Finite Group Databasebeta

← #14657248

Subgroups — #14657248

Order 2816.

518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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#13076662C211yesmaximal, characteristic
2#13069430C212yesmaximal, complemented
3C2×#10622102C212yesmaximal, complemented
4#13066497C211yesmaximal, characteristic, complemented
5C11×#1836C211yesmaximal, characteristic, complemented
6C2×#66928C2212yes—
7C2×C11×#97C2211yescharacteristic
8C11×#384C2211yescharacteristic
9C11×#382C2211yescharacteristic
10#10622604—22no—
11C2×#66874—22no—
12C2×#66873—22no—
13C2×#66867C2212yes—
14#10622286—22no—
15#10622284—22no—
16C11×#340—22no—
17#10622102—24no—
18C22×D44—22no—
19C22×D44D412yes—
20C22×Dic22D412yes—
21C22×C8×C11—21no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4D412yes—
25C2×C42×C11C2311yescharacteristic
26C2×(C2×D11)⋊C4—22no—
27C2×(C2×D11)⋊C4—22no—
28C2×(C2×D11)⋊C4—22no—
29C2×(C2×D11)⋊C4—22no—
30C22×C11⋊C8—22no—
31#66928—22no—
32#66928—22no—
33#66928—22no—
34#66928—22no—
35C11×#97—21no—
36C11×#97D412yescomplemented
37C11×#95—22no—
38C11⋊#95—22no—
39#66874—44no—
40#66873—44no—
41#66867—22no—
42#66867—22no—
43#10425—111nomaximal, Sylow
44C23×D11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—41no—
47C22×C4×C11C2×D412yes—
48C22×C4×C11C2×D411yescharacteristic
49C22×Dic11—22no—
50C2×D44—22no—
51C2×D44—22no—
52C2×D44—42no—
53C2×D44—42no—
54C2×D44—82no—
55C2×D44—82no—
56C2×D44—82no—
57C2×Dic22—22no—
58C2×Dic22—22no—
59C2×Dic22—42no—
60C2×Dic22—42no—
61C2×C8×C11—22no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C11×C4⋊C4—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4112yes—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—82no—
76(C2×D11)⋊C4—82no—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—42no—
79C2×C11⋊C8—42no—
80#2819—111no—
81#1959—112no—
82#1836D1111yescharacteristic, complemented
83C2×#329—112no—
84#1295—111no—
85C23×C11#12011yescharacteristic
86C22×D11—42no—
87C22×D11—42no—
88C22×D11—42no—
89C22×D11—42no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—82no—
101C2×C4×C11—81no—
102C2×C4×C11#12112yes—
103C2×C4×C11#12111yescharacteristic
104C2×C4×C11#12312yes—
105C2×C4×C11#12411yescharacteristic
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109D44—44no—
110D44—82no—
111D44—88no—
112Dic22—44no—
113Dic22—82no—
114C8×C11—42no—
115C11⋊C8—44no—
116C2×#124—112no—
117C2×#103—222no—
118C2×#102—222no—
119C2×#97—112no—
120C2×#97C2×D1111yescharacteristic
121#394—222no—
122#393—222no—
123#392—222no—
124#384C2×D1111yescharacteristic
125#382C2×D1111yescharacteristic
126#340—22no—
127#329—224no—
128C22×C11#39411yescharacteristic
129C22×C11#45312yes—
130C22×C11#45411yescharacteristic
131C22×C11#45512yes—
132C22×C11#45511yescharacteristic
133C2×D11—82no—
134C2×D11—82no—
135C2×D11—82no—
136C2×D11—82no—
137C2×D11—82no—
138C2×D11—82no—
139C2×D11—82no—
140C4×C11—22no—
141C4×C11—22no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—82no—
145C4×C11—161no—
146Dic11—82no—
147C22×Q8—112no—
148C22×D4—112no—
149C22×D4—222no—
150C22×C8—21no—
151C22×C8—222no—
152#124—222no—
153#124—222no—
154#124—222no—
155#124—222no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4C22⋊D1112yes—
159C2×C22⋊C4—222no—
160C2×C22⋊C4—222no—
161C2×C22⋊C4—222no—
162C2×C22⋊C4—222no—
163C2×C42C22×D1111yescharacteristic
164#103—444no—
165#102—444no—
166#97—21no—
167#97—222no—
168#97—222no—
169#97D4412yescomplemented
170#95—22no—
171#95—222no—
172C2×C11#165611yescharacteristic
173C2×C11#165912yes—
174C2×C11#166211yescharacteristic
175C2×C11#203712yes—
176C2×C11#204011yescharacteristic
177D11—162no—
178C24—222no—
179C2×Q8—222no—
180C2×Q8—222no—
181C2×Q8—442no—
182C2×Q8—442no—
183C2×D4—222no—
184C2×D4—222no—
185C2×D4—442no—
186C2×D4—442no—
187C2×D4—882no—
188C2×D4—882no—
189C2×D4—882no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—222no—
193C22×C4D4×D1112yes—
194C22×C4C2×C22⋊D1111yescharacteristic
195C2×C8—22no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—224no—
199C2×C8—442no—
200C2×C8—442no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—42no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C22⋊C4—442no—
208C22⋊C4—442no—
209C22⋊C4—882no—
210C22⋊C4—882no—
211C42C2×D4411yescharacteristic
212C42#433911yescharacteristic
213C42#434312yes—
214C11#1042511yescharacteristic, complemented, Sylow
215C23—442no—
216C23—442no—
217C23—442no—
218C23—442no—
219C23—442no—
220C23—442no—
221C23—442no—
222C23#6699011yescharacteristic
223Q8—444no—
224Q8—882no—
225D4—444no—
226D4—882no—
227D4—888no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—81no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4#6694712yes—
241C2×C4#6694812yes—
242C2×C4#6698311yescharacteristic
243C2×C4#6700011yescharacteristic
244C8—42no—
245C8—444no—
246C22—882no—
247C22—882no—
248C22—882no—
249C22—882no—
250C22—882no—
251C22—882no—
252C22—882no—
253C22#1062260411yescharacteristic
254C22#1062267411yescharacteristic
255C22#1062267511yescharacteristic
256C22#1062281112yes—
257C22#1062281512yes—
258C4—22no—
259C4—22no—
260C4—21no—
261C4—21no—
262C4—82no—
263C4—161no—
264C4—882no—
265C2—1762no—
266C2#1306790811yescharacteristic
267C2#1306792112yes—
268C2#1306793711yescharacteristic
269C2#1306982812yes—
270C2#1306984511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1836C2
socleC23×C11#120
prime radical#13076662C2
hypercenter#1836D11
hypocenterC11#10425
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
2. #13069430C2semidirect
3. C2×#10622102C2semidirect
4. #13066497C2semidirect
5. C11×#1836C2semidirect
36. C11×#97D4semidirect
82. #1836D11semidirect
169. #97D44semidirect
214. C11#10425semidirect

Maximal subgroups

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

subgroupindex
#130766622
#130694302
C2×#106221022
#130664972
C11×#18362
#1042511