Finite Group Databasebeta

← #14517987

Subgroups — #14517987

Order 1944.

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

normal subgroups only

This group has 211 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
1#11757849C211yesmaximal, characteristic, complemented
2C3×#6258C311yesmaximal, characteristic
3#67×3−1+2—31nomaximal
4#10619741C313yesmaximal, complemented
5#92283—41nomaximal
6C22×C3×3−1+2D311yescharacteristic, complemented
7C2×D3×3−1+2—31no—
8C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic
9C3×#1094—21no—
10Dic3×3−1+2—31no—
11#66357—23no—
12#66357C2×C313yescomplemented
13#6910—41noSylow
14C32×S4—91no—
15C32×#67—31no—
16#6258C3211yescharacteristic
17D4×3−1+2—91no—
18C9×#67—33no—
19C2×C3×3−1+2—31no—
20C3×#272—41no—
21D3×3−1+2—61no—
22#4176—43no—
23C22×C33C3×D311yescharacteristic
24C2×C32×D3—31no—
25C32×A4—31no—
26C32×Dic3—31no—
27C22×3−1+2—31no—
28C22×3−1+2—61no—
29C22×3−1+2—91no—
30C22×C3×C9C3×D313yescomplemented
31C2×D3×C9—33no—
32C22⋊H(3,𝔽3)—21no—
33C22⋊H(3,𝔽3)—61no—
34C22⋊H(3,𝔽3)C2×C3211yescharacteristic
35#1094—23no—
36#1094—61no—
37#1094—61no—
38C3×C22⋊C9—61no—
39C4×3−1+2—91no—
40C9×Dic3—33no—
41C3×3−1+2—81no—
42C3×3−1+2S411yescharacteristic, complemented
43C3×H(3,𝔽3)—41no—
44#731—43no—
45#731—83no—
46C3×S4—91no—
47C3×S4—93no—
48C32×D4—91no—
49C3×#67—31no—
50C3×#67—91no—
51D4×C9—93no—
52C2×C33—31no—
53C32×D3—61no—
54C32×D3—361no—
55C2×3−1+2—31no—
56C2×3−1+2—63no—
57C2×3−1+2—61no—
58C2×3−1+2—181no—
59C2×C3×C9—33no—
60#272—41no—
61D3×C9—63no—
62C22×C32—21no—
63C22×C32—91no—
64C22×C32—91no—
65C22×C32(C3⋊D3)⋊C311yescharacteristic
66C22×C32C32×D311yescharacteristic
67C2×C3×D3—31no—
68C2×C3×D3—91no—
69C3×A4—31no—
70C3×A4—61no—
71C3×A4—93no—
72C32×C4—91no—
73C3×Dic3—31no—
74C3×Dic3—91no—
75C22×C9—33no—
76C22×C9—93no—
77C22⋊C9—63no—
78C4×C9—93no—
79C33—121no—
80C33C3×S411yescharacteristic
813−1+2—31no—
823−1+2—61no—
833−1+2—83no—
843−1+2—241no—
853−1+2—241no—
86H(3,𝔽3)—41no—
87H(3,𝔽3)—81no—
88H(3,𝔽3)—241no—
89C3×C9—241no—
90C3×C9C3×S413yescomplemented
91S4—91no—
92C3×D4—91no—
93C3×D4—271no—
94#67—31no—
95C2×C32—31no—
96C2×C32—31no—
97C2×C32—61no—
98C2×C32—91no—
99C2×C32—181no—
100C2×C32—181no—
101C3×D3—61no—
102C3×D3—181no—
103C3×D3—361no—
104C3×D3—363no—
105C2×C9—33no—
106C2×C9—63no—
107C2×C9—183no—
108C22×C3—31no—
109C22×C3—31no—
110C22×C3—61no—
111C22×C3—91no—
112C22×C3—271no—
113C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
114C2×D3—31no—
115A4—91no—
116A4—181no—
117C3×C4—91no—
118C3×C4—271no—
119Dic3—31no—
120C32—21no—
121C32—91no—
122C32—121no—
123C32—241no—
124C32—363no—
125C32(C3⋊S4)⋊C311yescharacteristic
126C32C32×S411yescharacteristic
127C9—33no—
128C9—243no—
129D4—91noSylow
130C2×C3—31no—
131C2×C3—31no—
132C2×C3—61no—
133C2×C3—91no—
134C2×C3—181no—
135C2×C3—181no—
136C2×C3—541no—
137D3—61no—
138D3—361no—
139C22—91no—
140C22#9228311yescharacteristic, complemented
141C4—91no—
142C3—31no—
143C3—31no—
144C3—61no—
145C3—361no—
146C3—721no—
147C3C3×(C3⋊S4)⋊C311yescharacteristic
148C2—31no—
149C2—181no—
subgroupG/H
centerC3C3×(C3⋊S4)⋊C3
commutator, cosocle, hypocenterC22⋊H(3,𝔽3)C2×C32
FrattiniC32C32×S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×(C3⋊D3)⋊C3
prime radicalC3×#6258C3
hypercenterC32(C3⋊S4)⋊C3
LCSG ▷ C22⋊H(3,𝔽3)
UCSC1 ◁ C3 ◁ C32

Complements

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

NH ≅ G/Ntype
1. #11757849C2semidirect
4. #10619741C3semidirect
6. C22×C3×3−1+2D3semidirect
12. #66357C2×C3semidirect
30. C22×C3×C9C3×D3semidirect
42. C3×3−1+2S4semidirect
90. C3×C9C3×S4semidirect
140. C22#92283semidirect

Maximal subgroups

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

subgroupindex
#117578492
C3×#62583
#67×3−1+23
#106197413
#922834