Finite Group Databasebeta

← #14515768

Subgroups — #14515768

Order 1944.

162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 30 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×#92206C211yesmaximal, characteristic, complemented
2C2×(C3⋊D3)⋊C27C211yesmaximal, characteristic, complemented
3#11757295C211yesmaximal, characteristic, complemented
4#10619899—31nomaximal
5#10619544—31nomaximal
6C2×C32⋊C27C2211yescharacteristic
7#92206—21no—
8(C3⋊D3)⋊C27—21no—
9C2×C9×C3⋊D3D311yescharacteristic
10C2×C3×C3⋊D9—31no—
11C3×C3⋊Dic9—31no—
12C2×D3×C27—31no—
13C2×C3×D27—31no—
14C2×C3×D27—61no—
15C3⋊Dic27D311yescharacteristic, complemented
16C32⋊C27D411yescharacteristic, complemented, Sylow
17#6295—91no—
18#6195—91no—
19#6194—91no—
20#6171—91no—
21C2×C32×C9C2×D311yescharacteristic
22C9×C3⋊D3—21no—
23C3×C3⋊D9—61no—
24C2×C3×C27—21no—
25C2×C3×C27C2×D311yescharacteristic
26D3×C27—61no—
27C3×D27—62no—
28C3×D27—61no—
29C2×C3×C3⋊D3—91no—
30C2×C3×C3⋊D3D911yescharacteristic
31C3×C3⋊Dic3—91no—
32C2×C3⋊D9—31no—
33C2×D3×C9—31no—
34C2×D3×C9—91no—
35C2×C3×D9—91no—
36C2×C3×D9—181no—
37C3⋊Dic9—31no—
38C3×Dic9—91no—
39C3×Dic9—181no—
40C22×C27—91no—
41C2×D27—31no—
42C2×D27—61no—
43Dic27—91no—
44C32×C9#6711yescharacteristic
45C3×C27—21no—
46C3×C27D1211yescharacteristic, complemented
47#626—271no—
48#626—271no—
49#625—271no—
50#611—271no—
51C2×C33C2×D911yescharacteristic
52C3×C3⋊D3—21no—
53C3×C3⋊D3—181no—
54C2×C3×C9—21no—
55C2×C3×C9—31no—
56C2×C3×C9—61no—
57C2×C3×C9D3211yescharacteristic
58C3⋊D9—61no—
59D3×C9—61no—
60D3×C9—181no—
61C3×D9—182no—
62C3×D9—181no—
63C2×C27—31no—
64C2×C27—61no—
65C2×C27—181no—
66D27—61no—
67D27—62no—
68C2×C3⋊D3—91no—
69C2×C3⋊D3D2711yescharacteristic, complemented
70C2×C3×D3—31no—
71C2×C3×D3—91no—
72C2×C3×D3—271no—
73C2×C3×D3—271no—
74C2×C3×D3—541no—
75C3⋊Dic3—91no—
76C3×Dic3—271no—
77C3×Dic3—271no—
78C3×Dic3—541no—
79C22×C9—91no—
80C2×D9—91no—
81C2×D9—181no—
82Dic9—91no—
83Dic9—181no—
84C33#61111yescharacteristic
85C3×C9—21no—
86C3×C9—31no—
87C3×C9—61no—
88C3×C9#62611yescharacteristic
89C27—31no—
90C27—61no—
91#67—811no—
92#67—811no—
93D12—811no—
94C2×C32—21no—
95C2×C32—31no—
96C2×C32—61no—
97C2×C32C2×D2711yescharacteristic
98C2×C32D3×D911yescharacteristic
99C3⋊D3—21no—
100C3⋊D3—181no—
101C3×D3—61no—
102C3×D3—181no—
103C3×D3—542no—
104C3×D3—541no—
105C3×D3—541no—
106C2×C9—21no—
107C2×C9—61no—
108C2×C9—181no—
109C2×C9((C3⋊D3)⋊C3)⋊C211yescharacteristic
110D9—182no—
111D9—181no—
112C22×C3—91no—
113C22×C3—811no—
114C2×D3—31no—
115C2×D3—91no—
116C2×D3—271no—
117C2×D3—271no—
118C2×D3—541no—
119C3×C4—811no—
120Dic3—271no—
121Dic3—271no—
122Dic3—541no—
123C32—21no—
124C32—31no—
125C32—61no—
126C32#617111yescharacteristic, complemented
127C32#619511yescharacteristic
128C9—21no—
129C9—61no—
130C9#620011yescharacteristic
131D4—2431noSylow
132C2×C3—21no—
133C2×C3—31no—
134C2×C3—61no—
135C2×C3—181no—
136C2×C3—1621no—
137C2×C3((C3⋊D3)⋊C9)⋊C211yescharacteristic
138C2×C3D3×D2711yescharacteristic
139D3—61no—
140D3—181no—
141D3—541no—
142D3—542no—
143D3—541no—
144C22—91no—
145C22—811no—
146C4—811no—
147C3—21no—
148C3—31no—
149C3—61no—
150C3#1061953511yescharacteristic
151C3#1061954511yescharacteristic
152C2—181no—
153C2—1621no—
154C2((C3⋊D3)⋊C27)⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2((C3⋊D3)⋊C27)⋊C2
commutator, Fitting, cosocleC2×C32⋊C27C22
FrattiniC2×C3×C9D32
socleC2×C32D3×D9
hypocenterC32⋊C27D4
LCSG ▷ C2×C32⋊C27 ▷ C32⋊C27
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×#92206C2semidirect
2. C2×(C3⋊D3)⋊C27C2semidirect
3. #11757295C2semidirect
15. C3⋊Dic27D3semidirect
16. C32⋊C27D4semidirect
46. C3×C27D12semidirect
69. C2×C3⋊D3D27semidirect
126. C32#6171semidirect

Maximal subgroups

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

subgroupindex
C2×#922062
C2×(C3⋊D3)⋊C272
#117572952
#106198993
#106195443