Finite Group Databasebeta

← #14647116

Subgroups — #14647116

Order 2816.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10622264C211yesmaximal, characteristic
2#13068682C212yesmaximal
3#13066459C211yesmaximal, characteristic
4#13066458C212yesmaximal
5C11×#1280C211yesmaximal, characteristic
6C22×C4×Dic11C2211yescharacteristic
7C2×C11×C22⋊C8C2212yes—
8C2×C11×#95C2211yescharacteristic
9C2×C11⋊#95C412yes—
10C2×C11⋊#95C412yes—
11C2×C11⋊#95C2211yescharacteristic
12C2×C22⋊(C11⋊C8)C2212yes—
13#10622264—24no—
14#10622188—24no—
15C23×C4×C11C2×C412yes—
16C23×C4×C11C2311yescharacteristic
17C23×Dic11C2×C411yescharacteristic
18C23×Dic11C2×C412yes—
19C23×Dic11C2×C411yescharacteristic
20C22×C8×C11—22no—
21C2×C4×Dic11—22no—
22C2×C4×Dic11—21no—
23C2×C4×Dic11—21no—
24C2×C4×Dic11D414yes—
25C22×C11⋊C8—22no—
26C11×C22⋊C8—22no—
27C11×C22⋊C8—22no—
28C11×#95—22no—
29C11⋊#95—22no—
30C11⋊#95—24no—
31C11⋊#95—24no—
32C22⋊(C11⋊C8)—22no—
33C22⋊(C11⋊C8)—22no—
34#8705—111nomaximal, Sylow
35C24×C11C22×C411yescharacteristic
36C22×C4×C11—22no—
37C22×C4×C11—22no—
38C22×C4×C11—22no—
39C22×C4×C11—42no—
40C22×C4×C11—42no—
41C22×C4×C11—42no—
42C22×C4×C11C2×D412yes—
43C22×C4×C11#4112yes—
44C22×C4×C11#4111yescharacteristic
45C22×C4×C11#4111yescharacteristic
46C22×Dic11—22no—
47C22×Dic11—21no—
48C22×Dic11—21no—
49C22×Dic11—21no—
50C22×Dic11—21no—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11—22no—
55C22×Dic11—41no—
56C22×Dic11—41no—
57C22×Dic11—42no—
58C22×Dic11—42no—
59C22×Dic11C22⋊C412yes—
60C22×Dic11C22⋊C412yes—
61C2×C8×C11—44no—
62C2×C8×C11—42no—
63C4×Dic11—24no—
64C4×Dic11—24no—
65C2×C11⋊C8—44no—
66C2×C11⋊C8—42no—
67C2×#383—111no—
68#1817—112no—
69#1280—112no—
70#1280—111no—
71#1280D1111yescharacteristic
72C23×C11—22no—
73C23×C11—21no—
74C23×C11—21no—
75C23×C11C2×C22⋊C411yescharacteristic
76C23×C11#11711yescharacteristic
77C23×C11#11711yescharacteristic
78C23×C11#13112yes—
79C23×C11#13112yes—
80C2×C4×C11—24no—
81C2×C4×C11—42no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—82no—
88C2×C4×C11—82no—
89C2×C4×C11#12312yes—
90C2×C4×C11#12312yes—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—24no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—42no—
97C2×Dic11—42no—
98C2×Dic11—41no—
99C2×Dic11—41no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—82no—
105C2×Dic11—82no—
106C8×C11—82no—
107C11⋊C8—82no—
108C22×C42—111no—
109C2×C22⋊C8—112no—
110C2×C22⋊C8C2×D1112yes—
111#383—224no—
112C2×#95—111no—
113C2×#95—112no—
114C2×#95—112no—
115C2×#95C2×D1111yescharacteristic
116#336—224no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11—21no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—22no—
125C22×C11#38111yescharacteristic
126C22×C11#40812yes—
127C22×C11#41012yes—
128C22×C11#41311yescharacteristic
129C22×C11#41311yescharacteristic
130C22×C11#43311yescharacteristic
131C22×C11#43311yescharacteristic
132C22×C11#43312yes—
133C4×C11—22no—
134C4×C11—22no—
135C4×C11—82no—
136Dic11—42no—
137Dic11—42no—
138Dic11—82no—
139C23×C4—111no—
140C23×C4—111no—
141C23×C4—112no—
142C23×C4C4×D1112yes—
143C23×C4C22×D1111yescharacteristic
144C22×C8—22no—
145C22×C8—222no—
146C2×C42—114no—
147C2×C42—222no—
148C2×C42—221no—
149C2×C42—221no—
150C22⋊C8—22no—
151C22⋊C8—22no—
152C22⋊C8—222no—
153C22⋊C8—222no—
154#95—22no—
155#95—224no—
156#95—224no—
157#95—222no—
158C2×C11—21no—
159C2×C11—21no—
160C2×C11—22no—
161C2×C11#147312yes—
162C2×C11#147312yes—
163C2×C11#181811yescharacteristic
164C2×C11#182011yescharacteristic
165C2×C11#182211yescharacteristic
166C24C2×C4×D1111yescharacteristic
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—112no—
174C22×C4—112no—
175C22×C4—221no—
176C22×C4—221no—
177C22×C4—221no—
178C22×C4—221no—
179C22×C4—222no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4—222no—
183C22×C4—222no—
184C22×C4—441no—
185C22×C4—441no—
186C22×C4—442no—
187C22×C4—442no—
188C22×C4#433912yes—
189C22×C4D4×D1112yes—
190C22×C4#434111yescharacteristic
191C22×C4#434311yescharacteristic
192C2×C8—44no—
193C2×C8—42no—
194C2×C8—444no—
195C2×C8—442no—
196C42—224no—
197C42—224no—
198C11#870511yescharacteristic, complemented, Sylow
199C23—22no—
200C23—21no—
201C23—21no—
202C23#6692511yescharacteristic
203C23C22⋊C4×D1111yescharacteristic
204C23#6694511yescharacteristic
205C23#6695412yes—
206C23#6696012yes—
207C2×C4—24no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—222no—
217C2×C4—222no—
218C2×C4—224no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—442no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4—441no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—882no—
230C2×C4—882no—
231C2×C4#6693612yes—
232C2×C4#6694712yes—
233C8—82no—
234C8—882no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22#1062227711yescharacteristic
244C22#1062230311yescharacteristic
245C22#1062232211yescharacteristic
246C22#1062234012yes—
247C22#1062235312yes—
248C22#1062235811yescharacteristic
249C22#1062236411yescharacteristic
250C22#1062245312yes—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—442no—
255C4—442no—
256C4—882no—
257C2—21no—
258C2—21no—
259C2—22no—
260C2#1306698212yes—
261C2#1306698412yes—
262C2#1306868611yescharacteristic
263C2#1306869211yescharacteristic
264C2#1306869811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#1280D11
hypocenterC11#8705
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
198. C11#8705semidirect

Maximal subgroups

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

subgroupindex
C2×#106222642
#130686822
#130664592
#130664582
C11×#12802
#870511