Finite Group Databasebeta

← #16844224

Subgroups — #16844224

Order 3968.

228 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521606C211yesmaximal, characteristic
2#14520895C211yesmaximal, characteristic
3#14520787C214yesmaximal
4C31×#432C211yesmaximal, characteristic
5C2×C42×C31C2211yescharacteristic
6#11758503—21no—
7#11758501—21no—
8#11758501C2212yes—
9C2×C4×Dic31—21no—
10#11758447—21no—
11#11758446C411yescharacteristic, complemented
12#11758446C411yescharacteristic, complemented
13C4×Dic62—21no—
14C4×Dic62C412yescomplemented
15C31×C4⋊C8—21no—
16C31×C22⋊C8C2212yes—
17C31×#97—21no—
18C31⋊#95—21no—
19C31⋊#95C2212yes—
20C22×C4×C31D411yescharacteristic
21C22×C4×C31D411yescharacteristic
22C22×C4×C31C2311yescharacteristic
23C22×Dic31—22no—
24C2×Dic62—21no—
25C2×Dic62C2×C412yes—
26C2×C8×C31—22no—
27C42×C31C2×C411yescharacteristic
28C42×C31C2×C411yescharacteristic
29C42×C31D411yescharacteristic
30C42×C31D411yescharacteristic
31C22⋊Dic31—22no—
32C4⋊Dic31—21no—
33C4⋊Dic31—21no—
34C4⋊Dic31—21no—
35C4⋊Dic31C2×C412yes—
36Dic31⋊C4—22no—
37Dic31⋊C4—22no—
38C4×Dic31—24no—
39C4×Dic31—22no—
40C23×C31C2×D411yescharacteristic
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—41no—
44C2×C4×C31C22⋊C411yescharacteristic
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C22⋊C411yescharacteristic
47C2×C4×C31C22⋊C411yescharacteristic
48C2×C4×C31C22×C411yescharacteristic
49C2×C4×C31C2×D411yescharacteristic
50C2×Dic31—24no—
51C2×Dic31—22no—
52C2×Dic31—22no—
53C2×Dic31—42no—
54C2×Dic31—42no—
55Dic62—42no—
56Dic62—42no—
57C8×C31—42no—
58#1506—311nomaximal, Sylow
59C22×C31—21no—
60C22×C31—21no—
61C22×C31C2×C22⋊C411yescharacteristic
62C22×C31#13712yes—
63C4×C31—21no—
64C4×C31—21no—
65C4×C31—21no—
66C4×C31—21no—
67C4×C31—21no—
68C4×C31#10412yes—
69Dic31—44no—
70Dic31—42no—
71Dic31—42no—
72#533—311no—
73#432D3111yescharacteristic
74#376—311no—
75#328—314no—
76C2×C31—22no—
77C2×C31#41011yescharacteristic
78C2×C31#41911yescharacteristic
79C2×C31C2×#10411yescharacteristic
80C4⋊Q8—311no—
81C4⋊Q8—311no—
82#125—621no—
83C22⋊Q8—312no—
84C22⋊Q8—621no—
85C4×Q8—312no—
86C4×Q8—621no—
87#117—621no—
88C2×C42—621no—
89C2×C42C2×D3111yescharacteristic
90C4⋊C8—21no—
91C22⋊C8C2×D3112yes—
92#97—21no—
93#95—312no—
94#95—621no—
95C31#150611yescharacteristic, complemented, Sylow
96C2×Q8—312no—
97C2×Q8—621no—
98C22×C4—622no—
99C22×C4D12411yescharacteristic
100C22×C4D12411yescharacteristic
101C22×C4C22×D3111yescharacteristic
102C2×C8—22no—
103C4⋊C4—312no—
104C4⋊C4—622no—
105C4⋊C4—621no—
106C4⋊C4—621no—
107C4⋊C4—621no—
108C4⋊C4—622no—
109C22⋊C4—622no—
110C42—624no—
111C42—622no—
112C42C4×D3111yescharacteristic
113C42C4×D3111yescharacteristic
114C42C22⋊D3111yescharacteristic
115C42C22⋊D3111yescharacteristic
116C23C2×D12411yescharacteristic
117Q8—1242no—
118Q8—1242no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—624no—
123C2×C4—622no—
124C2×C4—622no—
125C2×C4—1242no—
126C2×C4—1242no—
127C2×C4(C2×D31)⋊C411yescharacteristic
128C2×C4(C2×D31)⋊C411yescharacteristic
129C2×C4(C2×D31)⋊C411yescharacteristic
130C2×C4(C2×D31)⋊C411yescharacteristic
131C2×C4C2×C4×D3111yescharacteristic
132C2×C4C2×C22⋊D3111yescharacteristic
133C8—42no—
134C22—21no—
135C22—21no—
136C22#1175848612yes—
137C22C2×(C2×D31)⋊C411yescharacteristic
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—21no—
143C4—1244no—
144C4—1242no—
145C4—1242no—
146C4#1175841312yes—
147C2—22no—
148C2#1452102211yescharacteristic
149C2#1452105911yescharacteristic
150C2C2×#1175841311yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#432C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#432D31
hypocenterC31#1506
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
11. #11758446C4semidirect
12. #11758446C4semidirect
14. C4×Dic62C4semidirect
95. C31#1506semidirect

Maximal subgroups

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

subgroupindex
#145216062
#145208952
#145207872
C31×#4322
#150631