Finite Group Databasebeta

← C4×C3⋊#4185 #14517741

Subgroups — C4×C3⋊#4185 #14517741

Order 1944.

594 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 107 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×C3⋊#4185C211yesmaximal, characteristic
2C3×C4×#732C211yesmaximal, characteristic, complemented
3C3⋊#66332C211yesmaximal, characteristic, complemented
4C4×C3⋊((C3⋊D3)⋊C3)—33nomaximal
5C3×C4×C3⋊D9—31nomaximal
6C4×#4185—39nomaximal
7C2×C3×#732C2211yescharacteristic
8C3⋊#4185C412yesdirect product factor
9C2×C3⋊((C3⋊D3)⋊C3)—33no—
10C2×C3×C3⋊D9—31no—
11C3×C4×H(3,𝔽3)D313yescomplemented
12C32×C4×C9D311yescharacteristic, complemented
13C3⋊((C3⋊Dic3)⋊C3)—33no—
14C3×C3⋊Dic9—31no—
15C2×#4185—39no—
16C4×#732D319yescomplemented
17#66332—39no—
18C3×#732C2×C411yescharacteristic, complemented, Sylow
19C4×C3⋊(C3⋊D3)—33no—
20C3×C4×C3⋊D3—91no—
21C4×C3⋊D9—31no—
22C4×(C3⋊D3)⋊C3—99no—
23C3×C4×D9—93no—
24C2×C3×H(3,𝔽3)C2×D313yes—
25C2×C32×C9C2×D311yescharacteristic
26C3⋊((C3⋊D3)⋊C3)—36no—
27C3×C3⋊D9—32no—
28C2×#732C2×D319yes—
29#4185—318no—
30C2×C3⋊(C3⋊D3)—33no—
31C2×C3×C3⋊D3—91no—
32C33×C4—33no—
33C33×C4C3⋊D311yescharacteristic
34C3⋊(C3⋊Dic3)—33no—
35C3×C3⋊Dic3—91no—
36C2×C3⋊D9—31no—
37C2×(C3⋊D3)⋊C3—99no—
38C2×C3×D9—93no—
39C4×H(3,𝔽3)—63no—
40C4×H(3,𝔽3)C3⋊D319yescomplemented
41C3×C4×C9—31no—
42C3×C4×C9—61no—
43C3×C4×C9C3⋊D313yescomplemented
44C3⋊Dic9—31no—
45(C3⋊Dic3)⋊C3—99no—
46C3×Dic9—93no—
47C3×H(3,𝔽3)C4×D313yescomplemented
48C32×C9C4×D311yescharacteristic, complemented
49#732C4×D319yescomplemented
50C4×C3⋊D3—91no—
51C4×C3⋊D3—99no—
52C4×C3⋊D3—279no—
53C3×C4×D3—273no—
54C3×C4×D3—271no—
55C4×D9—93no—
56C2×C33—33no—
57C2×C33C2×C3⋊D311yescharacteristic
58C3⋊(C3⋊D3)—36no—
59C3×C3⋊D3—92no—
60C2×H(3,𝔽3)—63no—
61C2×H(3,𝔽3)C2×C3⋊D319yes—
62C2×C3×C9—31no—
63C2×C3×C9—61no—
64C2×C3×C9C2×C3⋊D313yes—
65C3⋊D9—32no—
66(C3⋊D3)⋊C3—918no—
67C3×D9—96no—
68C2×C3⋊D3—91no—
69C2×C3⋊D3—99no—
70C2×C3⋊D3—279no—
71C2×C3×D3—273no—
72C2×C3×D3—271no—
73C32×C4—21no—
74C32×C4—33no—
75C32×C4—39no—
76C32×C4—99no—
77C32×C4#27211yescharacteristic
78C32×C4C3⋊(C3⋊D3)11yescharacteristic
79C3⋊Dic3—91no—
80C3⋊Dic3—99no—
81C3⋊Dic3—279no—
82C3×Dic3—273no—
83C3×Dic3—271no—
84C2×D9—93no—
85C4×C9—33no—
86Dic9—93no—
87C33—33no—
88C33C4×C3⋊D311yescharacteristic
89H(3,𝔽3)—63no—
90H(3,𝔽3)C4×C3⋊D319yescomplemented
91C3×C9—31no—
92C3×C9—61no—
93C3×C9C4×C3⋊D313yescomplemented
94C2×C3×C4—811no—
95C4×D3—273no—
96C4×D3—271no—
97C4×D3—819no—
98C2×C32—21no—
99C2×C32—33no—
100C2×C32—39no—
101C2×C32—99no—
102C2×C32C2×#27211yescharacteristic
103C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
104C3⋊D3—92no—
105C3⋊D3—918no—
106C3⋊D3—2718no—
107C3×D3—276no—
108C3×D3—272no—
109C2×C9—33no—
110D9—96no—
111C22×C3—811no—
112C2×D3—273no—
113C2×D3—271no—
114C2×D3—819no—
115C3×C4—31no—
116C3×C4—61no—
117C3×C4—99no—
118C3×C4—811no—
119C3×C4#418513yescomplemented
120C3×C4C3⋊#27211yescharacteristic
121Dic3—273no—
122Dic3—271no—
123Dic3—819no—
124C32—21no—
125C32—33no—
126C32—39no—
127C32—99no—
128C32C4×#27211yescharacteristic
129C32C4×C3⋊(C3⋊D3)11yescharacteristic
130C9—33no—
131C2×C4—811noSylow
132C2×C3—31no—
133C2×C3—61no—
134C2×C3—99no—
135C2×C3—812no—
136C2×C3C2×#418513yes—
137C2×C3C2×C3⋊#27211yescharacteristic
138D3—276no—
139D3—272no—
140D3—8118no—
141C22—811no—
142C4—811no—
143C4C3⋊#418511yescharacteristic, direct product factor
144C3—31no—
145C3—61no—
146C3—99no—
147C3C4×#418513yescomplemented
148C3C4×C3⋊#27211yescharacteristic
149C2—812no—
150C2C2×C3⋊#418511yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊#4185
commutator, hypocenterC3×#732C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×#732C2
socleC2×C32C2×#272
prime radicalC2×C3⋊#4185C2
cosocleC2×C3×#732C22
LCSG ▷ C3×#732
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#732C2semidirect
3. C3⋊#66332C2semidirect
8. C3⋊#4185C4direct (N × H)
11. C3×C4×H(3,𝔽3)D3semidirect
12. C32×C4×C9D3semidirect
16. C4×#732D3semidirect
18. C3×#732C2×C4semidirect
40. C4×H(3,𝔽3)C3⋊D3semidirect
43. C3×C4×C9C3⋊D3semidirect
47. C3×H(3,𝔽3)C4×D3semidirect
48. C32×C9C4×D3semidirect
49. #732C4×D3semidirect
90. H(3,𝔽3)C4×C3⋊D3semidirect
93. C3×C9C4×C3⋊D3semidirect
119. C3×C4#4185semidirect
143. C4C3⋊#4185direct (N × H)
147. C3C4×#4185semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41852
C3×C4×#7322
C3⋊#663322
C4×C3⋊((C3⋊D3)⋊C3)3
C3×C4×C3⋊D93
C4×#41853