Finite Group Databasebeta

← #14521275

Subgroups — #14521275

Order 1984.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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, complemented
2#11758523C211yesmaximal, characteristic, complemented
3#11758515C211yesmaximal, characteristic
4C2×C8×D31C211yesmaximal, characteristic, complemented
5#11758423C211yesmaximal, characteristic, complemented
6#11758420C211yesmaximal, characteristic, complemented
7#11758405C211yesmaximal, characteristic, complemented
8C2×Q8×C31C2211yescharacteristic
9C2×D4×C31C2211yescharacteristic
10C2×C22⋊D31—21no—
11C2×C4×D31C2211yescharacteristic
12SD16×C31—22no—
13C2×C8×C31C2211yescharacteristic
14C22⋊Dic31—21no—
15(C2×D31)⋊C4—21no—
16C4⋊Dic31C2211yescharacteristic
17C4⋊Dic31C2211yescharacteristic
18Dic31⋊C4—21no—
19C2×C31⋊C8C2211yescharacteristic
20C8×D31—22no—
21C23×C31—21no—
22C22×D31D411yescharacteristic
23Q8×C31—21no—
24Q8×C31—21no—
25D4×C31—21no—
26D4×C31—21no—
27C2×C4×C31—21no—
28C2×C4×C31C2311yescharacteristic
29C22⋊D31—42no—
30C2×Dic31—21no—
31C2×Dic31—21no—
32C2×Dic31D411yescharacteristic
33C4×D31—21no—
34C4×D31—21no—
35C8×C31D412yescomplemented
36C31⋊C8—21no—
37C22×C31—41no—
38C22×C31—41no—
39C22×C31—41no—
40C22×C31C2×D411yescharacteristic
41C2×D31—21no—
42C2×D31—21no—
43C2×D31SD1612yescomplemented
44C4×C31—41no—
45C4×C31C2×D411yescharacteristic
46C4×C31#4111yescharacteristic
47Dic31—21no—
48Dic31—41no—
49Dic31—41no—
50#465—311nomaximal, Sylow
51C2×C31—81no—
52C2×C31#12111yescharacteristic
53C2×C31C2×SD1611yescharacteristic
54C2×C31#13511yescharacteristic
55D31—22no—
56C2×SD16D3111yescharacteristic, complemented
57C22×C8—311no—
58C22⋊Q8—311no—
59#121—311no—
60#106—311no—
61#103—311no—
62#102—311no—
63C31#46511yescharacteristic, complemented, Sylow
64C2×Q8C2×D3111yescharacteristic
65C2×D4—621no—
66C2×D4C2×D3111yescharacteristic
67C22×C4—311no—
68SD16—22no—
69C2×C8—311no—
70C2×C8—622no—
71C2×C8C2×D3111yescharacteristic
72C4⋊C4—311no—
73C4⋊C4—311no—
74C4⋊C4—621no—
75C22⋊C4—621no—
76C22⋊C4—621no—
77C23—21no—
78C23—311no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—1242no—
84C2×C4—21no—
85C2×C4—311no—
86C2×C4—621no—
87C2×C4—621no—
88C2×C4—621no—
89C2×C4—621no—
90C2×C4C22×D3111yescharacteristic
91C8—621no—
92C8C22⋊D3112yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—312no—
97C22—621no—
98C22—621no—
99C22D4×D3111yescharacteristic
100C4—41no—
101C4—621no—
102C4—1241no—
103C4—1241no—
104C4#9249711yescharacteristic
105C4C2×C22⋊D3111yescharacteristic
106C2—81no—
107C2—622no—
108C2SD16×D3111yescharacteristic
109C2#1175849311yescharacteristic
110C2#1175851511yescharacteristic
subgroupG/H
centerC22D4×D31
commutator, cosocleC2×C4×C31C23
FrattiniC2×C4C22×D31
FittingC2×SD16×C31C2
socleC22×C31C2×D4
prime radical#11758515C2
hypercenterC2×SD16D31
hypocenterC31#465
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×C31C2semidirect
2. #11758523C2semidirect
4. C2×C8×D31C2semidirect
5. #11758423C2semidirect
6. #11758420C2semidirect
7. #11758405C2semidirect
35. C8×C31D4semidirect
43. C2×D31SD16semidirect
56. C2×SD16D31semidirect
63. C31#465semidirect
92. C8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C312
#117585232
#117585152
C2×C8×D312
#117584232
#117584202
#117584052
#46531