Finite Group Databasebeta

← #16847386

Subgroups — #16847386

Order 3968.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521023C212yesmaximal
2#14520844C214yesmaximal, complemented
3C31×#536C211yesmaximal, characteristic
4C2×#41×C31C2211yescharacteristic
5C22×Q8×C31C411yescharacteristic, complemented
6C31×C4⋊Q8C412yescomplemented
7C31×#124C2212yes—
8C31×#123—22no—
9C31×C22⋊Q8—22no—
10C31×#117C411yescharacteristic, complemented
11#11758503—22no—
12#11758422—22no—
13#11758422C2214yes—
14#41×C31—42no—
15C2×Q8×C31—21no—
16C2×Q8×C31—42no—
17C2×Q8×C31C2×C412yes—
18C2×Q8×C31C2×C411yescharacteristic
19C2×D4×C31D412yes—
20C2×D4×C31C2311yescharacteristic
21C22×C4×C31—21no—
22C22×C4×C31C2×C411yescharacteristic
23C22×C4×C31D412yes—
24C4⋊C4×C31—21no—
25C4⋊C4×C31—24no—
26C22⋊C4×C31—21no—
27C22⋊C4×C31—24no—
28C42×C31C2×C412yes—
29C22⋊Dic31—24no—
30C4⋊Dic31—42no—
31C4×Dic31—42no—
32C23×C31C22⋊C411yescharacteristic
33C23×C31C2×D412yes—
34Q8×C31—41no—
35Q8×C31—42no—
36Q8×C31—42no—
37D4×C31—42no—
38D4×C31—41no—
39C2×C4×C31—22no—
40C2×C4×C31—22no—
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—22no—
44C2×C4×C31—42no—
45C2×C4×C31C22⋊C412yes—
46C2×C4×C31C22⋊C411yescharacteristic
47C2×C4×C31C22×C411yescharacteristic
48C2×Dic31—44no—
49#2129—311nomaximal, Sylow
50C22×C31—22no—
51C22×C31—21no—
52C22×C31—41no—
53C22×C31—42no—
54C22×C31C2×C22⋊C411yescharacteristic
55C4×C31—22no—
56C4×C31—21no—
57C4×C31—42no—
58C4×C31—42no—
59C4×C31#9912yes—
60Dic31—84no—
61#536D3111yescharacteristic
62#410—312no—
63#354—314no—
64C2×C31—21no—
65C2×C31—42no—
66C2×C31—41no—
67C2×C31C2×#9911yescharacteristic
68C2×#41C2×D3111yescharacteristic
69C22×Q8Dic3111yescharacteristic, complemented
70C4⋊Q8Dic3112yescomplemented
71#124C2×D3112yes—
72#123—22no—
73C22⋊Q8—22no—
74#117—622no—
75#117Dic3111yescharacteristic, complemented
76#99—314no—
77#99—622no—
78C31#212911yescharacteristic, complemented, Sylow
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×Dic3112yes—
83C2×Q8C2×Dic3111yescharacteristic
84C2×D4C22⋊D3112yes—
85C2×D4C22×D3111yescharacteristic
86C22×C4—21no—
87C22×C4C2×Dic3111yescharacteristic
88C22×C4C22⋊D3112yes—
89C4⋊C4—24no—
90C4⋊C4—21no—
91C4⋊C4—1242no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—624no—
95C42—1242no—
96C42C2×Dic3112yes—
97C23C22⋊Dic3111yescharacteristic
98C23C2×C22⋊D3112yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—42no—
103D4—41no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—1244no—
111C2×C4C22⋊Dic3112yes—
112C2×C4C22⋊Dic3111yescharacteristic
113C2×C4C22×Dic3111yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊Dic3111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—2484no—
124C4#1175842212yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#1175842211yescharacteristic
subgroupG/H
centerC2C2×#11758422
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#536C2
socleC2×C31C2×#99
prime radicalC2×#41×C31C22
cosocleC2×D4×C31C23
hypercenter#536D31
hypocenterC31#2129
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #14520844C2semidirect
5. C22×Q8×C31C4semidirect
6. C31×C4⋊Q8C4semidirect
10. C31×#117C4semidirect
69. C22×Q8Dic31semidirect
70. C4⋊Q8Dic31semidirect
75. #117Dic31semidirect
78. C31#2129semidirect

Maximal subgroups

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

subgroupindex
#145210232
#145208442
C31×#5362
#212931