Finite Group Databasebeta

← #14517978

Subgroups — #14517978

Order 1944.

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

normal subgroups only

This group has 259 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#11757836C211yesmaximal, characteristic, complemented
2C3×#6258C311yesmaximal, characteristic, complemented
3#67×H(3,𝔽3)—31nomaximal
4#10619747C313yesmaximal, complemented
5#92281—41nomaximal
6C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
7C2×D3×H(3,𝔽3)—31no—
8C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic, complemented
9C3×#1094—21no—
10Dic3×H(3,𝔽3)—31no—
11#66368—23no—
12#66368C2×C313yescomplemented
13#6909—41noSylow
14C32×S4—91no—
15C32×#67—31no—
16C32×#67—33no—
17#6258C3211yescharacteristic
18D4×H(3,𝔽3)—91no—
19C2×C3×H(3,𝔽3)—31no—
20C3×#272—41no—
21D3×H(3,𝔽3)—61no—
22#4174—43no—
23C22×C33C3×D311yescharacteristic
24C22×C33C3×D313yescomplemented
25C2×C32×D3—31no—
26C2×C32×D3—33no—
27C32×A4—31no—
28C32×Dic3—31no—
29C32×Dic3—33no—
30C22×H(3,𝔽3)—31no—
31C22×H(3,𝔽3)—61no—
32C22×H(3,𝔽3)—91no—
33C22⋊H(3,𝔽3)—21no—
34C22⋊H(3,𝔽3)—61no—
35C22⋊H(3,𝔽3)C2×C3211yescharacteristic
36#1094—23no—
37#1094—61no—
38#1094—61no—
39C3×C22⋊C9—61no—
40C4×H(3,𝔽3)—91no—
41C3×3−1+2—81no—
42C3×H(3,𝔽3)—41no—
43C3×H(3,𝔽3)S411yescharacteristic, complemented
44AΣL(1,𝔽27)—43no—
45AΣL(1,𝔽27)—83no—
46C3×S4—91no—
47C3×S4—93no—
48C32×D4—93no—
49C32×D4—91no—
50C3×#67—31no—
51C3×#67—91no—
52C3×#67—93no—
53C2×C33—31no—
54C2×C33—33no—
55C32×D3—61no—
56C32×D3—63no—
57C32×D3—361no—
58C2×H(3,𝔽3)—31no—
59C2×H(3,𝔽3)—61no—
60C2×H(3,𝔽3)—63no—
61C2×H(3,𝔽3)—181no—
62#272—41no—
63C22×C32—21no—
64C22×C32—33no—
65C22×C32—91no—
66C22×C32—93no—
67C22×C32—93no—
68C22×C32—91no—
69C22×C32(C3⋊D3)⋊C311yescharacteristic
70C22×C32C32×D311yescharacteristic
71C2×C3×D3—31no—
72C2×C3×D3—91no—
73C2×C3×D3—93no—
74C3×A4—31no—
75C3×A4—61no—
76C3×A4—93no—
77C32×C4—93no—
78C32×C4—91no—
79C3×Dic3—31no—
80C3×Dic3—91no—
81C3×Dic3—93no—
82C22⋊C9—63no—
83C33—121no—
84C33C3×S411yescharacteristic
85C33C3×S413yescomplemented
863−1+2—83no—
873−1+2—241no—
883−1+2—241no—
89H(3,𝔽3)—31no—
90H(3,𝔽3)—41no—
91H(3,𝔽3)—61no—
92H(3,𝔽3)—81no—
93H(3,𝔽3)—241no—
94C3×C9—241no—
95S4—91no—
96C3×D4—91no—
97C3×D4—271no—
98C3×D4—273no—
99#67—31no—
100C2×C32—31no—
101C2×C32—33no—
102C2×C32—31no—
103C2×C32—61no—
104C2×C32—63no—
105C2×C32—91no—
106C2×C32—93no—
107C2×C32—181no—
108C2×C32—183no—
109C2×C32—183no—
110C2×C32—181no—
111C3×D3—61no—
112C3×D3—181no—
113C3×D3—183no—
114C3×D3—361no—
115C3×D3—363no—
116C22×C3—31no—
117C22×C3—31no—
118C22×C3—61no—
119C22×C3—91no—
120C22×C3—93no—
121C22×C3—271no—
122C22×C3—273no—
123C22×C3C3×(C3⋊D3)⋊C311yescharacteristic
124C2×D3—31no—
125A4—91no—
126A4—181no—
127C3×C4—91no—
128C3×C4—271no—
129C3×C4—273no—
130Dic3—31no—
131C32—21no—
132C32—33no—
133C32—91no—
134C32—93no—
135C32—121no—
136C32—241no—
137C32—363no—
138C32(C3⋊S4)⋊C311yescharacteristic
139C32C32×S411yescharacteristic
140C9—243no—
141D4—91noSylow
142C2×C3—31no—
143C2×C3—31no—
144C2×C3—61no—
145C2×C3—91no—
146C2×C3—93no—
147C2×C3—181no—
148C2×C3—183no—
149C2×C3—181no—
150C2×C3—541no—
151C2×C3—543no—
152D3—61no—
153D3—361no—
154C22—91no—
155C22#9228111yescharacteristic, complemented
156C4—91no—
157C3—31no—
158C3—31no—
159C3—61no—
160C3—93no—
161C3—361no—
162C3—721no—
163C3C3×(C3⋊S4)⋊C311yescharacteristic
164C2—31no—
165C2—181no—
subgroupG/H
centerC3C3×(C3⋊S4)⋊C3
commutator, cosocle, hypocenterC22⋊H(3,𝔽3)C2×C32
FrattiniC32C32×S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C3C3×(C3⋊D3)⋊C3
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. #11757836C2semidirect
2. C3×#6258C3semidirect
4. #10619747C3semidirect
6. C22×C3×H(3,𝔽3)D3semidirect
8. C3×C22⋊H(3,𝔽3)C2×C3semidirect
12. #66368C2×C3semidirect
24. C22×C33C3×D3semidirect
43. C3×H(3,𝔽3)S4semidirect
85. C33C3×S4semidirect
155. C22#92281semidirect

Maximal subgroups

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

subgroupindex
#117578362
C3×#62583
#67×H(3,𝔽3)3
#106197473
#922814