Finite Group Databasebeta

← C31×#1821 #16841754

Subgroups — C31×#1821 #16841754

Order 3968.

316 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C22×C4⋊C4×C31C211yesmaximal, characteristic
2C31×#407C212yesmaximal
3C31×#343C214yesmaximal, complemented
4C23×C4×C31C412yes—
5C23×C4×C31C2211yescharacteristic
6C2×M16×C31C2214yes—
7C2×C4⋊C4×C31—22no—
8C2×C4⋊C4×C31—22no—
9C2×C4⋊C4×C31C412yes—
10C2×C4⋊C4×C31C2212yes—
11C31×C22⋊C8—22no—
12C31×C22⋊C8—22no—
13C24×C31C2×C411yescharacteristic
14C22×C4×C31—24no—
15C22×C4×C31—22no—
16C22×C4×C31—22no—
17C22×C4×C31—44no—
18C22×C4×C31C2×C411yescharacteristic
19C22×C4×C31C2×C414yes—
20C22×C4×C31D412yes—
21C22×C4×C31D412yes—
22C22×C4×C31C2311yescharacteristic
23M16×C31—28no—
24C2×C8×C31—24no—
25C4⋊C4×C31—24no—
26C4⋊C4×C31—24no—
27C23×C31—22no—
28C23×C31—22no—
29C23×C31—22no—
30C23×C31C22⋊C411yescharacteristic
31C23×C31C22⋊C411yescharacteristic
32C23×C31C22×C411yescharacteristic
33C2×C4×C31—22no—
34C2×C4×C31—24no—
35C2×C4×C31—24no—
36C2×C4×C31—24no—
37C2×C4×C31—44no—
38C2×C4×C31—44no—
39C2×C4×C31—44no—
40C2×C4×C31C22⋊C412yes—
41C2×C4×C31C2×D412yes—
42C2×C4×C31#4114yes—
43C8×C31—44no—
44#1821C3111yesmaximal, characteristic, direct product factor, Sylow
45C22×C31—28no—
46C22×C31—21no—
47C22×C31—21no—
48C22×C31—21no—
49C22×C31—21no—
50C22×C31—21no—
51C22×C31—21no—
52C22×C31#10012yes—
53C22×C31#10112yes—
54C22×C31C2×C22⋊C411yescharacteristic
55C22×C31#11712yes—
56C4×C31—22no—
57C4×C31—44no—
58C4×C31#12314yes—
59C22×C4⋊C4C2×C3111yescharacteristic
60#407C2×C3112yes—
61#343C2×C3114yescomplemented
62C2×C31—22no—
63C2×C31—22no—
64C2×C31—22no—
65C2×C31#38111yescharacteristic
66C2×C31C2×#10011yescharacteristic
67C2×C31C2×#10111yescharacteristic
68C23×C4C4×C3112yes—
69C23×C4C22×C3111yescharacteristic
70C2×M16C22×C3114yes—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4C4×C3112yes—
74C2×C4⋊C4C22×C3112yes—
75C22⋊C8—22no—
76C22⋊C8—22no—
77C31#182111yescharacteristic, direct product factor, Sylow
78C24C2×C4×C3111yescharacteristic
79C22×C4—24no—
80C22×C4—22no—
81C22×C4—22no—
82C22×C4—44no—
83C22×C4C2×C4×C3111yescharacteristic
84C22×C4C2×C4×C3114yes—
85C22×C4D4×C3112yes—
86C22×C4D4×C3112yes—
87C22×C4C23×C3111yescharacteristic
88M16—28no—
89C2×C8—24no—
90C4⋊C4—24no—
91C4⋊C4—24no—
92C23—22no—
93C23—22no—
94C23—22no—
95C23C22⋊C4×C3111yescharacteristic
96C23C22⋊C4×C3111yescharacteristic
97C23C22×C4×C3111yescharacteristic
98C2×C4—22no—
99C2×C4—24no—
100C2×C4—24no—
101C2×C4—24no—
102C2×C4—44no—
103C2×C4—44no—
104C2×C4—44no—
105C2×C4C22⋊C4×C3112yes—
106C2×C4C2×D4×C3112yes—
107C2×C4#41×C3114yes—
108C8—44no—
109C22—28no—
110C22—21no—
111C22—21no—
112C22—21no—
113C22—21no—
114C22—21no—
115C22—21no—
116C22C31×#10012yes—
117C22C31×#10112yes—
118C22C2×C22⋊C4×C3111yescharacteristic
119C22C31×#11712yes—
120C4—22no—
121C4—44no—
122C4C31×#12314yes—
123C2—22no—
124C2—22no—
125C2—22no—
126C2C31×#38111yescharacteristic
127C2C2×C31×#10011yescharacteristic
128C2C2×C31×#10111yescharacteristic
subgroupG/H
center, socleC22×C31C2×C22⋊C4
commutatorC23C22×C4×C31
Frattini, cosocleC22×C4C23×C31
prime radicalC24×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#343C2semidirect
44. #1821C31direct (N × H)
61. #343C2×C31semidirect
77. C31#1821direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×C312
C31×#4072
C31×#3432
#182131