Finite Group Databasebeta

← #14767669

Subgroups — #14767669

Order 2816.

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

normal subgroups only

This group has 826 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#13077335C212yesmaximal, complemented
3#13069444C212yesmaximal, complemented
4#13068942C218yesmaximal, complemented
5#13068757C211yesmaximal, characteristic, complemented
6C11×#1745C211yesmaximal, characteristic, complemented
7C2×#66957C2214yes—
8C2×#66954C2214yes—
9#10623008C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C43×C11C2211yescharacteristic
13#10622723C2214yes—
14C2×#66869C2218yes—
15#10622537C2212yes—
16#10622328C414yescomplemented
17#10622325C414yescomplemented
18#10622319—28no—
19C11×#336C2214yes—
20#10622190C2214yes—
21C2×#4339C2314yes—
22C22×C8×C11C2312yes—
23C22×C8×C11C2312yes—
24C2×C42×C11—22no—
25C2×C42×C11C2312yes—
26C2×C42×C11C2311yescharacteristic
27#66983—24no—
28C2×#4318C2314yes—
29C2×Dic44C2×C414yes—
30#66957—48no—
31C2×D88C2×C414yes—
32C2×#4314C2×C418yes—
33#66954—48no—
34C2×#4313—24no—
35C2×C8×D11—24no—
36#66928C2×C414yes—
37#66927C2×C412yes—
38C4×D44—24no—
39#66922C2×C412yes—
40C11×#97C2×C414yes—
41C11×#97D414yes—
42(C2×D11)⋊C8—28no—
43#66869—48no—
44C4⋊(C11⋊C8)—24no—
45#22283—111nomaximal, Sylow
46C22×C4×C11—22no—
47C22×C4×C11#4112yes—
48C22×C4×C11C2411yescharacteristic
49C2×C22⋊D11—24no—
50#4339—28no—
51#4339—28no—
52C2×D44—24no—
53C2×D44C22×C414yes—
54C2×C4×D11—24no—
55C2×Dic22C22×C414yes—
56C2×C8×C11—24no—
57C2×C8×C11—24no—
58C2×C8×C11C22×C414yes—
59C2×C8×C11C2×D414yes—
60C42×C11—24no—
61C42×C11—44no—
62C42×C11C22×C412yes—
63C42×C11C2×D412yes—
64(C2×D11)⋊C4—28no—
65C4⋊Dic11—24no—
66#4318—28no—
67C2×C11⋊C8—24no—
68Dic44—44no—
69D88—44no—
70#4314—48no—
71#4313—48no—
72C8×D11—48no—
73#3150—111no—
74#2932—112no—
75#1962—112no—
76#1876—118no—
77#1838—111no—
78#1745D1111yescharacteristic, complemented
79C23×C11C2×#4111yescharacteristic
80C22×D11—24no—
81C2×C4×C11—24no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C4×D414yes—
86C2×C4×C11C23×C411yescharacteristic
87C2×C4×C11C22×D411yescharacteristic
88C2×C4×C11H(5,𝔽2)14yes—
89C22⋊D11—48no—
90C2×Dic11—24no—
91D44—28no—
92D44—84no—
93C4×D11—44no—
94C4×D11—44no—
95Dic22—28no—
96C8×C11—24no—
97C8×C11—24no—
98C11⋊C8—44no—
99C2×#135—114no—
100C2×#131—114no—
101#532—112no—
102#497—114no—
103#496—114no—
104#435—228no—
105#423—112no—
106C2×#104—118no—
107#408—114no—
108C2×#97C2×D1111yescharacteristic
109C2×#97C2×D1111yescharacteristic
110C43C2×D1111yescharacteristic
111#341—114no—
112#336C2×D1114yes—
113C22×C11—22no—
114C22×C11C2×C4×D411yescharacteristic
115C22×C11#54012yes—
116C2×D11—44no—
117C2×D11—48no—
118C4×C11—24no—
119C4×C11—44no—
120C4×C11#51812yes—
121C4×C11#53512yes—
122Dic11—44no—
123C2×#41—114no—
124#135—448no—
125C2×Q16—114no—
126C2×SD16—118no—
127C2×D8—114no—
128#131—448no—
129C2×M16—114no—
130C2×M16—224no—
131C22×C8—224no—
132C22×C8C22×D1112yes—
133C22×C8C22×D1112yes—
134C4⋊Q8—112no—
135#127—112no—
136#124—114no—
137#121—224no—
138C4×D4—224no—
139C2×C42—22no—
140C2×C42C22×D1112yes—
141C2×C42C22×D1111yescharacteristic
142C4⋊C8—224no—
143#104—448no—
144C22⋊C8—228no—
145#97C4×D1114yes—
146#97D4414yes—
147C2×C11—22no—
148C2×C11#232811yescharacteristic
149C2×C11#295612yes—
150D11—84no—
151#41—228no—
152#41—228no—
153C2×Q8—114no—
154C2×D4—114no—
155C2×D4—224no—
156C2×D4—224no—
157C22×C4—22no—
158C22×C4—224no—
159C22×C4#433912yes—
160C22×C4C23×D1111yescharacteristic
161Q16—444no—
162SD16—448no—
163D8—444no—
164M16—228no—
165M16—448no—
166C2×C8—24no—
167C2×C8—24no—
168C2×C8—224no—
169C2×C8—448no—
170C2×C8C2×C4×D1114yes—
171C2×C8C2×D4414yes—
172C4⋊C4—224no—
173C22⋊C4—228no—
174C42—24no—
175C42—44no—
176C42C2×C4×D1112yes—
177C42C2×D4412yes—
178C11#2228311yescharacteristic, complemented, Sylow
179C23—224no—
180C23C2×#433911yescharacteristic
181Q8—228no—
182D4—228no—
183D4—448no—
184D4—884no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—224no—
190C2×C4—444no—
191C2×C4—444no—
192C2×C4C4×D4414yes—
193C2×C4C22×C4×D1111yescharacteristic
194C2×C4C22×D4411yescharacteristic
195C2×C4#6704214yes—
196C8—24no—
197C8—24no—
198C8—444no—
199C22—22no—
200C22—448no—
201C22—444no—
202C22C2×C4×D4411yescharacteristic
203C22#1062306612yes—
204C4—24no—
205C4—44no—
206C4—444no—
207C4#1062305212yes—
208C4#1062305612yes—
209C2—22no—
210C2—884no—
211C2#1307134111yescharacteristic
212C2#1307752712yes—
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1745C2
socleC22×C11C2×C4×D4
prime radical#13079062C2
cosocleC22×C4×C11C24
hypercenter#1745D11
hypocenterC11#22283
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1745

Complements

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

NH ≅ G/Ntype
2. #13077335C2semidirect
3. #13069444C2semidirect
4. #13068942C2semidirect
5. #13068757C2semidirect
6. C11×#1745C2semidirect
16. #10622328C4semidirect
17. #10622325C4semidirect
78. #1745D11semidirect
178. C11#22283semidirect

Maximal subgroups

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

subgroupindex
#130790622
#130773352
#130694442
#130689422
#130687572
C11×#17452
#2228311