Finite Group Databasebeta

← C4×#92306 #14517539

Subgroups — C4×#92306 #14517539

Order 1944.

377 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 70 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×#92306C211yesmaximal, characteristic
2C4×#6893C211yesmaximal, characteristic, complemented
3#11757610C211yesmaximal, characteristic, complemented
4C4×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
5C4×C3⋊((C3⋊D3)⋊C3)—31nomaximal
6C4×#4169—33nomaximal
7C2×#6893C2211yescharacteristic
8#92306C412yesdirect product factor
9C2×C3⋊(C3⋊D9)C2×C311yescharacteristic
10C2×C3⋊((C3⋊D3)⋊C3)—31no—
11C3×C4×3−1+2—21no—
12C3×C4×H(3,𝔽3)D311yescharacteristic
13C32×C4×C9C2×C311yescharacteristic, complemented
14C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
15C3⋊((C3⋊Dic3)⋊C3)—31no—
16C2×#4169—33no—
17C4×C32⋊C9—23no—
18C4×C32⋊C9D313yescomplemented
19#66316—33no—
20#6893C2×C411yescharacteristic, complemented, Sylow
21C4×C3⋊(C3⋊D3)—31no—
22C3×C4×C3⋊D3—91no—
23C4×C3⋊D9—33no—
24C4×C3⋊D9—93no—
25C4×(C3⋊D3)⋊C3—93no—
26C2×C3×3−1+2—21no—
27C2×C3×H(3,𝔽3)C2×D311yescharacteristic
28C2×C32×C9C22×C311yescharacteristic
29C3⋊(C3⋊D9)C3×C412yescomplemented
30C3⋊((C3⋊D3)⋊C3)—32no—
31C2×C32⋊C9—23no—
32C2×C32⋊C9C2×D313yes—
33#4169—36no—
34C2×C3⋊(C3⋊D3)—31no—
35C2×C3×C3⋊D3—91no—
36C33×C4—21no—
37C33×C4C3×D311yescharacteristic
38C33×C4C3⋊D311yescharacteristic
39C3⋊(C3⋊Dic3)—31no—
40C3×C3⋊Dic3—91no—
41C2×C3⋊D9—33no—
42C2×C3⋊D9—93no—
43C2×(C3⋊D3)⋊C3—93no—
44C4×3−1+2—63no—
45C4×H(3,𝔽3)—33no—
46C3×C4×C9—23no—
47C3×C4×C9—33no—
48C3×C4×C9C3×D313yes—
49C3⋊Dic9—33no—
50C3⋊Dic9—93no—
51(C3⋊Dic3)⋊C3—93no—
52C3×3−1+2—21no—
53C3×H(3,𝔽3)C4×D311yescharacteristic
54C32×C9C2×C3×C411yescharacteristic, complemented
55C32⋊C9—23no—
56C32⋊C9C4×D313yescomplemented
57C4×C3⋊D3—91no—
58C4×C3⋊D3—93no—
59C4×C3⋊D3—273no—
60C3×C4×D3—271no—
61C3×C4×D3—273no—
62C4×D9—273no—
63C2×C33—21no—
64C2×C33C2×C3×D311yescharacteristic
65C2×C33C2×C3⋊D311yescharacteristic
66C3⋊(C3⋊D3)—32no—
67C3×C3⋊D3—92no—
68C2×3−1+2—63no—
69C2×H(3,𝔽3)—33no—
70C2×C3×C9—23no—
71C2×C3×C9—33no—
72C2×C3×C9C2×C3×D313yes—
73C3⋊D9—36no—
74C3⋊D9—96no—
75(C3⋊D3)⋊C3—96no—
76C2×C3⋊D3—91no—
77C2×C3⋊D3—93no—
78C2×C3⋊D3—273no—
79C2×C3×D3—271no—
80C2×C3×D3—273no—
81C32×C4—33no—
82C32×C4—31no—
83C32×C4—33no—
84C32×C4—61no—
85C32×C4—63no—
86C32×C4(C3⋊D3)⋊C313yes—
87C32×C4C3×C3⋊D311yescharacteristic
88C3⋊Dic3—91no—
89C3⋊Dic3—93no—
90C3⋊Dic3—273no—
91C3×Dic3—271no—
92C3×Dic3—273no—
93C2×D9—273no—
94C4×C9—33no—
95C4×C9—63no—
96Dic9—273no—
97C33—21no—
98C33C3×C4×D311yescharacteristic
99C33C4×C3⋊D311yescharacteristic
1003−1+2—63no—
101H(3,𝔽3)—33no—
102C3×C9—23no—
103C3×C9—33no—
104C3×C9C3×C4×D313yes—
105C2×C3×C4—811no—
106C4×D3—271no—
107C4×D3—273no—
108C4×D3—813no—
109C2×C32—33no—
110C2×C32—31no—
111C2×C32—33no—
112C2×C32—61no—
113C2×C32—63no—
114C2×C32C2×(C3⋊D3)⋊C313yes—
115C2×C32C2×C3×C3⋊D311yescharacteristic
116C3⋊D3—92no—
117C3⋊D3—96no—
118C3⋊D3—276no—
119C3×D3—272no—
120C3×D3—276no—
121C2×C9—33no—
122C2×C9—63no—
123D9—276no—
124C22×C3—811no—
125C2×D3—271no—
126C2×D3—273no—
127C2×D3—813no—
128C3×C4—33no—
129C3×C4—91no—
130C3×C4—181no—
131C3×C4—811no—
132C3×C4C3⋊((C3⋊D3)⋊C3)11yescharacteristic
133C3×C4#420713yes—
134Dic3—271no—
135Dic3—273no—
136Dic3—813no—
137C32—33no—
138C32—31no—
139C32—33no—
140C32—61no—
141C32—63no—
142C32C4×(C3⋊D3)⋊C313yes—
143C32C3×C4×C3⋊D311yescharacteristic
144C9—33no—
145C9—63no—
146C2×C4—811noSylow
147C2×C3—33no—
148C2×C3—91no—
149C2×C3—181no—
150C2×C3—812no—
151C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
152C2×C3C2×#420713yes—
153D3—272no—
154D3—276no—
155D3—816no—
156C22—811no—
157C4—811no—
158C4#9230611yescharacteristic, direct product factor
159C3—33no—
160C3—91no—
161C3—181no—
162C3C4×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
163C3C4×#420713yes—
164C2—812no—
165C2C2×#9230611yescharacteristic
subgroupG/H
center, hypercenterC4#92306
commutator, hypocenterC32×C9C2×C3×C4
Frattini, socleC2×C32C2×C3×C3⋊D3
FittingC4×#6893C2
prime radicalC2×#92306C2
cosocleC2×C32×C9C22×C3
LCSG ▷ C32×C9
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×#6893C2semidirect
3. #11757610C2semidirect
4. C4×C3⋊(C3⋊D9)C3semidirect
8. #92306C4direct (N × H)
13. C32×C4×C9C2×C3semidirect
14. C3⋊(C3⋊Dic9)C2×C3semidirect
18. C4×C32⋊C9D3semidirect
20. #6893C2×C4semidirect
29. C3⋊(C3⋊D9)C3×C4semidirect
54. C32×C9C2×C3×C4semidirect
56. C32⋊C9C4×D3semidirect
158. C4#92306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#923062
C4×#68932
#117576102
C4×C3⋊(C3⋊D9)3
C4×C3⋊((C3⋊D3)⋊C3)3
C4×#41693