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—42no—
267C4⋊C4—114no—
268C4⋊C4—222no—
269C22⋊C4—41no—
270C22⋊C4—228no—
271C22⋊C4—224no—
272C22⋊C4—224no—
273C42—41no—
274C42D4×D1112yes—
275C42C2×C22⋊D1111yescharacteristic
276C42C23×D1111yescharacteristic
277C11#1852911yescharacteristic, complemented, Sylow
278C23—24no—
279C23—48no—
280C23—44no—
281C23—228no—
282C23—224no—
283C23—444no—
284C23—4432no—
285C23—444no—
286C23—888no—
287C23—8832no—
288C23#6699011yescharacteristic
289Q8—44no—
290D4—44no—
291D4—48no—
292D4—48no—
293D4—82no—
294D4—118no—
295D4—228no—
296D4—224no—
297D4—4432no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—42no—
301C2×C4—224no—
302C2×C4—448no—
303C2×C4—444no—
304C2×C4—448no—
305C2×C4#6699011yescharacteristic
306C2×C4#6699012yes—
307C2×C4C2×D4×D1112yes—
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—42no—
310C8—444no—
311C22—22no—
312C22—48no—
313C22—44no—
314C22—88no—
315C22—228no—
316C22—4416no—
317C22—444no—
318C22—444no—
319C22—8832no—
320C22#1062267412yes—
321C22C2×#6699011yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—444no—
327C4D11×AGL(1,ℤ/8)14yes—
328C2—22no—
329C2—84no—
330C2—448no—
331C2#1307784112yes—
332C2C2×#1062267411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3138C2
socleC22×C11C2×#120
prime radicalC2×#10623248C2
hypercenter#3138D11
hypocenterC11#18529
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #13078711C2semidirect
3. #13067792C2semidirect
4. #13067330C2semidirect
5. #13067060C2semidirect
6. C11×#3138C2semidirect
8. C11×#533C22semidirect
17. C11×#486C22semidirect
19. C4×C11×M16C22semidirect
20. #10622700C22semidirect
21. #10622696C22semidirect
25. #10622539C22semidirect
26. #10622182C22semidirect
27. #10622097C22semidirect
38. C11×C4⋊Q8C23semidirect
61. C4×C8×C11C23semidirect
66. C4⋊(C11⋊C8)C23semidirect
113. #3138D11semidirect
155. #533C2×D11semidirect
161. #486C2×D11semidirect
169. C4×M16C2×D11semidirect
200. C4⋊Q8C22×D11semidirect
228. C4×C8C22×D11semidirect
277. C11#18529semidirect

Maximal subgroups

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

subgroupindex
C2×#106232482
#130787112
#130677922
#130673302
#130670602
C11×#31382
#1852911