Finite Group Databasebeta

← C2×#6912⋊C4 #14517717

Subgroups — C2×#6912⋊C4 #14517717

Order 1944.

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

normal subgroups only

This group has 364 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×#6912C211yesmaximal, characteristic
2#6912⋊C4C212yesmaximal, direct product factor
3C2×C3×3−1+2⋊C4—33nomaximal
4C2×C3×3−1+2⋊C4—31nomaximal
5C2×#733⋊C4C311yesmaximal, characteristic, complemented
6C2×#6912C412yescomplemented
7C2×#6912C2211yescharacteristic
8C22×C3×3−1+2D311yescharacteristic
9C22×C3×3−1+2D313yes—
10C3×3−1+2⋊C4—36no—
11C3×3−1+2⋊C4—32no—
12C22×#733—23no—
13C22×#733—21no—
14C22×#733C2×C311yescharacteristic
15#733⋊C4C2×C312yescomplemented
16#6912C2×C411yescharacteristic, complemented, Sylow
17C2×C32×Dic3—91no—
18C2×3−1+2⋊C4—36no—
19C2×3−1+2⋊C4—33no—
20C2×3−1+2⋊C4—33no—
21C2×C3×Dic9—33no—
22C2×C3×Dic9—31no—
23C2×C3×3−1+2Dic312yes—
24C2×C3×3−1+2Dic316yes—
25C2×C3×3−1+2C2×D311yescharacteristic
26C2×C3×3−1+2C2×D313yes—
27C2×#733—26no—
28C2×#733—23no—
29C2×#733—22no—
30C2×#733—21no—
31C2×#733C3×C412yescomplemented
32C2×#733C22×C311yescharacteristic
33C22×C33C3⋊D311yescharacteristic
34C32×Dic3—92no—
35C22×3−1+2—23no—
36C22×3−1+2—36no—
37C22×3−1+2—33no—
38C22×3−1+2C3×D313yes—
39C22×C3×C9—21no—
40C22×C3×C9—33no—
41C22×C3×C9C3×D311yescharacteristic
423−1+2⋊C4—312no—
433−1+2⋊C4—36no—
443−1+2⋊C4—36no—
45C3×Dic9—36no—
46C3×Dic9—32no—
47C3×3−1+2C2×Dic311yescharacteristic
48C3×3−1+2C2×Dic313yes—
49#733—23no—
50#733—21no—
51#733C2×C3×C411yescharacteristic, complemented
52C2×C32×C4—271no—
53C2×C3×Dic3—93no—
54C2×C3×Dic3—91no—
55C2×Dic9—33no—
56C2×Dic9—31no—
57C2×C33C3⋊Dic312yes—
58C2×C33C2×C3⋊D311yescharacteristic
59C2×3−1+2—26no—
60C2×3−1+2—23no—
61C2×3−1+2—312no—
62C2×3−1+2—36no—
63C2×3−1+2—36no—
64C2×3−1+2—33no—
65C2×3−1+2C3×Dic316yes—
66C2×3−1+2C2×C3×D313yes—
67C2×C3×C9—22no—
68C2×C3×C9—21no—
69C2×C3×C9—36no—
70C2×C3×C9—33no—
71C2×C3×C9C3×Dic312yes—
72C2×C3×C9C2×C3×D311yescharacteristic
73C22×C32—91no—
74C22×C32#27213yes—
75C22×C32C3×C3⋊D311yescharacteristic
76C32×C4—272no—
77C3×Dic3—96no—
78C3×Dic3—92no—
79C22×C9—33no—
80C22×C9—31no—
81C22×C9—61no—
82C22×C9—63no—
83Dic9—36no—
84Dic9—32no—
85C33C2×C3⋊Dic311yescharacteristic
863−1+2—23no—
873−1+2—36no—
883−1+2—33no—
893−1+2C2×C3×Dic313yes—
90C3×C9—21no—
91C3×C9—33no—
92C3×C9C2×C3×Dic311yescharacteristic
93C2×C3×C4—273no—
94C2×C3×C4—271no—
95C2×Dic3—91no—
96C2×C32—92no—
97C2×C32—91no—
98C2×C32#108416yes—
99C2×C32C2×#27213yes—
100C2×C32C3×C3⋊Dic312yes—
101C2×C32C2×C3×C3⋊D311yescharacteristic
102C2×C9—36no—
103C2×C9—32no—
104C2×C9—33no—
105C2×C9—31no—
106C2×C9—62no—
107C2×C9—66no—
108C2×C9—61no—
109C2×C9—63no—
110C22×C3—33no—
111C22×C3—31no—
112C22×C3C3×#27211yescharacteristic
113C3×C4—276no—
114C3×C4—272no—
115Dic3—92no—
116C32—91no—
117C32C2×#108413yes—
118C32C2×C3×C3⋊Dic311yescharacteristic
119C9—33no—
120C9—31no—
121C9—61no—
122C9—63no—
123C2×C4—271noSylow
124C2×C3—36no—
125C2×C3—32no—
126C2×C3—33no—
127C2×C3—31no—
128C2×C3C3×#108412yes—
129C2×C3C2×C3×#27211yescharacteristic
130C22#6912⋊C211yescharacteristic
131C4—272no—
132C3—33no—
133C3—31no—
134C3C2×C3×#108411yescharacteristic
135C2#6912⋊C412yesdirect product factor
136C2C2×#6912⋊C211yescharacteristic
subgroupG/H
center, hypercenterC22#6912⋊C2
commutator, hypocenter#733C2×C3×C4
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×#6912C2
socleC22×C3C3×#272
prime radicalC22×C33C3⋊D3
cosocleC2×#733C22×C3
LCSG ▷ #733
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #6912⋊C4C2direct (N × H)
5. C2×#733⋊C4C3semidirect
6. C2×#6912C4semidirect
15. #733⋊C4C2×C3semidirect
16. #6912C2×C4semidirect
31. C2×#733C3×C4semidirect
51. #733C2×C3×C4semidirect
135. C2#6912⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#69122
#6912⋊C42
C2×C3×3−1+2⋊C43
C2×#733⋊C43