Finite Group Databasebeta

← C2×#11757637 #14517715

Subgroups — C2×#11757637 #14517715

Order 1944.

442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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×#6911C211yesmaximal, characteristic
2#11757637C212yesmaximal, direct product factor
3C2×C3×3−1+2⋊C4—31nomaximal
4C2×C3×(C3⋊Dic3)⋊C3—33nomaximal
5C2×#66332C311yesmaximal, characteristic, complemented
6C2×#6911C412yescomplemented
7C2×#6911C2211yescharacteristic
8C22×C3×3−1+2D311yescharacteristic
9C22×C3×H(3,𝔽3)D313yes—
10C3×3−1+2⋊C4—32no—
11C3×(C3⋊Dic3)⋊C3—36no—
12C22×#732—23no—
13C22×#732—21no—
14C22×#732C2×C311yescharacteristic
15#66332C2×C312yescomplemented
16#6911C2×C411yescharacteristic, complemented, Sylow
17C2×C3×C3⋊Dic3—33no—
18C2×C32×Dic3—91no—
19C2×3−1+2⋊C4—33no—
20C2×(C3⋊Dic3)⋊C3—36no—
21C2×(C3⋊Dic3)⋊C3—33no—
22C2×C3×Dic9—31no—
23C2×C3×3−1+2Dic312yescomplemented
24C2×C3×3−1+2C2×D311yescharacteristic
25C2×C3×H(3,𝔽3)Dic316yescomplemented
26C2×C3×H(3,𝔽3)C2×D313yes—
27C2×#732—26no—
28C2×#732—23no—
29C2×#732—22no—
30C2×#732—21no—
31C2×#732C3×C412yescomplemented
32C2×#732C22×C311yescharacteristic
33C22×C33—33no—
34C22×C33C3⋊D311yescharacteristic
35C3×C3⋊Dic3—36no—
36C32×Dic3—92no—
37C22×3−1+2—33no—
38C22×H(3,𝔽3)—23no—
39C22×H(3,𝔽3)—36no—
40C22×H(3,𝔽3)C3×D313yes—
41C22×C3×C9—21no—
42C22×C3×C9C3×D311yescharacteristic
433−1+2⋊C4—36no—
44(C3⋊Dic3)⋊C3—312no—
45(C3⋊Dic3)⋊C3—36no—
46C3×Dic9—32no—
47C3×3−1+2C2×Dic311yescharacteristic, complemented
48C3×H(3,𝔽3)C2×Dic313yescomplemented
49#732—23no—
50#732—21no—
51#732C2×C3×C411yescharacteristic, complemented
52C2×C32×C4—271no—
53C2×C3⋊Dic3—33no—
54C2×C3×Dic3—93no—
55C2×C3×Dic3—91no—
56C2×C3×Dic3—273no—
57C2×Dic9—31no—
58C2×C33—36no—
59C2×C33—33no—
60C2×C33C3⋊Dic312yes—
61C2×C33C2×C3⋊D311yescharacteristic
62C2×3−1+2—36no—
63C2×3−1+2—33no—
64C2×H(3,𝔽3)—26no—
65C2×H(3,𝔽3)—23no—
66C2×H(3,𝔽3)—312no—
67C2×H(3,𝔽3)—36no—
68C2×H(3,𝔽3)C3×Dic316yescomplemented
69C2×H(3,𝔽3)C2×C3×D313yes—
70C2×C3×C9—22no—
71C2×C3×C9—21no—
72C2×C3×C9C3×Dic312yescomplemented
73C2×C3×C9C2×C3×D311yescharacteristic
74C22×C32—33no—
75C22×C32—63no—
76C22×C32—91no—
77C22×C32—93no—
78C22×C32—183no—
79C22×C32#27213yes—
80C22×C32C3×C3⋊D311yescharacteristic
81C32×C4—272no—
82C3⋊Dic3—36no—
83C3×Dic3—96no—
84C3×Dic3—92no—
85C3×Dic3—276no—
86C22×C9—31no—
87C22×C9—61no—
88Dic9—32no—
89C33—33no—
90C33C2×C3⋊Dic311yescharacteristic
913−1+2—33no—
92H(3,𝔽3)—23no—
93H(3,𝔽3)—36no—
94H(3,𝔽3)C2×C3×Dic313yescomplemented
95C3×C9—21no—
96C3×C9C2×C3×Dic311yescharacteristic, complemented
97C2×C3×C4—273no—
98C2×C3×C4—271no—
99C2×Dic3—91no—
100C2×Dic3—273no—
101C2×C32—36no—
102C2×C32—33no—
103C2×C32—66no—
104C2×C32—63no—
105C2×C32—92no—
106C2×C32—91no—
107C2×C32—93no—
108C2×C32—96no—
109C2×C32—186no—
110C2×C32—183no—
111C2×C32#108416yes—
112C2×C32C2×#27213yes—
113C2×C32C3×C3⋊Dic312yes—
114C2×C32C2×C3×C3⋊D311yescharacteristic
115C2×C9—32no—
116C2×C9—31no—
117C2×C9—62no—
118C2×C9—61no—
119C22×C3—33no—
120C22×C3—31no—
121C22×C3—93no—
122C22×C3—183no—
123C22×C3C3×#27211yescharacteristic
124C3×C4—276no—
125C3×C4—272no—
126Dic3—92no—
127Dic3—276no—
128C32—33no—
129C32—63no—
130C32—91no—
131C32—93no—
132C32—183no—
133C32C2×#108413yes—
134C32C2×C3×C3⋊Dic311yescharacteristic
135C9—31no—
136C9—61no—
137C2×C4—271noSylow
138C2×C3—36no—
139C2×C3—32no—
140C2×C3—33no—
141C2×C3—31no—
142C2×C3—96no—
143C2×C3—93no—
144C2×C3—186no—
145C2×C3—183no—
146C2×C3C3×#108412yes—
147C2×C3C2×C3×#27211yescharacteristic
148C22#9233311yescharacteristic
149C4—272no—
150C3—33no—
151C3—31no—
152C3—93no—
153C3—183no—
154C3C2×C3×#108411yescharacteristic
155C2#1175763712yesdirect product factor
156C2C2×#9233311yescharacteristic
subgroupG/H
center, hypercenterC22#92333
commutator, hypocenter#732C2×C3×C4
FrattiniC2×C32C2×C3×C3⋊D3
Fitting, prime radicalC22×#6911C2
socleC22×C3C3×#272
cosocleC2×#732C22×C3
LCSG ▷ #732
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #11757637C2direct (N × H)
5. C2×#66332C3semidirect
6. C2×#6911C4semidirect
15. #66332C2×C3semidirect
16. #6911C2×C4semidirect
23. C2×C3×3−1+2Dic3semidirect
25. C2×C3×H(3,𝔽3)Dic3semidirect
31. C2×#732C3×C4semidirect
47. C3×3−1+2C2×Dic3semidirect
48. C3×H(3,𝔽3)C2×Dic3semidirect
51. #732C2×C3×C4semidirect
68. C2×H(3,𝔽3)C3×Dic3semidirect
72. C2×C3×C9C3×Dic3semidirect
94. H(3,𝔽3)C2×C3×Dic3semidirect
96. C3×C9C2×C3×Dic3semidirect
155. C2#11757637direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69112
#117576372
C2×C3×3−1+2⋊C43
C2×C3×(C3⋊Dic3)⋊C33
C2×#663323