Finite Group Databasebeta

← C4×C3⋊#4181 #14517723

Subgroups — C4×C3⋊#4181 #14517723

Order 1944.

801 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 801 conjugacy classes of subgroups — too many to draw. Only its 173 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⋊#4181C211yesmaximal, characteristic
2C3×C4×C32⋊C9C211yesmaximal, characteristic, complemented
3C3⋊#66328C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊(C3⋊D3)—31nomaximal
5C3×C4×C3⋊D9—33nomaximal
6C4×#4181—39nomaximal
7C2×C3×C32⋊C9C2211yescharacteristic
8C3⋊#4181C412yesdirect product factor
9C2×C3×C3⋊(C3⋊D3)—31no—
10C34×C4D311yescharacteristic
11C3×C3⋊(C3⋊Dic3)—31no—
12C2×C3×C3⋊D9—33no—
13C32×C4×C9D313yescomplemented
14C3×C3⋊Dic9—33no—
15C2×#4181—39no—
16C4×C32⋊C9D319yescomplemented
17#66328—39no—
18C3×C32⋊C9C2×C411yescharacteristic, complemented, Sylow
19C4×C3⋊(C3⋊D3)—31no—
20C3×C4×C3⋊D3—99no—
21C3×C4×C3⋊D3—93no—
22C3×C4×C3⋊D3—91no—
23C4×C3⋊D9—33no—
24C3×C4×D9—99no—
25C2×C34C2×D311yescharacteristic
26C3×C3⋊(C3⋊D3)—32no—
27C2×C32×C9C2×D313yes—
28C3×C3⋊D9—36no—
29C2×C32⋊C9C2×D319yes—
30#4181—318no—
31C2×C3⋊(C3⋊D3)—31no—
32C2×C3×C3⋊D3—99no—
33C2×C3×C3⋊D3—93no—
34C2×C3×C3⋊D3—91no—
35C33×C4—31no—
36C33×C4—63no—
37C33×C4—61no—
38C33×C4D919yescomplemented
39C33×C4C3⋊D311yescharacteristic
40C33×C4C3⋊D313yes—
41C3⋊(C3⋊Dic3)—31no—
42C3×C3⋊Dic3—99no—
43C3×C3⋊Dic3—93no—
44C3×C3⋊Dic3—91no—
45C2×C3⋊D9—33no—
46C2×C3×D9—99no—
47C3×C4×C9—33no—
48C3×C4×C9—63no—
49C3×C4×C9C3⋊D319yescomplemented
50C3⋊Dic9—33no—
51C3×Dic9—99no—
52C34C4×D311yescharacteristic
53C32×C9C4×D313yescomplemented
54C32⋊C9C4×D319yescomplemented
55C4×C3⋊D3—99no—
56C4×C3⋊D3—93no—
57C4×C3⋊D3—91no—
58C3×C4×D3—273no—
59C3×C4×D3—279no—
60C3×C4×D3—271no—
61C4×D9—99no—
62C2×C33—31no—
63C2×C33—63no—
64C2×C33—61no—
65C2×C33C2×D919yes—
66C2×C33C2×C3⋊D311yescharacteristic
67C2×C33C2×C3⋊D313yes—
68C3⋊(C3⋊D3)—32no—
69C3×C3⋊D3—918no—
70C3×C3⋊D3—96no—
71C3×C3⋊D3—92no—
72C2×C3×C9—33no—
73C2×C3×C9—63no—
74C2×C3×C9C2×C3⋊D319yes—
75C3⋊D9—36no—
76C3×D9—918no—
77C2×C3⋊D3—99no—
78C2×C3⋊D3—93no—
79C2×C3⋊D3—91no—
80C2×C3×D3—279no—
81C2×C3×D3—273no—
82C2×C3×D3—271no—
83C32×C4—23no—
84C32×C4—21no—
85C32×C4—39no—
86C32×C4—33no—
87C32×C4—69no—
88C32×C4—63no—
89C32×C4C3⋊D913yes—
90C32×C4C3⋊D919yescomplemented
91C32×C4#27211yescharacteristic
92C32×C4C3⋊(C3⋊D3)11yescharacteristic
93C3⋊Dic3—99no—
94C3⋊Dic3—93no—
95C3⋊Dic3—91no—
96C3×Dic3—279no—
97C3×Dic3—273no—
98C3×Dic3—271no—
99C2×D9—99no—
100C4×C9—39no—
101Dic9—99no—
102C33—31no—
103C33—63no—
104C33—61no—
105C33C4×D919yescomplemented
106C33C4×C3⋊D311yescharacteristic
107C33C4×C3⋊D313yes—
108C3×C9—33no—
109C3×C9—63no—
110C3×C9C4×C3⋊D319yescomplemented
111C2×C3×C4—811no—
112C4×D3—279no—
113C4×D3—273no—
114C4×D3—271no—
115C2×C32—23no—
116C2×C32—21no—
117C2×C32—39no—
118C2×C32—33no—
119C2×C32—69no—
120C2×C32—63no—
121C2×C32C2×C3⋊D913yes—
122C2×C32C2×C3⋊D919yes—
123C2×C32C2×#27211yescharacteristic
124C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
125C3⋊D3—918no—
126C3⋊D3—96no—
127C3⋊D3—92no—
128C3×D3—276no—
129C3×D3—2718no—
130C3×D3—272no—
131C2×C9—39no—
132D9—918no—
133C22×C3—811no—
134C2×D3—279no—
135C2×D3—273no—
136C2×D3—271no—
137C3×C4—23no—
138C3×C4—21no—
139C3×C4—39no—
140C3×C4—811no—
141C3×C4#418113yescomplemented
142C3×C4C3⋊(C3⋊D9)11yescharacteristic
143C3×C4C3⋊#27211yescharacteristic
144Dic3—279no—
145Dic3—273no—
146Dic3—271no—
147C32—23no—
148C32—21no—
149C32—39no—
150C32—33no—
151C32—69no—
152C32—63no—
153C32C4×C3⋊D913yes—
154C32C4×C3⋊D919yescomplemented
155C32C4×#27211yescharacteristic
156C32C4×C3⋊(C3⋊D3)11yescharacteristic
157C9—39no—
158C2×C4—811noSylow
159C2×C3—23no—
160C2×C3—21no—
161C2×C3—39no—
162C2×C3—812no—
163C2×C3C2×#418113yes—
164C2×C3C2×C3⋊(C3⋊D9)11yescharacteristic
165C2×C3C2×C3⋊#27211yescharacteristic
166D3—2718no—
167D3—276no—
168D3—272no—
169C22—811no—
170C4—811no—
171C4C3⋊#418111yescharacteristic, direct product factor
172C3—23no—
173C3—21no—
174C3—39no—
175C3C4×#418113yescomplemented
176C3C4×C3⋊(C3⋊D9)11yescharacteristic
177C3C4×C3⋊#27211yescharacteristic
178C2—812no—
179C2C2×C3⋊#418111yescharacteristic
subgroupG/H
center, hypercenterC3×C4C3⋊(C3⋊D9)
commutator, hypocenterC3×C32⋊C9C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×C32⋊C9C2
socleC2×C33C2×C3⋊D3
prime radicalC2×C3⋊#4181C2
cosocleC2×C3×C32⋊C9C22
LCSG ▷ C3×C32⋊C9
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C32⋊C9C2semidirect
3. C3⋊#66328C2semidirect
8. C3⋊#4181C4direct (N × H)
13. C32×C4×C9D3semidirect
16. C4×C32⋊C9D3semidirect
18. C3×C32⋊C9C2×C4semidirect
38. C33×C4D9semidirect
49. C3×C4×C9C3⋊D3semidirect
53. C32×C9C4×D3semidirect
54. C32⋊C9C4×D3semidirect
90. C32×C4C3⋊D9semidirect
105. C33C4×D9semidirect
110. C3×C9C4×C3⋊D3semidirect
141. C3×C4#4181semidirect
154. C32C4×C3⋊D9semidirect
171. C4C3⋊#4181direct (N × H)
175. C3C4×#4181semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41812
C3×C4×C32⋊C92
C3⋊#663282
C3×C4×C3⋊(C3⋊D3)3
C3×C4×C3⋊D93
C4×#41813