Finite Group Databasebeta

← #14519204

Subgroups — #14519204

Order 1944.

427 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 427 conjugacy classes of subgroups — too many to draw. Only its 56 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#11758104C211yesmaximal, characteristic, complemented
2C3×#6258C311yesmaximal, characteristic
3#10620044C313yesmaximal, complemented
4S4×3−1+2—33nomaximal
5#67×3−1+2—31nomaximal
6#92394—41nomaximal
7C22×C3×3−1+2D311yescharacteristic, complemented
8C2×D3×3−1+2—31no—
9C3×C22⋊H(3,𝔽3)C2×C311yescharacteristic
10C3×#1094—21no—
11#66440—29no—
12A4×3−1+2—23no—
13A4×3−1+2D313yescomplemented
14#66436—23no—
15#66436C2×C313yescomplemented
16Dic3×3−1+2—31no—
173−1+4—41noSylow
18C32×S4—33no—
19C32×#67—31no—
20#6258C3211yescharacteristic
21C9×S4—39no—
22D4×3−1+2—91no—
23C9×#67—33no—
24C2×C3×3−1+2—31no—
25#4208—43no—
26C3×#272—41no—
27D3×3−1+2—61no—
28D3×3−1+2—123no—
29C22×C33C3×D311yescharacteristic
30C2×C32×D3—31no—
31C32×A4C3×D313yes—
32C32×Dic3—31no—
33C22×3−1+2—21no—
34C22×3−1+2—23no—
35C22×3−1+2—91no—
36C22×3−1+2C3⋊D311yescharacteristic
37C22×C3×C9C3×D313yescomplemented
38C2×D3×C9—33no—
39C22⋊H(3,𝔽3)—21no—
40C22⋊H(3,𝔽3)—23no—
41C22⋊H(3,𝔽3)C2×C3211yescharacteristic
42#1094—23no—
43#1094—23no—
44#1094—23no—
45C3×C22⋊C9—23no—
46C9⋊A4—29no—
47C9⋊A4—29no—
48C9⋊A4—29no—
49C9×A4—29no—
50C9×A4C3×D319yescomplemented
51C4×3−1+2—91no—
52C9×Dic3—33no—
53#737—43no—
54#737—89no—
55#737—83no—
56C3×3−1+2—43no—
57C3×3−1+2—83no—
58C3×3−1+2—81no—
59C3×3−1+2S411yescharacteristic, complemented
60C3×H(3,𝔽3)—41no—
61C3×S4—33no—
62C3×S4—93no—
63C32×D4—91no—
64C3×#67—31no—
65C3×#67—91no—
66D4×C9—93no—
67C2×C33—31no—
68C32×D3—61no—
69C32×D3—123no—
70C2×3−1+2—31no—
71C2×3−1+2—63no—
72C2×3−1+2—61no—
73C2×3−1+2—181no—
74C2×C3×C9—33no—
75#272—41no—
76D3×C9—63no—
77D3×C9—129no—
78C22×C32—21no—
79C22×C32—91no—
80C22×C32—91no—
81C22×C32C32×D311yescharacteristic
82C22×C32C3×C3⋊D311yescharacteristic
83C2×C3×D3—31no—
84C2×C3×D3—91no—
85C3×A4—23no—
86C3×A4—93no—
87C3×A4C32×D313yes—
88C32×C4—91no—
89C3×Dic3—31no—
90C3×Dic3—91no—
91C22×C9—23no—
92C22×C9—93no—
93C22×C9C3×C3⋊D313yes—
94C22⋊C9—29no—
95C4×C9—93no—
96C33—43no—
97C33C3×S411yescharacteristic
983−1+2—21no—
993−1+2—23no—
1003−1+2—89no—
1013−1+2—89no—
1023−1+2—83no—
1033−1+2—83no—
1043−1+2—83no—
1053−1+2—89no—
1063−1+2C3⋊S411yescharacteristic
107H(3,𝔽3)—41no—
108H(3,𝔽3)—83no—
109H(3,𝔽3)—81no—
110C3×C9—49no—
111C3×C9—89no—
112C3×C9—83no—
113C3×C9C3×S413yescomplemented
114S4—33no—
115C3×D4—91no—
116C3×D4—271no—
117#67—31no—
118C2×C32—31no—
119C2×C32—31no—
120C2×C32—61no—
121C2×C32—91no—
122C2×C32—181no—
123C2×C32—181no—
124C3×D3—61no—
125C3×D3—123no—
126C3×D3—181no—
127C3×D3—363no—
128C2×C9—33no—
129C2×C9—63no—
130C2×C9—183no—
131C22×C3—31no—
132C22×C3—31no—
133C22×C3—61no—
134C22×C3—91no—
135C22×C3—271no—
136C22×C3C32×C3⋊D311yescharacteristic
137C2×D3—31no—
138A4—33no—
139A4—63no—
140C3×C4—91no—
141C3×C4—271no—
142Dic3—31no—
143C32—21no—
144C32—43no—
145C32—83no—
146C32—91no—
147C32—363no—
148C32C32×S411yescharacteristic
149C32C3×C3⋊S411yescharacteristic
150C9—23no—
151C9—89no—
152C9C3×C3⋊S413yes—
153D4—91noSylow
154C2×C3—31no—
155C2×C3—31no—
156C2×C3—61no—
157C2×C3—91no—
158C2×C3—181no—
159C2×C3—181no—
160C2×C3—541no—
161D3—61no—
162D3—123no—
163C22—91no—
164C22#9239411yescharacteristic, complemented
165C4—91no—
166C3—31no—
167C3—31no—
168C3—61no—
169C3—123no—
170C3—243no—
171C3C32×C3⋊S411yescharacteristic
172C2—31no—
173C2—181no—
subgroupG/H
center, FrattiniC3C32×C3⋊S4
commutator, cosocle, hypocenterC22⋊H(3,𝔽3)C2×C32
FittingC22×C3×3−1+2D3
socleC22×C3C32×C3⋊D3
prime radicalC3×#6258C3
hypercenter3−1+2C3⋊S4
LCSG ▷ C22⋊H(3,𝔽3)
UCSC1 ◁ C3 ◁ 3−1+2

Complements

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

NH ≅ G/Ntype
1. #11758104C2semidirect
3. #10620044C3semidirect
7. C22×C3×3−1+2D3semidirect
13. A4×3−1+2D3semidirect
15. #66436C2×C3semidirect
37. C22×C3×C9C3×D3semidirect
50. C9×A4C3×D3semidirect
59. C3×3−1+2S4semidirect
113. C3×C9C3×S4semidirect
164. C22#92394semidirect

Maximal subgroups

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

subgroupindex
#117581042
C3×#62583
#106200443
S4×3−1+23
#67×3−1+23
#923944