Finite Group Databasebeta

← #14651605

Subgroups — #14651605

Order 2816.

518 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 99 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#13072903C211yesmaximal, characteristic
2#13071219C211yesmaximal, characteristic
3#13068713C212yesmaximal
4#13066470C212yesmaximal
5C11×#1463C211yesmaximal, characteristic
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66979C2211yescharacteristic
8C11×#407C2212yes—
9#10622825—21no—
10#10622824—21no—
11#10622824—21no—
12#10622824C2211yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11C2212yes—
15#10622599C412yescomplemented
16#10622596C412yescomplemented
17#10622594—24no—
18#10622591—22no—
19C11×#324—22no—
20#10622193—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C2×C11×M16—22no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4C2×C412yes—
28C2×C11×C4⋊C4D412yes—
29C2×C22⋊Dic11—21no—
30C2×C22⋊Dic11—22no—
31C2×C22⋊Dic11—21no—
32#66979—22no—
33#66979—22no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—22no—
38C2×C4×Dic11—21no—
39C2×C4×Dic11D414yes—
40C11×C22⋊C8—22no—
41C11×C22⋊C8—22no—
42C11⋊#95—24no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95C2×C412yes—
50#9482—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—21no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—42no—
57C22×C4×C11—42no—
58C22×C4×C11—42no—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22⋊C412yes—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D412yes—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11#4112yes—
65C22×Dic11—22no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—24no—
69C11×M16—44no—
70C2×C8×C11—42no—
71C11×C4⋊C4—24no—
72C11×C4⋊C4—24no—
73C22⋊Dic11—44no—
74C22⋊Dic11—42no—
75C22⋊Dic11—41no—
76C22⋊Dic11—41no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—82no—
80Dic11⋊C4—44no—
81C4×Dic11—44no—
82C4×Dic11—42no—
83#2484—111no—
84#2313—111no—
85#1826—112no—
86#1463D1111yescharacteristic
87#1284—112no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—41no—
91C23×C11C2×C22⋊C411yescharacteristic
92C23×C11#12011yescharacteristic
93C23×C11#12311yescharacteristic
94C2×C4×C11—24no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—81no—
107C2×C4×C11C4×D412yes—
108C2×C4×C11#12112yes—
109C2×Dic11—42no—
110C2×Dic11—44no—
111C2×Dic11—42no—
112C2×Dic11—44no—
113C2×Dic11—42no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—44no—
119C8×C11—82no—
120C2×#117—111no—
121C22×C4⋊C4C2×D1111yescharacteristic
122#407C2×D1112yes—
123#400—112no—
124#398—112no—
125#387—224no—
126#387—222no—
127#385—221no—
128#381—111no—
129#381—221no—
130#381—221no—
131#380—221no—
132C4×C22⋊C4—112no—
133#339—224no—
134#324—22no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—44no—
143C22×C11#38611yescharacteristic
144C22×C11#42112yes—
145C22×C11#45812yes—
146C4×C11—22no—
147C4×C11—22no—
148C4×C11—42no—
149C4×C11—42no—
150Dic11—84no—
151Dic11—82no—
152Dic11—81no—
153Dic11—81no—
154C23×C4D4411yescharacteristic
155C23×C4D4411yescharacteristic
156C23×C4C22×D1111yescharacteristic
157C2×M16—22no—
158#117—222no—
159#117—222no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—111no—
163C2×C4⋊C4—111no—
164C2×C4⋊C4—222no—
165C2×C4⋊C4—222no—
166C2×C4⋊C4C4×D1112yes—
167C2×C4⋊C4C22⋊D1112yes—
168C2×C22⋊C4—221no—
169C2×C22⋊C4—222no—
170C2×C22⋊C4—221no—
171C2×C42—114no—
172C2×C42—221no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—112no—
176#95—222no—
177#95—224no—
178#95—222no—
179#95—222no—
180#95—222no—
181#95—222no—
182#95—221no—
183C2×C11—22no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11#189011yescharacteristic
187C2×C11#189711yescharacteristic
188C2×C11#191211yescharacteristic
189C24C2×D4411yescharacteristic
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—224no—
198C22×C4—222no—
199C22×C4—221no—
200C22×C4—221no—
201C22×C4(C2×D11)⋊C412yes—
202C22×C4(C2×D11)⋊C412yes—
203C22×C4C2×C4×D1111yescharacteristic
204C22×C4D4×D1112yes—
205C22×C4#434112yes—
206C22×C4C2×C22⋊D1111yescharacteristic
207M16—44no—
208C2×C8—42no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—444no—
214C4⋊C4—882no—
215C22⋊C4—444no—
216C22⋊C4—442no—
217C22⋊C4—441no—
218C22⋊C4—441no—
219C42—444no—
220C42—442no—
221C11#948211yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23—41no—
225C23#6693511yescharacteristic
226C23#6693911yescharacteristic
227C23C2×(C2×D11)⋊C411yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—81no—
241C2×C4—444no—
242C2×C4—442no—
243C2×C4—444no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—441no—
249C2×C4—441no—
250C2×C4—444no—
251C2×C4(C22⋊D11)⋊C412yes—
252C2×C4#6699212yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1062235512yes—
263C22#1062257111yescharacteristic
264C22#1062275212yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—884no—
270C4—882no—
271C4—881no—
272C4—881no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#1306902711yescharacteristic
277C2#1306906211yescharacteristic
278C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1463C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1463D11
hypocenterC11#9482
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
15. #10622599C4semidirect
16. #10622596C4semidirect
221. C11#9482semidirect

Maximal subgroups

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

subgroupindex
#130729032
#130712192
#130687132
#130664702
C11×#14632
#948211