Finite Group Databasebeta

← #72254534

Subgroups — #72254534

Order 3520.

260 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×M16×C11⋊C5C211yesmaximal, characteristic, complemented
2#66983⋊C5C212yesmaximal, complemented
3C2×D88⋊C5C211yesmaximal, characteristic, complemented
4#66885⋊C5C212yesmaximal, complemented
5#66881⋊C5C211yesmaximal, characteristic, complemented
6C22×C4×C11⋊C5C2211yescharacteristic
7C2×C22⋊AGL(1,𝔽11)—22no—
8C2×C4⋊AGL(1,𝔽11)C2212yes—
9M16×C11⋊C5—22no—
10C2×C8×C11⋊C5C2211yescharacteristic
11C2×C8×C11⋊C5C2211yescharacteristic
12((C2×D11)⋊C4)⋊C5—22no—
13C4⋊(Dic11⋊C5)C2212yes—
14D88⋊C5—22no—
15#10622748C511yesmaximal, characteristic, complemented, Hall
16C23×C11⋊C5D411yescharacteristic
17C22×AGL(1,𝔽11)—22no—
18C2×C4×C11⋊C5—21no—
19C2×C4×C11⋊C5—21no—
20C2×C4×C11⋊C5D411yescharacteristic
21C2×C4×C11⋊C5C2311yescharacteristic
22C22⋊AGL(1,𝔽11)—44no—
23C2×Dic11⋊C5—22no—
24C4⋊AGL(1,𝔽11)—22no—
25C4⋊AGL(1,𝔽11)—22no—
26C8×C11⋊C5—21no—
27C8×C11⋊C5D412yescomplemented
28C2×C11×M16C2×C511yescharacteristic, complemented
29#66983C2×C512yescomplemented
30C2×D88C2×C511yescharacteristic, complemented
31#66885C2×C512yescomplemented
32#66881C2×C511yescharacteristic, complemented
33C5×#469—111nomaximal, Hall
34C22×C11⋊C5—21no—
35C22×C11⋊C5—22no—
36C22×C11⋊C5C2×D411yescharacteristic
37C2×AGL(1,𝔽11)—42no—
38C2×AGL(1,𝔽11)—42no—
39C2×AGL(1,𝔽11)—42no—
40C4×C11⋊C5—21no—
41C4×C11⋊C5C2×D411yescharacteristic
42C4×C11⋊C5#4111yescharacteristic
43Dic11⋊C5—42no—
44C22×C4×C11C22×C511yescharacteristic
45C2×C22⋊D11—22no—
46C2×D44C22×C512yes—
47C11×M16—22no—
48C2×C8×C11C22×C511yescharacteristic
49C2×C8×C11C22×C511yescharacteristic
50(C2×D11)⋊C4—22no—
51C4⋊Dic11C22×C512yes—
52D88—22no—
53C2×C5×D8—111no—
54C2×C5×M16—111no—
55C5×#121—112no—
56C5×#106—111no—
57C5×#102—112no—
58C2×C11⋊C5—41no—
59C2×C11⋊C5#12111yescharacteristic
60C2×C11⋊C5AGL(1,ℤ/8)12yes—
61AGL(1,𝔽11)—82no—
62C23×C11C5×D411yescharacteristic
63C22×D11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11C5×D411yescharacteristic
67C2×C4×C11C23×C511yescharacteristic
68C22⋊D11—44no—
69C2×Dic11—22no—
70D44—22no—
71D44—22no—
72C8×C11—21no—
73C8×C11C5×D412yescomplemented
74C2×C5×D4—112no—
75C2×C5×D4—222no—
76C22×C4×C5—111no—
77C5×D8—222no—
78C5×M16—222no—
79C2×C5×C8—111no—
80C2×C5×C8—111no—
81C5×C4⋊C4—112no—
82C5×C22⋊C4—222no—
83#469—111noSylow
84C11⋊C5#46911yescharacteristic, complemented, Hall
85C22×C11—21no—
86C22×C11—22no—
87C22×C11C2×C5×D411yescharacteristic
88C2×D11—42no—
89C2×D11—42no—
90C2×D11—42no—
91C4×C11—21no—
92C4×C11C2×C5×D411yescharacteristic
93C4×C11C5×#4111yescharacteristic
94Dic11—42no—
95C23×C5—111no—
96C23×C5—222no—
97C5×D4—222no—
98C5×D4—222no—
99C5×D4—444no—
100C2×C4×C5—111no—
101C2×C4×C5—111no—
102C2×C4×C5—221no—
103C2×C4×C5—221no—
104C2×C4×C5—222no—
105C5×C8—112no—
106C5×C8—221no—
107C2×D8—111no—
108C2×M16AGL(1,𝔽11)11yescharacteristic, complemented
109#121—112no—
110#106—111no—
111#102—112no—
112C2×C11—41no—
113C2×C11C5×#12111yescharacteristic
114C2×C11C5×AGL(1,ℤ/8)12yes—
115D11—82no—
116C22×C5—111no—
117C22×C5—221no—
118C22×C5—222no—
119C22×C5—442no—
120C22×C5—442no—
121C22×C5—442no—
122C4×C5—111no—
123C4×C5—111no—
124C4×C5—221no—
125C4×C5—442no—
126C2×D4—112no—
127C2×D4—222no—
128C22×C4C2×AGL(1,𝔽11)11yescharacteristic
129D8—222no—
130M16—22no—
131C2×C8C2×AGL(1,𝔽11)11yescharacteristic
132C2×C8C2×AGL(1,𝔽11)11yescharacteristic
133C4⋊C4—112no—
134C22⋊C4—222no—
135C11C5×#46911yescharacteristic, complemented, Sylow
136C2×C5—112no—
137C2×C5—111no—
138C2×C5—441no—
139C2×C5—882no—
140C23—222no—
141C23C4⋊AGL(1,𝔽11)11yescharacteristic
142D4—222no—
143D4—222no—
144D4—444no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—222no—
148C2×C4C4⋊AGL(1,𝔽11)11yescharacteristic
149C2×C4C22×AGL(1,𝔽11)11yescharacteristic
150C8—21no—
151C8C22⋊AGL(1,𝔽11)12yescomplemented
152C5—111noSylow
153C22—22no—
154C22—21no—
155C22—442no—
156C22—442no—
157C22—442no—
158C22C2×C4⋊AGL(1,𝔽11)11yescharacteristic
159C4—21no—
160C4—442no—
161C4#4339⋊C511yescharacteristic
162C4C2×C22⋊AGL(1,𝔽11)11yescharacteristic
163C2—41no—
164C2—882no—
165C2#66961⋊C512yes—
166C2#66983⋊C511yescharacteristic
subgroupG/H
centerC22C2×C4⋊AGL(1,𝔽11)
commutator, cosocleC2×C4×C11C23×C5
FrattiniC2×C4C22×AGL(1,𝔽11)
FittingC2×C11×M16C2×C5
socleC22×C11C2×C5×D4
hypercenterC2×M16AGL(1,𝔽11)
hypocenterC11C5×#469
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×M16×C11⋊C5C2semidirect
2. #66983⋊C5C2semidirect
3. C2×D88⋊C5C2semidirect
4. #66885⋊C5C2semidirect
5. #66881⋊C5C2semidirect
15. #10622748C5semidirect
27. C8×C11⋊C5D4semidirect
28. C2×C11×M16C2×C5semidirect
29. #66983C2×C5semidirect
30. C2×D88C2×C5semidirect
31. #66885C2×C5semidirect
32. #66881C2×C5semidirect
73. C8×C11C5×D4semidirect
84. C11⋊C5#469semidirect
108. C2×M16AGL(1,𝔽11)semidirect
135. C11C5×#469semidirect
151. C8C22⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C11⋊C52
#66983⋊C52
C2×D88⋊C52
#66885⋊C52
#66881⋊C52
#106227485
C5×#46911