Finite Group Databasebeta

← #16844261

Subgroups — #16844261

Order 3968.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521106C211yesmaximal, characteristic
3#14520785C214yesmaximal
4C31×#383C211yesmaximal, characteristic
5C2×C42×C31C2211yescharacteristic
6#11758503—21no—
7#11758501—21no—
8#11758501C2212yes—
9#11758447—21no—
10#11758446C411yescharacteristic, complemented
11#11758446C411yescharacteristic, complemented
12C4×Dic62—21no—
13C4×Dic62C412yescomplemented
14C31×#95—21no—
15C31×#95—21no—
16C31×#95C2212yes—
17C22⋊(C31⋊C8)C2212yes—
18C4⋊(C31⋊C8)—21no—
19#11758391—21no—
20C22×C4×C31—22no—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C2×Dic62—21no—
25C2×Dic62C2×C412yes—
26C42×C31C2×C411yescharacteristic
27C42×C31C2×C411yescharacteristic
28C42×C31D411yescharacteristic
29C42×C31D411yescharacteristic
30C22⋊Dic31—22no—
31C4⋊Dic31—21no—
32C4⋊Dic31—21no—
33C4⋊Dic31—21no—
34C4⋊Dic31C2×C412yes—
35Dic31⋊C4—22no—
36Dic31⋊C4—22no—
37C4×Dic31—22no—
38C2×C31⋊C8—22no—
39C23×C31C2×D411yescharacteristic
40C2×C4×C31—22no—
41C2×C4×C31—41no—
42C2×C4×C31—41no—
43C2×C4×C31—42no—
44C2×C4×C31—42no—
45C2×C4×C31—42no—
46C2×C4×C31C22⋊C411yescharacteristic
47C2×C4×C31C22⋊C411yescharacteristic
48C2×C4×C31C22⋊C411yescharacteristic
49C2×C4×C31C22⋊C411yescharacteristic
50C2×C4×C31C22×C411yescharacteristic
51C2×C4×C31C2×D411yescharacteristic
52C2×Dic31—22no—
53C2×Dic31—22no—
54Dic62—42no—
55Dic62—42no—
56C31⋊C8—42no—
57#1515—311nomaximal, Sylow
58C22×C31—21no—
59C22×C31—21no—
60C22×C31C2×C22⋊C411yescharacteristic
61C22×C31#13712yes—
62C4×C31—21no—
63C4×C31—21no—
64C4×C31—21no—
65C4×C31—21no—
66C4×C31—21no—
67C4×C31—21no—
68C4×C31—82no—
69Dic31—42no—
70Dic31—42no—
71#533—311no—
72#432—311no—
73#383D3111yescharacteristic
74#328—314no—
75C2×C31—22no—
76C2×C31#41011yescharacteristic
77C2×C31#41911yescharacteristic
78C2×C31#42111yescharacteristic
79C4⋊Q8—311no—
80C4⋊Q8—311no—
81#125—621no—
82C22⋊Q8—312no—
83C22⋊Q8—621no—
84C4×Q8—312no—
85C4×Q8—621no—
86#117—621no—
87C2×C42C2×D3111yescharacteristic
88C4⋊C8—621no—
89C22⋊C8—312no—
90#97—621no—
91#95—21no—
92#95—21no—
93#95C2×D3112yes—
94C31#151511yescharacteristic, complemented, Sylow
95C2×Q8—312no—
96C2×Q8—621no—
97C22×C4—22no—
98C22×C4C22⋊D3111yescharacteristic
99C22×C4C22⋊D3111yescharacteristic
100C22×C4C22×D3111yescharacteristic
101C2×C8—622no—
102C4⋊C4—312no—
103C4⋊C4—622no—
104C4⋊C4—621no—
105C4⋊C4—621no—
106C4⋊C4—621no—
107C4⋊C4—622no—
108C22⋊C4—622no—
109C42—622no—
110C42C4×D3111yescharacteristic
111C42C4×D3111yescharacteristic
112C42D12411yescharacteristic
113C42D12411yescharacteristic
114C23C2×C22⋊D3111yescharacteristic
115Q8—1242no—
116Q8—1242no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—622no—
124C2×C4—622no—
125C2×C4(C2×D31)⋊C411yescharacteristic
126C2×C4(C2×D31)⋊C411yescharacteristic
127C2×C4(C2×D31)⋊C411yescharacteristic
128C2×C4(C2×D31)⋊C411yescharacteristic
129C2×C4C2×C4×D3111yescharacteristic
130C2×C4C2×D12411yescharacteristic
131C8—1242no—
132C22—21no—
133C22—21no—
134C22C2×(C2×D31)⋊C411yescharacteristic
135C22#1175852812yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—1242no—
144C4—1242no—
145C2—22no—
146C2#1452102211yescharacteristic
147C2#1452105711yescharacteristic
148C2#1452106711yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#383C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#383D31
hypocenterC31#1515
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #11758446C4semidirect
11. #11758446C4semidirect
13. C4×Dic62C4semidirect
94. C31#1515semidirect

Maximal subgroups

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

subgroupindex
#145216062
#145211062
#145207852
C31×#3832
#151531