Finite Group Databasebeta

← #16844375

Subgroups — #16844375

Order 3968.

202 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 77 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#14521606C211yesmaximal, characteristic
2#14521102C211yesmaximal, characteristic
3#14520796C212yesmaximal, complemented
4#14520794C212yesmaximal, complemented
5C31×#431C211yesmaximal, characteristic
6C2×C42×C31C2211yescharacteristic
7#11758503C412yes—
8#11758501—21no—
9#11758501—21no—
10#11758447C412yes—
11#11758446C2211yescharacteristic
12#11758446C2211yescharacteristic
13C4×Dic62—21no—
14C4×Dic62—21no—
15C31×C4⋊C8C2212yes—
16C31×C22⋊C8—21no—
17C4×C8×C31—21no—
18C22⋊(C31⋊C8)—21no—
19C4⋊(C31⋊C8)C2212yes—
20C4×C31⋊C8—21no—
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31D411yescharacteristic
24C2×Dic62—21no—
25C2×Dic62—21no—
26C2×C8×C31—22no—
27C42×C31C2×C411yescharacteristic
28C42×C31D411yescharacteristic
29C42×C31D411yescharacteristic
30C42×C31C2311yescharacteristic
31C22⋊Dic31—22no—
32C4⋊Dic31—21no—
33C4⋊Dic31—21no—
34C4⋊Dic31C2×C412yes—
35C4⋊Dic31C2×C412yes—
36Dic31⋊C4—22no—
37Dic31⋊C4—22no—
38C4×Dic31—22no—
39C2×C31⋊C8—22no—
40C23×C31C22⋊C411yescharacteristic
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—22no—
44C2×C4×C31C22⋊C411yescharacteristic
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C22⋊C411yescharacteristic
47C2×C4×C31C22×C411yescharacteristic
48C2×C4×C31C2×D411yescharacteristic
49C2×C4×C31C2×D411yescharacteristic
50C2×Dic31—22no—
51C2×Dic31—22no—
52Dic62—42no—
53Dic62—42no—
54C8×C31—42no—
55C31⋊C8—42no—
56#1544—311nomaximal, Sylow
57C22×C31—21no—
58C22×C31—21no—
59C22×C31—21no—
60C22×C31C2×C22⋊C411yescharacteristic
61C4×C31—21no—
62C4×C31—21no—
63C4×C31—21no—
64C4×C31#10112yes—
65C4×C31#13512yes—
66C4×C31#13512yes—
67Dic31—42no—
68Dic31—42no—
69#533—311no—
70#431—311no—
71#431D3111yescharacteristic
72#332—312no—
73#332—312no—
74C2×C31—41no—
75C2×C31C2×#10111yescharacteristic
76C2×C31#41611yescharacteristic
77C2×C31#41611yescharacteristic
78C4⋊Q8—311no—
79C4⋊Q8—311no—
80#125—312no—
81C22⋊Q8—621no—
82C22⋊Q8—621no—
83C4×Q8—621no—
84C4×Q8—621no—
85#117—312no—
86C2×C42C2×D3111yescharacteristic
87C4⋊C8—312no—
88C4⋊C8C2×D3112yes—
89C22⋊C8—21no—
90C22⋊C8—621no—
91C4×C8—21no—
92C4×C8—621no—
93C31#154411yescharacteristic, complemented, Sylow
94C2×Q8—621no—
95C2×Q8—621no—
96C22×C4C4×D3111yescharacteristic
97C22×C4D12411yescharacteristic
98C22×C4C22⋊D3111yescharacteristic
99C2×C8—22no—
100C2×C8—622no—
101C4⋊C4—312no—
102C4⋊C4—312no—
103C4⋊C4—622no—
104C4⋊C4—622no—
105C4⋊C4—621no—
106C4⋊C4—621no—
107C22⋊C4—622no—
108C42—622no—
109C42C4×D3111yescharacteristic
110C42D12411yescharacteristic
111C42C22⋊D3111yescharacteristic
112C42C22×D3111yescharacteristic
113C23(C2×D31)⋊C411yescharacteristic
114Q8—1242no—
115Q8—1242no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—622no—
120C2×C4—622no—
121C2×C4(C2×D31)⋊C411yescharacteristic
122C2×C4(C2×D31)⋊C411yescharacteristic
123C2×C4(C2×D31)⋊C411yescharacteristic
124C2×C4C2×C4×D3111yescharacteristic
125C2×C4C2×D12411yescharacteristic
126C2×C4C2×C22⋊D3111yescharacteristic
127C8—42no—
128C8—1242no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22C2×(C2×D31)⋊C411yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—1242no—
137C4—1242no—
138C4#1175841212yes—
139C4#1175848112yes—
140C4#1175852712yes—
141C2—41no—
142C2C2×#1175841211yescharacteristic
143C2#1452104311yescharacteristic
144C2#1452104611yescharacteristic
subgroupG/H
centerC2×C4(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#431C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C22⋊C4
cosocleC42×C31C23
hypercenter#431D31
hypocenterC31#1544
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #14520796C2semidirect
4. #14520794C2semidirect
93. C31#1544semidirect

Maximal subgroups

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

subgroupindex
#145216062
#145211022
#145207962
#145207942
C31×#4312
#154431