Finite Group Databasebeta

← #14517425

Subgroups — #14517425

Order 1944.

753 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 753 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×C32⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×#92258C211yesmaximal, characteristic, complemented
3#11757562C211yesmaximal, characteristic, complemented
4C32×#638—31nomaximal
5#10619977C314yesmaximal, complemented
6C2×C32⋊H(3,𝔽3)—21no—
7C2×C32⋊H(3,𝔽3)C2211yescharacteristic
8#92258—21no—
9C22×C34D311yescharacteristic, complemented
10C2×C32×C3⋊D3—31no—
11C32×C3⋊Dic3—31no—
12C22×C3×H(3,𝔽3)—24no—
13C22×C3×H(3,𝔽3)C2×C314yescomplemented
14C2×C3⋊((C3⋊D3)⋊C3)C2×C314yescomplemented
15C3⋊((C3⋊Dic3)⋊C3)C2×C314yescomplemented
16C32⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
17#6312C3211yescharacteristic, complemented
18C3×#638—34no—
19C32×#67—94no—
20#638⋊C3—94no—
21C2×C34—21no—
22C2×C34C2×D311yescharacteristic
23C32×C3⋊D3—61no—
24C2×C3×H(3,𝔽3)—28no—
25C2×C3×H(3,𝔽3)—24no—
26C2×C3×H(3,𝔽3)—24no—
27C2×C3×H(3,𝔽3)C22×C314yes—
28C3⋊((C3⋊D3)⋊C3)—24no—
29C22×C33—24no—
30C22×C33—34no—
31C22×C33—64no—
32C22×C33C3×D314yes—
33C22×C33C2×C3211yescharacteristic, complemented
34C2×C3⋊(C3⋊D3)C2×C3211yescharacteristic, complemented
35C2×C3×C3⋊D3—34no—
36C2×C32×D3—94no—
37C3⋊(C3⋊Dic3)C2×C3211yescharacteristic, complemented
38C3×C3⋊Dic3—34no—
39C32×Dic3—94no—
40C22×H(3,𝔽3)—34no—
41C22×H(3,𝔽3)—64no—
42C22×H(3,𝔽3)—68no—
43C22×H(3,𝔽3)—64no—
44C2×(C3⋊D3)⋊C3—94no—
45(C3⋊Dic3)⋊C3—94no—
46C34#6711yescharacteristic, complemented
47C3×H(3,𝔽3)—24no—
48C3×H(3,𝔽3)C3×D414yescomplemented
49C32×D4—271no—
50#638—31no—
51#638—94no—
52C3×#67—912no—
53C3×#67—94no—
54C2×C33—24no—
55C2×C33—28no—
56C2×C33—21no—
57C2×C33—24no—
58C2×C33—34no—
59C2×C33—64no—
60C2×C33—64no—
61C2×C33—68no—
62C2×C33C2×C3×D314yes—
63C2×C33C22×C3211yescharacteristic
64C3⋊(C3⋊D3)—21no—
65C3×C3⋊D3—64no—
66C32×D3—184no—
67C2×H(3,𝔽3)—34no—
68C2×H(3,𝔽3)—64no—
69C2×H(3,𝔽3)—64no—
70C2×H(3,𝔽3)—68no—
71C2×H(3,𝔽3)—616no—
72C2×H(3,𝔽3)—68no—
73C2×H(3,𝔽3)—68no—
74C2×H(3,𝔽3)—64no—
75(C3⋊D3)⋊C3—184no—
76C22×C32—24no—
77C22×C32—31no—
78C22×C32—312no—
79C22×C32—34no—
80C22×C32—66no—
81C22×C32—64no—
82C22×C32—63no—
83C22×C32—64no—
84C22×C32—612no—
85C22×C32—271no—
86C22×C32(C3⋊D3)⋊C314yescomplemented
87C22×C32C32×D311yescharacteristic
88C2×C3⋊D3—31no—
89C2×C3⋊D3—94no—
90C2×C3×D3—912no—
91C2×C3×D3—94no—
92C32×C4—271no—
93C3⋊Dic3—31no—
94C3⋊Dic3—94no—
95C3×Dic3—912no—
96C3×Dic3—94no—
97C33—24no—
98C33—34no—
99C33—64no—
100C33C3×#6714yes—
101C33C32×D411yescharacteristic, complemented
102H(3,𝔽3)—34no—
103H(3,𝔽3)—64no—
104H(3,𝔽3)—68no—
105H(3,𝔽3)—64no—
106C3×D4—274no—
107#67—94no—
108#67—811no—
109C2×C32—21no—
110C2×C32—28no—
111C2×C32—24no—
112C2×C32—24no—
113C2×C32—31no—
114C2×C32—312no—
115C2×C32—34no—
116C2×C32—612no—
117C2×C32—64no—
118C2×C32—68no—
119C2×C32—624no—
120C2×C32—66no—
121C2×C32—64no—
122C2×C32—61no—
123C2×C32—612no—
124C2×C32—68no—
125C2×C32—66no—
126C2×C32—63no—
127C2×C32—64no—
128C2×C32—612no—
129C2×C32—541no—
130C2×C32C2×(C3⋊D3)⋊C314yes—
131C2×C32C2×C32×D311yescharacteristic
132C3⋊D3—61no—
133C3⋊D3—184no—
134C3×D3—1812no—
135C3×D3—184no—
136C22×C3—34no—
137C22×C3—64no—
138C22×C3—91no—
139C22×C3—184no—
140C22×C3—274no—
141C22×C3C3×(C3⋊D3)⋊C314yes—
142C2×D3—94no—
143C2×D3—811no—
144C3×C4—274no—
145Dic3—94no—
146Dic3—811no—
147C32—24no—
148C32—31no—
149C32—312no—
150C32—34no—
151C32—66no—
152C32—64no—
153C32—63no—
154C32—64no—
155C32—612no—
156C32#638⋊C314yescomplemented
157C32C32×#6711yescharacteristic
158D4—271noSylow
159C2×C3—24no—
160C2×C3—34no—
161C2×C3—64no—
162C2×C3—68no—
163C2×C3—64no—
164C2×C3—91no—
165C2×C3—181no—
166C2×C3—188no—
167C2×C3—184no—
168C2×C3—544no—
169C2×C3C2×C3×(C3⋊D3)⋊C314yes—
170D3—184no—
171D3—1621no—
172C22—271no—
173C22#9225811yescharacteristic, complemented
174C4—271no—
175C3—34no—
176C3—64no—
177C3—91no—
178C3—184no—
179C3C3×#638⋊C314yes—
180C2—21no—
181C2—541no—
182C2C2×#9225811yescharacteristic
subgroupG/H
centerC2C2×#92258
commutator, cosocleC2×C33C22×C32
Frattini, socleC2×C32C2×C32×D3
FittingC22×C32⋊H(3,𝔽3)C2
hypercenterC22#92258
hypocenterC33C32×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C32⋊H(3,𝔽3)C2semidirect
2. C2×#92258C2semidirect
3. #11757562C2semidirect
5. #10619977C3semidirect
9. C22×C34D3semidirect
13. C22×C3×H(3,𝔽3)C2×C3semidirect
14. C2×C3⋊((C3⋊D3)⋊C3)C2×C3semidirect
15. C3⋊((C3⋊Dic3)⋊C3)C2×C3semidirect
16. C32⋊H(3,𝔽3)D4semidirect
17. #6312C32semidirect
33. C22×C33C2×C32semidirect
34. C2×C3⋊(C3⋊D3)C2×C32semidirect
37. C3⋊(C3⋊Dic3)C2×C32semidirect
46. C34#67semidirect
48. C3×H(3,𝔽3)C3×D4semidirect
86. C22×C32(C3⋊D3)⋊C3semidirect
101. C33C32×D4semidirect
156. C32#638⋊C3semidirect
173. C22#92258semidirect

Maximal subgroups

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

subgroupindex
C22×C32⋊H(3,𝔽3)2
C2×#922582
#117575622
C32×#6383
#106199773