Finite Group Databasebeta

← C4×C3⋊#4183 #14517735

Subgroups — C4×C3⋊#4183 #14517735

Order 1944.

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

normal subgroups only

This group has 813 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⋊#4183C211yesmaximal, characteristic
2C3×C4×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
3C3⋊#66330C211yesmaximal, characteristic, complemented
4C3×C4×C3⋊(C3⋊D3)—31nomaximal
5C4×C3⋊AGL(1,ℤ/9)—32nomaximal
6C4×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7C4×#4183—39nomaximal
8C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
9C3⋊#4183C412yesdirect product factor
10C2×C3×C3⋊(C3⋊D3)—31no—
11C34×C4D311yescharacteristic, complemented
12C3×C3⋊(C3⋊Dic3)—31no—
13C2×C3⋊AGL(1,ℤ/9)—32no—
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C3×C4×3−1+2D312yescomplemented
16C3×C4×H(3,𝔽3)D311yescharacteristic, complemented
17C3⋊(3−1+2⋊C4)—32no—
18C3⋊((C3⋊Dic3)⋊C3)—31no—
19C2×#4183—39no—
20C4×AΣL(1,𝔽27)D319yescomplemented
21#66330—39no—
22C3×AΣL(1,𝔽27)C2×C411yescharacteristic, complemented, Sylow
23C4×C3⋊(C3⋊D3)—31no—
24C4×C3⋊(C3⋊D3)—31no—
25C3×C4×C3⋊D3—99no—
26C3×C4×C3⋊D3—91no—
27C3×C4×C3⋊D3—93no—
28C4×C3⋊D9—32no—
29C4×AGL(1,ℤ/9)—96no—
30C4×(C3⋊D3)⋊C3—93no—
31C2×C34C2×D311yescharacteristic
32C3×C3⋊(C3⋊D3)—32no—
33C2×C3×3−1+2C2×D312yes—
34C2×C3×H(3,𝔽3)C2×D311yescharacteristic
35C3⋊AGL(1,ℤ/9)—34no—
36C3⋊((C3⋊D3)⋊C3)—32no—
37C2×AΣL(1,𝔽27)C2×D319yes—
38#4183—318no—
39C2×C3⋊(C3⋊D3)—31no—
40C2×C3⋊(C3⋊D3)—31no—
41C2×C3×C3⋊D3—99no—
42C2×C3×C3⋊D3—93no—
43C2×C3×C3⋊D3—91no—
44C33×C4—31no—
45C33×C4—39no—
46C33×C4—31no—
47C33×C4—61no—
48C33×C4C3⋊D311yescharacteristic
49C33×C4C3⋊D313yescomplemented
50C3⋊(C3⋊Dic3)—31no—
51C3⋊(C3⋊Dic3)—31no—
52C3×C3⋊Dic3—99no—
53C3×C3⋊Dic3—93no—
54C3×C3⋊Dic3—91no—
55C2×C3⋊D9—32no—
56C2×AGL(1,ℤ/9)—96no—
57C2×(C3⋊D3)⋊C3—93no—
58C4×3−1+2—62no—
59C4×3−1+2C3⋊D316yescomplemented
60C4×H(3,𝔽3)—61no—
61C4×H(3,𝔽3)C3⋊D313yescomplemented
62C3×C4×C9—32no—
63C3⋊Dic9—32no—
643−1+2⋊C4—96no—
65(C3⋊Dic3)⋊C3—93no—
66C34C4×D311yescharacteristic, complemented
67C3×3−1+2C4×D312yescomplemented
68C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
69AΣL(1,𝔽27)C4×D319yescomplemented
70C4×C3⋊D3—99no—
71C4×C3⋊D3—93no—
72C4×C3⋊D3—91no—
73C4×C3⋊D3—93no—
74C4×C3⋊D3—273no—
75C3×C4×D3—279no—
76C3×C4×D3—273no—
77C3×C4×D3—271no—
78C4×D9—96no—
79C2×C33—31no—
80C2×C33—39no—
81C2×C33—31no—
82C2×C33—61no—
83C2×C33C2×C3⋊D311yescharacteristic
84C2×C33C2×C3⋊D313yes—
85C3⋊(C3⋊D3)—32no—
86C3⋊(C3⋊D3)—32no—
87C3×C3⋊D3—918no—
88C3×C3⋊D3—92no—
89C3×C3⋊D3—96no—
90C2×3−1+2—62no—
91C2×3−1+2C2×C3⋊D316yes—
92C2×H(3,𝔽3)—61no—
93C2×H(3,𝔽3)C2×C3⋊D313yes—
94C2×C3×C9—32no—
95C3⋊D9—34no—
96AGL(1,ℤ/9)—912no—
97(C3⋊D3)⋊C3—96no—
98C2×C3⋊D3—99no—
99C2×C3⋊D3—93no—
100C2×C3⋊D3—91no—
101C2×C3⋊D3—93no—
102C2×C3⋊D3—273no—
103C2×C3×D3—279no—
104C2×C3×D3—273no—
105C2×C3×D3—271no—
106C32×C4—21no—
107C32×C4—39no—
108C32×C4—33no—
109C32×C4—39no—
110C32×C4—33no—
111C32×C4—33no—
112C32×C4—69no—
113C32×C4—93no—
114C32×C4#27211yescharacteristic
115C32×C4C3⋊(C3⋊D3)11yescharacteristic
116C3⋊Dic3—99no—
117C3⋊Dic3—93no—
118C3⋊Dic3—91no—
119C3⋊Dic3—93no—
120C3⋊Dic3—273no—
121C3×Dic3—279no—
122C3×Dic3—273no—
123C3×Dic3—271no—
124C2×D9—96no—
125C4×C9—36no—
126Dic9—96no—
127C33—31no—
128C33—39no—
129C33—31no—
130C33—61no—
131C33C4×C3⋊D311yescharacteristic
132C33C4×C3⋊D313yescomplemented
1333−1+2—62no—
1343−1+2C4×C3⋊D316yescomplemented
135H(3,𝔽3)—61no—
136H(3,𝔽3)C4×C3⋊D313yescomplemented
137C3×C9—32no—
138C2×C3×C4—811no—
139C4×D3—279no—
140C4×D3—273no—
141C4×D3—271no—
142C4×D3—813no—
143C2×C32—21no—
144C2×C32—39no—
145C2×C32—33no—
146C2×C32—39no—
147C2×C32—33no—
148C2×C32—33no—
149C2×C32—69no—
150C2×C32—93no—
151C2×C32C2×#27211yescharacteristic
152C2×C32C2×C3⋊(C3⋊D3)11yescharacteristic
153C3⋊D3—918no—
154C3⋊D3—96no—
155C3⋊D3—92no—
156C3⋊D3—96no—
157C3⋊D3—276no—
158C3×D3—2718no—
159C3×D3—276no—
160C3×D3—272no—
161C2×C9—36no—
162D9—912no—
163C22×C3—811no—
164C2×D3—279no—
165C2×D3—273no—
166C2×D3—271no—
167C2×D3—813no—
168C3×C4—39no—
169C3×C4—31no—
170C3×C4—61no—
171C3×C4—93no—
172C3×C4—811no—
173C3×C4#418313yescomplemented
174C3×C4C3⋊#27211yescharacteristic
175Dic3—279no—
176Dic3—273no—
177Dic3—271no—
178Dic3—813no—
179C32—21no—
180C32—39no—
181C32—39no—
182C32—33no—
183C32—33no—
184C32—33no—
185C32—69no—
186C32—93no—
187C32C4×#27211yescharacteristic
188C32C4×C3⋊(C3⋊D3)11yescharacteristic
189C9—36no—
190C2×C4—811noSylow
191C2×C3—39no—
192C2×C3—31no—
193C2×C3—61no—
194C2×C3—93no—
195C2×C3—812no—
196C2×C3C2×#418313yes—
197C2×C3C2×C3⋊#27211yescharacteristic
198D3—2718no—
199D3—276no—
200D3—272no—
201D3—816no—
202C22—811no—
203C4—811no—
204C4C3⋊#418311yescharacteristic, direct product factor
205C3—39no—
206C3—31no—
207C3—61no—
208C3—93no—
209C3C4×#418313yescomplemented
210C3C4×C3⋊#27211yescharacteristic
211C2—812no—
212C2C2×C3⋊#418311yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊#4183
commutator, hypocenterC3×AΣL(1,𝔽27)C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×AΣL(1,𝔽27)C2
socleC2×C32C2×#272
prime radicalC2×C3⋊#4183C2
cosocleC2×C3×AΣL(1,𝔽27)C22
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×AΣL(1,𝔽27)C2semidirect
3. C3⋊#66330C2semidirect
9. C3⋊#4183C4direct (N × H)
11. C34×C4D3semidirect
15. C3×C4×3−1+2D3semidirect
16. C3×C4×H(3,𝔽3)D3semidirect
20. C4×AΣL(1,𝔽27)D3semidirect
22. C3×AΣL(1,𝔽27)C2×C4semidirect
49. C33×C4C3⋊D3semidirect
59. C4×3−1+2C3⋊D3semidirect
61. C4×H(3,𝔽3)C3⋊D3semidirect
66. C34C4×D3semidirect
67. C3×3−1+2C4×D3semidirect
68. C3×H(3,𝔽3)C4×D3semidirect
69. AΣL(1,𝔽27)C4×D3semidirect
132. C33C4×C3⋊D3semidirect
134. 3−1+2C4×C3⋊D3semidirect
136. H(3,𝔽3)C4×C3⋊D3semidirect
173. C3×C4#4183semidirect
204. C4C3⋊#4183direct (N × H)
209. C3C4×#4183semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41832
C3×C4×AΣL(1,𝔽27)2
C3⋊#663302
C3×C4×C3⋊(C3⋊D3)3
C4×C3⋊AGL(1,ℤ/9)3
C4×C3⋊((C3⋊D3)⋊C3)3
C4×#41833