Finite Group Databasebeta

← #14909616

Subgroups — #14909616

Order 2816.

616 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 143 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#13078264C212yesmaximal, complemented
2#13070808C214yesmaximal, complemented
3#13070719C212yesmaximal, complemented
4#13070702C212yesmaximal, complemented
5#13070530C214yesmaximal, complemented
6C11×#2113C211yesmaximal, characteristic, complemented
7C2×C11×#131C2211yescharacteristic
8#10623361—22no—
9C22×D88C2212yescomplemented
10C2×C11×M32C2211yescharacteristic, complemented
11C22×C11×C16C2211yescharacteristic, complemented
12#10622748—22no—
13#10622748—22no—
14#10622744—22no—
15#10622728C2214yes—
16#10622728C2214yescomplemented
17#10622719C2212yescomplemented
18C2×D176C2212yes—
19C2×D176C2212yes—
20C11×C22⋊C16C2214yescomplemented
21#10622147C2214yescomplemented
22#10622147C2214yescomplemented
23#10622143C2212yescomplemented
24#10622142C2212yescomplemented
25C2×C11×#41D411yescharacteristic
26C22×D44—22no—
27C11×#131—41no—
28C11×#131—41no—
29C2×C11×M16D412yes—
30C2×C11×M16D411yescharacteristic
31C22×C8×C11C2312yes—
32C22×C8×C11C2311yescharacteristic
33#67000—42no—
34#66993—42no—
35#66990—42no—
36#66990—42no—
37#66983—24no—
38#66983—24no—
39#66979—22no—
40C2×D88—22no—
41C2×D88—42no—
42C2×D88—42no—
43C2×D88C2314yes—
44C11×M32—41no—
45C2×C11×C16—41no—
46C2×C11×C16C2312yes—
47C2×C11×C16C2312yes—
48#66885—24no—
49#66885—24no—
50#66882C2314yes—
51#66881—22no—
52D176—42no—
53D176—42no—
54#33765—111nomaximal, Sylow
55C23×D11—42no—
56C11×#41—41no—
57C11×#41—41no—
58C2×Q8×C11D811yescharacteristic
59C2×D4×C11D811yescharacteristic
60C2×D4×C11D812yes—
61C22×C4×C11C2×D412yes—
62C22×C4×C11C2×D411yescharacteristic
63C2×C22⋊D11—44no—
64C2×C22⋊D11—44no—
65C2×D44—24no—
66C2×D44—44no—
67C2×D44—44no—
68C2×D44—42no—
69C11×M16—42no—
70C11×M16—41no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11C2×D412yes—
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2411yescharacteristic
78C22⋊Dic11—42no—
79(C2×D11)⋊C4—44no—
80(C2×D11)⋊C4—44no—
81C4⋊Dic11—24no—
82C4×Dic11—42no—
83D88—24no—
84D88—24no—
85D88—44no—
86C11×C16—22no—
87C11×C16—22no—
88#3058—112no—
89#2234—114no—
90#2218—112no—
91#2215—112no—
92#2184—114no—
93#2113D1111yescharacteristic, complemented
94C23×C11C2×D812yes—
95C23×C11C2×D811yescharacteristic
96C22×D11—44no—
97C22×D11—84no—
98C22×D11—164no—
99Q8×C11—41no—
100D4×C11—41no—
101D4×C11—42no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11C2×D812yes—
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11C22×D411yescharacteristic
109C22⋊D11—164no—
110C22⋊D11—164no—
111C2×Dic11—44no—
112D44—44no—
113D44—44no—
114D44—84no—
115C8×C11—22no—
116C8×C11—21no—
117C8×C11H(5,𝔽2)11yescharacteristic
118C8×C11H(5,𝔽2)11yescharacteristic
119C22×D8—112no—
120C2×#131C2×D1111yescharacteristic
121#535—222no—
122C2×D16—112no—
123C2×D16—112no—
124C2×M32C2×D1111yescharacteristic, complemented
125C22×C16C2×D1111yescharacteristic, complemented
126#469—222no—
127#469—222no—
128#466—114no—
129#466—114no—
130#427—112no—
131#418—222no—
132#367—112no—
133#366—112no—
134#357—114no—
135#357—114no—
136C22⋊C16C2×D1114yescomplemented
137C22×C11—24no—
138C22×C11—22no—
139C22×C11—22no—
140C22×C11—21no—
141C22×C11C22×D811yescharacteristic
142C2×D11—84no—
143C2×D11—84no—
144C2×D11—84no—
145C2×D11—168no—
146C4×C11—21no—
147C4×C11—22no—
148C4×C11#53411yescharacteristic
149C4×C11#57511yescharacteristic
150Dic11—84no—
151C2×#41D4411yescharacteristic
152C22×D4—222no—
153C2×D8—114no—
154C2×D8—222no—
155C2×D8—442no—
156C2×D8—442no—
157#131—41no—
158#131—41no—
159C2×M16D4412yes—
160C2×M16D4411yescharacteristic
161C22×C8C22×D1112yes—
162C22×C8C22×D1111yescharacteristic
163#127—442no—
164#124—442no—
165#121—224no—
166#121—224no—
167#120—442no—
168#120—442no—
169#117—222no—
170D16—442no—
171D16—442no—
172M32—41no—
173C2×C16—41no—
174C2×C16C22×D1112yes—
175C2×C16C22×D1112yes—
176#107—114no—
177#106—222no—
178#102—224no—
179#102—224no—
180C2×C11—42no—
181C2×C11—41no—
182C2×C11#318611yescharacteristic
183C2×C11#341512yes—
184D11—164no—
185C24—442no—
186#41—41no—
187#41—41no—
188C2×Q8D8811yescharacteristic
189C2×D4—224no—
190C2×D4—444no—
191C2×D4—444no—
192C2×D4—444no—
193C2×D4—444no—
194C2×D4—442no—
195C2×D4D8811yescharacteristic
196C2×D4D8812yes—
197C22×C4C2×D4412yes—
198C22×C4C2×D4411yescharacteristic
199D8—224no—
200D8—224no—
201D8—444no—
202M16—41no—
203M16—42no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—22no—
207C2×C8—22no—
208C2×C8C2×D4411yescharacteristic
209C2×C8C2×D4412yes—
210C2×C8C23×D1111yescharacteristic
211C4⋊C4—224no—
212C22⋊C4—442no—
213C22⋊C4—444no—
214C22⋊C4—444no—
215C42—442no—
216C16—22no—
217C16—22no—
218C11#3376511yescharacteristic, complemented, Sylow
219C23—444no—
220C23—884no—
221C23—1764no—
222C23C2×D8812yes—
223C23C2×D8811yescharacteristic
224Q8—41no—
225D4—42no—
226D4—41no—
227D4—444no—
228D4—444no—
229D4—884no—
230D4—1764no—
231D4—1764no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—444no—
237C2×C4C2×D8812yes—
238C2×C4C2×D8811yescharacteristic
239C2×C4C22×D4411yescharacteristic
240C8—22no—
241C8—21no—
242C8#6703711yescharacteristic
243C8#6703711yescharacteristic
244C22—22no—
245C22—21no—
246C22—22no—
247C22—24no—
248C22—884no—
249C22—884no—
250C22—884no—
251C22—1768no—
252C22C22×D8811yescharacteristic
253C4—22no—
254C4—21no—
255C4—884no—
256C4#1062302411yescharacteristic
257C4#1062327911yescharacteristic
258C2—42no—
259C2—41no—
260C2—1764no—
261C2#1307936711yescharacteristic
262C2#1308175712yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
hypercenter#2113D11
hypocenterC11#33765
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
1. #13078264C2semidirect
2. #13070808C2semidirect
3. #13070719C2semidirect
4. #13070702C2semidirect
5. #13070530C2semidirect
6. C11×#2113C2semidirect
9. C22×D88C22semidirect
10. C2×C11×M32C22semidirect
11. C22×C11×C16C22semidirect
16. #10622728C22semidirect
17. #10622719C22semidirect
20. C11×C22⋊C16C22semidirect
21. #10622147C22semidirect
22. #10622147C22semidirect
23. #10622143C22semidirect
24. #10622142C22semidirect
93. #2113D11semidirect
124. C2×M32C2×D11semidirect
125. C22×C16C2×D11semidirect
136. C22⋊C16C2×D11semidirect
218. C11#33765semidirect

Maximal subgroups

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

subgroupindex
#130782642
#130708082
#130707192
#130707022
#130705302
C11×#21132
#3376511