Finite Group Databasebeta

← #14517015

Subgroups — #14517015

Order 1944.

653 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 653 conjugacy classes of subgroups — too many to draw. Only its 50 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#10620144—31nomaximal
5#10619901—31nomaximal
6#4175⋊C4—33nomaximal
7C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
8C3⋊#4175C412yescomplemented
9C2×C3⋊(C3⋊(C3⋊D3))D311yescharacteristic
10C3×C3⋊(C3⋊Dic3)—31no—
11C33×Dic3—31no—
12C2×C3⋊((C3⋊D3)⋊C3)—31no—
13C3⋊(3−1+2⋊C4)—61no—
14C3×#1084D311yescharacteristic, complemented
15C3⋊((C3⋊Dic3)⋊C3)—31no—
16C2×#4175—33no—
17#66330—33no—
18#66330—63no—
19#66321D313yescomplemented
20C3×AΣL(1,𝔽27)C2×C411yescharacteristic, complemented, Sylow
21C4×C3⋊(C3⋊D3)—91no—
22#6289—93no—
23#6289—91no—
24#6289—99no—
25Dic3×C3⋊D3—91no—
26((C3⋊D3)⋊C3)⋊C4—91no—
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#4175—36no—
35C2×C3⋊(C3⋊D3)—31no—
36C2×C3⋊(C3⋊D3)—33no—
37C2×C3⋊(C3⋊D3)—91no—
38C2×C3⋊(C3⋊D3)—99no—
39C2×C3⋊(C3⋊D3)—181no—
40C2×C3×C3⋊D3—91no—
41C33×C4—91no—
42C3⋊(C3⋊Dic3)—31no—
43C3⋊(C3⋊Dic3)—31no—
44C3×C3⋊Dic3—99no—
45C3×C3⋊Dic3—93no—
46C3×C3⋊Dic3—91no—
47C32×Dic3—39no—
48C32×Dic3—33no—
49C32×Dic3—31no—
50C32×Dic3—91no—
51C2×(C3⋊D3)⋊C3—91no—
52C2×(C3⋊D3)⋊C3—181no—
53#1084C3⋊D311yescharacteristic, complemented
54C3⋊Dic9—61no—
553−1+2⋊C4—183no—
56(C3⋊Dic3)⋊C3—91no—
57(C3⋊Dic3)⋊C3—181no—
58C34C2×Dic311yescharacteristic, complemented
59C3×3−1+2—21no—
60C3×H(3,𝔽3)C4×D311yescharacteristic, complemented
61AΣL(1,𝔽27)—23no—
62AΣL(1,𝔽27)C4×D313yescomplemented
63C4×C3⋊D3—271no—
64C4×C3⋊D3—273no—
65C4×C3⋊D3—279no—
66#624—271no—
67#624—273no—
68#624—279no—
69D3×Dic3—271no—
70D3×Dic3—273no—
71C2×C33—31no—
72C2×C33—39no—
73C2×C33—31no—
74C2×C33—61no—
75C2×C33D3211yescharacteristic
76C2×C33D3213yes—
77C3⋊(C3⋊D3)—32no—
78C3⋊(C3⋊D3)—36no—
79C3⋊(C3⋊D3)—92no—
80C3⋊(C3⋊D3)—918no—
81C3⋊(C3⋊D3)—182no—
82C3×C3⋊D3—92no—
83C2×3−1+2—23no—
84C2×3−1+2—121no—
85C2×H(3,𝔽3)—21no—
86C2×H(3,𝔽3)—61no—
87C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
88C2×C3×C9—61no—
89(C3⋊D3)⋊C3—92no—
90(C3⋊D3)⋊C3—182no—
91C2×C3⋊D3—91no—
92C2×C3⋊D3—91no—
93C2×C3⋊D3—181no—
94C2×C3⋊D3—273no—
95C2×C3⋊D3—279no—
96C2×C3⋊D3—273no—
97C2×C3⋊D3—279no—
98C2×C3⋊D3—549no—
99C2×C3×D3—271no—
100C2×C3×D3—273no—
101C32×C4—99no—
102C32×C4—93no—
103C32×C4—91no—
104C3⋊Dic3—99no—
105C3⋊Dic3—93no—
106C3⋊Dic3—91no—
107C3⋊Dic3—91no—
108C3⋊Dic3—181no—
109C3⋊Dic3—273no—
110C3×Dic3—39no—
111C3×Dic3—33no—
112C3×Dic3—31no—
113C3×Dic3—91no—
114C3×Dic3—93no—
115C3×Dic3—279no—
116C3×Dic3—273no—
117C3×Dic3—271no—
118Dic9—183no—
119C33—31no—
120C33—39no—
121C33—31no—
122C33—61no—
123C33D3×Dic311yescharacteristic
124C33D3×Dic313yescomplemented
1253−1+2—23no—
1263−1+2—121no—
127H(3,𝔽3)—21no—
128H(3,𝔽3)—61no—
129H(3,𝔽3)C4×C3⋊D311yescharacteristic, complemented
130C3×C9—61no—
131C2×Dic3—811no—
132C4×D3—811no—
133C4×D3—813no—
134C4×D3—811no—
135C4×D3—819no—
136C2×C32—21no—
137C2×C32—39no—
138C2×C32—33no—
139C2×C32—39no—
140C2×C32—33no—
141C2×C32—31no—
142C2×C32—69no—
143C2×C32—61no—
144C2×C32—93no—
145C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
146C2×C32D3×C3⋊D311yescharacteristic
147C3⋊D3—92no—
148C3⋊D3—92no—
149C3⋊D3—182no—
150C3⋊D3—276no—
151C3⋊D3—2718no—
152C3⋊D3—276no—
153C3⋊D3—2718no—
154C3⋊D3—5418no—
155C3×D3—272no—
156C3×D3—276no—
157C2×C9—63no—
158C22×C3—811no—
159C2×D3—273no—
160C2×D3—271no—
161C2×D3—811no—
162C2×D3—819no—
163C2×D3—1621no—
164C3×C4—99no—
165C3×C4—93no—
166C3×C4—91no—
167C3×C4—811no—
168Dic3—31no—
169Dic3—91no—
170Dic3—279no—
171Dic3—273no—
172Dic3—271no—
173Dic3—811no—
174Dic3—1621no—
175C32—21no—
176C32—39no—
177C32—39no—
178C32—33no—
179C32—33no—
180C32—31no—
181C32—69no—
182C32—61no—
183C32—93no—
184C32((C3⋊D3)⋊C3)⋊C411yescharacteristic
185C32Dic3×C3⋊D311yescharacteristic
186C9—63no—
187C2×C4—2431noSylow
188C2×C3—31no—
189C2×C3—39no—
190C2×C3—61no—
191C2×C3—91no—
192C2×C3—181no—
193C2×C3—812no—
194C2×C3#4174⋊C213yes—
195C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
196D3—276no—
197D3—272no—
198D3—812no—
199D3—8118no—
200D3—1622no—
201C22—811no—
202C4—91no—
203C4—811no—
204C3—31no—
205C3—39no—
206C3—61no—
207C3—91no—
208C3—181no—
209C3#4175⋊C413yescomplemented
210C3#1061988311yescharacteristic
211C2—812no—
212C2#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⋊#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
14. C3×#1084D3semidirect
19. #66321D3semidirect
20. C3×AΣL(1,𝔽27)C2×C4semidirect
28. C3⋊(C3⋊(C3⋊D3))Dic3semidirect
53. #1084C3⋊D3semidirect
58. C34C2×Dic3semidirect
60. C3×H(3,𝔽3)C4×D3semidirect
62. AΣL(1,𝔽27)C4×D3semidirect
124. C33D3×Dic3semidirect
129. H(3,𝔽3)C4×C3⋊D3semidirect
209. 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
#106201443
#106199013
#4175⋊C43