Finite Group Databasebeta

← C3×D4×D27 #13047343

Subgroups — C3×D4×D27 #13047343

Order 1296.

240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×C3×D27C212yesmaximal, complemented
2C3×D4×C27C211yesmaximal, characteristic, complemented
3C3×#6171C212yesmaximal, complemented
4C3×D108C211yesmaximal, characteristic, complemented
5C3×C4×D27C211yesmaximal, characteristic, complemented
6C3×D4×D9—31nomaximal
7D4×D27C311yesmaximal, characteristic, direct product factor
8C22×C3×C27C2212yescomplemented
9C2×C3×D27—24no—
10C2×C3×D27C2211yescharacteristic
11C2×C3×D27C2212yescomplemented
12C3×C4×C27C2211yescharacteristic, complemented
13C3×Dic27C2211yescharacteristic, complemented
14C22×C3×D9—32no—
15C3×D4×C9D311yescharacteristic
16C3×#611—32no—
17C3×D36—31no—
18C3×C4×D9—31no—
19C22×D27C2×C312yescomplemented
20D4×C27—21no—
21D4×C27C2×C311yescharacteristic, complemented
22#6171C2×C312yescomplemented
23D108C2×C311yescharacteristic, complemented
24C4×D27C2×C311yescharacteristic, complemented
25C2×C3×C27—22no—
26C2×C3×C27C2311yescharacteristic
27C3×D27—22no—
28C3×D27D412yesdirect product factor
29C3×D3×D4—91no—
30D4×D9—31no—
31C22×C3×C9C2×D312yes—
32C2×C3×D9—31no—
33C2×C3×D9—32no—
34C2×C3×D9—64no—
35C3×C4×C9C2×D311yescharacteristic
36C3×Dic9—31no—
37C22×C27—22no—
38C22×C27C22×C312yescomplemented
39C2×D27—24no—
40C2×D27C22×C311yescharacteristic
41C2×D27C22×C312yescomplemented
42C4×C27—21no—
43C4×C27C22×C311yescharacteristic, complemented
44Dic27C22×C311yescharacteristic, complemented
45C3×C27C2×D411yescharacteristic, complemented, Sylow
46C22×C3×D3—92no—
47C32×D4D911yescharacteristic
48C3×#67—92no—
49C3×D12—91no—
50C3×C4×D3—91no—
51C22×D9—32no—
52D4×C9—21no—
53D4×C9C3×D311yescharacteristic
54#611—32no—
55D36—31no—
56C4×D9—31no—
57C2×C3×C9—22no—
58C2×C3×C9C22×D311yescharacteristic
59C3×D9—32no—
60C3×D9—62no—
61C2×C27—22no—
62C2×C27—21no—
63C2×C27—42no—
64C2×C27C23×C311yescharacteristic
65D27—22no—
66D27C3×D412yesdirect product factor
67C2×C3×D4—271no—
68D3×D4—91no—
69C22×C32C2×D912yes—
70C2×C3×D3—91no—
71C2×C3×D3—92no—
72C2×C3×D3—184no—
73C32×C4C2×D911yescharacteristic
74C3×Dic3—91no—
75C22×C9—22no—
76C22×C9C2×C3×D312yes—
77C2×D9—31no—
78C2×D9—32no—
79C2×D9—64no—
80C4×C9—21no—
81C4×C9C2×C3×D311yescharacteristic
82Dic9—31no—
83C3×C9D3×D411yescharacteristic
84C27—21no—
85C27C2×C3×D411yescharacteristic, complemented
86C23×C3—272no—
87C22×D3—92no—
88C3×D4—21no—
89C3×D4—272no—
90C3×D4—271no—
91C3×D4D2711yescharacteristic, direct product factor
92C3×D4C3×D911yescharacteristic
93C2×C3×C4—271no—
94#67—92no—
95D12—91no—
96C4×D3—91no—
97C2×C32—22no—
98C2×C32C22×D911yescharacteristic
99C3×D3—92no—
100C3×D3—182no—
101C2×C9—22no—
102C2×C9—21no—
103C2×C9—42no—
104C2×C9C22×C3×D311yescharacteristic
105D9—32no—
106D9—62no—
107C2×D4—271noSylow
108C22×C3—22no—
109C22×C3—271no—
110C22×C3—272no—
111C22×C3—544no—
112C22×C3C2×D2712yescomplemented
113C22×C3C2×C3×D912yes—
114C2×D3—91no—
115C2×D3—92no—
116C2×D3—184no—
117C3×C4—21no—
118C3×C4—271no—
119C3×C4C2×D2711yescharacteristic, complemented
120C3×C4C2×C3×D911yescharacteristic
121Dic3—91no—
122C32D4×D911yescharacteristic
123C9—21no—
124C9C3×D3×D411yescharacteristic
125C23—272no—
126D4—272no—
127D4—271no—
128D4C3×D2711yescharacteristic, direct product factor
129C2×C4—271no—
130C2×C3—22no—
131C2×C3—22no—
132C2×C3—21no—
133C2×C3—42no—
134C2×C3—272no—
135C2×C3—542no—
136C2×C3C22×D2711yescharacteristic
137C2×C3C22×C3×D911yescharacteristic
138D3—92no—
139D3—182no—
140C22—271no—
141C22—272no—
142C22—544no—
143C22C2×C3×D2712yescomplemented
144C4—271no—
145C4C2×C3×D2711yescharacteristic, complemented
146C3—21no—
147C3D4×D2711yescharacteristic, direct product factor
148C3C3×D4×D911yescharacteristic
149C2—22no—
150C2—272no—
151C2—542no—
152C2C22×C3×D2711yescharacteristic
subgroupG/H
centerC2×C3C22×D27
commutator, cosocleC2×C27C23×C3
FrattiniC2×C9C22×C3×D3
FittingC3×D4×C27C2
socleC2×C32C22×D9
hypercenterC3×D4D27
hypocenterC27C2×C3×D4
LCSG ▷ C2×C27 ▷ C27
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×D27C2semidirect
2. C3×D4×C27C2semidirect
3. C3×#6171C2semidirect
4. C3×D108C2semidirect
5. C3×C4×D27C2semidirect
7. D4×D27C3direct (N × H)
8. C22×C3×C27C22semidirect
11. C2×C3×D27C22semidirect
12. C3×C4×C27C22semidirect
13. C3×Dic27C22semidirect
19. C22×D27C2×C3semidirect
21. D4×C27C2×C3semidirect
22. #6171C2×C3semidirect
23. D108C2×C3semidirect
24. C4×D27C2×C3semidirect
28. C3×D27D4direct (N × H)
38. C22×C27C22×C3semidirect
41. C2×D27C22×C3semidirect
43. C4×C27C22×C3semidirect
44. Dic27C22×C3semidirect
45. C3×C27C2×D4semidirect
66. D27C3×D4direct (N × H)
85. C27C2×C3×D4semidirect
91. C3×D4D27direct (N × H)
112. C22×C3C2×D27semidirect
119. C3×C4C2×D27semidirect
128. D4C3×D27direct (N × H)
143. C22C2×C3×D27semidirect
145. C4C2×C3×D27semidirect
147. C3D4×D27direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D272
C3×D4×C272
C3×#61712
C3×D1082
C3×C4×D272
C3×D4×D93
D4×D273