Finite Group Databasebeta

← #14767655

Subgroups — #14767655

Order 2816.

818 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 203 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#13079062C211yesmaximal, characteristic
2#13077327C212yesmaximal, complemented
3#13069447C212yesmaximal, complemented
4#13068944C218yesmaximal, complemented
5#13068369C211yesmaximal, characteristic, complemented
6C11×#1838C211yesmaximal, characteristic, complemented
7C2×#66960C2214yes—
8C2×#66957C2214yes—
9#10623008C2212yes—
10C11×#423C2212yes—
11C2×C11×#97C2211yescharacteristic
12C2×#66889C2218yes—
13#10622742C2214yes—
14#10622545C2211yescharacteristic
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622451—22no—
17#10622451—22no—
18#10622447—22no—
19#10622447—22no—
20#10622328C414yescomplemented
21#10622325C414yescomplemented
22C11×#341C2214yes—
23#10622188C2214yes—
24C2×#4339C2314yes—
25C2×C11×M16C2314yes—
26C22×C8×C11C2312yes—
27C2×C42×C11C2311yescharacteristic
28#66983—22no—
29#66983—22no—
30C2×C4×Dic11C2312yes—
31C22×C11⋊C8C2312yes—
32#66960—48no—
33C2×Dic44C2×C414yes—
34#66957—48no—
35C2×D88C2×C414yes—
36C2×#4314C2×C418yes—
37C2×#4313—24no—
38C2×C8×D11—24no—
39#66928C2×C414yes—
40#66927C2×C412yes—
41C4×D44—22no—
42C4×D44—22no—
43#66922C2×C412yes—
44C11×C4⋊C8—22no—
45C11×C4⋊C8—22no—
46C11×#97C2×C414yes—
47C11⋊#95—22no—
48#66889—48no—
49(C2×D11)⋊C8—24no—
50(C2×D11)⋊C8—24no—
51C4×C11⋊C8D411yescharacteristic
52C4×C11⋊C8D412yes—
53C4×C11⋊C8D411yescharacteristic
54#22281—111nomaximal, Sylow
55C22×C4×C11#4112yes—
56C22×C4×C11C2411yescharacteristic
57C2×C22⋊D11—24no—
58C22×Dic11—22no—
59#4339—28no—
60#4339—28no—
61C2×D44—22no—
62C2×D44—22no—
63C2×D44C22×C414yes—
64C2×C4×D11—24no—
65C2×Dic22C22×C414yes—
66C11×M16—28no—
67C2×C8×C11—24no—
68C2×C8×C11—24no—
69C2×C8×C11C22×C414yes—
70C42×C11C22×C412yes—
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D411yescharacteristic
73(C2×D11)⋊C4—24no—
74(C2×D11)⋊C4—24no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4×Dic11—24no—
78C2×C11⋊C8—24no—
79C2×C11⋊C8C2×D412yes—
80C2×C11⋊C8C2×D412yes—
81Dic44—44no—
82D88—44no—
83#4314—48no—
84#4313—48no—
85C8×D11—48no—
86#3150—111no—
87#2931—112no—
88#1963—112no—
89#1876—118no—
90#1838D1111yescharacteristic, complemented
91#1746—111no—
92C23×C11C2×#4111yescharacteristic
93C22×D11—24no—
94C2×C4×C11—42no—
95C2×C4×C11C4×D412yes—
96C2×C4×C11C4×D412yes—
97C2×C4×C11C23×C411yescharacteristic
98C2×C4×C11C22×D411yescharacteristic
99C2×C4×C11H(5,𝔽2)14yes—
100C22⋊D11—48no—
101C2×Dic11—24no—
102C2×Dic11—44no—
103C2×Dic11—42no—
104D44—28no—
105D44—44no—
106D44—44no—
107C4×D11—44no—
108C4×D11—44no—
109Dic22—28no—
110C8×C11—24no—
111C8×C11—44no—
112C11⋊C8—22no—
113C11⋊C8—22no—
114C2×#135—114no—
115C2×#131—114no—
116#532—112no—
117#497—114no—
118#496—114no—
119#436—222no—
120#436—222no—
121C8×D4—222no—
122C8×D4—222no—
123#423C2×D1112yes—
124C2×#104—118no—
125#408—114no—
126C2×#97C2×D1111yescharacteristic
127C2×C4×C8—111no—
128#376—111no—
129#341C2×D1114yes—
130#336—114no—
131C22×C11—22no—
132C22×C11C2×C4×D411yescharacteristic
133C22×C11#54012yes—
134C2×D11—44no—
135C2×D11—44no—
136C2×D11—44no—
137C4×C11—22no—
138C4×C11—22no—
139C4×C11#51812yes—
140C4×C11#53512yes—
141Dic11—44no—
142Dic11—82no—
143C2×#41—114no—
144#135—448no—
145C2×Q16—114no—
146C2×SD16—118no—
147C2×D8—114no—
148#131—448no—
149C2×M16—224no—
150C2×M16C22×D1114yes—
151C22×C8—112no—
152C22×C8—224no—
153C22×C8C22×D1112yes—
154C4⋊Q8—112no—
155#127—112no—
156#124—114no—
157#121—222no—
158#121—222no—
159C4×D4—222no—
160C4×D4—222no—
161C2×C42—112no—
162C2×C42C22×D1111yescharacteristic
163C4⋊C8—22no—
164C4⋊C8—22no—
165#104—448no—
166C22⋊C8—224no—
167C22⋊C8—224no—
168#97C4×D1114yes—
169C4×C8—111no—
170C4×C8—112no—
171C4×C8—111no—
172#95—222no—
173C2×C11—22no—
174C2×C11#232811yescharacteristic
175C2×C11#295512yes—
176D11—84no—
177#41—228no—
178#41—228no—
179C2×Q8—114no—
180C2×D4—114no—
181C2×D4—224no—
182C2×D4—222no—
183C2×D4—222no—
184C22×C4—224no—
185C22×C4—222no—
186C22×C4#434312yes—
187C22×C4C23×D1111yescharacteristic
188Q16—444no—
189SD16—448no—
190D8—444no—
191M16—28no—
192M16—448no—
193C2×C8—24no—
194C2×C8—24no—
195C2×C8—112no—
196C2×C8—112no—
197C2×C8—224no—
198C2×C8—448no—
199C2×C8C2×C4×D1114yes—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C22⋊C4—224no—
203C22⋊C4—224no—
204C42—224no—
205C42C2×C4×D1112yes—
206C42D4×D1111yescharacteristic
207C42D4×D1111yescharacteristic
208C11#2228111yescharacteristic, complemented, Sylow
209C23—224no—
210C23C2×#434311yescharacteristic
211Q8—228no—
212D4—228no—
213D4—444no—
214D4—444no—
215D4—448no—
216C2×C4—42no—
217C2×C4—224no—
218C2×C4—444no—
219C2×C4—444no—
220C2×C4—444no—
221C2×C4—442no—
222C2×C4#6694612yes—
223C2×C4#6694612yes—
224C2×C4C22×C4×D1111yescharacteristic
225C2×C4C2×D4×D1111yescharacteristic
226C2×C4#6704214yes—
227C8—24no—
228C8—44no—
229C8—222no—
230C8—222no—
231C22—22no—
232C22—444no—
233C22—444no—
234C22—444no—
235C22C2×#6694611yescharacteristic
236C22#1062322912yes—
237C4—22no—
238C4—22no—
239C4—444no—
240C4—882no—
241C4#1062305212yes—
242C4#1062320512yes—
243C2—22no—
244C2—884no—
245C2#1307133911yescharacteristic
246C2#1307751812yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1838C2
socleC22×C11C2×C4×D4
prime radical#13079062C2
cosocleC22×C4×C11C24
hypercenter#1838D11
hypocenterC11#22281
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #13077327C2semidirect
3. #13069447C2semidirect
4. #13068944C2semidirect
5. #13068369C2semidirect
6. C11×#1838C2semidirect
20. #10622328C4semidirect
21. #10622325C4semidirect
90. #1838D11semidirect
208. C11#22281semidirect

Maximal subgroups

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

subgroupindex
#130790622
#130773272
#130694472
#130689442
#130683692
C11×#18382
#2228111