Finite Group Databasebeta

← #14767657

Subgroups — #14767657

Order 2816.

818 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 211 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#13077329C212yesmaximal, complemented
3#13069448C212yesmaximal, complemented
4#13068942C218yesmaximal, complemented
5#13068757C211yesmaximal, characteristic, complemented
6C11×#1746C211yesmaximal, characteristic, complemented
7C2×#66957C2214yes—
8C2×#66954C2214yes—
9#10623008C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C11×#376C2211yescharacteristic
13#10622723C2214yes—
14C2×#66869C2218yes—
15#10622537C2212yes—
16#10622328C414yescomplemented
17#10622325C414yescomplemented
18#10622301—22no—
19#10622301—22no—
20C8×D44—22no—
21C8×D44—22no—
22C11×#336C2214yes—
23#10622190C2214yes—
24C2×#4339C2314yes—
25C22×C8×C11C2312yes—
26C22×C8×C11C2312yes—
27C2×C42×C11C2312yes—
28C2×C42×C11C2311yescharacteristic
29#66983—22no—
30#66983—22no—
31C2×#4318C2314yes—
32C2×Dic44C2×C414yes—
33#66957—48no—
34C2×D88C2×C414yes—
35C2×#4314C2×C418yes—
36#66954—48no—
37C2×#4313—24no—
38C2×C8×D11—24no—
39#66928C2×C414yes—
40#66927C2×C412yes—
41C4×D44—22no—
42C4×D44—22no—
43#66922C2×C412yes—
44C11×#97C2×C414yes—
45C4×C8×C11D411yescharacteristic
46C4×C8×C11D412yes—
47C4×C8×C11D411yescharacteristic
48C11×#95—22no—
49(C2×D11)⋊C8—24no—
50(C2×D11)⋊C8—24no—
51#66869—48no—
52C4⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#22281—111nomaximal, Sylow
55C22×C4×C11—22no—
56C22×C4×C11#4112yes—
57C22×C4×C11C2411yescharacteristic
58C2×C22⋊D11—24no—
59#4339—28no—
60#4339—28no—
61C2×D44—22no—
62C2×D44—22no—
63C2×D44C22×C414yes—
64C2×C4×D11—24no—
65C2×Dic22C22×C414yes—
66C2×C8×C11—24no—
67C2×C8×C11—24no—
68C2×C8×C11C22×C414yes—
69C2×C8×C11C2×D412yes—
70C2×C8×C11C2×D412yes—
71C42×C11—24no—
72C42×C11C22×C412yes—
73C42×C11C2×D411yescharacteristic
74C42×C11C2×D411yescharacteristic
75(C2×D11)⋊C4—24no—
76(C2×D11)⋊C4—24no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79#4318—28no—
80C2×C11⋊C8—24no—
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#1838—111no—
91#1746D1111yescharacteristic, complemented
92C23×C11C2×#4111yescharacteristic
93C22×D11—24no—
94C2×C4×C11—42no—
95C2×C4×C11—44no—
96C2×C4×C11—42no—
97C2×C4×C11C4×D412yes—
98C2×C4×C11C4×D412yes—
99C2×C4×C11C23×C411yescharacteristic
100C2×C4×C11C22×D411yescharacteristic
101C2×C4×C11H(5,𝔽2)14yes—
102C22⋊D11—48no—
103C2×Dic11—24no—
104D44—28no—
105D44—44no—
106D44—44no—
107C4×D11—44no—
108C4×D11—44no—
109Dic22—28no—
110C8×C11—24no—
111C8×C11—22no—
112C8×C11—22no—
113C11⋊C8—44no—
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#423—112no—
124C2×#104—118no—
125#408—114no—
126C2×#97C2×D1111yescharacteristic
127C2×C4×C8C2×D1111yescharacteristic
128#376C2×D1111yescharacteristic
129#341—114no—
130#336C2×D1114yes—
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—82no—
140C4×C11#51812yes—
141C4×C11#53512yes—
142Dic11—44no—
143C2×#41—114no—
144#135—448no—
145C2×Q16—114no—
146C2×SD16—118no—
147C2×D8—114no—
148#131—448no—
149C2×M16—114no—
150C2×M16—224no—
151C22×C8—224no—
152C22×C8C22×D1112yes—
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×C42C22×D1112yes—
162C2×C42C22×D1111yescharacteristic
163C4⋊C8—222no—
164C4⋊C8—222no—
165#104—448no—
166C22⋊C8—224no—
167C22⋊C8—224no—
168#97C4×D1114yes—
169C4×C8D4411yescharacteristic
170C4×C8D4412yes—
171C4×C8D4411yescharacteristic
172#95—22no—
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—22no—
185C22×C4—224no—
186C22×C4#433912yes—
187C22×C4C23×D1111yescharacteristic
188Q16—444no—
189SD16—448no—
190D8—444no—
191M16—228no—
192M16—448no—
193C2×C8—24no—
194C2×C8—24no—
195C2×C8—224no—
196C2×C8—448no—
197C2×C8C2×C4×D1114yes—
198C2×C8C2×D4412yes—
199C2×C8C2×D4412yes—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C22⋊C4—224no—
203C22⋊C4—224no—
204C42—24no—
205C42C2×C4×D1112yes—
206C42C2×D4411yescharacteristic
207C42C2×D4411yescharacteristic
208C11#2228111yescharacteristic, complemented, Sylow
209C23—224no—
210C23C2×#433911yescharacteristic
211Q8—228no—
212D4—228no—
213D4—444no—
214D4—444no—
215D4—448no—
216C2×C4—42no—
217C2×C4—44no—
218C2×C4—42no—
219C2×C4—224no—
220C2×C4—444no—
221C2×C4—444no—
222C2×C4C4×D4412yes—
223C2×C4C4×D4412yes—
224C2×C4C22×C4×D1111yescharacteristic
225C2×C4C22×D4411yescharacteristic
226C2×C4#6704214yes—
227C8—24no—
228C8—22no—
229C8—22no—
230C8—444no—
231C22—22no—
232C22—444no—
233C22—444no—
234C22—444no—
235C22C2×C4×D4411yescharacteristic
236C22#1062306612yes—
237C4—22no—
238C4—22no—
239C4—82no—
240C4—444no—
241C4#1062305212yes—
242C4#1062305612yes—
243C2—22no—
244C2—884no—
245C2#1307134111yescharacteristic
246C2#1307752012yes—
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC22×C11C2×C4×D4
prime radical#13079062C2
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22281
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #13077329C2semidirect
3. #13069448C2semidirect
4. #13068942C2semidirect
5. #13068757C2semidirect
6. C11×#1746C2semidirect
16. #10622328C4semidirect
17. #10622325C4semidirect
91. #1746D11semidirect
208. C11#22281semidirect

Maximal subgroups

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

subgroupindex
#130790622
#130773292
#130694482
#130689422
#130687572
C11×#17462
#2228111