Finite Group Databasebeta

← C3⋊(#376⋊C9) #13136822

Subgroups — C3⋊(#376⋊C9) #13136822

Order 1728.

177 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 177 conjugacy classes of subgroups — too many to draw. Only its 29 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×#95⋊C9C211yesmaximal, characteristic
2C3×#4648C311yesmaximal, characteristic
3#376⋊C9—31nomaximal
4Dic3×C22⋊C9—41nomaximal
5C2×C3×C4×Dic3—31no—
6C32×#95C2×C311yescharacteristic
7C3×C3⋊#95—31no—
8#95⋊C9—21no—
9#95⋊C9D311yescharacteristic
10C2×C3×C22⋊C9—41no—
11C3×#376—31no—
12#4648C911yescharacteristic, complemented
13C22×C32×C4—31no—
14C22×C3×Dic3—31no—
15C22×C3×Dic3A411yescharacteristic
16C3×C4×Dic3—32no—
17C3×C4×Dic3—32no—
18C4×C22⋊C9—121no—
19C3×C22⋊C9—41no—
20C9×Dic3—161no—
21C2×C3×C42—91no—
22C2×C4×Dic3—31no—
23C3×#95—21no—
24C3×#95—91no—
25C3×#95C2×C911yescharacteristic
26C3×#95C3×D311yescharacteristic
27C3⋊#95—31no—
28C23×C32C2×A411yescharacteristic
29C2×C32×C4—32no—
30C2×C32×C4—62no—
31C2×C3×Dic3—31no—
32C2×C3×Dic3—31no—
33C2×C3×Dic3—32no—
34C2×C3×Dic3—61no—
35C2×C3×Dic3—61no—
36C2×C22⋊C9—41no—
37C2×C22⋊C9—81no—
38#376—31noSylow
39C2×C3×C9—161no—
40C22×C3×C4—31no—
41C22×C3×C4—31no—
42C22×C3×C4—31no—
43C22×C3×C4—61no—
44C22×C3×C4—91no—
45C22×Dic3—31no—
46C22×Dic3C22⋊C911yescharacteristic
47C3×C42—92no—
48C3×C42—92no—
49C4×Dic3—32no—
50C4×Dic3—32no—
51C22×C32—31no—
52C22×C32—31no—
53C22×C32#41⋊C311yescharacteristic
54C32×C4—62no—
55C3×Dic3—31no—
56C3×Dic3—62no—
57C3×Dic3C42⋊C311yescharacteristic
58C22⋊C9—41no—
59C22⋊C9—81no—
60C4×C9—481no—
61C2×C42—91no—
62#95—91no—
63#95D3×C911yescharacteristic
64C3×C9—161noSylow
65C23×C3—21no—
66C23×C3C2×C22⋊C911yescharacteristic
67C23×C3D3×A411yescharacteristic
68C2×C3×C4—32no—
69C2×C3×C4—32no—
70C2×C3×C4—62no—
71C2×C3×C4—62no—
72C2×C3×C4—62no—
73C2×C3×C4—91no—
74C2×C3×C4—91no—
75C2×C3×C4—92no—
76C2×C3×C4—122no—
77C2×C3×C4—181no—
78C2×C3×C4—181no—
79C2×Dic3—31no—
80C2×Dic3—31no—
81C2×Dic3—32no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C2×C32—31no—
85C2×C32—31no—
86C2×C32C2×C42⋊C311yescharacteristic
87C2×C9—161no—
88C2×C9—321no—
89C22×C4—31no—
90C22×C4—31no—
91C22×C4—91no—
92C42—92no—
93C42—92no—
94C22×C3—21no—
95C22×C3—31no—
96C22×C3—31no—
97C22×C3—31no—
98C22×C3—31no—
99C22×C3—61no—
100C22×C3—61no—
101C22×C3#41⋊C911yescharacteristic
102C22×C3C3⋊(#41⋊C3)11yescharacteristic
103C3×C4—31no—
104C3×C4—62no—
105C3×C4—62no—
106C3×C4—91no—
107C3×C4—122no—
108C3×C4—182no—
109Dic3—31no—
110Dic3—62no—
111Dic3C42⋊C911yescharacteristic
112C32#376⋊C311yescharacteristic
113C9—161no—
114C9—321no—
115C23D3×C22⋊C911yescharacteristic
116C2×C4—32no—
117C2×C4—62no—
118C2×C4—91no—
119C2×C4—91no—
120C2×C4—92no—
121C2×C4—181no—
122C2×C4—181no—
123C2×C3—21no—
124C2×C3—31no—
125C2×C3—31no—
126C2×C3—31no—
127C2×C3—31no—
128C2×C3—61no—
129C2×C3—61no—
130C2×C3C2×C42⋊C911yescharacteristic
131C2×C3D3×C42⋊C311yescharacteristic
132C22—31no—
133C22—31no—
134C22C3⋊(#41⋊C9)11yescharacteristic
135C4—31no—
136C4—62no—
137C4—91no—
138C4—182no—
139C3—21no—
140C3#376⋊C911yescharacteristic, complemented
141C3C3⋊(#376⋊C3)11yescharacteristic
142C2—31no—
143C2—31no—
144C2D3×C42⋊C911yescharacteristic
subgroupG/H
center, hypercenterC2×C3D3×C42⋊C3
commutator, hypocenterC3×#95C2×C9
FrattiniC23×C3D3×A4
Fitting, cosocleC32×#95C2×C3
socle, prime radicalC23×C32C2×A4
LCSG ▷ C3×#95
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
12. #4648C9semidirect
140. C3#376⋊C9semidirect

Maximal subgroups

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

subgroupindex
C3×#95⋊C92
C3×#46483
#376⋊C93
Dic3×C22⋊C94