Finite Group Databasebeta

← #14735707

Subgroups — #14735707

Order 2816.

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

normal subgroups only

This group has 784 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
1#13079830C212yesmaximal
2#13079138C211yesmaximal, characteristic
3#13067944C218yesmaximal, complemented
4#13067254C211yesmaximal, characteristic
5#13067231C212yesmaximal
6C11×#3556C211yesmaximal, characteristic
7C11×#564C2214yes—
8C11×#557—22no—
9C11×#557—22no—
10C11×#557—22no—
11C11×#541—24no—
12C11×#541—22no—
13C11×#533C2212yes—
14C11×#533C2211yescharacteristic
15#10623001C2211yescharacteristic
16#10622707—22no—
17#10622704—22no—
18#10622693—22no—
19#10622682C2214yes—
20#10622678C2214yes—
21#10622678C2214yes—
22#10622611—22no—
23#10622609—24no—
24#10622539C2212yes—
25C2×#66867C2211yescharacteristic
26#10622181C2218yes—
27#10622181C2214yes—
28C11×C4⋊Q8—24no—
29C11×C4⋊Q8—22no—
30C11×C4⋊Q8D412yes—
31C11×C4⋊Q8D412yes—
32C11×C4⋊Q8D412yes—
33C11×#126—28no—
34C11×#125—24no—
35C11×#125—22no—
36C11×#125—28no—
37C11×#125—28no—
38C11×#125—28no—
39C11×#125C2312yes—
40C11×#125C2314yes—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C4×Q8×C11—24no—
45C4×Q8×C11—24no—
46C4×Q8×C11—24no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C11×#117D414yes—
51C11×#117D412yes—
52C2×C42×C11C2311yescharacteristic
53#66979—21no—
54#66977—22no—
55C22×C11⋊C8—21no—
56#66923—21no—
57#66922C2312yes—
58C4×Dic22—22no—
59C22⋊(C11⋊C8)—22no—
60#66874—24no—
61#66874—24no—
62#66872—24no—
63#66872—24no—
64#66871—24no—
65#66871—24no—
66C4⋊(C11⋊C8)—22no—
67#66867—21no—
68#66867C2312yes—
69#66867C2314yes—
70#19067—111nomaximal, Sylow
71C2×Q8×C11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C2×Dic22—22no—
77C11×C4⋊C4—28no—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—28no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—24no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—24no—
86C11×C4⋊C4C2×D414yes—
87C11×C4⋊C4C2×D414yes—
88C11×C4⋊C4C2×D414yes—
89C11×C22⋊C4—24no—
90C11×C22⋊C4—22no—
91C42×C11—28no—
92C42×C11—24no—
93C42×C11—22no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D412yes—
96C42×C11C2411yescharacteristic
97C22⋊Dic11—41no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100Dic11⋊C4—42no—
101C4×Dic11—41no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—24no—
105#3556D1111yescharacteristic
106#3237—112no—
107#3162—111no—
108#1663—118no—
109#1537—111no—
110#1531—112no—
111C23×C11#12011yescharacteristic
112Q8×C11—44no—
113Q8×C11—44no—
114Q8×C11—44no—
115C2×C4×C11—22no—
116C2×C4×C11—24no—
117C2×C4×C11—24no—
118C2×C4×C11—24no—
119C2×C4×C11—42no—
120C2×C4×C11#12012yes—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11C22×D411yescharacteristic
123C2×C4×C11C22×D412yes—
124C2×Dic11—42no—
125Dic22—44no—
126C11⋊C8—24no—
127C11⋊C8—44no—
128#564C2×D1114yes—
129#557—22no—
130#557—22no—
131#557—22no—
132#541—22no—
133#541—24no—
134#533—111no—
135#533C2×D1111yescharacteristic
136#533C2×D1112yes—
137#501—114no—
138#501—114no—
139#501—222no—
140#491—114no—
141#485—224no—
142#477—222no—
143#475—222no—
144#432—112no—
145#427—222no—
146C2×#97—111no—
147#330—114no—
148#330—118no—
149C22×C11—21no—
150C22×C11—22no—
151C22×C11C2×#12011yescharacteristic
152C4×C11—21no—
153C4×C11—22no—
154C4×C11—22no—
155C4×C11—44no—
156C4×C11—44no—
157C4×C11—44no—
158C4×C11#45612yes—
159Dic11—82no—
160C22×C8—221no—
161C4⋊Q8—24no—
162C4⋊Q8—22no—
163C4⋊Q8—112no—
164C4⋊Q8C22⋊D1112yes—
165C4⋊Q8C22⋊D1112yes—
166C4⋊Q8C22⋊D1112yes—
167#126—28no—
168#125—24no—
169#125—22no—
170#125—28no—
171#125—28no—
172#125—28no—
173#125—221no—
174#125C22×D1114yes—
175#125C22×D1112yes—
176C22⋊Q8—22no—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—222no—
180C4×Q8—24no—
181C4×Q8—24no—
182C4×Q8—24no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8—222no—
187#117—221no—
188#117C22⋊D1112yes—
189#117C22⋊D1114yes—
190C2×C42C22×D1111yescharacteristic
191#107—224no—
192#107—224no—
193#106—224no—
194#106—224no—
195C4⋊C8—222no—
196#103—224no—
197#103—224no—
198C22⋊C8—222no—
199#97—112no—
200#97—114no—
201#97—221no—
202C2×C11—41no—
203C2×C11C2×#45611yescharacteristic
204C2×C11#302012yes—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—222no—
209C22×C4C2×C22⋊D1111yescharacteristic
210C22×C4C2×C22⋊D1112yes—
211C2×C8—224no—
212C2×C8—222no—
213C2×C8—224no—
214C4⋊C4—28no—
215C4⋊C4—28no—
216C4⋊C4—28no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—222no—
224C4⋊C4—222no—
225C4⋊C4—442no—
226C4⋊C4C2×C22⋊D1114yes—
227C4⋊C4C2×C22⋊D1114yes—
228C4⋊C4C2×C22⋊D1114yes—
229C22⋊C4—22no—
230C22⋊C4—24no—
231C22⋊C4—441no—
232C42—28no—
233C42—24no—
234C42—22no—
235C42—441no—
236C42C2×C22⋊D1111yescharacteristic
237C42C2×C22⋊D1112yes—
238C42C23×D1111yescharacteristic
239C11#1906711yescharacteristic, complemented, Sylow
240C23#6700611yescharacteristic
241Q8—44no—
242Q8—44no—
243Q8—44no—
244Q8—444no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—42no—
250C2×C4—442no—
251C2×C4#6700612yes—
252C2×C4#6700611yescharacteristic
253C2×C4C22×C22⋊D1111yescharacteristic
254C2×C4C22×C22⋊D1112yes—
255C8—224no—
256C8—444no—
257C22—21no—
258C22—22no—
259C22C2×#6700611yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—44no—
264C4—44no—
265C4—44no—
266C4—882no—
267C4#1062285912yes—
268C2—41no—
269C2C2×#1062285911yescharacteristic
270C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3556C2
socleC22×C11C2×#120
prime radicalC23×C11#120
hypercenter#3556D11
hypocenterC11#19067
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
3. #13067944C2semidirect
239. C11#19067semidirect

Maximal subgroups

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

subgroupindex
#130798302
#130791382
#130679442
#130672542
#130672312
C11×#35562
#1906711