Finite Group Databasebeta

← D4×C3⋊D27 #13047445

Subgroups — D4×C3⋊D27 #13047445

Order 1296.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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
3#10619677C212yesmaximal, complemented
4C4⋊(C3⋊D27)C211yesmaximal, characteristic, complemented
5C4×C3⋊D27C211yesmaximal, characteristic, complemented
6D4×C3⋊D9—31nomaximal
7D4×D27—33nomaximal
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
16#6233—32no—
17C4⋊(C3⋊D9)—31no—
18C4×C3⋊D9—31no—
19C22×D27—36no—
20D4×C27D313yescomplemented
21#6171—36no—
22D108—33no—
23C4×D27—33no—
24C2×C3×C27—22no—
25C2×C3×C27C2311yescharacteristic
26C3⋊D27—22no—
27C3⋊D27D412yesdirect product factor
28D4×C3⋊D3—91no—
29D4×D9—92no—
30D4×D9—91no—
31C22×C3×C9C2×D312yes—
32C2×C3⋊D9—31no—
33C2×C3⋊D9—32no—
34C2×C3⋊D9—64no—
35C3×C4×C9C2×D311yescharacteristic
36C3⋊Dic9—31no—
37C22×C27C2×D316yescomplemented
38C2×D27—33no—
39C2×D27—36no—
40C2×D27—612no—
41C4×C27C2×D313yescomplemented
42Dic27—33no—
43C3×C27C2×D411yescharacteristic, complemented, Sylow
44C22×C3⋊D3—92no—
45C32×D4D911yescharacteristic
46#638—92no—
47C4⋊(C3⋊D3)—91no—
48C4×C3⋊D3—91no—
49C22×D9—94no—
50C22×D9—92no—
51D4×C9D912yes—
52D4×C9C3⋊D311yescharacteristic
53#611—94no—
54#611—92no—
55D36—92no—
56D36—91no—
57C4×D9—92no—
58C4×D9—91no—
59C2×C3×C9—22no—
60C2×C3×C9C22×D311yescharacteristic
61C3⋊D9—32no—
62C3⋊D9—62no—
63C2×C27—26no—
64C2×C27C22×D313yes—
65D27—36no—
66D27—66no—
67D3×D4—273no—
68D3×D4—271no—
69C22×C32C2×D912yes—
70C2×C3⋊D3—91no—
71C2×C3⋊D3—92no—
72C2×C3⋊D3—184no—
73C32×C4C2×D911yescharacteristic
74C3⋊Dic3—91no—
75C22×C9C2×D914yes—
76C22×C9C2×C3⋊D312yes—
77C2×D9—92no—
78C2×D9—91no—
79C2×D9—94no—
80C2×D9—92no—
81C2×D9—184no—
82C2×D9—188no—
83C4×C9C2×D912yes—
84C4×C9C2×C3⋊D311yescharacteristic
85Dic9—92no—
86Dic9—91no—
87C3×C9D3×D411yescharacteristic
88C27D3×D413yescomplemented
89C22×D3—276no—
90C22×D3—272no—
91C3×D4D2713yescomplemented
92C3×D4C3⋊D911yescharacteristic
93#67—276no—
94#67—272no—
95D12—273no—
96D12—271no—
97C4×D3—273no—
98C4×D3—271no—
99C2×C32—22no—
100C2×C32C22×D911yescharacteristic
101C3⋊D3—92no—
102C3⋊D3—182no—
103C2×C9—24no—
104C2×C9—22no—
105C2×C9C22×D912yes—
106C2×C9C22×C3⋊D311yescharacteristic
107D9—94no—
108D9—92no—
109D9—184no—
110D9—182no—
111C2×D4—811noSylow
112C22×C3C2×D2716yescomplemented
113C22×C3C2×C3⋊D912yes—
114C2×D3—273no—
115C2×D3—271no—
116C2×D3—276no—
117C2×D3—272no—
118C2×D3—544no—
119C2×D3—5412no—
120C3×C4C2×D2713yescomplemented
121C3×C4C2×C3⋊D911yescharacteristic
122Dic3—273no—
123Dic3—271no—
124C32D4×D911yescharacteristic
125C9D4×D912yes—
126C9D4×C3⋊D311yescharacteristic
127C23—812no—
128D4—812no—
129D4—811no—
130D4C3⋊D2711yescharacteristic, direct product factor
131C2×C4—811no—
132C2×C3—26no—
133C2×C3—22no—
134C2×C3C22×D2713yes—
135C2×C3C22×C3⋊D911yescharacteristic
136D3—276no—
137D3—272no—
138D3—546no—
139D3—542no—
140C22—811no—
141C22—812no—
142C22—1624no—
143C22C2×C3⋊D2712yescomplemented
144C4—811no—
145C4C2×C3⋊D2711yescharacteristic, complemented
146C3D4×D2713yescomplemented
147C3D4×C3⋊D911yescharacteristic
148C2—22no—
149C2—812no—
150C2—1622no—
151C2C22×C3⋊D2711yescharacteristic
subgroupG/H
centerC2C22×C3⋊D27
commutator, cosocleC2×C3×C27C23
FrattiniC2×C9C22×C3⋊D3
FittingC3×D4×C27C2
socleC2×C32C22×D9
hypercenterD4C3⋊D27
hypocenterC3×C27C2×D4
LCSG ▷ C2×C3×C27 ▷ C3×C27
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×C3⋊D27C2semidirect
2. C3×D4×C27C2semidirect
3. #10619677C2semidirect
4. C4⋊(C3⋊D27)C2semidirect
5. C4×C3⋊D27C2semidirect
8. C22×C3×C27C22semidirect
11. C2×C3⋊D27C22semidirect
12. C3×C4×C27C22semidirect
13. C3⋊Dic27C22semidirect
20. D4×C27D3semidirect
27. C3⋊D27D4direct (N × H)
37. C22×C27C2×D3semidirect
41. C4×C27C2×D3semidirect
43. C3×C27C2×D4semidirect
88. C27D3×D4semidirect
91. C3×D4D27semidirect
112. C22×C3C2×D27semidirect
120. C3×C4C2×D27semidirect
130. D4C3⋊D27direct (N × H)
143. C22C2×C3⋊D27semidirect
145. C4C2×C3⋊D27semidirect
146. C3D4×D27semidirect

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
#106196772
C4⋊(C3⋊D27)2
C4×C3⋊D272
D4×C3⋊D93
D4×D273