Finite Group Databasebeta

← C4×D9×3−1+2 #14517304

Subgroups — C4×D9×3−1+2 #14517304

Order 1944.

267 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 98 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×D9×3−1+2C211yesmaximal, characteristic
2C4×C9×3−1+2C211yesmaximal, characteristic, complemented
33−1+2×Dic9C211yesmaximal, characteristic, complemented
4C4×D3×3−1+2—31nomaximal
5C32×C4×D9C311yesmaximal, characteristic
6C4×C9×D9C313yesmaximal, complemented
7C2×C9×3−1+2C2211yescharacteristic
8D9×3−1+2C412yesdirect product factor
9C2×D3×3−1+2—31no—
10C2×C32×D9C2×C311yescharacteristic
11C3×C4×3−1+2D311yescharacteristic
12C32×C4×C9C2×C311yescharacteristic
13Dic3×3−1+2—31no—
14C32×Dic9C2×C311yescharacteristic
15C2×C9×D9C2×C313yes—
16C4×C9⋊C9—23no—
17C4×C32⋊C9—21no—
18C4×C92C2×C313yescomplemented
19C9×Dic9C2×C313yescomplemented
20C9×3−1+2C2×C411yescharacteristic, complemented, Sylow
21C32×C4×D3—31no—
22C2×C4×3−1+2—91no—
23C4×D3×C9—33no—
24C3×C4×D9—31no—
25C3×C4×D9C3211yescharacteristic
26C2×C3×3−1+2C2×D311yescharacteristic
27C2×C32×C9C22×C311yescharacteristic
28D3×3−1+2—32no—
29C32×D9C3×C412yes—
30C2×C9⋊C9—23no—
31C2×C32⋊C9—21no—
32C2×C92C22×C313yes—
33C9×D9C3×C416yescomplemented
34C2×C32×D3—31no—
35C33×C4C3×D311yescharacteristic
36C32×Dic3—31no—
37C22×3−1+2—91no—
38C2×D3×C9—33no—
39C2×C3×D9—31no—
40C2×C3×D9C2×C3211yescharacteristic
41C4×3−1+2—21no—
42C4×3−1+2—23no—
43C4×3−1+2—91no—
44C4×3−1+2D911yescharacteristic, direct product factor
45C3×C4×C9—23no—
46C3×C4×C9—21no—
47C3×C4×C9—31no—
48C3×C4×C9—61no—
49C3×C4×C9C3×D313yes—
50C3×C4×C9C2×C3211yescharacteristic
51C9×Dic3—33no—
52C3×Dic9—31no—
53C3×Dic9C2×C3211yescharacteristic
54C3×3−1+2C4×D311yescharacteristic
55C32×C9C2×C3×C411yescharacteristic
56C9⋊C9—23no—
57C32⋊C9—21no—
58C92C2×C3×C413yescomplemented
59C2×C32×C4—91no—
60C3×C4×D3—31no—
61C3×C4×D3—91no—
62C2×C4×C9—93no—
63C4×D93−1+211yescharacteristic, direct product factor
64C2×C33C2×C3×D311yescharacteristic
65C32×D3—32no—
66C2×3−1+2—21no—
67C2×3−1+2—23no—
68C2×3−1+2—92no—
69C2×3−1+2C2×D911yescharacteristic
70C2×C3×C9—23no—
71C2×C3×C9—21no—
72C2×C3×C9—31no—
73C2×C3×C9—61no—
74C2×C3×C9C2×C3×D313yes—
75C2×C3×C9C22×C3211yescharacteristic
76D3×C9—36no—
77C3×D9—32no—
78C3×D9C32×C412yes—
79C22×C32—91no—
80C2×C3×D3—31no—
81C2×C3×D3—91no—
82C32×C4—21no—
83C32×C4—31no—
84C32×C4—61no—
85C32×C4—91no—
86C32×C4C3×D911yescharacteristic
87C32×C4C32×D311yescharacteristic
88C3×Dic3—31no—
89C3×Dic3—91no—
90C22×C9—93no—
91C2×D9C2×3−1+211yescharacteristic
92C4×C9—23no—
93C4×C9—21no—
94C4×C9—63no—
95C4×C9—61no—
96C4×C9—93no—
97C4×C9C3×D913yescomplemented
98C4×C9C2×3−1+211yescharacteristic, complemented
99Dic9C2×3−1+211yescharacteristic, complemented
100C33C3×C4×D311yescharacteristic
1013−1+2—21no—
1023−1+2—23no—
1033−1+2C4×D911yescharacteristic, direct product factor
104C3×C9—23no—
105C3×C9—21no—
106C3×C9—31no—
107C3×C9—61no—
108C3×C9C3×C4×D313yes—
109C3×C9C2×C32×C411yescharacteristic
110C2×C3×C4—91no—
111C2×C3×C4—271no—
112C4×D3—31no—
113C2×C32—21no—
114C2×C32—31no—
115C2×C32—61no—
116C2×C32—92no—
117C2×C32C2×C3×D911yescharacteristic
118C2×C32C2×C32×D311yescharacteristic
119C3×D3—32no—
120C3×D3—92no—
121C2×C9—23no—
122C2×C9—21no—
123C2×C9—63no—
124C2×C9—61no—
125C2×C9—96no—
126C2×C9C2×C3×D913yes—
127C2×C9C22×3−1+211yescharacteristic
128D9C4×3−1+212yesdirect product factor
129C22×C3—91no—
130C22×C3—271no—
131C2×D3—31no—
132C3×C4—21no—
133C3×C4—31no—
134C3×C4—61no—
135C3×C4—91no—
136C3×C4—271no—
137C3×C4C32×D911yescharacteristic
138C3×C4D3×3−1+211yescharacteristic
139Dic3—31no—
140C32—21no—
141C32—31no—
142C32—61no—
143C32C3×C4×D911yescharacteristic
144C32C32×C4×D311yescharacteristic
145C9—23no—
146C9—21no—
147C9—63no—
148C9—61no—
149C9C3×C4×D913yescomplemented
150C9C2×C4×3−1+211yescharacteristic, complemented
151C2×C4—91noSylow
152C2×C3—21no—
153C2×C3—31no—
154C2×C3—61no—
155C2×C3—92no—
156C2×C3—272no—
157C2×C3C2×C32×D911yescharacteristic
158C2×C3C2×D3×3−1+211yescharacteristic
159D3—32no—
160C22—91no—
161C4—91no—
162C4D9×3−1+211yescharacteristic, direct product factor
163C3—21no—
164C3—31no—
165C3—61no—
166C3C32×C4×D911yescharacteristic
167C3C4×D3×3−1+211yescharacteristic
168C2—92no—
169C2C2×D9×3−1+211yescharacteristic
subgroupG/H
centerC3×C4C32×D9
commutatorC3×C9C2×C32×C4
Frattini, socleC2×C32C2×C32×D3
FittingC4×C9×3−1+2C2
prime radicalC2×C32×D9C2×C3
cosocleC2×C3×C9C22×C32
hypercenterC4×3−1+2D9
hypocenterC9C2×C4×3−1+2
LCSG ▷ C3×C9 ▷ C9
UCSC1 ◁ C3×C4 ◁ C4×3−1+2

Complements

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

NH ≅ G/Ntype
2. C4×C9×3−1+2C2semidirect
3. 3−1+2×Dic9C2semidirect
6. C4×C9×D9C3semidirect
8. D9×3−1+2C4direct (N × H)
18. C4×C92C2×C3semidirect
19. C9×Dic9C2×C3semidirect
20. C9×3−1+2C2×C4semidirect
33. C9×D9C3×C4semidirect
44. C4×3−1+2D9direct (N × H)
58. C92C2×C3×C4semidirect
63. C4×D93−1+2direct (N × H)
97. C4×C9C3×D9semidirect
98. C4×C9C2×3−1+2semidirect
99. Dic9C2×3−1+2semidirect
103. 3−1+2C4×D9direct (N × H)
128. D9C4×3−1+2direct (N × H)
149. C9C3×C4×D9semidirect
150. C9C2×C4×3−1+2semidirect
162. C4D9×3−1+2direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D9×3−1+22
C4×C9×3−1+22
3−1+2×Dic92
C4×D3×3−1+23
C32×C4×D93
C4×C9×D93