Finite Group Databasebeta

← C2×2−1+4⋊C9 #10593119

Subgroups — C2×2−1+4⋊C9 #10593119

Order 576.

365 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 365 conjugacy classes of subgroups — too many to draw. Only its 86 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
12−1+4⋊C9C214yesmaximal, direct product factor
2C2×#41⋊C9C211yesmaximal, characteristic, complemented
3C22×Q8⋊C9C212yesmaximal, complemented
4C2×C3×2−1+4C311yesmaximal, characteristic
5C2×D4×C9—41nomaximal
6#41⋊C9C2212yescomplemented
7C2×Q8⋊C9C2211yescharacteristic
8C2×Q8⋊C9C2214yescomplemented
9C3×2−1+4—34no—
10C3×2−1+4C2×C314yes—
11C2×C3×#41—31no—
12C2×C3×#41—32no—
13C2×C3×#41C2×C311yescharacteristic
14C22×C3×Q8—31no—
15C22×C3×Q8C2×C312yes—
16C23×C9—42no—
17D4×C9—44no—
18C2×C4×C9—41no—
19Q8⋊C9C2311yescharacteristic
20C2×2−1+4C911yescharacteristic, complemented, Sylow
21C3×#41—38no—
22C3×#41—34no—
23C3×#41—34no—
24C3×#41—38no—
25C3×#41—32no—
26C3×#41C22×C312yes—
27C2×C3×Q8—34no—
28C2×C3×Q8—34no—
29C2×C3×Q8—31no—
30C2×C3×Q8—32no—
31C2×C3×Q8—34no—
32C2×C3×Q8C22×C311yescharacteristic
33C2×C3×Q8C22×C314yes—
34C2×C3×D4—31no—
35C2×C3×D4—32no—
36C2×C3×D4A411yescharacteristic
37C22×C3×C4—32no—
38C22×C3×C4—32no—
39C22×C3×C4—31no—
40C22×C9—44no—
41C22×C9—41no—
42C22×C9—84no—
43C4×C9—42no—
442−1+4—34no—
452−1+4C2×C914yescomplemented
46C2×#41—31no—
47C2×#41—32no—
48C2×#41C2×C911yescharacteristic, complemented
49C22×Q8—31no—
50C22×Q8C2×C912yescomplemented
51C23×C3—31no—
52C23×C3C2×A412yes—
53C3×Q8—31no—
54C3×Q8—34no—
55C3×Q8—34no—
56C3×Q8—34no—
57C3×Q8C23×C311yescharacteristic
58C3×D4—32no—
59C3×D4—32no—
60C3×D4—38no—
61C3×D4C2×A414yes—
62C2×C3×C4—38no—
63C2×C3×C4—34no—
64C2×C3×C4—34no—
65C2×C3×C4—32no—
66C2×C3×C4—31no—
67C2×C3×C4—32no—
68C2×C3×C4—32no—
69C2×C3×C4C2×A411yescharacteristic
70C2×C9—42no—
71C2×C9—41no—
72C2×C9—84no—
73#41—38no—
74#41—34no—
75#41—34no—
76#41—38no—
77#41—32no—
78#41C22×C912yescomplemented
79C2×Q8—34no—
80C2×Q8—34no—
81C2×Q8—31no—
82C2×Q8—32no—
83C2×Q8—34no—
84C2×Q8C22×C911yescharacteristic
85C2×Q8C22×C914yescomplemented
86C2×D4—31no—
87C2×D4—32no—
88C2×D4C22⋊C911yescharacteristic
89C22×C4—32no—
90C22×C4—32no—
91C22×C4—31no—
92C22×C3—24no—
93C22×C3—32no—
94C22×C3—62no—
95C22×C3C22×A414yes—
96C22×C3C22×A411yescharacteristic
97C3×C4—34no—
98C3×C4—31no—
99C3×C4—31no—
100C3×C4C22×A412yes—
101C9—41noSylow
102C23—31no—
103C23C2×C22⋊C912yes—
104Q8—31no—
105Q8—34no—
106Q8—34no—
107Q8—34no—
108Q8C23×C911yescharacteristic
109D4—32no—
110D4—32no—
111D4—38no—
112D4C2×C22⋊C914yes—
113C2×C4—38no—
114C2×C4—31no—
115C2×C4—32no—
116C2×C4—34no—
117C2×C4—34no—
118C2×C4—32no—
119C2×C4—32no—
120C2×C4C2×C22⋊C911yescharacteristic
121C2×C3—24no—
122C2×C3—62no—
123C2×C32−1+4⋊C312yes—
124C2×C3C23×A411yescharacteristic
125C22—24no—
126C22—32no—
127C22—62no—
128C22C22×C22⋊C914yes—
129C22C22×C22⋊C911yescharacteristic
130C4—31no—
131C4—34no—
132C4—31no—
133C4C22×C22⋊C912yes—
134C3C2×2−1+4⋊C311yescharacteristic
135C2—24no—
136C2—62no—
137C22−1+4⋊C912yesdirect product factor
138C2C23×C22⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3C22×A4
commutator, hypocenterQ8C23×C9
FrattiniC2×C3C23×A4
Fitting, prime radicalC2×C3×2−1+4C3
cosocleC3×Q8C23×C3
hypercenterC2×C3×D4A4
LCSG ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. 2−1+4⋊C9C2direct (N × H)
2. C2×#41⋊C9C2semidirect
3. C22×Q8⋊C9C2semidirect
6. #41⋊C9C22semidirect
8. C2×Q8⋊C9C22semidirect
20. C2×2−1+4C9semidirect
45. 2−1+4C2×C9semidirect
48. C2×#41C2×C9semidirect
50. C22×Q8C2×C9semidirect
78. #41C22×C9semidirect
85. C2×Q8C22×C9semidirect
137. C22−1+4⋊C9direct (N × H)

Maximal subgroups

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

subgroupindex
2−1+4⋊C92
C2×#41⋊C92
C22×Q8⋊C92
C2×C3×2−1+43
C2×D4×C94