Finite Group Databasebeta

← C3×C4×#4181 #14517493

Subgroups — C3×C4×#4181 #14517493

Order 1944.

580 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 94 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
4C32×C4×C3⋊D3—31nomaximal
5C32×C4×D9—33nomaximal
6C4×#4181C311yesmaximal, characteristic, direct product factor
7C2×C3×C32⋊C9C2211yescharacteristic
8C3×#4181C412yesdirect product factor
9C2×C32×C3⋊D3—31no—
10C34×C4D311yescharacteristic
11C32×C3⋊Dic3—31no—
12C2×C32×D9—33no—
13C32×C4×C9D313yescomplemented
14C32×Dic9—33no—
15C2×#4181C2×C311yescharacteristic
16C4×C32⋊C9—21no—
17C4×C32⋊C9—23no—
18C4×C32⋊C9C2×C311yescharacteristic, complemented
19#66328C2×C311yescharacteristic, complemented
20C3×C32⋊C9C2×C411yescharacteristic, complemented, Sylow
21C3×C4×C3⋊D3—33no—
22C3×C4×C3⋊D3—31no—
23C32×C4×D3—93no—
24C32×C4×D3—91no—
25C3×C4×D9—39no—
26C3×C4×D9—33no—
27C2×C34C2×D311yescharacteristic
28C32×C3⋊D3—32no—
29C2×C32×C9C2×D313yes—
30C32×D9—36no—
31C2×C32⋊C9—21no—
32C2×C32⋊C9—23no—
33C2×C32⋊C9C22×C311yescharacteristic
34#4181C3×C412yesdirect product factor
35C2×C3×C3⋊D3—33no—
36C2×C3×C3⋊D3—31no—
37C2×C32×D3—93no—
38C2×C32×D3—91no—
39C33×C4—23no—
40C33×C4—21no—
41C33×C4—33no—
42C33×C4—63no—
43C33×C4D913yescomplemented
44C33×C4C3×D311yescharacteristic
45C33×C4C3⋊D311yescharacteristic
46C3×C3⋊Dic3—33no—
47C3×C3⋊Dic3—31no—
48C32×Dic3—93no—
49C32×Dic3—91no—
50C2×C3×D9—39no—
51C2×C3×D9—33no—
52C3×C4×C9—23no—
53C3×C4×C9—39no—
54C3×C4×C9C3×D313yescomplemented
55C3×Dic9—39no—
56C3×Dic9—33no—
57C34C4×D311yescharacteristic
58C32×C9C4×D313yescomplemented
59C32⋊C9—21no—
60C32⋊C9—23no—
61C32⋊C9C2×C3×C411yescharacteristic, complemented
62C2×C32×C4—271no—
63C4×C3⋊D3—31no—
64C3×C4×D3—99no—
65C3×C4×D3—93no—
66C3×C4×D3—93no—
67C3×C4×D3—91no—
68C4×D9—33no—
69C2×C33—23no—
70C2×C33—21no—
71C2×C33—33no—
72C2×C33—63no—
73C2×C33C2×D913yes—
74C2×C33C2×C3×D311yescharacteristic
75C2×C33C2×C3⋊D311yescharacteristic
76C3×C3⋊D3—36no—
77C3×C3⋊D3—32no—
78C32×D3—96no—
79C32×D3—92no—
80C2×C3×C9—23no—
81C2×C3×C9—39no—
82C2×C3×C9C2×C3×D313yes—
83C3×D9—318no—
84C3×D9—36no—
85C22×C32—271no—
86C2×C3⋊D3—31no—
87C2×C3×D3—99no—
88C2×C3×D3—93no—
89C2×C3×D3—93no—
90C2×C3×D3—91no—
91C32×C4—23no—
92C32×C4—21no—
93C32×C4—23no—
94C32×C4—31no—
95C32×C4—39no—
96C32×C4—61no—
97C32×C4—69no—
98C32×C4—62no—
99C32×C4—61no—
100C32×C4—271no—
101C32×C4C3×D913yescomplemented
102C32×C4C3⋊D911yescharacteristic
103C32×C4#27213yes—
104C32×C4C3×C3⋊D311yescharacteristic
105C3⋊Dic3—31no—
106C3×Dic3—99no—
107C3×Dic3—93no—
108C3×Dic3—93no—
109C3×Dic3—91no—
110C2×D9—33no—
111C4×C9—33no—
112C4×C9—63no—
113Dic9—33no—
114C33—23no—
115C33—21no—
116C33—33no—
117C33—63no—
118C33C4×D913yescomplemented
119C33C3×C4×D311yescharacteristic
120C33C4×C3⋊D311yescharacteristic
121C3×C9—23no—
122C3×C9—39no—
123C3×C9C3×C4×D313yescomplemented
124C2×C3×C4—273no—
125C2×C3×C4—271no—
126C4×D3—93no—
127C4×D3—91no—
128C2×C32—23no—
129C2×C32—21no—
130C2×C32—23no—
131C2×C32—31no—
132C2×C32—39no—
133C2×C32—61no—
134C2×C32—69no—
135C2×C32—62no—
136C2×C32—61no—
137C2×C32—272no—
138C2×C32C2×C3×D913yes—
139C2×C32C2×C3⋊D911yescharacteristic
140C2×C32C2×#27213yes—
141C2×C32C2×C3×C3⋊D311yescharacteristic
142C3⋊D3—32no—
143C3×D3—918no—
144C3×D3—96no—
145C3×D3—96no—
146C3×D3—92no—
147C2×C9—33no—
148C2×C9—63no—
149D9—36no—
150C22×C3—273no—
151C22×C3—271no—
152C2×D3—93no—
153C2×D3—91no—
154C3×C4—23no—
155C3×C4—21no—
156C3×C4—33no—
157C3×C4—63no—
158C3×C4—273no—
159C3×C4—271no—
160C3×C4#418113yesdirect product factor
161C3×C4C3×C3⋊D911yescharacteristic
162C3×C4C3×#27211yescharacteristic
163Dic3—93no—
164Dic3—91no—
165C32—23no—
166C32—21no—
167C32—23no—
168C32—31no—
169C32—39no—
170C32—61no—
171C32—69no—
172C32—62no—
173C32—61no—
174C32C3×C4×D913yescomplemented
175C32C4×C3⋊D911yescharacteristic
176C32C4×#27213yes—
177C32C3×C4×C3⋊D311yescharacteristic
178C9—33no—
179C9—63no—
180C2×C4—271noSylow
181C2×C3—23no—
182C2×C3—21no—
183C2×C3—33no—
184C2×C3—63no—
185C2×C3—276no—
186C2×C3—272no—
187C2×C3C2×#418113yes—
188C2×C3C2×C3×C3⋊D911yescharacteristic
189C2×C3C2×C3×#27211yescharacteristic
190D3—96no—
191D3—92no—
192C22—271no—
193C4—271no—
194C4C3×#418111yescharacteristic, direct product factor
195C3—23no—
196C3—21no—
197C3—33no—
198C3—63no—
199C3C4×#418113yesdirect product factor
200C3C3×C4×C3⋊D911yescharacteristic
201C3C3×C4×#27211yescharacteristic
202C2—272no—
203C2C2×C3×#418111yescharacteristic
subgroupG/H
center, hypercenterC32×C4C3⋊D9
commutator, hypocenterC32⋊C9C2×C3×C4
FrattiniC2×C32C2×C3×C3⋊D3
FittingC3×C4×C32⋊C9C2
socleC2×C33C2×C3⋊D3
prime radicalC2×C3×#4181C2
cosocleC2×C32⋊C9C22×C3
LCSG ▷ C32⋊C9
UCSC1 ◁ C32×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C32⋊C9C2semidirect
3. C3×#66328C2semidirect
6. C4×#4181C3direct (N × H)
8. C3×#4181C4direct (N × H)
13. C32×C4×C9D3semidirect
18. C4×C32⋊C9C2×C3semidirect
19. #66328C2×C3semidirect
20. C3×C32⋊C9C2×C4semidirect
34. #4181C3×C4direct (N × H)
43. C33×C4D9semidirect
54. C3×C4×C9C3×D3semidirect
58. C32×C9C4×D3semidirect
61. C32⋊C9C2×C3×C4semidirect
101. C32×C4C3×D9semidirect
118. C33C4×D9semidirect
123. C3×C9C3×C4×D3semidirect
160. C3×C4#4181direct (N × H)
174. C32C3×C4×D9semidirect
194. C4C3×#4181direct (N × H)
199. C3C4×#4181direct (N × H)

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
C32×C4×C3⋊D33
C32×C4×D93
C4×#41813