Finite Group Databasebeta

← #16846654

Subgroups — #16846654

Order 3968.

260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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
2C4×#92474C211yesmaximal, characteristic
3#14520809C214yesmaximal
4C4×C4⋊C4×C31C211yesmaximal, characteristic
5C2×C4⋊C4×C31—21no—
6C2×C42×C31C2212yes—
7C2×C42×C31C2211yescharacteristic
8#11758503C2212yes—
9#11758501—21no—
10#11758501—21no—
11C2×#92474C2212yes—
12#11758447C412yescomplemented
13#11758446C411yescharacteristic, complemented
14#11758446C411yescharacteristic, complemented
15C4×Dic62—21no—
16C4×Dic62—21no—
17C31×#95—21no—
18#11758391—21no—
19C4×C31⋊C8—21no—
20C22×C4×C31—22no—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C2×Dic62—21no—
25C2×Dic62—21no—
26C4⋊C4×C31—24no—
27C42×C31—24no—
28C42×C31C2×C411yescharacteristic
29C42×C31C2×C411yescharacteristic
30C42×C31D411yescharacteristic
31C42×C31D411yescharacteristic
32C22⋊Dic31—22no—
33C4⋊Dic31—21no—
34C4⋊Dic31—21no—
35C4⋊Dic31C2×C412yes—
36C4⋊Dic31C2×C412yes—
37Dic31⋊C4—22no—
38Dic31⋊C4—22no—
39C4×Dic31—22no—
40#92474—22no—
41#92474Q814yescomplemented
42C2×C31⋊C8—22no—
43C23×C31C2×D411yescharacteristic
44C2×C4×C31—22no—
45C2×C4×C31—24no—
46C2×C4×C31—41no—
47C2×C4×C31—42no—
48C2×C4×C31—42no—
49C2×C4×C31C22⋊C411yescharacteristic
50C2×C4×C31C22⋊C411yescharacteristic
51C2×C4×C31C22⋊C411yescharacteristic
52C2×C4×C31C22⋊C411yescharacteristic
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×Q812yes—
56C2×C4×C31#4112yes—
57C2×Dic31—22no—
58C2×Dic31—22no—
59Dic62—42no—
60Dic62—42no—
61C31⋊C8—24no—
62#1986—311nomaximal, Sylow
63C22×C31—21no—
64C22×C31—21no—
65C22×C31C2×C22⋊C411yescharacteristic
66C22×C31#12411yescharacteristic
67C22×C31C4⋊Q811yescharacteristic
68C4×C31—21no—
69C4×C31—21no—
70C4×C31—21no—
71C4×C31—44no—
72C4×C31#10412yes—
73C4×C31C4×Q812yes—
74C4×C31C22⋊Q812yes—
75Dic31—42no—
76Dic31—42no—
77#533—311no—
78C4×M16—311no—
79C4×C4⋊C4D3111yescharacteristic
80#339—314no—
81C2×C31—21no—
82C2×C31—21no—
83C2×C31#39111yescharacteristic
84C2×C31C2×#10411yescharacteristic
85C2×C31#42111yescharacteristic
86C2×M16—312no—
87C4⋊Q8—311no—
88C4⋊Q8—311no—
89#125—312no—
90C22⋊Q8—621no—
91C22⋊Q8—621no—
92C4×Q8—621no—
93C4×Q8—621no—
94#117—312no—
95C2×C4⋊C4—21no—
96C2×C42C2×D3112yes—
97C2×C42C2×D3111yescharacteristic
98#97—621no—
99C4×C8—621no—
100#95—21no—
101C31#198611yescharacteristic, complemented, Sylow
102C2×Q8—621no—
103C2×Q8—621no—
104C22×C4—22no—
105C22×C4C22⋊D3111yescharacteristic
106C22×C4C22⋊D3111yescharacteristic
107C22×C4C22×D3111yescharacteristic
108M16—314no—
109M16—622no—
110C2×C8—622no—
111C4⋊C4—24no—
112C4⋊C4—312no—
113C4⋊C4—312no—
114C4⋊C4—622no—
115C4⋊C4—622no—
116C4⋊C4—621no—
117C4⋊C4—621no—
118C22⋊C4—622no—
119C42—24no—
120C42—622no—
121C42C4×D3111yescharacteristic
122C42C4×D3111yescharacteristic
123C42D12411yescharacteristic
124C42D12411yescharacteristic
125C23C2×C22⋊D3111yescharacteristic
126Q8—1242no—
127Q8—1242no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—42no—
133C2×C4—622no—
134C2×C4—622no—
135C2×C4(C2×D31)⋊C411yescharacteristic
136C2×C4(C2×D31)⋊C411yescharacteristic
137C2×C4(C2×D31)⋊C411yescharacteristic
138C2×C4(C2×D31)⋊C411yescharacteristic
139C2×C4C2×C4×D3111yescharacteristic
140C2×C4C2×D12411yescharacteristic
141C2×C4#9249712yes—
142C2×C4Q8×D3112yes—
143C8—624no—
144C22—21no—
145C22—21no—
146C22C2×(C2×D31)⋊C411yescharacteristic
147C22#1175851311yescharacteristic
148C22#1175852111yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—44no—
153C4—1242no—
154C4—1242no—
155C4#1175839312yes—
156C4#1175846412yes—
157C4#1175847412yes—
158C2—21no—
159C2—21no—
160C2#1452095411yescharacteristic
161C2C2×#1175839311yescharacteristic
162C2#1452106711yescharacteristic
subgroupG/H
centerC2×C4C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC4×C4⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC4×C4⋊C4D31
hypocenterC31#1986
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. #11758447C4semidirect
13. #11758446C4semidirect
14. #11758446C4semidirect
41. #92474Q8semidirect
101. C31#1986semidirect

Maximal subgroups

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

subgroupindex
#145216062
C4×#924742
#145208092
C4×C4⋊C4×C312
#198631