Finite Group Databasebeta

← #16847403

Subgroups — #16847403

Order 3968.

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

normal subgroups only

This group has 262 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#14521033C212yesmaximal, complemented
2#14520846C214yesmaximal, complemented
3C31×#535C211yesmaximal, characteristic
4C2×#41×C31C2211yescharacteristic
5C22×D4×C31C411yescharacteristic
6C31×#127C412yes—
7C31×#124C2212yes—
8C31×#121—22no—
9C31×#120—22no—
10C31×#117C411yescharacteristic
11C2×#92474—22no—
12#11758424C2214yescomplemented
13#11758421—22no—
14C24×C31—21no—
15#41×C31—42no—
16C2×Q8×C31C2311yescharacteristic
17C2×D4×C31—24no—
18C2×D4×C31—21no—
19C2×D4×C31—42no—
20C2×D4×C31C2×C412yes—
21C2×D4×C31C2×C411yescharacteristic
22C2×D4×C31D412yes—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31D412yes—
25C4⋊C4×C31—21no—
26C22⋊C4×C31—21no—
27C22⋊C4×C31—24no—
28C42×C31C2×C412yes—
29#92474—24no—
30#92474—42no—
31C2×C31⋊C8—42no—
32C23×C31—22no—
33C23×C31—42no—
34C23×C31—82no—
35C23×C31C22⋊C411yescharacteristic
36C23×C31C22⋊C412yes—
37Q8×C31—41no—
38D4×C31—41no—
39D4×C31—42no—
40D4×C31—42no—
41D4×C31—42no—
42D4×C31—84no—
43C2×C4×C31—22no—
44C2×C4×C31—22no—
45C2×C4×C31—22no—
46C2×C4×C31—22no—
47C2×C4×C31C22⋊C411yescharacteristic
48C2×C4×C31C22×C411yescharacteristic
49C2×C4×C31C2×D412yes—
50C31⋊C8—44no—
51#2134—311nomaximal, Sylow
52C22×C31—21no—
53C22×C31—22no—
54C22×C31—42no—
55C22×C31—41no—
56C22×C31—44no—
57C22×C31—42no—
58C22×C31—84no—
59C22×C31C2×C22⋊C411yescharacteristic
60C4×C31—22no—
61C4×C31—21no—
62C4×C31—42no—
63C4×C31#9912yes—
64#535D3111yescharacteristic
65#413—312no—
66#355—314no—
67C2×C31—21no—
68C2×C31—42no—
69C2×C31—41no—
70C2×C31—82no—
71C2×C31C2×#9911yescharacteristic
72C2×#41C2×D3111yescharacteristic
73C22×D4Dic3111yescharacteristic
74C2×M16—622no—
75#127Dic3112yes—
76#124C2×D3112yes—
77#121—22no—
78#120—22no—
79#117Dic3111yescharacteristic
80#101—314no—
81#100—622no—
82C31#213411yescharacteristic, complemented, Sylow
83C24—21no—
84#41—42no—
85C2×Q8C22×D3111yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic3112yes—
90C2×D4C2×Dic3111yescharacteristic
91C2×D4C22⋊D3112yes—
92C22×C4C2×Dic3111yescharacteristic
93C22×C4C22⋊D3112yes—
94M16—624no—
95M16—1242no—
96C2×C8—1242no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic3112yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic3111yescharacteristic
105C23C22⋊Dic3112yes—
106Q8—41no—
107D4—41no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—84no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4C22⋊Dic3111yescharacteristic
117C2×C4C22×Dic3111yescharacteristic
118C2×C4C2×C22⋊D3112yes—
119C8—1244no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic3111yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#1175842212yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#1175842211yescharacteristic
subgroupG/H
centerC2C2×#11758422
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
Fitting, prime radicalC31×#535C2
socleC2×C31C2×#99
cosocleC2×Q8×C31C23
hypercenter#535D31
hypocenterC31#2134
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14521033C2semidirect
2. #14520846C2semidirect
12. #11758424C22semidirect
82. C31#2134semidirect

Maximal subgroups

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

subgroupindex
#145210332
#145208462
C31×#5352
#213431