Finite Group Databasebeta

← #14517014

Subgroups — #14517014

Order 1944.

655 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 655 conjugacy classes of subgroups — too many to draw. Only its 48 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⋊#66322C211yesmaximal, characteristic, complemented
3C3×#66321C211yesmaximal, characteristic, complemented
4Dic3×C3⋊(C3⋊D3)—31nomaximal
5#10619901—31nomaximal
6#4183⋊C4—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3⋊#4183C412yescomplemented
9C2×C3×C3⋊(C3⋊D3)—31no—
10C3⋊(C3⋊(C3⋊Dic3))D311yescharacteristic, complemented
11C33×Dic3—31no—
12C2×C3⋊AGL(1,ℤ/9)—61no—
13C2×C3⋊((C3⋊D3)⋊C3)—31no—
14C3×#1084D311yescharacteristic, complemented
15C3⋊((C3⋊Dic3)⋊C3)—31no—
16C2×#4183—33no—
17C2×#4183—63no—
18#66322—33no—
19#66321D313yescomplemented
20C3×AΣL(1,𝔽27)C2×C411yescharacteristic, complemented, Sylow
21C4×C3⋊(C3⋊D3)—91no—
22#6289—91no—
23Dic3×C3⋊D3—93no—
24Dic3×C3⋊D3—91no—
25Dic3×C3⋊D3—99no—
26((C3⋊D3)⋊C3)⋊C4—91no—
27C2×C34C2×D311yescharacteristic
28C3×C3⋊(C3⋊D3)—32no—
29C2×C3×3−1+2—21no—
30C2×C3×H(3,𝔽3)C2×D311yescharacteristic
31C3⋊AGL(1,ℤ/9)—62no—
32C3⋊((C3⋊D3)⋊C3)—32no—
33C2×AΣL(1,𝔽27)—23no—
34C2×AΣL(1,𝔽27)C2×D313yes—
35#4183—36no—
36#4183—66no—
37C2×C3⋊(C3⋊D3)—31no—
38C2×C3⋊(C3⋊D3)—31no—
39C2×C3×C3⋊D3—99no—
40C2×C3×C3⋊D3—93no—
41C2×C3×C3⋊D3—91no—
42C33×C4—91no—
43C3⋊(C3⋊Dic3)—31no—
44C3⋊(C3⋊Dic3)—33no—
45C3⋊(C3⋊Dic3)—91no—
46C3⋊(C3⋊Dic3)—99no—
47C3⋊(C3⋊Dic3)—181no—
48C3×C3⋊Dic3—91no—
49C32×Dic3—39no—
50C32×Dic3—33no—
51C32×Dic3—31no—
52C32×Dic3—91no—
53C2×C3⋊D9—61no—
54C2×AGL(1,ℤ/9)—183no—
55C2×(C3⋊D3)⋊C3—91no—
56C2×(C3⋊D3)⋊C3—181no—
57#1084C3⋊D311yescharacteristic, complemented
58(C3⋊Dic3)⋊C3—91no—
59(C3⋊Dic3)⋊C3—181no—
60C34C4×D311yescharacteristic, complemented
61C3×3−1+2—21no—
62C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
63AΣL(1,𝔽27)—23no—
64AΣL(1,𝔽27)C4×D313yescomplemented
65C4×C3⋊D3—271no—
66C4×C3⋊D3—273no—
67C4×C3⋊D3—279no—
68#624—271no—
69#624—273no—
70D3×Dic3—271no—
71D3×Dic3—273no—
72D3×Dic3—279no—
73C2×C33—31no—
74C2×C33—39no—
75C2×C33—31no—
76C2×C33—61no—
77C2×C33D3211yescharacteristic
78C2×C33D3213yes—
79C3⋊(C3⋊D3)—32no—
80C3⋊(C3⋊D3)—32no—
81C3×C3⋊D3—918no—
82C3×C3⋊D3—92no—
83C3×C3⋊D3—96no—
84C2×3−1+2—23no—
85C2×3−1+2—121no—
86C2×H(3,𝔽3)—21no—
87C2×H(3,𝔽3)—61no—
88C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
89C2×C3×C9—61no—
90C3⋊D9—62no—
91AGL(1,ℤ/9)—186no—
92(C3⋊D3)⋊C3—92no—
93(C3⋊D3)⋊C3—182no—
94C2×C3⋊D3—99no—
95C2×C3⋊D3—93no—
96C2×C3⋊D3—91no—
97C2×C3⋊D3—91no—
98C2×C3⋊D3—181no—
99C2×C3⋊D3—273no—
100C2×C3×D3—279no—
101C2×C3×D3—273no—
102C2×C3×D3—271no—
103C32×C4—99no—
104C32×C4—93no—
105C32×C4—91no—
106C3⋊Dic3—91no—
107C3⋊Dic3—91no—
108C3⋊Dic3—181no—
109C3⋊Dic3—273no—
110C3⋊Dic3—279no—
111C3⋊Dic3—273no—
112C3⋊Dic3—279no—
113C3⋊Dic3—549no—
114C3×Dic3—39no—
115C3×Dic3—33no—
116C3×Dic3—31no—
117C3×Dic3—91no—
118C3×Dic3—93no—
119C3×Dic3—271no—
120C3×Dic3—273no—
121C2×D9—183no—
122C33—31no—
123C33—39no—
124C33—31no—
125C33—61no—
126C33#62411yescharacteristic
127C33#62413yescomplemented
1283−1+2—23no—
1293−1+2—121no—
130H(3,𝔽3)—21no—
131H(3,𝔽3)—61no—
132H(3,𝔽3)C4×C3⋊D311yescharacteristic, complemented
133C3×C9—61no—
134C2×Dic3—811no—
135C4×D3—811no—
136C4×D3—813no—
137C4×D3—811no—
138C4×D3—819no—
139C2×C32—21no—
140C2×C32—39no—
141C2×C32—33no—
142C2×C32—39no—
143C2×C32—33no—
144C2×C32—31no—
145C2×C32—69no—
146C2×C32—61no—
147C2×C32—93no—
148C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
149C2×C32D3×C3⋊D311yescharacteristic
150C3⋊D3—918no—
151C3⋊D3—96no—
152C3⋊D3—92no—
153C3⋊D3—92no—
154C3⋊D3—182no—
155C3⋊D3—276no—
156C3×D3—2718no—
157C3×D3—276no—
158C3×D3—272no—
159C2×C9—63no—
160D9—186no—
161C22×C3—811no—
162C2×D3—279no—
163C2×D3—273no—
164C2×D3—271no—
165C2×D3—811no—
166C2×D3—1621no—
167C3×C4—99no—
168C3×C4—93no—
169C3×C4—91no—
170C3×C4—811no—
171Dic3—31no—
172Dic3—91no—
173Dic3—273no—
174Dic3—271no—
175Dic3—819no—
176Dic3—811no—
177Dic3—1621no—
178C32—21no—
179C32—39no—
180C32—39no—
181C32—33no—
182C32—33no—
183C32—31no—
184C32—69no—
185C32—61no—
186C32—93no—
187C32#619911yescharacteristic
188C32#628911yescharacteristic
189C9—63no—
190C2×C4—2431noSylow
191C2×C3—31no—
192C2×C3—39no—
193C2×C3—61no—
194C2×C3—91no—
195C2×C3—181no—
196C2×C3—812no—
197C2×C3#4174⋊C213yes—
198C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
199D3—2718no—
200D3—276no—
201D3—272no—
202D3—812no—
203D3—1622no—
204C22—811no—
205C4—91no—
206C4—811no—
207C3—39no—
208C3—31no—
209C3—61no—
210C3—91no—
211C3—181no—
212C3#4183⋊C413yescomplemented
213C3#1061988511yescharacteristic
214C2—812no—
215C2#1175773511yescharacteristic
subgroupG/H
center, hypercenterC2#11757735
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⋊#4183C2
LCSG ▷ C3×AΣL(1,𝔽27)
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3⋊#66322C2semidirect
3. C3×#66321C2semidirect
8. C3⋊#4183C4semidirect
10. C3⋊(C3⋊(C3⋊Dic3))D3semidirect
14. C3×#1084D3semidirect
19. #66321D3semidirect
20. C3×AΣL(1,𝔽27)C2×C4semidirect
57. #1084C3⋊D3semidirect
60. C34C4×D3semidirect
62. C3×H(3,𝔽3)C4×D3semidirect
64. AΣL(1,𝔽27)C4×D3semidirect
127. C33#624semidirect
132. H(3,𝔽3)C4×C3⋊D3semidirect
212. C3#4183⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41832
C3⋊#663222
C3×#663212
Dic3×C3⋊(C3⋊D3)3
#106199013
#4183⋊C43