Finite Group Databasebeta

← Dic3×D27⋊C3 #14516844

Subgroups — Dic3×D27⋊C3 #14516844

Order 1944.

186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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×C3×D27⋊C3C211yesmaximal, characteristic
2C3⋊((C27⋊C3)⋊C4)C211yesmaximal, characteristic, complemented
3Dic3×C27⋊C3C211yesmaximal, characteristic, complemented
4C3×Dic3×D9—31nomaximal
5C4×D27⋊C3—31nomaximal
6Dic3×D27C311yesmaximal, characteristic, complemented
7C2×C3×C27⋊C3C2211yescharacteristic
8C3×D27⋊C3C412yescomplemented
9C2×C32×D9—31no—
10C3×C3⋊Dic9—31no—
11C3×C9×Dic3D311yescharacteristic
12C2×D27⋊C3—21no—
13C2×D27⋊C3D311yescharacteristic
14C2×C3×D27C2×C311yescharacteristic
15C4×C27⋊C3—31no—
16C3⋊Dic27C2×C311yescharacteristic, complemented
17(C27⋊C3)⋊C4—31no—
18(C27⋊C3)⋊C4—61no—
19Dic3×C27—21no—
20Dic3×C27C2×C311yescharacteristic, complemented
21C3×C27⋊C3C2×C411yescharacteristic, complemented, Sylow
22C3×D3×Dic3—91no—
23C3×C4×D9—91no—
24Dic3×D9—31no—
25C4×D27—31no—
26C2×C32×C9C2×D311yescharacteristic
27C32×D9—32no—
28C2×C27⋊C3—21no—
29C2×C27⋊C3—21no—
30C2×C27⋊C3—41no—
31C2×C27⋊C3C2×D311yescharacteristic
32C2×C3×C27—21no—
33C2×C3×C27C22×C311yescharacteristic
34D27⋊C3—22no—
35D27⋊C3Dic312yesdirect product factor
36C3×D27C3×C412yescomplemented
37C2×C32×D3—91no—
38C3×C3⋊Dic3—91no—
39C32×Dic3D911yescharacteristic
40C2×C3×D9—31no—
41C2×C3×D9—31no—
42C2×C3×D9—61no—
43C3×C4×C9—31no—
44C3⋊Dic9—31no—
45C9×Dic3—21no—
46C9×Dic3C3×D311yescharacteristic
47C3×Dic9—91no—
48C3×Dic9—181no—
49C2×D27C3×D311yescharacteristic
50C4×C27—31no—
51C4×C27—61no—
52Dic27—31no—
53Dic27—61no—
54C32×C9C4×D311yescharacteristic
55C27⋊C3—21no—
56C27⋊C3—21no—
57C27⋊C3—41no—
58C27⋊C3C2×Dic311yescharacteristic, complemented
59C3×C27—21no—
60C3×C27C2×C3×C411yescharacteristic, complemented
61C2×C3×Dic3—271no—
62C3×C4×D3—271no—
63D3×Dic3—91no—
64C4×D9—91no—
65C2×C33C2×D911yescharacteristic
66C32×D3—92no—
67C2×C3×C9—21no—
68C2×C3×C9—21no—
69C2×C3×C9—21no—
70C2×C3×C9—41no—
71C2×C3×C9D3211yescharacteristic
72C2×C3×C9C2×C3×D311yescharacteristic
73C3×D9—32no—
74C3×D9—32no—
75C3×D9—62no—
76C2×C27—21no—
77C2×C27—21no—
78C2×C27—41no—
79C2×C27C2×C3×D311yescharacteristic
80D27C3×Dic312yescomplemented
81C22×C32—271no—
82C2×C3×D3—91no—
83C2×C3×D3—91no—
84C2×C3×D3—181no—
85C32×C4—31no—
86C3⋊Dic3—91no—
87C3×Dic3—31no—
88C3×Dic3—271no—
89C3×Dic3—271no—
90C3×Dic3—541no—
91C3×Dic3C3×D911yescharacteristic
92C2×D9—31no—
93C4×C9—31no—
94C4×C9—61no—
95Dic9—91no—
96Dic9—181no—
97C33C4×D911yescharacteristic
98C3×C9—21no—
99C3×C9—21no—
100C3×C9—21no—
101C3×C9—41no—
102C3×C9D3×Dic311yescharacteristic
103C3×C9C3×C4×D311yescharacteristic
104C27—21no—
105C27—21no—
106C27—41no—
107C27C2×C3×Dic311yescharacteristic, complemented
108C2×C3×C4—811no—
109C2×Dic3—271no—
110C4×D3—271no—
111C2×C32—21no—
112C2×C32—31no—
113C2×C32—61no—
114C2×C32—272no—
115C2×C32D3×D911yescharacteristic
116C2×C32C2×C3×D911yescharacteristic
117C3×D3—92no—
118C3×D3—92no—
119C3×D3—182no—
120C2×C9—21no—
121C2×C9—21no—
122C2×C9—41no—
123C2×C9C3×D3211yescharacteristic
124D9—32no—
125C22×C3—271no—
126C22×C3—271no—
127C22×C3—541no—
128C2×D3—91no—
129C3×C4—31no—
130C3×C4—91no—
131C3×C4—811no—
132Dic3—271no—
133Dic3—271no—
134Dic3—541no—
135Dic3D27⋊C311yescharacteristic, direct product factor
136C32—21no—
137C32—31no—
138C32—61no—
139C32Dic3×D911yescharacteristic
140C32C3×C4×D911yescharacteristic
141C9—21no—
142C9—21no—
143C9—41no—
144C9C3×D3×Dic311yescharacteristic
145C2×C4—811noSylow
146C2×C3—21no—
147C2×C3—31no—
148C2×C3—61no—
149C2×C3—272no—
150C2×C3—272no—
151C2×C3—542no—
152C2×C3C2×D27⋊C311yescharacteristic
153C2×C3C3×D3×D911yescharacteristic
154D3—92no—
155C22—271no—
156C4—31no—
157C4—811no—
158C3—21no—
159C3—31no—
160C3—61no—
161C3C4×D27⋊C311yescharacteristic, complemented
162C3C3×Dic3×D911yescharacteristic
163C2—272no—
164C2D3×D27⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×D27⋊C3
commutator, hypocenterC3×C27C2×C3×C4
FrattiniC2×C9C3×D32
FittingC2×C3×C27⋊C3C22
socleC2×C32C2×C3×D9
prime radicalC2×C3×D27⋊C3C2
cosocleC2×C3×C27C22×C3
LCSG ▷ C3×C27
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊((C27⋊C3)⋊C4)C2semidirect
3. Dic3×C27⋊C3C2semidirect
6. Dic3×D27C3semidirect
8. C3×D27⋊C3C4semidirect
16. C3⋊Dic27C2×C3semidirect
20. Dic3×C27C2×C3semidirect
21. C3×C27⋊C3C2×C4semidirect
35. D27⋊C3Dic3direct (N × H)
36. C3×D27C3×C4semidirect
58. C27⋊C3C2×Dic3semidirect
60. C3×C27C2×C3×C4semidirect
80. D27C3×Dic3semidirect
107. C27C2×C3×Dic3semidirect
135. Dic3D27⋊C3direct (N × H)
161. C3C4×D27⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D27⋊C32
C3⋊((C27⋊C3)⋊C4)2
Dic3×C27⋊C32
C3×Dic3×D93
C4×D27⋊C33
Dic3×D273