Finite Group Databasebeta

← #14735829

Subgroups — #14735829

Order 2816.

936 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 179 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
1#13079009C212yesmaximal, complemented
2#13078998C211yesmaximal, characteristic, complemented
3#13067939C218yesmaximal, complemented
4#13067211C211yesmaximal, characteristic, complemented
5#13067208C212yesmaximal, complemented
6C11×#3548C211yesmaximal, characteristic
7C11×#562C2214yes—
8C11×#554—22no—
9C11×#550—22no—
10C11×#547—22no—
11C11×#540—22no—
12C11×#537—24no—
13C11×#533C2211yescharacteristic
14C11×#532C2212yes—
15C2×#66922C2211yescharacteristic
16#10622845—24no—
17#10622706—22no—
18#10622694—22no—
19#10622683—22no—
20#10622682C2214yes—
21#10622668C2218yes—
22#10622617—22no—
23C4×#4318C2211yescharacteristic
24C4×#4318C2212yes—
25#10622181C2214yes—
26#10622178C2218yes—
27C2×C11×#41—24no—
28C2×C11×#41D414yes—
29C22×Dic22—21no—
30C11×C4⋊Q8D412yes—
31C11×C4⋊Q8D412yes—
32C11×#127—22no—
33C11×#127D412yes—
34C11×#125—22no—
35C11×#125C2312yes—
36C11×#124C2314yes—
37C11×#123—28no—
38C11×C22⋊Q8—24no—
39C11×C22⋊Q8—28no—
40C11×C22⋊Q8—22no—
41C11×#121—28no—
42C11×#121—24no—
43C11×#121—28no—
44C11×#121—22no—
45C11×#121—22no—
46C4×Q8×C11—22no—
47C4×D4×C11—24no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C11×#117D412yes—
51C2×C11×C4⋊C4—24no—
52C2×C42×C11C2311yescharacteristic
53C2×C4⋊Dic11—22no—
54C2×#4318—22no—
55C2×#4318—21no—
56#66922—22no—
57#66922—21no—
58#66922C2312yes—
59#66899—28no—
60#66896—28no—
61#66874—28no—
62#66867C2314yes—
63#66867C2312yes—
64C4×C11⋊C8—22no—
65C4×C11⋊C8—21no—
66#19080—111nomaximal, Sylow
67C11×#41—48no—
68C11×#41—88no—
69C2×Q8×C11—22no—
70C2×Q8×C11C2×D414yes—
71C2×D4×C11—28no—
72C2×D4×C11—24no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11C2×D414yes—
76C22×C4×C11—28no—
77C22×C4×C11—24no—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—41no—
81C2×Dic22—22no—
82C2×Dic22—44no—
83C2×Dic22—41no—
84C11×C4⋊C4—28no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4C2×D414yes—
90C11×C22⋊C4—28no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—24no—
93C11×C22⋊C4—24no—
94C42×C11—22no—
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D412yes—
97C42×C11C2411yescharacteristic
98C4⋊Dic11—24no—
99C4⋊Dic11—42no—
100#4318—42no—
101#4318—44no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—24no—
104#3548D1111yescharacteristic
105#3141—112no—
106#3139—111no—
107#1662—118no—
108#1526—111no—
109#1525—112no—
110C23×C11—24no—
111C23×C11#12011yescharacteristic
112Q8×C11—44no—
113Q8×C11—44no—
114D4×C11—44no—
115D4×C11—44no—
116D4×C11—44no—
117D4×C11—84no—
118D4×C11—88no—
119C2×C4×C11—22no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—24no—
123C2×C4×C11—48no—
124C2×C4×C11—88no—
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12012yes—
127C2×C4×C11C22×D412yes—
128C2×C4×C11C22×D411yescharacteristic
129C2×Dic11—42no—
130C2×Dic11—82no—
131Dic22—44no—
132Dic22—82no—
133C11⋊C8—44no—
134C11⋊C8—42no—
135#562C2×D1114yes—
136#554—22no—
137#550—22no—
138#547—22no—
139#540—22no—
140#537—24no—
141#533C2×D1111yescharacteristic
142#532C2×D1112yes—
143C2×C4⋊Q8—111no—
144#491—114no—
145#489—118no—
146#487—222no—
147#487—222no—
148#486—222no—
149#419—222no—
150#417—224no—
151C4×M16—111no—
152C4×M16—112no—
153#330—114no—
154#329—118no—
155C22×C11—22no—
156C22×C11—21no—
157C22×C11—44no—
158C22×C11—44no—
159C22×C11—44no—
160C22×C11C2×#12011yescharacteristic
161C4×C11—22no—
162C4×C11—21no—
163C4×C11—44no—
164C4×C11—44no—
165C4×C11#45412yes—
166C4×C11#45514yes—
167Dic11—82no—
168C2×#41—24no—
169C2×#41C22⋊D1114yes—
170C22×Q8—221no—
171C2×M16—222no—
172C2×M16—221no—
173C4⋊Q8—112no—
174C4⋊Q8—222no—
175C4⋊Q8—221no—
176C4⋊Q8C22⋊D1112yes—
177C4⋊Q8C22⋊D1112yes—
178#127—22no—
179#127C22⋊D1112yes—
180#125—22no—
181#125C22×D1112yes—
182#124C22×D1114yes—
183#123—28no—
184C22⋊Q8—24no—
185C22⋊Q8—28no—
186C22⋊Q8—22no—
187#121—28no—
188#121—24no—
189#121—28no—
190#121—22no—
191#121—22no—
192C4×Q8—22no—
193C4×D4—24no—
194C4×D4—22no—
195C4×D4—22no—
196#117C22⋊D1112yes—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—222no—
199C2×C42C22×D1111yescharacteristic
200#103—228no—
201#103—228no—
202#102—228no—
203#97—112no—
204#97—114no—
205C4×C8—222no—
206C4×C8—221no—
207C2×C11—41no—
208C2×C11—84no—
209C2×C11C2×#45512yes—
210C2×C11C2×#45411yescharacteristic
211#41—48no—
212#41—88no—
213C2×Q8—22no—
214C2×Q8—222no—
215C2×Q8—444no—
216C2×Q8—441no—
217C2×Q8C2×C22⋊D1114yes—
218C2×D4—28no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4C2×C22⋊D1114yes—
223C22×C4—28no—
224C22×C4—24no—
225C22×C4—441no—
226C22×C4C2×C22⋊D1112yes—
227C22×C4C2×C22⋊D1111yescharacteristic
228M16—444no—
229M16—442no—
230C2×C8—224no—
231C2×C8—222no—
232C4⋊C4—28no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—24no—
237C4⋊C4—224no—
238C4⋊C4—442no—
239C4⋊C4C2×C22⋊D1114yes—
240C22⋊C4—28no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—24no—
244C42—22no—
245C42C2×C22⋊D1111yescharacteristic
246C42C2×C22⋊D1112yes—
247C42C23×D1111yescharacteristic
248C11#1908011yescharacteristic, complemented, Sylow
249C23—24no—
250C23#6700611yescharacteristic
251Q8—44no—
252Q8—44no—
253Q8—444no—
254Q8—882no—
255D4—44no—
256D4—44no—
257D4—44no—
258D4—84no—
259D4—88no—
260C2×C4—24no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—48no—
265C2×C4—88no—
266C2×C4—442no—
267C2×C4—882no—
268C2×C4#6700612yes—
269C2×C4#6700611yescharacteristic
270C2×C4C22×C22⋊D1111yescharacteristic
271C2×C4C22×C22⋊D1112yes—
272C8—444no—
273C8—442no—
274C22—22no—
275C22—21no—
276C22—44no—
277C22—44no—
278C22—44no—
279C22C2×#6700611yescharacteristic
280C4—22no—
281C4—21no—
282C4—44no—
283C4—44no—
284C4—882no—
285C4#1062285514yes—
286C4#1062285812yes—
287C2—41no—
288C2—84no—
289C2C2×#1062285512yes—
290C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3548C2
socleC22×C11C2×#120
hypercenter#3548D11
hypocenterC11#19080
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. #13078998C2semidirect
3. #13067939C2semidirect
4. #13067211C2semidirect
5. #13067208C2semidirect
248. C11#19080semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130789982
#130679392
#130672112
#130672082
C11×#35482
#1908011