Finite Group Databasebeta

← #92164⋊C4 #14515739

Subgroups — #92164⋊C4 #14515739

Order 1944.

210 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 26 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
1C2×#92164C211yesmaximal, characteristic
2#11757324C211yesmaximal, characteristic, complemented
3#11757286C211yesmaximal, characteristic, complemented
4#10619885—31nomaximal
5((C3⋊D3)⋊C9)⋊C4—31nomaximal
6C2×#6859C2211yescharacteristic
7#92164C412yescomplemented
8C2×C3⋊#272D311yescharacteristic
9C3⋊((C3⋊Dic3)⋊C3)—31no—
10C3×(C3⋊Dic3)⋊C3—31no—
11C2×(C3⋊D3)⋊C9—31no—
12#66328D311yescharacteristic, complemented
13#66316—31no—
14#66316—61no—
15#6859C2×C411yescharacteristic, complemented, Sylow
16#6294—91no—
17Dic3×C3⋊D3—91no—
18#6199—93no—
19D3×Dic9—91no—
20C2×C3×H(3,𝔽3)C2×D311yescharacteristic
21C3⋊#272Dic312yes—
22C2×C32⋊C9—21no—
23C2×C32⋊C9C2×D311yescharacteristic
24(C3⋊D3)⋊C9—32no—
25C2×C3×C3⋊D3—31no—
26C2×C3×C3⋊D3—91no—
27C3⋊(C3⋊Dic3)—31no—
28C3×C3⋊Dic3—31no—
29C3×C3⋊Dic3—91no—
30C32×Dic3—91no—
31C2×#272—93no—
32C2×D3×C9—91no—
33C3⋊Dic9—31no—
34C3⋊Dic9—61no—
35(C3⋊Dic3)⋊C3—33no—
36(C3⋊Dic3)⋊C3—93no—
37C3×Dic9—91no—
38C3×H(3,𝔽3)C2×Dic311yescharacteristic
39C32⋊C9—21no—
40C32⋊C9C4×D311yescharacteristic, complemented
41C4×C3⋊D3—271no—
42#624—271no—
43D3×Dic3—271no—
44D3×Dic3—273no—
45D3×Dic3—271no—
46C2×Dic9—271no—
47C2×C33—31no—
48C2×C33D3211yescharacteristic
49C3×C3⋊D3—32no—
50C3×C3⋊D3—92no—
51C2×H(3,𝔽3)—33no—
52C2×C3×C9—31no—
53C2×C3×C9—61no—
54#272—96no—
55D3×C9—92no—
56C2×C3⋊D3—31no—
57C2×C3⋊D3—91no—
58C2×C3×D3—91no—
59C2×C3×D3—271no—
60C2×C3×D3—273no—
61C32×C4—271no—
62C3⋊Dic3—31no—
63C3⋊Dic3—91no—
64C3⋊Dic3—93no—
65C3⋊Dic3—271no—
66C3⋊Dic3—541no—
67C3×Dic3—93no—
68C3×Dic3—91no—
69C3×Dic3—271no—
70C3×Dic3—271no—
71C3×Dic3—271no—
72C3×Dic3—541no—
73C22×C9—271no—
74Dic9—91no—
75Dic9—271no—
76Dic9—541no—
77C33—31no—
78C33D3×Dic311yescharacteristic
79H(3,𝔽3)—33no—
80C3×C9—31no—
81C3×C9—61no—
82C2×Dic3—811no—
83C4×D3—811no—
84C4×D3—811no—
85C4×D3—813no—
86C2×C32—31no—
87C2×C32—33no—
88C2×C32—31no—
89C2×C32—61no—
90C2×C32—91no—
91C2×C32—181no—
92C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
93C3⋊D3—32no—
94C3⋊D3—92no—
95C3×D3—92no—
96C3×D3—272no—
97C3×D3—276no—
98C2×C9—91no—
99C2×C9—181no—
100C2×C9—272no—
101C22×C3—271no—
102C2×D3—91no—
103C2×D3—271no—
104C2×D3—273no—
105C3×C4—273no—
106C3×C4—271no—
107C3×C4—811no—
108Dic3—91no—
109Dic3—271no—
110Dic3—271no—
111Dic3—271no—
112Dic3—541no—
113Dic3—813no—
114C32—31no—
115C32—33no—
116C32—31no—
117C32—61no—
118C32—91no—
119C32—181no—
120C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
121C9—91no—
122C9—181no—
123C2×C4—2431noSylow
124C2×C3—21no—
125C2×C3—91no—
126C2×C3—93no—
127C2×C3—272no—
128C2×C3#4174⋊C211yescharacteristic
129C2×C3#4178⋊C211yescharacteristic
130D3—92no—
131D3—272no—
132D3—276no—
133C22—271no—
134C4—271no—
135C4—811no—
136C3—21no—
137C3—91no—
138C3—93no—
139C3#4175⋊C411yescharacteristic
140C3#4178⋊C411yescharacteristic
141C2—272no—
142C2#92163⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#92163⋊C2
commutator, hypocenter#6859C2×C4
FrattiniC2×C33D32
Fitting, cosocleC2×#6859C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
prime radicalC2×C3⋊#272D3
LCSG ▷ #6859
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #11757324C2semidirect
3. #11757286C2semidirect
7. #92164C4semidirect
12. #66328D3semidirect
15. #6859C2×C4semidirect
40. C32⋊C9C4×D3semidirect

Maximal subgroups

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

subgroupindex
C2×#921642
#117573242
#117572862
#106198853
((C3⋊D3)⋊C9)⋊C43