Finite Group Databasebeta

← #16844854

Subgroups — #16844854

Order 3968.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#14521765C211yesmaximal, characteristic
2#14521336C212yesmaximal, complemented
3#14520798C211yesmaximal, characteristic, complemented
4#14520778C212yesmaximal, complemented
5C31×#494C211yesmaximal, characteristic, complemented
6C2×Q16×C31—22no—
7C31×C4⋊Q8C2211yescharacteristic
8C31×C4⋊Q8C2211yescharacteristic
9#11758524—22no—
10#11758472—22no—
11#11758469—22no—
12C4×D124C2212yes—
13C4×C8×C31C2211yescharacteristic
14#11758397—22no—
15#11758396—22no—
16C4⋊(C31⋊C8)C2212yes—
17C2×Q8×C31—21no—
18C2×Q8×C31D412yes—
19C2×D124—22no—
20C2×D124D412yes—
21C2×C4×D31—22no—
22Q16×C31—44no—
23C2×C8×C31—21no—
24C4⋊C4×C31—22no—
25C4⋊C4×C31—22no—
26C42×C31C2311yescharacteristic
27(C2×D31)⋊C4—24no—
28(C2×D31)⋊C4—22no—
29C4⋊Dic31D412yes—
30C4×Dic31—22no—
31C2×C31⋊C8—22no—
32C22×D31—22no—
33Q8×C31—42no—
34Q8×C31—42no—
35C2×C4×C31—22no—
36C2×C4×C31—41no—
37C2×C4×C31C2×D412yes—
38C2×C4×C31C2×D411yescharacteristic
39C2×Dic31—22no—
40D124—22no—
41D124—22no—
42D124—82no—
43C4×D31—42no—
44C4×D31—42no—
45C8×C31—22no—
46C31⋊C8—42no—
47#1634—311nomaximal, Sylow
48C22×C31#12011yescharacteristic
49C2×D31—42no—
50C2×D31—42no—
51C2×D31—42no—
52C4×C31—21no—
53C4×C31—42no—
54C4×C31—81no—
55C4×C31#13512yes—
56C4×C31#13712yes—
57Dic31—42no—
58#555—311no—
59#494D3111yescharacteristic, complemented
60#476—312no—
61#333—311no—
62D4⋊C8—312no—
63C2×C31#45212yes—
64C2×C31#45311yescharacteristic
65D31—82no—
66C2×Q16—22no—
67C4⋊Q8C2×D3111yescharacteristic
68C4⋊Q8C2×D3111yescharacteristic
69#124—622no—
70#121—622no—
71C4×D4—312no—
72#117—622no—
73#106—622no—
74C4⋊C8—312no—
75#102—622no—
76C4×C8C2×D3111yescharacteristic
77C31#163411yescharacteristic, complemented, Sylow
78C2×Q8—21no—
79C2×Q8C22⋊D3112yes—
80C2×D4—312no—
81C2×D4—622no—
82C22×C4—622no—
83Q16—44no—
84C2×C8—21no—
85C2×C8—622no—
86C4⋊C4—22no—
87C4⋊C4—22no—
88C4⋊C4—312no—
89C22⋊C4—624no—
90C22⋊C4—622no—
91C42—622no—
92C42C22×D3111yescharacteristic
93C23—622no—
94Q8—42no—
95Q8—42no—
96D4—622no—
97D4—622no—
98D4—2482no—
99C2×C4—22no—
100C2×C4—41no—
101C2×C4—622no—
102C2×C4—1242no—
103C2×C4—1242no—
104C2×C4D4×D3112yes—
105C2×C4C2×C22⋊D3111yescharacteristic
106C8—22no—
107C8—1242no—
108C22—1242no—
109C22—1242no—
110C22—1242no—
111C22#1175851411yescharacteristic
112C4—21no—
113C4—42no—
114C4—81no—
115C4—1242no—
116C4#1175849512yes—
117C4#1175849612yes—
118C2—2482no—
119C2#1452121012yes—
120C2#1452121611yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#494C2
socleC22×C31#120
prime radical#14521765C2
hypercenter#494D31
hypocenterC31#1634
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #14521336C2semidirect
3. #14520798C2semidirect
4. #14520778C2semidirect
5. C31×#494C2semidirect
59. #494D31semidirect
77. C31#1634semidirect

Maximal subgroups

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

subgroupindex
#145217652
#145213362
#145207982
#145207782
C31×#4942
#163431