Finite Group Databasebeta

← C31×#7359 #21464118

Subgroups — C31×#7359 #21464118

Order 7936.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C31×#1991C211yesmaximal, characteristic
2C31×#1324C212yesmaximal
3C2×C31×#125C411yescharacteristic
4C2×C4×C8×C31C411yescharacteristic
5C31×#382C2211yescharacteristic
6C31×#340—22no—
7C31×#324—22no—
8C22×C8×C31—21no—
9C31×#125—21no—
10C31×#125—41no—
11C31×#125C812yescomplemented
12C2×C4⋊C4×C31—21no—
13C2×C4⋊C4×C31—41no—
14C2×C4⋊C4×C31D412yes—
15C2×C42×C31C2×C411yescharacteristic
16C31×C22⋊C8—42no—
17C4×C8×C31—41no—
18C31×#95—41no—
19C22×C4×C31—21no—
20C22×C4×C31—22no—
21C22×C4×C31—41no—
22C22×C4×C31C22⋊C411yescharacteristic
23C2×C8×C31—22no—
24C2×C8×C31—41no—
25C2×C8×C31—41no—
26C2×C8×C31—82no—
27C4⋊C4×C31—22no—
28C4⋊C4×C31—42no—
29C4⋊C4×C31—42no—
30C4⋊C4×C31—42no—
31C4⋊C4×C31—41no—
32C42×C31—21no—
33C42×C31C2×C811yescharacteristic
34C42×C31M1611yescharacteristic
35#7359C3111yesmaximal, characteristic, direct product factor, Sylow
36C23×C31#9911yescharacteristic
37C2×C4×C31—21no—
38C2×C4×C31—21no—
39C2×C4×C31—21no—
40C2×C4×C31—21no—
41C2×C4×C31—42no—
42C2×C4×C31—42no—
43C2×C4×C31—42no—
44C2×C4×C31—82no—
45C2×C4×C31—82no—
46C2×C4×C31C22⋊C811yescharacteristic
47C2×C4×C31#10011yescharacteristic
48C8×C31—42no—
49C8×C31—162no—
50#1991C2×C3111yescharacteristic
51#1324C2×C3112yes—
52C22×C31—22no—
53C22×C31#32311yescharacteristic
54C22×C31#35411yescharacteristic
55C22×C31#35611yescharacteristic
56C4×C31—21no—
57C4×C31—21no—
58C4×C31—41no—
59C4×C31—41no—
60C4×C31—82no—
61C4×C31—82no—
62C2×#125C4×C3111yescharacteristic
63C2×C4×C8C4×C3111yescharacteristic
64#382C22×C3111yescharacteristic
65#340—22no—
66#324—22no—
67C2×C31—21no—
68C2×C31—21no—
69C2×C31#131911yescharacteristic
70C2×C31#141412yes—
71C22×C8—21no—
72#125—21no—
73#125—41no—
74#125C8×C3112yescomplemented
75C2×C4⋊C4—21no—
76C2×C4⋊C4—41no—
77C2×C4⋊C4D4×C3112yes—
78C2×C42C2×C4×C3111yescharacteristic
79C22⋊C8—42no—
80C4×C8—41no—
81#95—41no—
82C31#735911yescharacteristic, direct product factor, Sylow
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—41no—
86C22×C4C22⋊C4×C3111yescharacteristic
87C2×C8—22no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—82no—
91C4⋊C4—22no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C4⋊C4—42no—
95C4⋊C4—41no—
96C42—21no—
97C42C2×C8×C3111yescharacteristic
98C42M16×C3111yescharacteristic
99C23C31×#9911yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4—82no—
108C2×C4—82no—
109C2×C4C31×C22⋊C811yescharacteristic
110C2×C4C31×#10011yescharacteristic
111C8—42no—
112C8—162no—
113C22—22no—
114C22C31×#32311yescharacteristic
115C22C31×#35411yescharacteristic
116C22C31×#35611yescharacteristic
117C4—21no—
118C4—21no—
119C4—41no—
120C4—41no—
121C4—82no—
122C4—82no—
123C2—21no—
124C2—21no—
125C2C31×#131911yescharacteristic
126C2C31×#141412yes—
subgroupG/H
center, socleC22×C31#354
commutatorC42C2×C8×C31
Frattini, cosocle#382C22×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#382 ◁ G

Complements

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

NH ≅ G/Ntype
11. C31×#125C8semidirect
35. #7359C31direct (N × H)
74. #125C8×C31semidirect
82. C31#7359direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19912
C31×#13242
#735931