Finite Group Databasebeta

← D4×C9⋊Dic9 #72244266

Subgroups — D4×C9⋊Dic9 #72244266

Order 2592.

1081 conjugacy classes of subgroups; only the 450 normal subgroups are shown.

normal subgroups only

This group has 1081 conjugacy classes of subgroups — too many to draw. Only its 450 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×D4×C92C211yesmaximal, characteristic
2C22×C9⋊Dic9C212yesmaximal, complemented
3#13046833C212yesmaximal, complemented
4C4⋊(C9⋊Dic9)C211yesmaximal, characteristic, complemented
5C4×C9⋊Dic9C211yesmaximal, characteristic, complemented
6D4×C3⋊Dic9—34nomaximal
7C23×C92C2212yes—
8D4×C92C414yescomplemented
9C2×C4×C92C2211yescharacteristic
10C2×C9⋊Dic9—24no—
11C2×C9⋊Dic9C2211yescharacteristic
12C2×C9⋊Dic9C2212yes—
13C2×C9⋊Dic9C2211yescharacteristic
14C2×C3×D4×C9D314yes—
15C22×C3⋊Dic9—38no—
16#88551—38no—
17C4⋊(C3⋊Dic9)—34no—
18C4×C3⋊Dic9—34no—
19C22×C92—22no—
20C22×C92—22no—
21C22×C92C2×C414yescomplemented
22C22×C92C2311yescharacteristic
23C4×C92C2×C412yescomplemented
24C9⋊Dic9—22no—
25C9⋊Dic9—21no—
26C9⋊Dic9D412yesdirect product factor
27D4×C3⋊Dic3—91no—
28D4×Dic9—912no—
29C23×C3×C9C2×D318yes—
30C3×D4×C9Dic3116yes—
31C2×C3×C4×C9C2×D314yes—
32C2×C3⋊Dic9—34no—
33C2×C3⋊Dic9—38no—
34C2×C3⋊Dic9—34no—
35C2×C3⋊Dic9—616no—
36C2×C92—24no—
37C2×C92C22×C411yescharacteristic
38C2×C92C2×D411yescharacteristic
39C2×C92#4111yescharacteristic
40C2×C32×D4C3⋊D311yescharacteristic
41C22×C3⋊Dic3—92no—
42#3757—92no—
43C4⋊(C3⋊Dic3)—91no—
44C4×C3⋊Dic3—91no—
45C2×D4×C9D9112yes—
46C22×Dic9—924no—
47#3676—924no—
48C4⋊Dic9—912no—
49C4×Dic9—912no—
50C22×C3×C9—28no—
51C22×C3×C9—28no—
52C22×C3×C9C2×Dic3116yes—
53C22×C3×C9C22×D314yes—
54C3×C4×C9C2×Dic318yes—
55C3⋊Dic9—38no—
56C3⋊Dic9—68no—
57C3⋊Dic9—64no—
58D4×Dic3—274no—
59C92C4×D411yescharacteristic, complemented, Sylow
60C23×C32C2×C3⋊D312yes—
61C32×D4C3⋊Dic314yes—
62C2×C32×C4C2×C3⋊D311yescharacteristic
63C2×C3⋊Dic3—91no—
64C2×C3⋊Dic3—91no—
65C2×C3⋊Dic3—92no—
66C2×C3⋊Dic3—184no—
67C23×C9C2×D9124yes—
68D4×C9Dic9148yescomplemented
69C2×C4×C9C2×D9112yes—
70C2×Dic9—912no—
71C2×Dic9—912no—
72C2×Dic9—924no—
73C2×Dic9—1848no—
74C2×C3×C9—216no—
75C2×C3×C9D3×D414yes—
76C2×C3×C9#23714yes—
77C2×C3×C9C22×Dic314yes—
78C2×C3×D4C3⋊D914yes—
79C22×Dic3—278no—
80#217—278no—
81C4⋊Dic3—274no—
82C4×Dic3—274no—
83C22×C32—22no—
84C22×C32—22no—
85C22×C32C2×C3⋊Dic314yes—
86C22×C32C22×C3⋊D311yescharacteristic
87C32×C4C2×C3⋊Dic312yes—
88C3⋊Dic3—92no—
89C3⋊Dic3—182no—
90C3⋊Dic3—181no—
91C22×C9—224no—
92C22×C9—224no—
93C22×C9C2×Dic9148yescomplemented
94C22×C9C22×D9112yes—
95C4×C9C2×Dic9124yescomplemented
96Dic9—924no—
97Dic9—1824no—
98Dic9—1812no—
99C4×D4—811noSylow
100C3×C9D4×Dic314yes—
101C23×C3C2×C3⋊D918yes—
102C3×D4C3⋊Dic9116yes—
103C2×C3×C4C2×C3⋊D914yes—
104C2×Dic3—274no—
105C2×Dic3—274no—
106C2×Dic3—278no—
107C2×Dic3—5416no—
108C2×C32—24no—
109C2×C32D4×C3⋊D311yescharacteristic
110C2×C32#383011yescharacteristic
111C2×C32C22×C3⋊Dic311yescharacteristic
112C2×C9—248no—
113C2×C9D4×D9112yes—
114C2×C9#3699112yes—
115C2×C9C22×Dic9112yes—
116C2×D4C9⋊D911yescharacteristic
117C22×C4—812no—
118C4⋊C4—811no—
119C22⋊C4—812no—
120C42—811no—
121C22×C3—28no—
122C22×C3—28no—
123C22×C3C2×C3⋊Dic9116yes—
124C22×C3C22×C3⋊D914yes—
125C3×C4C2×C3⋊Dic918yes—
126Dic3—278no—
127Dic3—548no—
128Dic3—544no—
129C32D4×C3⋊Dic311yescharacteristic
130C9D4×Dic9112yescomplemented
131C23C2×C9⋊D912yes—
132D4C9⋊Dic914yesdirect product factor
133C2×C4—811no—
134C2×C4—811no—
135C2×C4—812no—
136C2×C4—1624no—
137C2×C4C2×C9⋊D911yescharacteristic
138C2×C3—216no—
139C2×C3D4×C3⋊D914yes—
140C2×C3#8874214yes—
141C2×C3C22×C3⋊Dic914yes—
142C22—22no—
143C22—22no—
144C22C2×C9⋊Dic914yescomplemented
145C22C22×C9⋊D911yescharacteristic
146C4—812no—
147C4—1622no—
148C4—1621no—
149C4C2×C9⋊Dic912yescomplemented
150C3D4×C3⋊Dic914yes—
151C2—24no—
152C2D4×C9⋊D911yescharacteristic
153C2#1304744211yescharacteristic
154C2C22×C9⋊Dic911yescharacteristic
subgroupG/H
centerC22C22×C9⋊D9
commutatorC2×C92C22×C4
Frattini, socleC22×C32C22×C3⋊D3
FittingC2×D4×C92C2
prime radicalC2×C32×D4C3⋊D3
cosocleC22×C92C23
hypercenterC2×D4C9⋊D9
hypocenterC92C4×D4
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C22×C9⋊Dic9C2semidirect
3. #13046833C2semidirect
4. C4⋊(C9⋊Dic9)C2semidirect
5. C4×C9⋊Dic9C2semidirect
8. D4×C92C4semidirect
21. C22×C92C2×C4semidirect
23. C4×C92C2×C4semidirect
26. C9⋊Dic9D4direct (N × H)
59. C92C4×D4semidirect
68. D4×C9Dic9semidirect
93. C22×C9C2×Dic9semidirect
95. C4×C9C2×Dic9semidirect
130. C9D4×Dic9semidirect
132. D4C9⋊Dic9direct (N × H)
144. C22C2×C9⋊Dic9semidirect
149. C4C2×C9⋊Dic9semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C922
C22×C9⋊Dic92
#130468332
C4⋊(C9⋊Dic9)2
C4×C9⋊Dic92
D4×C3⋊Dic93