Finite Group Databasebeta

← #16847383

Subgroups — #16847383

Order 3968.

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

normal subgroups only

This group has 270 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, complemented
2#14520842C214yesmaximal, complemented
3C31×#535C211yesmaximal, characteristic
4C2×#41×C31C2211yescharacteristic
5C22×D4×C31C411yescharacteristic, complemented
6C31×#127C2212yes—
7C31×#124C412yescomplemented
8C31×#121—22no—
9C31×#120—22no—
10C31×#117C411yescharacteristic, complemented
11#11758503—22no—
12#11758422—22no—
13#11758422C2214yescomplemented
14C24×C31—21no—
15#41×C31—42no—
16C2×Q8×C31C2×C411yescharacteristic
17C2×D4×C31—24no—
18C2×D4×C31—21no—
19C2×D4×C31—42no—
20C2×D4×C31C2×C412yes—
21C2×D4×C31D412yes—
22C2×D4×C31C2311yescharacteristic
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31D412yes—
25C4⋊C4×C31—21no—
26C22⋊C4×C31—21no—
27C22⋊C4×C31—24no—
28C42×C31C2×C412yes—
29C22⋊Dic31—24no—
30C4⋊Dic31—42no—
31C4×Dic31—42no—
32C23×C31—22no—
33C23×C31—42no—
34C23×C31—82no—
35C23×C31C22⋊C411yescharacteristic
36C23×C31C2×D412yes—
37Q8×C31—41no—
38D4×C31—42no—
39D4×C31—41no—
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⋊C412yes—
48C2×C4×C31C22⋊C411yescharacteristic
49C2×C4×C31C22×C411yescharacteristic
50C2×Dic31—44no—
51#2128—311nomaximal, Sylow
52C22×C31—22no—
53C22×C31—21no—
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—
64Dic31—84no—
65#535D3111yescharacteristic
66#410—312no—
67#353—314no—
68C2×C31—21no—
69C2×C31—42no—
70C2×C31—41no—
71C2×C31—82no—
72C2×C31C2×#9911yescharacteristic
73C2×#41C2×D3111yescharacteristic
74C22×D4Dic3111yescharacteristic, complemented
75#127C2×D3112yes—
76#124Dic3112yescomplemented
77#121—22no—
78#120—22no—
79#117—622no—
80#117Dic3111yescharacteristic, complemented
81#99—314no—
82#99—622no—
83C31#212811yescharacteristic, complemented, Sylow
84C24—21no—
85#41—42no—
86C2×Q8C2×Dic3111yescharacteristic
87C2×D4—24no—
88C2×D4—21no—
89C2×D4—42no—
90C2×D4C2×Dic3112yes—
91C2×D4C22⋊D3112yes—
92C2×D4C22×D3111yescharacteristic
93C22×C4C2×Dic3111yescharacteristic
94C22×C4C22⋊D3112yes—
95C4⋊C4—21no—
96C4⋊C4—1242no—
97C22⋊C4—21no—
98C22⋊C4—24no—
99C22⋊C4—624no—
100C42—1242no—
101C42C2×Dic3112yes—
102C23—22no—
103C23—42no—
104C23—82no—
105C23C22⋊Dic3111yescharacteristic
106C23C2×C22⋊D3112yes—
107Q8—41no—
108D4—42no—
109D4—41no—
110D4—42no—
111D4—42no—
112D4—84no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—1244no—
118C2×C4C22⋊Dic3112yes—
119C2×C4C22⋊Dic3111yescharacteristic
120C2×C4C22×Dic3111yescharacteristic
121C22—22no—
122C22—21no—
123C22—42no—
124C22—41no—
125C22—44no—
126C22—42no—
127C22—84no—
128C22C2×C22⋊Dic3111yescharacteristic
129C4—22no—
130C4—21no—
131C4—42no—
132C4—2484no—
133C4#1175842212yes—
134C2—21no—
135C2—42no—
136C2—41no—
137C2—82no—
138C2C2×#1175842211yescharacteristic
subgroupG/H
centerC2C2×#11758422
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
Fitting, prime radicalC31×#535C2
socleC2×C31C2×#99
cosocleC2×D4×C31C23
hypercenter#535D31
hypocenterC31#2128
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. #14521023C2semidirect
2. #14520842C2semidirect
5. C22×D4×C31C4semidirect
7. C31×#124C4semidirect
10. C31×#117C4semidirect
13. #11758422C22semidirect
74. C22×D4Dic31semidirect
76. #124Dic31semidirect
80. #117Dic31semidirect
83. C31#2128semidirect

Maximal subgroups

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

subgroupindex
#145210232
#145208422
C31×#5352
#212831