Finite Group Databasebeta

← #14517652

Subgroups — #14517652

Order 1944.

1072 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 93 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×#92301C211yesmaximal, characteristic, complemented
3#11757605C211yesmaximal, characteristic, complemented
4#10620179C311yesmaximal, characteristic, complemented
5#10619977—34nomaximal
6C2×C32⋊H(3,𝔽3)—21no—
7C2×C32⋊H(3,𝔽3)C2211yescharacteristic
8#92301—21no—
9C22×C34C2×C311yescharacteristic, complemented
10C2×C3⋊(C3⋊(C3⋊D3))C2×C311yescharacteristic, complemented
11C3⋊(C3⋊(C3⋊Dic3))C2×C311yescharacteristic, complemented
12C22×C3×H(3,𝔽3)—24no—
13C22×C3×H(3,𝔽3)D314yescomplemented
14C2×C3⋊((C3⋊D3)⋊C3)—34no—
15C3⋊((C3⋊Dic3)⋊C3)—34no—
16C32⋊H(3,𝔽3)D411yescharacteristic, complemented, Sylow
17#6312—34no—
18#6312—912no—
19C3×#638—91no—
20#638⋊C3—912no—
21C2×C34—21no—
22C2×C34C22×C311yescharacteristic
23C3⋊(C3⋊(C3⋊D3))—21no—
24C2×C3×H(3,𝔽3)—28no—
25C2×C3×H(3,𝔽3)—24no—
26C2×C3×H(3,𝔽3)—24no—
27C2×C3×H(3,𝔽3)C2×D314yes—
28C3⋊((C3⋊D3)⋊C3)—64no—
29C22×C33—24no—
30C22×C33—312no—
31C22×C33C3×D314yes—
32C22×C33C3⋊D311yescharacteristic, complemented
33C2×C3⋊(C3⋊D3)—34no—
34C2×C3⋊(C3⋊D3)—912no—
35C2×C3×C3⋊D3—91no—
36C3⋊(C3⋊Dic3)—34no—
37C3⋊(C3⋊Dic3)—912no—
38C3×C3⋊Dic3—91no—
39C22×H(3,𝔽3)—312no—
40C22×H(3,𝔽3)—612no—
41C2×(C3⋊D3)⋊C3—912no—
42(C3⋊Dic3)⋊C3—912no—
43C34C3×D411yescharacteristic, complemented
44C3×H(3,𝔽3)—24no—
45C3×H(3,𝔽3)#6714yescomplemented
46#638—91no—
47#638—912no—
48#638—2712no—
49#638—2727no—
50C3×#67—274no—
51C2×C33—24no—
52C2×C33—28no—
53C2×C33—21no—
54C2×C33—24no—
55C2×C33—312no—
56C2×C33—612no—
57C2×C33C2×C3×D314yes—
58C2×C33C2×C3⋊D311yescharacteristic
59C3⋊(C3⋊D3)—64no—
60C3⋊(C3⋊D3)—1812no—
61C3×C3⋊D3—181no—
62C2×H(3,𝔽3)—312no—
63C2×H(3,𝔽3)—612no—
64C2×H(3,𝔽3)—624no—
65C2×H(3,𝔽3)—612no—
66(C3⋊D3)⋊C3—1812no—
67C22×C32—327no—
68C22×C32—312no—
69C22×C32—34no—
70C22×C32—64no—
71C22×C32—612no—
72C22×C32(C3⋊D3)⋊C3112yescomplemented
73C22×C32C3×C3⋊D311yescharacteristic
74C2×C3⋊D3—91no—
75C2×C3⋊D3—912no—
76C2×C3⋊D3—2712no—
77C2×C3⋊D3—2727no—
78C2×C3×D3—274no—
79C3⋊Dic3—91no—
80C3⋊Dic3—912no—
81C3⋊Dic3—2712no—
82C3⋊Dic3—2727no—
83C3×Dic3—274no—
84C33—24no—
85C33—312no—
86C33C3×#6714yes—
87C33#63811yescharacteristic, complemented
88H(3,𝔽3)—312no—
89H(3,𝔽3)—612no—
90C3×D4—811no—
91#67—274no—
92#67—8112no—
93C2×C32—21no—
94C2×C32—212no—
95C2×C32—327no—
96C2×C32—312no—
97C2×C32—34no—
98C2×C32—612no—
99C2×C32—64no—
100C2×C32—68no—
101C2×C32—624no—
102C2×C32—627no—
103C2×C32—64no—
104C2×C32—612no—
105C2×C32C2×(C3⋊D3)⋊C3112yes—
106C2×C32C2×C3×C3⋊D311yescharacteristic
107C3⋊D3—181no—
108C3⋊D3—1812no—
109C3⋊D3—5412no—
110C3⋊D3—5427no—
111C3×D3—544no—
112C22×C3—312no—
113C22×C3—91no—
114C22×C3—184no—
115C22×C3—811no—
116C22×C3C3⋊((C3⋊D3)⋊C3)14yes—
117C2×D3—274no—
118C2×D3—8112no—
119C3×C4—811no—
120Dic3—274no—
121Dic3—8112no—
122C32—327no—
123C32—312no—
124C32—34no—
125C32—64no—
126C32—612no—
127C32#638⋊C3112yescomplemented
128C32C3×#63811yescharacteristic
129D4—811noSylow
130C2×C3—24no—
131C2×C3—312no—
132C2×C3—612no—
133C2×C3—91no—
134C2×C3—181no—
135C2×C3—188no—
136C2×C3—184no—
137C2×C3—1621no—
138C2×C3C2×C3⋊((C3⋊D3)⋊C3)14yes—
139D3—544no—
140D3—16212no—
141C22—811no—
142C22#9230111yescharacteristic, complemented
143C4—811no—
144C3—312no—
145C3—91no—
146C3—184no—
147C3#1061997714yes—
148C2—21no—
149C2—1621no—
150C2C2×#9230111yescharacteristic
subgroupG/H
centerC2C2×#92301
commutator, cosocleC2×C34C22×C3
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC22×C32⋊H(3,𝔽3)C2
hypercenterC22#92301
hypocenterC34C3×D4
LCSG ▷ C2×C34 ▷ C34
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×#92301C2semidirect
3. #11757605C2semidirect
4. #10620179C3semidirect
9. C22×C34C2×C3semidirect
10. C2×C3⋊(C3⋊(C3⋊D3))C2×C3semidirect
11. C3⋊(C3⋊(C3⋊Dic3))C2×C3semidirect
13. C22×C3×H(3,𝔽3)D3semidirect
16. C32⋊H(3,𝔽3)D4semidirect
32. C22×C33C3⋊D3semidirect
43. C34C3×D4semidirect
45. C3×H(3,𝔽3)#67semidirect
72. C22×C32(C3⋊D3)⋊C3semidirect
87. C33#638semidirect
127. C32#638⋊C3semidirect
142. C22#92301semidirect

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×#923012
#117576052
#106201793
#106199773