Finite Group Databasebeta

← C31×#440 #14520621

Subgroups — C31×#440 #14520621

Order 1984.

120 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 70 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×SD16×C31C211yesmaximal, characteristic
2C4×Q8×C31C211yesmaximal, characteristic, complemented
3C4×D4×C31C211yesmaximal, characteristic
4C31×#107C211yesmaximal, characteristic, complemented
5C31×#103C211yesmaximal, characteristic, complemented
6C31×#102C211yesmaximal, characteristic
7C31×#97C211yesmaximal, characteristic, complemented
8C2×Q8×C31C2211yescharacteristic
9C2×D4×C31C2211yescharacteristic
10C22×C4×C31—21no—
11SD16×C31C414yescomplemented
12C2×C8×C31C2211yescharacteristic
13C2×C8×C31C2211yescharacteristic
14C4⋊C4×C31—21no—
15C4⋊C4×C31C2211yescharacteristic
16C4⋊C4×C31C2211yescharacteristic
17C22⋊C4×C31—21no—
18C42×C31—21no—
19C42×C31C2211yescharacteristic
20C23×C31—21no—
21Q8×C31—21no—
22Q8×C31C2×C412yescomplemented
23D4×C31—21no—
24D4×C31C2×C412yes—
25C2×C4×C31—21no—
26C2×C4×C31—21no—
27C2×C4×C31—21no—
28C2×C4×C31—42no—
29C2×C4×C31D411yescharacteristic
30C2×C4×C31D411yescharacteristic
31C2×C4×C31C2311yescharacteristic
32C8×C31—21no—
33C8×C31C2×C412yescomplemented
34C22×C31—22no—
35C22×C31—41no—
36C22×C31—41no—
37C22×C31C2×D411yescharacteristic
38C4×C31—22no—
39C4×C31—21no—
40C4×C31—21no—
41C4×C31—41no—
42C4×C31—41no—
43C4×C31C22×C411yescharacteristic
44C4×C31#4111yescharacteristic
45#440C3111yesmaximal, characteristic, direct product factor, Sylow
46C2×C31—42no—
47C2×C31C4×D411yescharacteristic
48C2×C31AGL(1,ℤ/8)11yescharacteristic
49C2×C31#13711yescharacteristic
50C2×SD16C2×C3111yescharacteristic
51C4×Q8C2×C3111yescharacteristic, complemented
52C4×D4C2×C3111yescharacteristic
53#107C2×C3111yescharacteristic, complemented
54#103C2×C3111yescharacteristic, complemented
55#102C2×C3111yescharacteristic
56#97C2×C3111yescharacteristic, complemented
57C31#44011yescharacteristic, direct product factor, Sylow
58C2×Q8C22×C3111yescharacteristic
59C2×D4C22×C3111yescharacteristic
60C22×C4—21no—
61SD16C4×C3114yescomplemented
62C2×C8C22×C3111yescharacteristic
63C2×C8C22×C3111yescharacteristic
64C4⋊C4—21no—
65C4⋊C4C22×C3111yescharacteristic
66C4⋊C4C22×C3111yescharacteristic
67C22⋊C4—21no—
68C42—21no—
69C42C22×C3111yescharacteristic
70C23—21no—
71Q8—21no—
72Q8C2×C4×C3112yescomplemented
73D4—21no—
74D4C2×C4×C3112yes—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—42no—
79C2×C4D4×C3111yescharacteristic
80C2×C4D4×C3111yescharacteristic
81C2×C4C23×C3111yescharacteristic
82C8—21no—
83C8C2×C4×C3112yescomplemented
84C22—22no—
85C22—41no—
86C22—41no—
87C22C2×D4×C3111yescharacteristic
88C4—22no—
89C4—21no—
90C4—21no—
91C4—41no—
92C4—41no—
93C4C22×C4×C3111yescharacteristic
94C4#41×C3111yescharacteristic
95C2—42no—
96C2C4×D4×C3111yescharacteristic
97C2C31×AGL(1,ℤ/8)11yescharacteristic
98C2C31×#13711yescharacteristic
subgroupG/H
center, socleC22×C31C2×D4
commutatorC4C22×C4×C31
Frattini, cosocleC2×C4C23×C31
prime radicalC2×D4×C31C22
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×Q8×C31C2semidirect
4. C31×#107C2semidirect
5. C31×#103C2semidirect
7. C31×#97C2semidirect
11. SD16×C31C4semidirect
22. Q8×C31C2×C4semidirect
33. C8×C31C2×C4semidirect
45. #440C31direct (N × H)
51. C4×Q8C2×C31semidirect
53. #107C2×C31semidirect
54. #103C2×C31semidirect
56. #97C2×C31semidirect
57. C31#440direct (N × H)
61. SD16C4×C31semidirect
72. Q8C2×C4×C31semidirect
83. C8C2×C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C312
C4×Q8×C312
C4×D4×C312
C31×#1072
C31×#1032
C31×#1022
C31×#972
#44031