Finite Group Databasebeta

← #14651136

Subgroups — #14651136

Order 2816.

558 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 131 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#13077640C211yesmaximal, characteristic
2#13073608C211yesmaximal, characteristic
3#13067289C212yesmaximal, complemented
4#13066517C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66989—21no—
8C2×#66922C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#100—21no—
11#10622825—22no—
12C2×C22⋊(C11⋊C8)—22no—
13D4×C11⋊C8—24no—
14#10622587—21no—
15#10622566C414yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622538C2212yes—
18C11×#343—21no—
19#10622120—24no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D412yes—
22C22×Dic22—21no—
23C2×C11×M16—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—24no—
30#66989—42no—
31#66989—42no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C412yes—
35C2×C4×Dic11—21no—
36C22×C11⋊C8—24no—
37#66922—22no—
38#66922—22no—
39C11×C4⋊C8—22no—
40C11×C4⋊C8—22no—
41C11×#100—42no—
42C11⋊#95—24no—
43C11⋊#95C2×C412yes—
44C22⋊(C11⋊C8)—24no—
45C22⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)D414yes—
47C4×C11⋊C8—22no—
48#9393—111nomaximal, Sylow
49C24×C11C22⋊C412yes—
50C2×D4×C11—22no—
51C2×D4×C11—22no—
52C2×D4×C11D812yes—
53C2×D4×C11SD1612yes—
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—44no—
57C22×C4×C11C22⋊C412yes—
58C22×C4×C11C22×C411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×Dic11—22no—
62C22×Dic11—22no—
63C2×Dic22—42no—
64C2×Dic22—41no—
65C2×Dic22—41no—
66C2×Dic22—42no—
67C11×M16—42no—
68C11×M16—42no—
69C2×C8×C11—42no—
70C11×C4⋊C4—22no—
71C11×C22⋊C4—24no—
72C42×C11C2×D412yes—
73C42×C11#4112yes—
74C22⋊Dic11—48no—
75C4⋊Dic11—24no—
76C4⋊Dic11—42no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4×Dic11—41no—
80C4×Dic11—41no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—84no—
83#2972—111no—
84#2547—111no—
85#1800D1111yescharacteristic
86#1546—112no—
87#1303—112no—
88C23×C11—22no—
89C23×C11—22no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11#10214yes—
93C23×C11C2×C22⋊C411yescharacteristic
94D4×C11—24no—
95D4×C11—24no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—41no—
99C2×C4×C11—44no—
100C2×C4×C11—42no—
101C2×C4×C11—82no—
102C2×C4×C11C4×D412yes—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11#12112yes—
105C2×C4×C11#12311yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11C2×SD1611yescharacteristic
108C2×C4×C11#13512yes—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115Dic22—82no—
116Dic22—82no—
117C8×C11—82no—
118C11⋊C8—44no—
119C2×C4⋊Q8—111no—
120C2×#124—221no—
121C2×C4×D4C2×D1111yescharacteristic
122C8×D4—224no—
123#431—112no—
124#423C2×D1112yes—
125C2×#100—21no—
126C2×C22⋊C8—222no—
127#397—114no—
128#391—221no—
129#380—222no—
130C4×C4⋊C4—111no—
131#343—21no—
132#332—224no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11—24no—
136C22×C11—44no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11—82no—
140C22×C11#38611yescharacteristic
141C22×C11C2×#10211yescharacteristic
142C22×C11#41611yescharacteristic
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11#45512yes—
147C4×C11#46512yes—
148C4×C11#46612yes—
149Dic11—82no—
150Dic11—82no—
151C22×Q8—221no—
152C22×D4C22⋊D1111yescharacteristic
153C23×C4D4412yes—
154C2×M16—22no—
155C22×C8—224no—
156C4⋊Q8—222no—
157C4⋊Q8—222no—
158#124—442no—
159#124—442no—
160C4×D4—22no—
161C4×D4—22no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4—221no—
164C2×C4⋊C4—221no—
165C2×C4⋊C4C22⋊D1111yescharacteristic
166C2×C22⋊C4—224no—
167C2×C22⋊C4C4×D1112yes—
168C2×C42—221no—
169C2×C42C22×D1111yescharacteristic
170C4⋊C8—22no—
171C4⋊C8—22no—
172C4⋊C8—114no—
173#100—42no—
174C22⋊C8—224no—
175C22⋊C8—222no—
176C4×C8—222no—
177#95—112no—
178#95—224no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11—44no—
182C2×C11#188511yescharacteristic
183C2×C11#189311yescharacteristic
184C2×C11#191511yescharacteristic
185C24(C2×D11)⋊C412yes—
186C2×Q8—441no—
187C2×Q8—442no—
188C2×Q8—441no—
189C2×Q8—442no—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4#432312yes—
193C2×D4#432512yes—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—44no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4(C2×D11)⋊C412yes—
200C22×C4C2×C4×D1111yescharacteristic
201C22×C4C2×D4411yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203M16—42no—
204M16—42no—
205C2×C8—42no—
206C2×C8—224no—
207C2×C8—884no—
208C4⋊C4—22no—
209C4⋊C4—224no—
210C4⋊C4—442no—
211C4⋊C4—441no—
212C4⋊C4—441no—
213C22⋊C4—24no—
214C22⋊C4—448no—
215C42—441no—
216C42—441no—
217C42D4×D1112yes—
218C42#434112yes—
219C11#939311yescharacteristic, complemented, Sylow
220C23—22no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23#6687314yes—
225C23C2×(C2×D11)⋊C411yescharacteristic
226Q8—882no—
227Q8—882no—
228D4—24no—
229D4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—442no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4(C22⋊D11)⋊C412yes—
243C2×C4#6693511yescharacteristic
244C2×C4#6693911yescharacteristic
245C2×C4C2×#432311yescharacteristic
246C2×C4#6699212yes—
247C2×C4C2×#432511yescharacteristic
248C2×C4#6700312yes—
249C8—82no—
250C8—444no—
251C22—21no—
252C22—21no—
253C22—24no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22—82no—
258C22#1062257111yescharacteristic
259C22C2×#6687311yescharacteristic
260C22#1062261511yescharacteristic
261C4—22no—
262C4—21no—
263C4—42no—
264C4—882no—
265C4—882no—
266C4#1062235912yes—
267C4#1062265112yes—
268C4#1062266112yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1306900211yescharacteristic
273C2#1306904211yescharacteristic
274C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#9393
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13067289C2semidirect
4. #13066517C2semidirect
219. C11#9393semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130736082
#130672892
#130665172
C11×#18002
#939311