Finite Group Databasebeta

← C4×#131⋊C9 #11919521

Subgroups — C4×#131⋊C9 #11919521

Order 1152.

277 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#131⋊C9C212yesmaximal
2C4×#41⋊C9C211yesmaximal, characteristic
3C3×C4×#131C311yesmaximal, characteristic
4C2×#41⋊C9C2211yescharacteristic
5#131⋊C9C414yesdirect product factor
6C4×Q8⋊C9C412yes—
7C4×C8×C9—41nomaximal
8C2×C3×#131C2×C312yes—
9C3×C4×#41C2×C311yescharacteristic
10C3×#405—32no—
11C3×C4×M16—31no—
12C2×C3×C4×C8—31no—
13#41⋊C9C2×C412yes—
14C2×Q8⋊C9C2×C411yescharacteristic
15C2×C8×C9—42no—
16C42×C9—41no—
17C4×#131C911yescharacteristic, complemented, Sylow
18C2×C3×#41C22×C311yescharacteristic
19C3×#131—34no—
20C3×#131C3×C414yes—
21C2×C3×M16—32no—
22C22×C3×C8—32no—
23C3×C4×Q8C3×C412yes—
24C3×C4×D4—32no—
25C3×#117—31no—
26C2×C3×C42—31no—
27C3×#97—32no—
28C3×C4×C8—32no—
29C3×C4×C8—31no—
30C3×C4×C8A411yescharacteristic
31C2×C4×C9—42no—
32C2×C4×C9—41no—
33Q8⋊C9C4211yescharacteristic
34C8×C9—44no—
35C2×#131C2×C912yes—
36C4×#41C2×C911yescharacteristic
37#405—32no—
38C4×M16—31no—
39C2×C4×C8—31no—
40C3×#41—32no—
41C3×#41C2×C3×C412yes—
42C2×C3×Q8C2×C3×C411yescharacteristic
43C2×C3×D4—31no—
44C22×C3×C4—31no—
45C22×C3×C4—32no—
46C3×M16—34no—
47C3×M16—34no—
48C2×C3×C8—32no—
49C2×C3×C8—34no—
50C2×C3×C8—34no—
51C2×C3×C8C2×A412yes—
52C3×C4⋊C4—32no—
53C3×C22⋊C4—32no—
54C3×C42—32no—
55C3×C42—31no—
56C3×C42C2×A411yescharacteristic
57C22×C9—41no—
58C4×C9—44no—
59C4×C9—42no—
60C2×#41C22×C911yescharacteristic
61#131—34no—
62#131C4×C914yescomplemented
63C2×M16—32no—
64C22×C8—32no—
65C4×Q8C4×C912yes—
66C4×D4—32no—
67#117—31no—
68C2×C42—31no—
69#97—32no—
70C4×C8—32no—
71C4×C8—31no—
72C4×C8C22⋊C911yescharacteristic
73C23×C3—31no—
74C3×Q8—31no—
75C3×Q8C3×C4211yescharacteristic
76C3×D4—32no—
77C3×D4—32no—
78C2×C3×C4—31no—
79C2×C3×C4—32no—
80C2×C3×C4—32no—
81C2×C3×C4—32no—
82C2×C3×C4—64no—
83C2×C3×C4C4×A412yes—
84C2×C3×C4C22×A411yescharacteristic
85C3×C8—34no—
86C3×C8C4×A414yes—
87C2×C9—41no—
88C2×C9—42no—
89#41—32no—
90#41C2×C4×C912yes—
91C2×Q8C2×C4×C911yescharacteristic
92C2×D4—31no—
93C22×C4—31no—
94C22×C4—32no—
95M16—34no—
96M16—34no—
97C2×C8—32no—
98C2×C8—34no—
99C2×C8—34no—
100C2×C8C2×C22⋊C912yes—
101C4⋊C4—32no—
102C22⋊C4—32no—
103C42—32no—
104C42—31no—
105C42C2×C22⋊C911yescharacteristic
106C22×C3—32no—
107C22×C3—62no—
108C22×C3C2×C4×A411yescharacteristic
109C3×C4—31no—
110C3×C4—31no—
111C3×C4—62no—
112C3×C4#131⋊C314yes—
113C3×C4C2×C4×A412yes—
114C9—41noSylow
115C23—31no—
116Q8—31no—
117Q8C42×C911yescharacteristic
118D4—32no—
119D4—32no—
120C2×C4—31no—
121C2×C4—32no—
122C2×C4—32no—
123C2×C4—32no—
124C2×C4—64no—
125C2×C4C4×C22⋊C912yes—
126C2×C4C22×C22⋊C911yescharacteristic
127C8—34no—
128C8C4×C22⋊C914yes—
129C2×C3—62no—
130C2×C3C42×A411yescharacteristic
131C2×C3C2×#131⋊C312yes—
132C22—32no—
133C22—62no—
134C22C2×C4×C22⋊C911yescharacteristic
135C4—31no—
136C4—31no—
137C4—62no—
138C4#131⋊C914yesdirect product factor
139C4C2×C4×C22⋊C912yes—
140C3C4×#131⋊C311yescharacteristic
141C2—62no—
142C2C42×C22⋊C911yescharacteristic
143C2C2×#131⋊C912yes—
subgroupG/H
center, hypercenterC3×C4×C8A4
commutator, hypocenterQ8C42×C9
FrattiniC2×C3×C4C22×A4
FittingC3×C4×#131C3
socleC22×C3C2×C4×A4
prime radical, cosocleC2×C3×#41C22×C3
LCSG ▷ Q8
UCSC1 ◁ C3×C4×C8

Complements

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

NH ≅ G/Ntype
5. #131⋊C9C4direct (N × H)
17. C4×#131C9semidirect
62. #131C4×C9semidirect
138. C4#131⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#131⋊C92
C4×#41⋊C92
C3×C4×#1313
C4×C8×C94