Finite Group Databasebeta

← #14518087

Subgroups — #14518087

Order 1944.

178 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 36 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
1#11757860C211yesmaximal, characteristic, complemented
2#10619983—31nomaximal
3C3⋊((C22⋊C27)⋊C2)C311yesmaximal, characteristic, complemented
4C3×(C22⋊C27)⋊C2—31nomaximal
5((C22⋊C27)⋊C2)⋊C3—32nomaximal
6#92318—41nomaximal
7C22×#737D311yescharacteristic
8C2×#4207—31no—
9#66409—31no—
10#66353—21no—
11#66353—22no—
12#66353D312yescomplemented
13C3×C22⋊C27—21no—
14C3×C22⋊C27D311yescharacteristic, complemented
15C3×C22⋊C27C2×C311yescharacteristic, complemented
16#6903—41noSylow
17#6233—31no—
18#611⋊C3—92no—
19#638⋊C3—91no—
20C3×#611—91no—
21(C22⋊C27)⋊C2—32no—
22(C22⋊C27)⋊C2—31no—
23C2×#737—31no—
24#4207—61no—
25C3⋊D27—41no—
26D27⋊C3—122no—
27C3×D27—121no—
28C22×3−1+2—21no—
29C22×3−1+2—22no—
30C22×3−1+2D912yes—
31C22×H(3,𝔽3)D911yescharacteristic
32C22×C3×C9—21no—
33C22×C3×C9C3×D311yescharacteristic
34C22×C3×C9C3⋊D311yescharacteristic
35C2×C3⋊D9—31no—
36C2×AGL(1,ℤ/9)—92no—
37C2×(C3⋊D3)⋊C3—91no—
38C2×C3×D9—91no—
39C3⋊Dic9—31no—
403−1+2⋊C4—92no—
41(C3⋊Dic3)⋊C3—91no—
42C3×Dic9—91no—
43C22⋊C27—22no—
44C22⋊C27—21no—
45C22⋊C27C3×D311yescharacteristic
46C22⋊C27C3×D312yes—
47#737S411yescharacteristic
48C27⋊C3—42no—
49C27⋊C3—82no—
50C27⋊C3—81no—
51C3×C27—41no—
52C3×C27—41no—
53C3×C27—81no—
54#638—91no—
55C3×#67—271no—
56#611—92no—
57#611—91no—
58C2×3−1+2—32no—
59C2×3−1+2—62no—
60C2×3−1+2—61no—
61C2×H(3,𝔽3)—31no—
62C2×C3×C9—31no—
63C2×C3×C9—31no—
64C2×C3×C9—61no—
65C3⋊D9—61no—
66AGL(1,ℤ/9)—182no—
67(C3⋊D3)⋊C3—181no—
68C3×D9—181no—
69D27—121no—
70D27—122no—
71C22×C32—21no—
72C22×C32C3×D911yescharacteristic
73C22×C32C3⋊D911yescharacteristic
74C2×C3⋊D3—91no—
75C2×C3×D3—271no—
76C3⋊Dic3—91no—
77C3×Dic3—271no—
78C22×C9—22no—
79C22×C9—21no—
80C22×C9C3×D912yes—
81C22×C9C3×C3⋊D311yescharacteristic
82C2×D9—91no—
83C2×D9—92no—
84Dic9—91no—
85Dic9—92no—
863−1+2—21no—
873−1+2—22no—
883−1+2(C22⋊C9)⋊C212yes—
89H(3,𝔽3)(C22⋊C9)⋊C211yescharacteristic
90C3×C9—21no—
91C3×C9C3×S411yescharacteristic
92C3×C9C3⋊S411yescharacteristic
93C27—41no—
94C27—42no—
95C27—81no—
96C27—82no—
97C3×D4—811no—
98#67—271no—
99#67—811no—
100C2×C32—31no—
101C2×C32—31no—
102C2×C32—61no—
103C3⋊D3—181no—
104C3×D3—541no—
105C2×C9—32no—
106C2×C9—31no—
107C2×C9—61no—
108C2×C9—62no—
109D9—182no—
110D9—181no—
111C22×C3—31no—
112C22×C3—31no—
113C22×C3—61no—
114C22×C3—811no—
115C22×C3C3×C3⋊D911yescharacteristic
116C2×D3—271no—
117C2×D3—811no—
118C3×C4—811no—
119Dic3—271no—
120Dic3—811no—
121C32—21no—
122C32C3×(C22⋊C9)⋊C211yescharacteristic
123C32C3⋊((C22⋊C9)⋊C2)11yescharacteristic
124C9—22no—
125C9—21no—
126C9C3×(C22⋊C9)⋊C212yes—
127C9C3×C3⋊S411yescharacteristic
128D4—811noSylow
129C2×C3—31no—
130C2×C3—91no—
131C2×C3—91no—
132C2×C3—181no—
133C2×C3—1621no—
134D3—541no—
135D3—1621no—
136C22—811no—
137C22#9231811yescharacteristic, complemented
138C4—811no—
139C3—31no—
140C3—31no—
141C3—61no—
142C3C3×C3⋊((C22⋊C9)⋊C2)11yescharacteristic
143C2—31no—
144C2—1621no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×C22⋊C27C2×C3
FrattiniC9C3×C3⋊S4
FittingC22×#737D3
socleC22×C3C3×C3⋊D9
LCSG ▷ C3×C22⋊C27
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757860C2semidirect
3. C3⋊((C22⋊C27)⋊C2)C3semidirect
12. #66353D3semidirect
14. C3×C22⋊C27D3semidirect
15. C3×C22⋊C27C2×C3semidirect
137. C22#92318semidirect

Maximal subgroups

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

subgroupindex
#117578602
#106199833
C3⋊((C22⋊C27)⋊C2)3
C3×(C22⋊C27)⋊C23
((C22⋊C27)⋊C2)⋊C33
#923184