Finite Group Databasebeta

← C3×#157⋊(C3⋊D3) #14519519

Subgroups — C3×#157⋊(C3⋊D3) #14519519

Order 1944.

884 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C3×C3⋊#1113C212yesmaximal, complemented
2C33×#157C211yesmaximal, characteristic, complemented
3#157⋊(C3⋊D3)C311yesmaximal, characteristic, direct product factor
4C3×#157⋊D3—34nomaximal
5C32×C3⋊(C3⋊D3)—22no—
6C33×C3⋊D3C2211yescharacteristic
7C3⋊#1113C2×C312yescomplemented
8C3×#1113—38no—
9C3×D3×C3⋊D3—62no—
10C32×#157—24no—
11C32×#157D314yescomplemented
12C32×#157C2×C311yescharacteristic, complemented
13C35D411yescharacteristic, complemented, Sylow
14#157⋊D3—34no—
15C3×GO+(4,𝔽2)—91no—
16C3×C4⋊(C3⋊D3)—91nomaximal
17C3×C3⋊(C3⋊D3)—22no—
18C3×C3⋊(C3⋊D3)—22no—
19C3×C3⋊(C3⋊D3)—42no—
20C32×C3⋊D3—24no—
21C32×C3⋊D3—62no—
22C32×C3⋊D3—68no—
23C32×C3⋊D3—128no—
24C32×C3⋊D3C2×D314yes—
25C32×C3⋊D3C22×C311yescharacteristic
26C33×D3—62no—
27C2×C3×C3⋊D3—92no—
28#1113—38no—
29D3×C3⋊D3—62no—
30C3×D32—92no—
31C3×D32—188no—
32C3×#157—24no—
33C3×#157C3×D314yescomplemented
34C3×#157C3⋊D311yescharacteristic, complemented
35C33×C4—91no—
36C34—22no—
37C34—24no—
38C34—42no—
39C34—48no—
40C34—88no—
41C34D1214yescomplemented
42C34C3×D411yescharacteristic, complemented
43GO+(4,𝔽2)—91no—
44C4⋊(C3⋊D3)—91no—
45C3×D12—274no—
46C2×C33—91no—
47C3⋊(C3⋊D3)—22no—
48C3×C3⋊D3—24no—
49C3×C3⋊D3—62no—
50C3×C3⋊D3—62no—
51C3×C3⋊D3—68no—
52C3×C3⋊D3—68no—
53C3×C3⋊D3—128no—
54C3×C3⋊D3—128no—
55C3×C3⋊D3—122no—
56C3×C3⋊D3—128no—
57C3×C3⋊D3—1216no—
58C3×C3⋊D3C2×C3×D314yes—
59C3×C3⋊D3C2×C3⋊D311yescharacteristic
60C32×D3—62no—
61C32×D3—68no—
62C32×D3—128no—
63C32×D3—188no—
64C32×D3—182no—
65C32×D3—368no—
66C2×C3⋊D3—92no—
67C2×C3×D3—278no—
68C2×C3×D3—542no—
69D32—92no—
70D32—188no—
71#157C3×C3⋊D311yescharacteristic, complemented
72C32×C4—91no—
73C32×C4—94no—
74C32×C4—184no—
75C33—22no—
76C33—28no—
77C33—24no—
78C33—48no—
79C33—48no—
80C33—48no—
81C33—48no—
82C33—416no—
83C33—42no—
84C33—48no—
85C33—88no—
86C33—88no—
87C33—88no—
88C33—86no—
89C33—824no—
90C33—816no—
91C33—848no—
92C33C3×D1214yescomplemented
93C33C4⋊(C3⋊D3)11yescharacteristic, complemented
94C33GO+(4,𝔽2)11yescharacteristic, complemented
95C3×D4—811no—
96D12—274no—
97C2×C32—91no—
98C2×C32—94no—
99C2×C32—184no—
100C2×C32—542no—
101C3⋊D3—62no—
102C3⋊D3—68no—
103C3⋊D3—128no—
104C3⋊D3C2×C3×C3⋊D311yescharacteristic
105C3×D3—62no—
106C3×D3—68no—
107C3×D3—128no—
108C3×D3—182no—
109C3×D3—188no—
110C3×D3—182no—
111C3×D3—188no—
112C3×D3—362no—
113C3×D3—368no—
114C3×D3—368no—
115C3×D3—368no—
116C3×D3—3616no—
117C22×C3—812no—
118C2×D3—278no—
119C2×D3—542no—
120C3×C4—94no—
121C3×C4—91no—
122C3×C4—184no—
123C32—24no—
124C32—28no—
125C32—22no—
126C32—48no—
127C32—48no—
128C32—42no—
129C32—48no—
130C32—416no—
131C32—48no—
132C32—48no—
133C32—88no—
134C32—824no—
135C32—88no—
136C32—86no—
137C32—816no—
138C32—848no—
139C32—88no—
140C32C3×C4⋊(C3⋊D3)11yescharacteristic, complemented
141C32C3×GO+(4,𝔽2)11yescharacteristic, complemented
142C32#157⋊D314yescomplemented
143D4—811noSylow
144C2×C3—94no—
145C2×C3—91no—
146C2×C3—184no—
147C2×C3—542no—
148C2×C3—542no—
149C2×C3—1082no—
150D3—62no—
151D3—182no—
152D3—188no—
153D3—368no—
154C22—812no—
155C4—91no—
156C3—22no—
157C3—24no—
158C3—48no—
159C3—42no—
160C3—88no—
161C3C3×#157⋊D314yescomplemented
162C3#157⋊(C3⋊D3)11yescharacteristic, direct product factor
163C2—91no—
164C2—542no—
subgroupG/H
center, hypercenterC3#157⋊(C3⋊D3)
commutator, cosocleC32×C3⋊D3C22×C3
FrattiniC1G
Fitting, socleC35D4
hypocenterC34C3×D4
LCSG ▷ C32×C3⋊D3 ▷ C34
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊#1113C2semidirect
2. C33×#157C2semidirect
3. #157⋊(C3⋊D3)C3direct (N × H)
7. C3⋊#1113C2×C3semidirect
11. C32×#157D3semidirect
12. C32×#157C2×C3semidirect
13. C35D4semidirect
33. C3×#157C3×D3semidirect
34. C3×#157C3⋊D3semidirect
41. C34D12semidirect
42. C34C3×D4semidirect
71. #157C3×C3⋊D3semidirect
92. C33C3×D12semidirect
93. C33C4⋊(C3⋊D3)semidirect
94. C33GO+(4,𝔽2)semidirect
140. C32C3×C4⋊(C3⋊D3)semidirect
141. C32C3×GO+(4,𝔽2)semidirect
142. C32#157⋊D3semidirect
161. C3C3×#157⋊D3semidirect
162. C3#157⋊(C3⋊D3)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C3⋊#11132
C33×#1572
#157⋊(C3⋊D3)3
C3×#157⋊D33
C3×C4⋊(C3⋊D3)9