Finite Group Databasebeta

← #14657245

Subgroups — #14657245

Order 2816.

518 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069433C212yesmaximal, complemented
2#13068749C211yesmaximal, characteristic, complemented
3C2×#10622178C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#2819C211yesmaximal, characteristic
6C2×C11×#124C2212yes—
7C11×#394—22no—
8C11×#393—22no—
9C11×#392—22no—
10C11×#382C2211yescharacteristic
11C2×#66899—22no—
12C2×#66896—22no—
13#10622548C2211yescharacteristic
14C2×#66867C2212yes—
15C2×#66867C2211yescharacteristic
16#10622178—24no—
17#10622167—22no—
18C22×Q8×C11D412yes—
19C22×D4×C11—22no—
20C22×D4×C11D412yes—
21C11×#124—22no—
22C11×#124—22no—
23C11×#124—22no—
24C11×#124—22no—
25C2×C11×C4⋊C4D412yes—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—22no—
32C2×C4⋊Dic11—21no—
33C22×C11⋊C8—22no—
34C22×C11⋊C8—21no—
35C11×#95—22no—
36C11×#95—22no—
37#66899—44no—
38#66896—44no—
39#66867—21no—
40#66867—22no—
41#66867—22no—
42#66867D412yescomplemented
43#10425—111nomaximal, Sylow
44C24×C11—22no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11—42no—
48C2×Q8×C11—42no—
49C2×D4×C11—22no—
50C2×D4×C11—22no—
51C2×D4×C11—42no—
52C2×D4×C11—42no—
53C2×D4×C11—82no—
54C2×D4×C11—82no—
55C2×D4×C11—82no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11C2×D412yes—
59C22×C4×C11C2×D411yescharacteristic
60C22×Dic11—41no—
61C11×C4⋊C4—42no—
62C11×C22⋊C4—42no—
63C11×C22⋊C4—42no—
64C11×C22⋊C4—42no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—82no—
67C11×C22⋊C4—82no—
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4112yes—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C4⋊Dic11—42no—
74C2×C11⋊C8—24no—
75C2×C11⋊C8—22no—
76C2×C11⋊C8—41no—
77C2×C11⋊C8—41no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2819D1111yescharacteristic
81#1959—112no—
82#1836—111no—
83C2×#329—112no—
84#1295—111no—
85C23×C11—42no—
86C23×C11—42no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11—42no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11#12011yescharacteristic
93Q8×C11—44no—
94Q8×C11—82no—
95D4×C11—44no—
96D4×C11—82no—
97D4×C11—88no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—42no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11—42no—
108C2×C4×C11#12111yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12312yes—
111C2×C4×C11#12411yescharacteristic
112C2×Dic11—82no—
113C2×Dic11—81no—
114C11⋊C8—44no—
115C11⋊C8—42no—
116C2×#124C2×D1112yes—
117C2×#103—222no—
118C2×#102—222no—
119C2×#97—111no—
120C2×#97—112no—
121#394—22no—
122#393—22no—
123#392—22no—
124#384—111no—
125#382C2×D1111yescharacteristic
126#340—222no—
127#329—224no—
128C22×C11—82no—
129C22×C11—82no—
130C22×C11—82no—
131C22×C11—82no—
132C22×C11—82no—
133C22×C11—82no—
134C22×C11—82no—
135C22×C11#39411yescharacteristic
136C22×C11#45312yes—
137C22×C11#45411yescharacteristic
138C22×C11#45511yescharacteristic
139C22×C11#45512yes—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—82no—
145C4×C11—82no—
146Dic11—161no—
147C22×Q8C22⋊D1112yes—
148C22×D4—22no—
149C22×D4C22⋊D1112yes—
150C22×C8—221no—
151C22×C8—222no—
152#124—22no—
153#124—22no—
154#124—22no—
155#124—22no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4C22⋊D1112yes—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C42C22×D1111yescharacteristic
164#103—444no—
165#102—444no—
166#97—112no—
167#97—222no—
168#97—221no—
169#97—222no—
170#95—22no—
171#95—22no—
172C2×C11—162no—
173C2×C11#165611yescharacteristic
174C2×C11#165912yes—
175C2×C11#166211yescharacteristic
176C2×C11#203712yes—
177C2×C11#204011yescharacteristic
178C24—22no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×D4—22no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—82no—
188C2×D4—82no—
189C2×D4—82no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—441no—
193C22×C4C2×C22⋊D1112yes—
194C22×C4C2×C22⋊D1111yescharacteristic
195C2×C8—224no—
196C2×C8—222no—
197C2×C8—441no—
198C2×C8—442no—
199C2×C8—441no—
200C2×C8—442no—
201C4⋊C4—42no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C22⋊C4—82no—
210C22⋊C4—82no—
211C42D4×D1111yescharacteristic
212C42#434111yescharacteristic
213C42#434112yes—
214C11#1042511yescharacteristic, complemented, Sylow
215C23—42no—
216C23—42no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—42no—
222C23#6700611yescharacteristic
223Q8—44no—
224Q8—82no—
225D4—44no—
226D4—82no—
227D4—88no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—882no—
239C2×C4—881no—
240C2×C4#6698812yes—
241C2×C4#6698911yescharacteristic
242C2×C4#6699111yescharacteristic
243C2×C4#6699212yes—
244C8—442no—
245C8—444no—
246C22—82no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—82no—
251C22—82no—
252C22—82no—
253C22#1062283511yescharacteristic
254C22#1062285412yes—
255C22#1062285511yescharacteristic
256C22#1062285512yes—
257C22#1062285811yescharacteristic
258C4—21no—
259C4—21no—
260C4—22no—
261C4—22no—
262C4—82no—
263C4—82no—
264C4—1761no—
265C2—162no—
266C2#1306790911yescharacteristic
267C2#1306792212yes—
268C2#1306793911yescharacteristic
269C2#1306982312yes—
270C2#1306984211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2819C2
socleC23×C11#120
hypercenter#2819D11
hypocenterC11#10425
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2819

Complements

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

NH ≅ G/Ntype
1. #13069433C2semidirect
2. #13068749C2semidirect
3. C2×#10622178C2semidirect
4. #13066497C2semidirect
42. #66867D4semidirect
214. C11#10425semidirect

Maximal subgroups

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

subgroupindex
#130694332
#130687492
C2×#106221782
#130664972
C11×#28192
#1042511