Finite Group Databasebeta

← C31×#1466 #16841399

Subgroups — C31×#1466 #16841399

Order 3968.

300 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 100 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×C4×D4×C31C211yesmaximal, characteristic
2C31×#432C212yesmaximal, complemented
3C31×#323C214yesmaximal, complemented
4C22×D4×C31C411yescharacteristic
5C23×C4×C31C412yes—
6C4×D4×C31—22no—
7C4×D4×C31—22no—
8C2×C4⋊C4×C31C411yescharacteristic
9C2×C22⋊C4×C31C2212yes—
10C2×C42×C31C2211yescharacteristic
11C31×C4⋊C8—22no—
12C31×C22⋊C8C2214yes—
13C31×#97—22no—
14C24×C31C2×C412yes—
15C2×D4×C31—24no—
16C2×D4×C31—22no—
17C22×C4×C31—22no—
18C22×C4×C31—22no—
19C22×C4×C31—44no—
20C22×C4×C31C2×C411yescharacteristic
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31C2×C412yes—
23C22×C4×C31C2311yescharacteristic
24C2×C8×C31—24no—
25C4⋊C4×C31—22no—
26C22⋊C4×C31—24no—
27C42×C31D412yes—
28C42×C31D412yes—
29C23×C31—22no—
30C23×C31—22no—
31C23×C31—42no—
32C23×C31—42no—
33C23×C31M1614yes—
34C23×C31C22×C411yescharacteristic
35D4×C31—28no—
36C2×C4×C31—22no—
37C2×C4×C31—22no—
38C2×C4×C31—22no—
39C2×C4×C31—41no—
40C2×C4×C31—44no—
41C2×C4×C31—44no—
42C2×C4×C31—42no—
43C2×C4×C31C22⋊C412yes—
44C2×C4×C31C22⋊C411yescharacteristic
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C2×D412yes—
47C8×C31—44no—
48#1466C3111yesmaximal, characteristic, direct product factor, Sylow
49C22×C31—21no—
50C22×C31—21no—
51C22×C31—24no—
52C22×C31—44no—
53C22×C31—44no—
54C22×C31—42no—
55C22×C31—42no—
56C22×C31C2×C22⋊C411yescharacteristic
57C22×C31C2×M1612yes—
58C4×C31—22no—
59C4×C31—22no—
60C4×C31—21no—
61C4×C31—42no—
62C4×C31#10012yes—
63C2×C4×D4C2×C3111yescharacteristic
64#432C2×C3112yescomplemented
65#323C2×C3114yescomplemented
66C2×C31—22no—
67C2×C31—44no—
68C2×C31#40711yescharacteristic
69C2×C31#41011yescharacteristic
70C2×C31C2×#10011yescharacteristic
71C22×D4C4×C3111yescharacteristic
72C23×C4C4×C3112yes—
73C4×D4—22no—
74C4×D4—22no—
75C2×C4⋊C4C4×C3111yescharacteristic
76C2×C22⋊C4C22×C3112yes—
77C2×C42C22×C3111yescharacteristic
78C4⋊C8—22no—
79C22⋊C8C22×C3114yes—
80#97—22no—
81C31#146611yescharacteristic, direct product factor, Sylow
82C24C2×C4×C3112yes—
83C2×D4—24no—
84C2×D4—22no—
85C22×C4—22no—
86C22×C4—22no—
87C22×C4—44no—
88C22×C4C2×C4×C3111yescharacteristic
89C22×C4C2×C4×C3111yescharacteristic
90C22×C4C2×C4×C3112yes—
91C22×C4C23×C3111yescharacteristic
92C2×C8—24no—
93C4⋊C4—22no—
94C22⋊C4—24no—
95C42D4×C3112yes—
96C42D4×C3112yes—
97C23—22no—
98C23—22no—
99C23—42no—
100C23—42no—
101C23M16×C3114yes—
102C23C22×C4×C3111yescharacteristic
103D4—28no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—41no—
108C2×C4—44no—
109C2×C4—44no—
110C2×C4—42no—
111C2×C4C22⋊C4×C3112yes—
112C2×C4C22⋊C4×C3111yescharacteristic
113C2×C4C22⋊C4×C3111yescharacteristic
114C2×C4C2×D4×C3112yes—
115C8—44no—
116C22—21no—
117C22—21no—
118C22—24no—
119C22—44no—
120C22—44no—
121C22—42no—
122C22—42no—
123C22C2×C22⋊C4×C3111yescharacteristic
124C22C2×M16×C3112yes—
125C4—22no—
126C4—22no—
127C4—21no—
128C4—42no—
129C4C31×#10012yes—
130C2—22no—
131C2—44no—
132C2C31×#40711yescharacteristic
133C2C31×#41011yescharacteristic
134C2C2×C31×#10011yescharacteristic
subgroupG/H
center, socleC22×C31C2×C22⋊C4
commutatorC23C22×C4×C31
Frattini, cosocleC22×C4C23×C31
prime radicalC22×D4×C31C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#432C2semidirect
3. C31×#323C2semidirect
48. #1466C31direct (N × H)
64. #432C2×C31semidirect
65. #323C2×C31semidirect
81. C31#1466direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C312
C31×#4322
C31×#3232
#146631