Finite Group Databasebeta

← #4175⋊Dic3 #14517016

Subgroups — #4175⋊Dic3 #14517016

Order 1944.

433 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 433 conjugacy classes of subgroups — too many to draw. Only its 54 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×#4175C211yesmaximal, characteristic
2C3⋊#66330C211yesmaximal, characteristic, complemented
3C3⋊#66321C211yesmaximal, characteristic, complemented
4#10620154—31nomaximal
5((C3⋊D3)⋊C3)⋊Dic3—31nomaximal
6#4175⋊C4—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3×#4175C412yescomplemented
9C2×C3×C3⋊(C3⋊D3)D311yescharacteristic
10C3×C3⋊(C3⋊Dic3)—31no—
11C32×C3⋊Dic3—31no—
12C2×C3×(C3⋊D3)⋊C3—31no—
13C3⋊#1084D311yescharacteristic, complemented
14C3⋊(3−1+2⋊C4)—61no—
15C3⋊((C3⋊Dic3)⋊C3)—31no—
16C2×#4175D313yes—
17#66330—33no—
18#66330—63no—
19#66321—33no—
20C3×AΣL(1,𝔽27)C2×C411yescharacteristic, complemented, Sylow
21#6294—91no—
22#6294—93no—
23#6289—91no—
24Dic3×C3⋊D3—91no—
25D3×C3⋊Dic3—91no—
26((C3⋊D3)⋊C3)⋊C4—93no—
27C2×C34C2×D311yescharacteristic
28C3×C3⋊(C3⋊D3)Dic312yescomplemented
29C2×C3×3−1+2—21no—
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3×(C3⋊D3)⋊C3—32no—
32C2×AΣL(1,𝔽27)—23no—
33C2×AΣL(1,𝔽27)C2×D313yes—
34#4175Dic316yescomplemented
35C2×C3⋊(C3⋊D3)C3⋊D311yescharacteristic
36C2×C3×C3⋊D3—31no—
37C2×C3×C3⋊D3—91no—
38C2×C3×C3⋊D3—93no—
39C2×C32×D3—91no—
40C3⋊(C3⋊Dic3)—31no—
41C3⋊(C3⋊Dic3)—31no—
42C3×C3⋊Dic3—33no—
43C3×C3⋊Dic3—31no—
44C3×C3⋊Dic3—91no—
45C3×C3⋊Dic3—93no—
46C3×C3⋊Dic3—91no—
47C3×C3⋊Dic3—91no—
48C3×C3⋊Dic3—181no—
49C3×C3⋊Dic3—183no—
50C32×Dic3—91no—
51C32×Dic3—91no—
52C32×Dic3—181no—
53C2×(C3⋊D3)⋊C3—33no—
54#1084—33no—
55#1084—181no—
56C3⋊Dic9—61no—
573−1+2⋊C4—183no—
58(C3⋊Dic3)⋊C3—93no—
59C34C2×Dic311yescharacteristic, complemented
60C3×3−1+2—21no—
61C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
62AΣL(1,𝔽27)—23no—
63AΣL(1,𝔽27)C2×Dic313yescomplemented
64C2×C3⋊Dic3—271no—
65C4×C3⋊D3—271no—
66#624—271no—
67#624—273no—
68D3×Dic3—271no—
69D3×Dic3—273no—
70D3×Dic3—271no—
71D3×Dic3—273no—
72C2×C33—21no—
73C2×C33—31no—
74C2×C33—33no—
75C2×C33—31no—
76C2×C33—61no—
77C2×C33—63no—
78C2×C33D3211yescharacteristic
79C2×C33C2×C3⋊D311yescharacteristic
80C3⋊(C3⋊D3)C3⋊Dic312yescomplemented
81C3×C3⋊D3—32no—
82C3×C3⋊D3—92no—
83C3×C3⋊D3—96no—
84C32×D3—92no—
85C2×3−1+2—23no—
86C2×3−1+2—121no—
87C2×H(3,𝔽3)—61no—
88C2×H(3,𝔽3)D3213yes—
89C2×C3×C9—61no—
90(C3⋊D3)⋊C3—36no—
91C22×C32—271no—
92C2×C3⋊D3—31no—
93C2×C3⋊D3—91no—
94C2×C3⋊D3—93no—
95C2×C3×D3—93no—
96C2×C3×D3—91no—
97C2×C3×D3—271no—
98C2×C3×D3—273no—
99C32×C4—271no—
100C3⋊Dic3—31no—
101C3⋊Dic3—91no—
102C3⋊Dic3—91no—
103C3⋊Dic3—93no—
104C3⋊Dic3—91no—
105C3⋊Dic3—93no—
106C3⋊Dic3—183no—
107C3⋊Dic3—181no—
108C3⋊Dic3—271no—
109C3⋊Dic3—541no—
110C3×Dic3—93no—
111C3×Dic3—93no—
112C3×Dic3—91no—
113C3×Dic3—91no—
114C3×Dic3—181no—
115C3×Dic3—183no—
116C3×Dic3—273no—
117C3×Dic3—271no—
118C3×Dic3—273no—
119C3×Dic3—271no—
120C3×Dic3—541no—
121C3×Dic3—543no—
122Dic9—183no—
123C33—21no—
124C33—31no—
125C33—33no—
126C33—31no—
127C33—61no—
128C33—63no—
129C33D3×Dic311yescharacteristic
130C33C2×C3⋊Dic311yescharacteristic, complemented
1313−1+2—23no—
1323−1+2—121no—
133H(3,𝔽3)—61no—
134H(3,𝔽3)D3×Dic313yescomplemented
135C3×C9—61no—
136C2×Dic3—811no—
137C2×Dic3—813no—
138C4×D3—811no—
139C4×D3—811no—
140C4×D3—813no—
141C2×C32—21no—
142C2×C32—31no—
143C2×C32—33no—
144C2×C32—31no—
145C2×C32—33no—
146C2×C32—33no—
147C2×C32—63no—
148C2×C32—61no—
149C2×C32—63no—
150C2×C32—63no—
151C2×C32—61no—
152C2×C32—91no—
153C2×C32—123no—
154C2×C32—181no—
155C2×C32—272no—
156C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
157C2×C32D3×C3⋊D311yescharacteristic
158C3⋊D3—32no—
159C3⋊D3—92no—
160C3⋊D3—96no—
161C3×D3—96no—
162C3×D3—92no—
163C3×D3—272no—
164C3×D3—276no—
165C2×C9—63no—
166C22×C3—273no—
167C22×C3—271no—
168C2×D3—91no—
169C2×D3—271no—
170C2×D3—273no—
171C3×C4—273no—
172C3×C4—271no—
173C3×C4—811no—
174Dic3—91no—
175Dic3—91no—
176Dic3—181no—
177Dic3—273no—
178Dic3—273no—
179Dic3—271no—
180Dic3—271no—
181Dic3—541no—
182Dic3—543no—
183Dic3—813no—
184C32—21no—
185C32—33no—
186C32—31no—
187C32—33no—
188C32—31no—
189C32—33no—
190C32—61no—
191C32—63no—
192C32—63no—
193C32—63no—
194C32—61no—
195C32—91no—
196C32—123no—
197C32—181no—
198C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
199C32D3×C3⋊Dic311yescharacteristic
200C9—63no—
201C2×C4—2431noSylow
202C2×C3—21no—
203C2×C3—31no—
204C2×C3—33no—
205C2×C3—61no—
206C2×C3—63no—
207C2×C3—93no—
208C2×C3—276no—
209C2×C3—272no—
210C2×C3#4174⋊C211yescharacteristic
211C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
212D3—92no—
213D3—272no—
214D3—276no—
215C22—271no—
216C4—271no—
217C4—811no—
218C3—21no—
219C3—31no—
220C3—33no—
221C3—61no—
222C3—63no—
223C3—93no—
224C3#4175⋊C411yescharacteristic, complemented
225C3((C3⋊D3)⋊C3)⋊Dic311yescharacteristic
226C2—272no—
227C2#4175⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4175⋊D3
commutator, hypocenterC3×AΣL(1,𝔽27)C2×C4
FrattiniC2×C32D3×C3⋊D3
Fitting, cosocleC2×C3×AΣL(1,𝔽27)C22
socleC2×C32((C3⋊D3)⋊C3)⋊C2
prime radicalC2×C3×#4175C2
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66330C2semidirect
3. C3⋊#66321C2semidirect
8. C3×#4175C4semidirect
13. C3⋊#1084D3semidirect
20. C3×AΣL(1,𝔽27)C2×C4semidirect
28. C3×C3⋊(C3⋊D3)Dic3semidirect
34. #4175Dic3semidirect
59. C34C2×Dic3semidirect
61. C3×H(3,𝔽3)C4×D3semidirect
63. AΣL(1,𝔽27)C2×Dic3semidirect
80. C3⋊(C3⋊D3)C3⋊Dic3semidirect
130. C33C2×C3⋊Dic3semidirect
134. H(3,𝔽3)D3×Dic3semidirect
224. C3#4175⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41752
C3⋊#663302
C3⋊#663212
#106201543
((C3⋊D3)⋊C3)⋊Dic33
#4175⋊C43