Finite Group Databasebeta

← C3⋊D3×#689 #13086992

Subgroups — C3⋊D3×#689 #13086992

Order 1440.

360 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C5×Q8×C3⋊D3C211yesmaximal, characteristic
2C3⋊D3×Dic10C211yesmaximal, characteristic
3#10623912C211yesmaximal, characteristic, complemented
4C32×#689C211yesmaximal, characteristic, complemented
5#10623768C211yesmaximal, characteristic, complemented
6#10623766C211yesmaximal, characteristic, complemented
7C3⋊D3×#168C211yesmaximal, characteristic
8D3×#689—34nomaximal
9C32×C5×Q8C2211yescharacteristic
10#67180C2211yescharacteristic
11C4×C5×C3⋊D3—21no—
12C4×C5×C3⋊D3C2211yescharacteristic
13C5×#634—21no—
14C5×#634C2211yescharacteristic
15C32×Dic10C2211yescharacteristic
16#67141—21no—
17C3⋊D3×Dic5—21no—
18C3⋊(C3⋊#168)C2211yescharacteristic
19C32×#168C2211yescharacteristic
20Q16×C3⋊D3—51nomaximal, Hall
21C5×D3×Q8—34no—
22D3×Dic10—34no—
23#6718—34no—
24C3×#689D314yescomplemented
25#6663—34no—
26#6661—34no—
27D3×#168—34no—
28C2×C5×C3⋊D3D411yescharacteristic
29C32×C4×C5—21no—
30C32×C4×C5C2311yescharacteristic
31C3⋊Dic15—21no—
32C5×C3⋊Dic3—21no—
33C5×C3⋊Dic3D411yescharacteristic
34C32×Dic5—21no—
35C2×#689—91noHall
36Q8×C3⋊D3—51no—
37Q8×C3⋊D3D511yescharacteristic
38C32×Q16—51no—
39#3756—51no—
40#3756—51no—
41#3746—51no—
42C8×C3⋊D3—51no—
43C3×C5×Q8C2×D314yes—
44Dic30—34no—
45C4×C5×D3—34no—
46C4×C5×D3—64no—
47C5×Dic6—34no—
48C5×Dic6—64no—
49C3×Dic10C2×D314yes—
50#1204—64no—
51D3×Dic5—64no—
52C3⋊#168—34no—
53C3×#168C2×D314yes—
54D3×Q16—154no—
55C2×C32×C5C2×D411yescharacteristic
56C5×C3⋊D3Q1612yescomplemented
57C2×C5×Q8—91no—
58C2×Dic10—91no—
59#689—91no—
60#689—91no—
61#689—91no—
62#689C3⋊D311yescharacteristic, direct product factor
63C2×#168—91no—
64C32×Q8—51no—
65C32×Q8C2×D511yescharacteristic
66C4×C3⋊D3—21no—
67C4×C3⋊D3—101no—
68C4×C3⋊D3C2×D511yescharacteristic
69#634—21no—
70#634—51no—
71#634—101no—
72#634C2×D511yescharacteristic
73C32×C8—51no—
74C3⋊(C3⋊C8)—51no—
75C2×C5×D3—34no—
76C3×C4×C5—24no—
77C3×C4×C5C22×D314yes—
78Dic15—64no—
79C3×Dic5—24no—
80C5×Dic3—34no—
81C5×Dic3—64no—
82D3×Q8—34no—
83D3×Q8—154no—
84C3×Q16—54no—
85#216—154no—
86#216—154no—
87Dic12—154no—
88D3×C8—154no—
89C32×C5C2×Q1611yescharacteristic, complemented, Hall
90C5×Q8—91no—
91C5×Q8—181no—
92C5×Q8C2×C3⋊D311yescharacteristic
93C2×C4×C5—91no—
94C2×C4×C5—181no—
95C2×Dic5—181no—
96Dic10—91no—
97Dic10—181no—
98Dic10C2×C3⋊D311yescharacteristic
99#168—91no—
100#168C2×C3⋊D311yescharacteristic
101C2×C3⋊D3C22⋊D511yescharacteristic
102C32×C4—21no—
103C32×C4—101no—
104C32×C4C22×D511yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3—101no—
107C3⋊Dic3C22⋊D511yescharacteristic
108C2×Q16—451noSylow
109C2×C3×C5D3×D414yes—
110C5×D3—38no—
111C3×Q8—54no—
112C3×Q8D3×D514yes—
113C4×D3—34no—
114C4×D3—64no—
115C4×D3—304no—
116Dic6—34no—
117Dic6—64no—
118Dic6—154no—
119Dic6—304no—
120C3×C8—54no—
121C3⋊C8—154no—
122C22×C5—91no—
123C4×C5—21no—
124C4×C5—91no—
125C4×C5—181no—
126C4×C5C22×C3⋊D311yescharacteristic
127Dic5—21no—
128Dic5—181no—
129C2×C32C2×C22⋊D511yescharacteristic
130C3⋊D3#68912yesdirect product factor
131C2×Q8—91no—
132C2×Q8—451no—
133Q16—51no—
134Q16—451no—
135Q16—451no—
136Q16—451no—
137C2×C8—451no—
138C3×C5D3×Q1614yescomplemented
139C2×D3—34no—
140C3×C4—24no—
141C3×C4—104no—
142C3×C4C2×D3×D514yes—
143Dic3—34no—
144Dic3—64no—
145Dic3—304no—
146C2×C5—92no—
147C2×C5D4×C3⋊D311yescharacteristic
148C32C2×#68911yescharacteristic, complemented, Sylow
149Q8—51no—
150Q8—91no—
151Q8—181no—
152Q8—451no—
153Q8—901no—
154Q8D5×C3⋊D311yescharacteristic
155C2×C4—91no—
156C2×C4—181no—
157C2×C4—901no—
158C8—51no—
159C8—451no—
160C2×C3D3×C22⋊D514yes—
161D3—38no—
162C5Q16×C3⋊D311yescharacteristic, complemented, Sylow
163C22—91no—
164C4—21no—
165C4—91no—
166C4—101no—
167C4—181no—
168C4—901no—
169C4C2×D5×C3⋊D311yescharacteristic
170C3D3×#68914yescomplemented
171C2—92no—
172C2C3⋊D3×C22⋊D511yescharacteristic
subgroupG/H
centerC2C3⋊D3×C22⋊D5
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D5×C3⋊D3
FittingC32×C5×Q8C22
socleC2×C32×C5C2×D4
prime radicalC2×C5×C3⋊D3D4
hypercenterQ8D5×C3⋊D3
hypocenterC32×C5C2×Q16
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ Q8

Complements

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

NH ≅ G/Ntype
3. #10623912C2semidirect
4. C32×#689C2semidirect
5. #10623768C2semidirect
6. #10623766C2semidirect
24. C3×#689D3semidirect
56. C5×C3⋊D3Q16semidirect
62. #689C3⋊D3direct (N × H)
89. C32×C5C2×Q16semidirect
130. C3⋊D3#689direct (N × H)
138. C3×C5D3×Q16semidirect
148. C32C2×#689semidirect
162. C5Q16×C3⋊D3semidirect
170. C3D3×#689semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×C3⋊D32
C3⋊D3×Dic102
#106239122
C32×#6892
#106237682
#106237662
C3⋊D3×#1682
D3×#6893
Q16×C3⋊D35