Finite Group Databasebeta

← #14767658

Subgroups — #14767658

Order 2816.

818 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 243 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#13077328C212yesmaximal, complemented
2#13069449C212yesmaximal, complemented
3#13068945C218yesmaximal, complemented
4#13068757C211yesmaximal, characteristic, complemented
5#13068369C211yesmaximal, characteristic, complemented
6C11×#3150C211yesmaximal, characteristic
7C2×C11×#135C2214yes—
8C11×#532C2212yes—
9C2×#67001C2214yes—
10C11×#497C414yescomplemented
11C11×#496C414yescomplemented
12C2×C11×#97C2211yescharacteristic
13C2×#66901C2218yes—
14#10622847C2214yes—
15#10622625—22no—
16#10622625—22no—
17D4×C11⋊C8—22no—
18D4×C11⋊C8—22no—
19#10622545C2211yescharacteristic
20#10622537C2212yes—
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622190C2214yes—
23#10622188C2214yes—
24C2×C11×#41C2314yes—
25C11×#135—48no—
26C2×C11×Q16C2×C414yes—
27C2×C11×SD16C2×C418yes—
28C2×C11×D8C2×C414yes—
29C22×C8×C11C2312yes—
30C11×C4⋊Q8C2×C412yes—
31C11×#127C2×C412yes—
32C11×#124C2×C414yes—
33C11×#121—22no—
34C11×#121—22no—
35C4×D4×C11—22no—
36C4×D4×C11—22no—
37C2×C42×C11C2311yescharacteristic
38#67001—48no—
39C2×C4×Dic11C2312yes—
40C2×#4318—24no—
41C2×#4318C2314yes—
42C22×C11⋊C8—24no—
43C22×C11⋊C8C2312yes—
44C11×#97C2×C414yes—
45#66901—48no—
46C11⋊#95—22no—
47C22⋊(C11⋊C8)—24no—
48C22⋊(C11⋊C8)—24no—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51C4×C11⋊C8D411yescharacteristic
52C4×C11⋊C8D412yes—
53C4×C11⋊C8D411yescharacteristic
54#22281—111nomaximal, Sylow
55C11×#41—28no—
56C11×#41—28no—
57C2×Q8×C11C22×C414yes—
58C2×D4×C11—24no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11C22×C414yes—
62C22×C4×C11—24no—
63C22×C4×C11#4112yes—
64C22×C4×C11C2411yescharacteristic
65C22×Dic11—22no—
66C11×Q16—44no—
67C11×SD16—48no—
68C11×D8—44no—
69C2×C8×C11—24no—
70C2×C8×C11C22×C414yes—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—24no—
74C11×C22⋊C4—24no—
75C42×C11C22×C412yes—
76C42×C11C2×D411yescharacteristic
77C42×C11C2×D411yescharacteristic
78C4×Dic11—24no—
79#4318—28no—
80#4318—48no—
81C2×C11⋊C8—24no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—48no—
84C2×C11⋊C8C2×D412yes—
85C2×C11⋊C8C2×D412yes—
86#3150D1111yescharacteristic
87#2931—112no—
88#1963—112no—
89#1876—118no—
90#1838—111no—
91#1746—111no—
92C23×C11—24no—
93C23×C11C2×#4111yescharacteristic
94Q8×C11—28no—
95D4×C11—28no—
96D4×C11—44no—
97D4×C11—44no—
98D4×C11—48no—
99C2×C4×C11—24no—
100C2×C4×C11—42no—
101C2×C4×C11—44no—
102C2×C4×C11—44no—
103C2×C4×C11C4×D412yes—
104C2×C4×C11C4×D412yes—
105C2×C4×C11C23×C411yescharacteristic
106C2×C4×C11C22×D411yescharacteristic
107C2×C4×C11H(5,𝔽2)14yes—
108C2×Dic11—44no—
109C2×Dic11—42no—
110C8×C11—24no—
111C11⋊C8—22no—
112C11⋊C8—22no—
113C11⋊C8—44no—
114C2×#135C2×D1114yes—
115C2×#131—114no—
116#532C2×D1112yes—
117#497Dic1114yescomplemented
118#496Dic1114yescomplemented
119#436—222no—
120#436—222no—
121C8×D4—222no—
122C8×D4—222no—
123#423—112no—
124C2×#104—118no—
125#408—114no—
126C2×#97C2×D1111yescharacteristic
127C2×C4×C8—111no—
128#376—111no—
129#341—114no—
130#336—114no—
131C22×C11—22no—
132C22×C11—44no—
133C22×C11—44no—
134C22×C11—44no—
135C22×C11C2×C4×D411yescharacteristic
136C22×C11#54012yes—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11—44no—
140C4×C11#51812yes—
141C4×C11#53512yes—
142Dic11—82no—
143C2×#41C22×D1114yes—
144#135—48no—
145C2×Q16C2×Dic1114yes—
146C2×SD16C2×Dic1118yes—
147C2×D8C2×Dic1114yes—
148#131—448no—
149C2×M16—114no—
150C2×M16—224no—
151C22×C8—112no—
152C22×C8—224no—
153C22×C8C22×D1112yes—
154C4⋊Q8C2×Dic1112yes—
155#127C2×Dic1112yes—
156#124C2×Dic1114yes—
157#121—22no—
158#121—22no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C42—112no—
162C2×C42C22×D1111yescharacteristic
163C4⋊C8—222no—
164C4⋊C8—222no—
165#104—448no—
166C22⋊C8—224no—
167C22⋊C8—224no—
168#97C2×Dic1114yes—
169C4×C8—111no—
170C4×C8—112no—
171C4×C8—111no—
172#95—222no—
173C2×C11—22no—
174C2×C11—84no—
175C2×C11#232811yescharacteristic
176C2×C11#295512yes—
177#41—28no—
178#41—28no—
179C2×Q8C22×Dic1114yes—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4C22×Dic1114yes—
184C22×C4—24no—
185C22×C4—222no—
186C22×C4#434112yes—
187C22×C4C23×D1111yescharacteristic
188Q16—44no—
189SD16—48no—
190D8—44no—
191M16—228no—
192M16—448no—
193C2×C8—24no—
194C2×C8—112no—
195C2×C8—112no—
196C2×C8—224no—
197C2×C8—224no—
198C2×C8—448no—
199C2×C8C22×Dic1114yes—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C42—224no—
205C42D4×D1111yescharacteristic
206C42D4×D1111yescharacteristic
207C42C22×Dic1112yes—
208C11#2228111yescharacteristic, complemented, Sylow
209C23—24no—
210C23C2×#434111yescharacteristic
211Q8—28no—
212D4—28no—
213D4—44no—
214D4—44no—
215D4—48no—
216C2×C4—24no—
217C2×C4—42no—
218C2×C4—44no—
219C2×C4—44no—
220C2×C4—444no—
221C2×C4—442no—
222C2×C4D4×Dic1112yes—
223C2×C4D4×Dic1112yes—
224C2×C4C2×D4×D1111yescharacteristic
225C2×C4#6703714yes—
226C2×C4C23×Dic1111yescharacteristic
227C8—24no—
228C8—222no—
229C8—222no—
230C8—444no—
231C22—22no—
232C22—44no—
233C22—44no—
234C22—44no—
235C22#1062325012yes—
236C22C2×D4×Dic1111yescharacteristic
237C4—22no—
238C4—22no—
239C4—44no—
240C4—882no—
241C4#1062324612yes—
242C4#1062332912yes—
243C2—22no—
244C2—84no—
245C2#1307134211yescharacteristic
246C2#1307751912yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3150C2
socleC22×C11C2×C4×D4
cosocleC22×C4×C11C24
hypercenter#3150D11
hypocenterC11#22281
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3150

Complements

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

NH ≅ G/Ntype
1. #13077328C2semidirect
2. #13069449C2semidirect
3. #13068945C2semidirect
4. #13068757C2semidirect
5. #13068369C2semidirect
10. C11×#497C4semidirect
11. C11×#496C4semidirect
117. #497Dic11semidirect
118. #496Dic11semidirect
208. C11#22281semidirect

Maximal subgroups

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

subgroupindex
#130773282
#130694492
#130689452
#130687572
#130683692
C11×#31502
#2228111