Finite Group Databasebeta

← #14516155

Subgroups — #14516155

Order 1944.

376 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 39 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×#6856C211yesmaximal, characteristic, complemented
2C2×#92198C211yesmaximal, characteristic, complemented
3#11757321C211yesmaximal, characteristic, complemented
4#10619977—32nomaximal
5#10619630—32nomaximal
6C2×#6856—21no—
7C2×#6856C2211yescharacteristic
8#92198—21no—
9C22×C3×H(3,𝔽3)D312yescomplemented
10C2×C3⋊((C3⋊D3)⋊C3)—32no—
11C3⋊((C3⋊Dic3)⋊C3)—32no—
12C22×C32⋊C9D312yescomplemented
13C2×#4169—32no—
14#66316—32no—
15#6856D411yescharacteristic, complemented, Sylow
16#6312—32no—
17C3×#638—91no—
18#6233—32no—
19#638⋊C3—96no—
20C2×C3×H(3,𝔽3)—22no—
21C2×C3×H(3,𝔽3)C2×D312yes—
22C3⋊((C3⋊D3)⋊C3)—62no—
23C2×C32⋊C9—22no—
24C2×C32⋊C9C2×D312yes—
25#4169—62no—
26C22×C33—32no—
27C22×C33C3⋊D311yescharacteristic
28C2×C3⋊(C3⋊D3)—32no—
29C2×C3×C3⋊D3—91no—
30C3⋊(C3⋊Dic3)—32no—
31C3×C3⋊Dic3—91no—
32C22×H(3,𝔽3)—36no—
33C22×C3×C9—32no—
34C2×C3⋊D9—32no—
35C2×(C3⋊D3)⋊C3—96no—
36C3⋊Dic9—32no—
37(C3⋊Dic3)⋊C3—96no—
38C3×H(3,𝔽3)#6712yescomplemented
39C32⋊C9#6712yescomplemented
40#638—91no—
41#638—96no—
42#638—272no—
43#638—274no—
44C3×#67—272no—
45C3×#67—272no—
46#611—272no—
47C2×C33—21no—
48C2×C33—32no—
49C2×C33—62no—
50C2×C33C2×C3⋊D311yescharacteristic
51C3⋊(C3⋊D3)—62no—
52C3×C3⋊D3—181no—
53C2×H(3,𝔽3)—36no—
54C2×H(3,𝔽3)—66no—
55C2×C3×C9—32no—
56C2×C3×C9—62no—
57C3⋊D9—62no—
58(C3⋊D3)⋊C3—186no—
59C22×C32—32no—
60C22×C32—36no—
61C22×C32—32no—
62C22×C32—92no—
63C22×C32—94no—
64C22×C32#27211yescharacteristic
65C2×C3⋊D3—91no—
66C2×C3⋊D3—96no—
67C2×C3⋊D3—272no—
68C2×C3⋊D3—274no—
69C2×C3×D3—272no—
70C2×C3×D3—272no—
71C3⋊Dic3—91no—
72C3⋊Dic3—96no—
73C3⋊Dic3—272no—
74C3⋊Dic3—274no—
75C3×Dic3—272no—
76C3×Dic3—272no—
77C22×C9—92no—
78C2×D9—272no—
79Dic9—272no—
80C33—32no—
81C33#63811yescharacteristic
82H(3,𝔽3)—36no—
83C3×C9—32no—
84C3×D4—811no—
85#67—272no—
86#67—272no—
87#67—816no—
88C2×C32—21no—
89C2×C32—32no—
90C2×C32—36no—
91C2×C32—32no—
92C2×C32—62no—
93C2×C32—66no—
94C2×C32—62no—
95C2×C32—92no—
96C2×C32—94no—
97C2×C32—182no—
98C2×C32—184no—
99C2×C32C2×#27211yescharacteristic
100C3⋊D3—181no—
101C3⋊D3—186no—
102C3⋊D3—542no—
103C3⋊D3—544no—
104C3×D3—542no—
105C3×D3—542no—
106C2×C9—92no—
107C2×C9—182no—
108D9—542no—
109C22×C3—96no—
110C22×C3—91no—
111C22×C3—811no—
112C22×C3#418312yes—
113C22×C3#418512yes—
114C2×D3—272no—
115C2×D3—272no—
116C2×D3—816no—
117C3×C4—811no—
118Dic3—272no—
119Dic3—272no—
120Dic3—816no—
121C32—32no—
122C32—36no—
123C32—32no—
124C32—92no—
125C32—94no—
126C32#623511yescharacteristic
127C9—92no—
128D4—811noSylow
129C2×C3—22no—
130C2×C3—22no—
131C2×C3—96no—
132C2×C3—91no—
133C2×C3—181no—
134C2×C3—186no—
135C2×C3—1621no—
136C2×C3C2×#418312yes—
137C2×C3C2×#418512yes—
138D3—542no—
139D3—542no—
140D3—1626no—
141C22—811no—
142C22#9219811yescharacteristic, complemented
143C4—811no—
144C3—96no—
145C3—91no—
146C3#1061967912yes—
147C3#1061968312yes—
148C2—21no—
149C2—1621no—
150C2C2×#9219811yescharacteristic
subgroupG/H
centerC2C2×#92198
commutator, cosocleC2×#6856C22
FrattiniC2×C33C2×C3⋊D3
FittingC22×#6856C2
socleC2×C32C2×#272
hypercenterC22#92198
hypocenter#6856D4
LCSG ▷ C2×#6856 ▷ #6856
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×#6856C2semidirect
2. C2×#92198C2semidirect
3. #11757321C2semidirect
9. C22×C3×H(3,𝔽3)D3semidirect
12. C22×C32⋊C9D3semidirect
15. #6856D4semidirect
38. C3×H(3,𝔽3)#67semidirect
39. C32⋊C9#67semidirect
142. C22#92198semidirect

Maximal subgroups

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

subgroupindex
C22×#68562
C2×#921982
#117573212
#106199773
#106196303