Finite Group Databasebeta

← #14517039

Subgroups — #14517039

Order 1944.

340 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊#4184C211yesmaximal, characteristic, complemented
2C2×C3×#4176C211yesmaximal, characteristic, complemented
3C3⋊#66324C211yesmaximal, characteristic, complemented
4#10619904—31nomaximal
5#10619879—31nomaximal
6#10619556—33nomaximal
7C2×C3×#731C2211yescharacteristic
8C3⋊#4184—21no—
9C3×#4176—21no—
10C2×C3⋊AGL(1,ℤ/9)—61no—
11C2×C3×#272D311yescharacteristic
12C2×C3⋊((C3⋊D3)⋊C3)—31no—
13C2×C3×C3⋊D9—31no—
14C2×C3×D3×C9—31no—
15C3⋊(C3⋊Dic9)D311yescharacteristic, complemented
16C3⋊((C3⋊Dic3)⋊C3)—31no—
17C2×#4184—33no—
18C2×#4184—63no—
19C2×#4176D313yescomplemented
20#66324—33no—
21C3×#731D411yescharacteristic, complemented, Sylow
22#6291—91no—
23#6290—91no—
24#6233—91no—
25#6200—91no—
26#6194—93no—
27C2×C3×3−1+2—21no—
28C2×C3×H(3,𝔽3)C2×D311yescharacteristic
29C2×C32×C9C2×D311yescharacteristic
30C3⋊AGL(1,ℤ/9)—62no—
31C3×#272—21no—
32C3⋊((C3⋊D3)⋊C3)—61no—
33C3×C3⋊D9—61no—
34C3×D3×C9—61no—
35C2×#731—23no—
36C2×#731C2×D313yes—
37#4184—66no—
38#4184—63no—
39#4176—23no—
40C2×C3⋊(C3⋊D3)—31no—
41C2×C3×C3⋊D3—91no—
42C2×C32×D3—31no—
43C2×C32×D3—91no—
44C3⋊(C3⋊Dic3)—31no—
45C3×C3⋊Dic3—91no—
46C22×C3×C9—91no—
47C2×#272C3⋊D311yescharacteristic
48C2×C3⋊D9—31no—
49C2×C3⋊D9—61no—
50C2×AGL(1,ℤ/9)—183no—
51C2×(C3⋊D3)⋊C3—91no—
52C2×(C3⋊D3)⋊C3—181no—
53C2×D3×C9—33no—
54C2×C3×D9—93no—
55C3⋊Dic9—33no—
56C3⋊Dic9—91no—
57C3⋊Dic9—181no—
58(C3⋊Dic3)⋊C3—91no—
59(C3⋊Dic3)⋊C3—181no—
60C3×3−1+2—21no—
61C3×H(3,𝔽3)#6711yescharacteristic
62C32×C9D1211yescharacteristic, complemented
63#731—23no—
64#731#6713yescomplemented
65#638—271no—
66#626—271no—
67#626—273no—
68#625—271no—
69#625—273no—
70#611—273no—
71C2×C33—31no—
72C2×C33D3211yescharacteristic
73C3⋊(C3⋊D3)—61no—
74C3×C3⋊D3—181no—
75C32×D3—61no—
76C32×D3—181no—
77C2×3−1+2—23no—
78C2×3−1+2—121no—
79C2×H(3,𝔽3)—21no—
80C2×H(3,𝔽3)—61no—
81C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
82C2×C3×C9—31no—
83C2×C3×C9—61no—
84C2×C3×C9—61no—
85C2×C3×C9—181no—
86C2×C3×C9D3213yes—
87#272—21no—
88C3⋊D9—61no—
89C3⋊D9—62no—
90AGL(1,ℤ/9)—186no—
91(C3⋊D3)⋊C3—182no—
92(C3⋊D3)⋊C3—181no—
93D3×C9—63no—
94C3×D9—183no—
95C22×C32—91no—
96C2×C3⋊D3—91no—
97C2×C3⋊D3—91no—
98C2×C3⋊D3—181no—
99C2×C3⋊D3—273no—
100C2×C3×D3—33no—
101C2×C3×D3—31no—
102C2×C3×D3—91no—
103C2×C3×D3—93no—
104C2×C3×D3—273no—
105C2×C3×D3—271no—
106C3⋊Dic3—91no—
107C3⋊Dic3—91no—
108C3⋊Dic3—181no—
109C3⋊Dic3—273no—
110C3×Dic3—271no—
111C3×Dic3—273no—
112C22×C9—93no—
113C2×D9—93no—
114C2×D9—183no—
115Dic9—273no—
116C33—31no—
117C33#62611yescharacteristic
1183−1+2—23no—
1193−1+2—121no—
120H(3,𝔽3)—21no—
121H(3,𝔽3)—61no—
122H(3,𝔽3)#63811yescharacteristic
123C3×C9—31no—
124C3×C9—61no—
125C3×C9—61no—
126C3×C9#62613yescomplemented
127#67—811no—
128#67—813no—
129#67—811no—
130D12—811no—
131C2×C32—21no—
132C2×C32—33no—
133C2×C32—31no—
134C2×C32—61no—
135C2×C32—93no—
136C2×C32—181no—
137C2×C32((C3⋊D3)⋊C3)⋊C211yescharacteristic
138C2×C32D3×C3⋊D311yescharacteristic
139C3⋊D3—181no—
140C3⋊D3—181no—
141C3⋊D3—182no—
142C3⋊D3—543no—
143C3×D3—63no—
144C3×D3—61no—
145C3×D3—181no—
146C3×D3—183no—
147C3×D3—543no—
148C3×D3—541no—
149C2×C9—33no—
150C2×C9—63no—
151C2×C9—183no—
152D9—183no—
153D9—186no—
154C22×C3—93no—
155C22×C3—91no—
156C22×C3—811no—
157C2×D3—31no—
158C2×D3—91no—
159C2×D3—273no—
160C2×D3—271no—
161C2×D3—811no—
162C2×D3—1621no—
163C3×C4—811no—
164Dic3—273no—
165Dic3—271no—
166Dic3—811no—
167Dic3—1621no—
168C32—21no—
169C32—33no—
170C32—31no—
171C32—61no—
172C32—93no—
173C32#620011yescharacteristic
174C32#629111yescharacteristic
175C9—33no—
176C9—63no—
177D4—2431noSylow
178C2×C3—31no—
179C2×C3—61no—
180C2×C3—91no—
181C2×C3—183no—
182C2×C3—181no—
183C2×C3—181no—
184C2×C3—1621no—
185C2×C3#4176⋊C213yes—
186C2×C3((C3⋊D3)⋊C3)⋊D311yescharacteristic
187D3—61no—
188D3—181no—
189D3—543no—
190D3—541no—
191D3—1621no—
192D3—1622no—
193C22—91no—
194C22—811no—
195C4—811no—
196C3—31no—
197C3—61no—
198C3—91no—
199C3—181no—
200C3#1061955613yescomplemented
201C3#1061988611yescharacteristic
202C2—181no—
203C2—1621no—
204C2#1175773811yescharacteristic
subgroupG/H
center, hypercenterC2#11757738
commutator, Fitting, cosocleC2×C3×#731C22
FrattiniC2×C32D3×C3⋊D3
socleC2×C32((C3⋊D3)⋊C3)⋊C2
hypocenterC3×#731D4
LCSG ▷ C2×C3×#731 ▷ C3×#731
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4184C2semidirect
2. C2×C3×#4176C2semidirect
3. C3⋊#66324C2semidirect
15. C3⋊(C3⋊Dic9)D3semidirect
19. C2×#4176D3semidirect
21. C3×#731D4semidirect
62. C32×C9D12semidirect
64. #731#67semidirect
126. C3×C9#626semidirect
200. C3#10619556semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41842
C2×C3×#41762
C3⋊#663242
#106199043
#106198793
#106195563