Finite Group Databasebeta

← C31×#7371 #21464130

Subgroups — C31×#7371 #21464130

Order 7936.

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

normal subgroups only

This group has 190 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×#1844C211yesmaximal, characteristic
2C31×#1325C212yesmaximal
3C2×C31×#106—22no—
4C2×C4×C8×C31C411yescharacteristic
5C31×#384C411yescharacteristic
6C31×#384C2211yescharacteristic
7C31×#324—22no—
8C22×C8×C31—21no—
9C2×C4⋊C4×C31—21no—
10C2×C4⋊C4×C31—41no—
11C2×C4⋊C4×C31—41no—
12C2×C4⋊C4×C31D412yes—
13C2×C42×C31C2×C411yescharacteristic
14C31×#106—44no—
15C31×C22⋊C8—42no—
16C4×C8×C31—21no—
17C4×C8×C31C812yescomplemented
18C22×C4×C31—21no—
19C22×C4×C31—22no—
20C22×C4×C31—41no—
21C22×C4×C31C22⋊C411yescharacteristic
22C2×C8×C31—22no—
23C2×C8×C31—22no—
24C2×C8×C31—22no—
25C2×C8×C31—82no—
26C4⋊C4×C31—42no—
27C4⋊C4×C31—42no—
28C4⋊C4×C31—82no—
29C4⋊C4×C31—82no—
30C42×C31—21no—
31C42×C31C2×C811yescharacteristic
32C42×C31M1611yescharacteristic
33#7371C3111yesmaximal, characteristic, direct product factor, Sylow
34C23×C31#9911yescharacteristic
35C2×C4×C31—22no—
36C2×C4×C31—22no—
37C2×C4×C31—21no—
38C2×C4×C31—21no—
39C2×C4×C31—21no—
40C2×C4×C31—21no—
41C2×C4×C31—42no—
42C2×C4×C31—82no—
43C2×C4×C31—82no—
44C2×C4×C31—81no—
45C2×C4×C31C22⋊C811yescharacteristic
46C2×C4×C31#10111yescharacteristic
47C8×C31—24no—
48C8×C31—162no—
49#1844C2×C3111yescharacteristic
50#1325C2×C3112yes—
51C22×C31—21no—
52C22×C31—21no—
53C22×C31#32411yescharacteristic
54C22×C31#35311yescharacteristic
55C22×C31#35611yescharacteristic
56C4×C31—22no—
57C4×C31—22no—
58C4×C31—21no—
59C4×C31—21no—
60C4×C31—82no—
61C4×C31—161no—
62C2×#106—22no—
63C2×C4×C8C4×C3111yescharacteristic
64#384C4×C3111yescharacteristic
65#384C22×C3111yescharacteristic
66#324—22no—
67C2×C31—21no—
68C2×C31—21no—
69C2×C31#132511yescharacteristic
70C2×C31#140911yescharacteristic
71C2×C31#141011yescharacteristic
72C22×C8—21no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4D4×C3112yes—
77C2×C42C2×C4×C3111yescharacteristic
78#106—44no—
79C22⋊C8—42no—
80C4×C8—21no—
81C4×C8C8×C3112yescomplemented
82C31#737111yescharacteristic, direct product factor, Sylow
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—41no—
86C22×C4C22⋊C4×C3111yescharacteristic
87C2×C8—22no—
88C2×C8—22no—
89C2×C8—22no—
90C2×C8—82no—
91C4⋊C4—42no—
92C4⋊C4—42no—
93C4⋊C4—82no—
94C4⋊C4—82no—
95C42—21no—
96C42C2×C8×C3111yescharacteristic
97C42M16×C3111yescharacteristic
98C23C31×#9911yescharacteristic
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—42no—
106C2×C4—82no—
107C2×C4—82no—
108C2×C4—81no—
109C2×C4C31×C22⋊C811yescharacteristic
110C2×C4C31×#10111yescharacteristic
111C8—24no—
112C8—162no—
113C22—21no—
114C22—21no—
115C22C31×#32411yescharacteristic
116C22C31×#35311yescharacteristic
117C22C31×#35611yescharacteristic
118C4—22no—
119C4—22no—
120C4—21no—
121C4—21no—
122C4—82no—
123C4—161no—
124C2—21no—
125C2—21no—
126C2C31×#132511yescharacteristic
127C2C31×#140911yescharacteristic
128C2C31×#141011yescharacteristic
subgroupG/H
center, socleC22×C31#353
commutatorC42C2×C8×C31
Frattini, cosocle#384C22×C31
prime radicalC23×C31#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#384 ◁ G

Complements

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

NH ≅ G/Ntype
17. C4×C8×C31C8semidirect
33. #7371C31direct (N × H)
81. C4×C8C8×C31semidirect
82. C31#7371direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#18442
C31×#13252
#737131