Finite Group Databasebeta

← #14517706

Subgroups — #14517706

Order 1944.

430 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C22×C3×#732C211yesmaximal, characteristic, complemented
2C2×C3⋊#4179C211yesmaximal, characteristic, complemented
3C3⋊#66326C211yesmaximal, characteristic, complemented
4#10619992C311yesmaximal, characteristic, complemented
5#10619977—31nomaximal
6#10619650—33nomaximal
7C2×C3×#732—21no—
8C2×C3×#732C2211yescharacteristic
9C3⋊#4179—21no—
10C22×C3×H(3,𝔽3)—21no—
11C22×C3×H(3,𝔽3)D311yescharacteristic
12C22×C32×C9C2×C311yescharacteristic, complemented
13C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
14C2×C3⋊((C3⋊D3)⋊C3)—31no—
15C3⋊(C3⋊Dic9)C2×C311yescharacteristic, complemented
16C3⋊((C3⋊Dic3)⋊C3)—31no—
17C22×#732—23no—
18C22×#732D313yescomplemented
19C2×#4179—33no—
20#66326—33no—
21C3×#732D411yescharacteristic, complemented, Sylow
22#6312—31no—
23C3×#638—91no—
24#6233—33no—
25#6233—91no—
26#6233—92no—
27#638⋊C3—92no—
28#638⋊C3—91no—
29C2×C3×H(3,𝔽3)—22no—
30C2×C3×H(3,𝔽3)—21no—
31C2×C3×H(3,𝔽3)—21no—
32C2×C3×H(3,𝔽3)C2×D311yescharacteristic
33C2×C32×C9—21no—
34C2×C32×C9C22×C311yescharacteristic
35C3⋊(C3⋊D9)—21no—
36C3⋊((C3⋊D3)⋊C3)—61no—
37C2×#732—26no—
38C2×#732—23no—
39C2×#732—23no—
40C2×#732C2×D313yes—
41#4179—63no—
42C22×C33—31no—
43C22×C33—61no—
44C22×C33C3×D311yescharacteristic
45C2×C3⋊(C3⋊D3)—31no—
46C2×C3×C3⋊D3—91no—
47C3⋊(C3⋊Dic3)—31no—
48C3×C3⋊Dic3—91no—
49C22×H(3,𝔽3)—21no—
50C22×H(3,𝔽3)—23no—
51C22×H(3,𝔽3)—32no—
52C22×H(3,𝔽3)—62no—
53C22×H(3,𝔽3)C3⋊D311yescharacteristic
54C22×C3×C9—32no—
55C22×C3×C9—31no—
56C22×C3×C9C3×D313yescomplemented
57C2×C3⋊D9—33no—
58C2×C3⋊D9—91no—
59C2×C3⋊D9—92no—
60C2×(C3⋊D3)⋊C3—92no—
61C2×(C3⋊D3)⋊C3—91no—
62C3⋊Dic9—33no—
63C3⋊Dic9—91no—
64C3⋊Dic9—92no—
65(C3⋊Dic3)⋊C3—92no—
66(C3⋊Dic3)⋊C3—91no—
67C3×H(3,𝔽3)—21no—
68C3×H(3,𝔽3)#6711yescharacteristic
69C32×C9C3×D411yescharacteristic, complemented
70#732—23no—
71#732#6713yescomplemented
72#638—91no—
73#638—92no—
74#638—91no—
75#638—273no—
76C3×#67—271no—
77C3×#67—273no—
78#611—273no—
79C2×C33—21no—
80C2×C33—31no—
81C2×C33—61no—
82C2×C33—62no—
83C2×C33—61no—
84C2×C33C2×C3×D311yescharacteristic
85C3⋊(C3⋊D3)—61no—
86C3×C3⋊D3—181no—
87C2×H(3,𝔽3)—22no—
88C2×H(3,𝔽3)—26no—
89C2×H(3,𝔽3)—21no—
90C2×H(3,𝔽3)—21no—
91C2×H(3,𝔽3)—23no—
92C2×H(3,𝔽3)—32no—
93C2×H(3,𝔽3)—62no—
94C2×H(3,𝔽3)—64no—
95C2×H(3,𝔽3)—62no—
96C2×H(3,𝔽3)C2×C3⋊D311yescharacteristic
97C2×C3×C9—23no—
98C2×C3×C9—32no—
99C2×C3×C9—31no—
100C2×C3×C9—61no—
101C2×C3×C9—62no—
102C2×C3×C9C2×C3×D313yes—
103C3⋊D9—63no—
104C3⋊D9—181no—
105C3⋊D9—182no—
106(C3⋊D3)⋊C3—182no—
107(C3⋊D3)⋊C3—181no—
108C22×C32—33no—
109C22×C32—31no—
110C22×C32—61no—
111C22×C32—63no—
112C22×C32—93no—
113C22×C32—183no—
114C22×C32(C3⋊D3)⋊C312yes—
115C22×C32(C3⋊D3)⋊C311yescharacteristic
116C22×C32C3×C3⋊D311yescharacteristic
117C2×C3⋊D3—91no—
118C2×C3⋊D3—92no—
119C2×C3⋊D3—91no—
120C2×C3⋊D3—273no—
121C2×C3×D3—271no—
122C2×C3×D3—273no—
123C3⋊Dic3—91no—
124C3⋊Dic3—92no—
125C3⋊Dic3—91no—
126C3⋊Dic3—273no—
127C3×Dic3—271no—
128C3×Dic3—273no—
129C22×C9—33no—
130C2×D9—273no—
131Dic9—273no—
132C33—31no—
133C33—61no—
134C33C3×#6711yescharacteristic
135H(3,𝔽3)—21no—
136H(3,𝔽3)—23no—
137H(3,𝔽3)—32no—
138H(3,𝔽3)—62no—
139H(3,𝔽3)#63811yescharacteristic
140C3×C9—32no—
141C3×C9—31no—
142C3×C9C3×#6713yescomplemented
143C3×D4—811no—
144#67—273no—
145#67—271no—
146#67—812no—
147#67—811no—
148C2×C32—21no—
149C2×C32—22no—
150C2×C32—21no—
151C2×C32—33no—
152C2×C32—31no—
153C2×C32—63no—
154C2×C32—61no—
155C2×C32—62no—
156C2×C32—66no—
157C2×C32—61no—
158C2×C32—63no—
159C2×C32—93no—
160C2×C32—183no—
161C2×C32—186no—
162C2×C32—183no—
163C2×C32C2×(C3⋊D3)⋊C312yes—
164C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
165C2×C32C2×C3×C3⋊D311yescharacteristic
166C3⋊D3—181no—
167C3⋊D3—182no—
168C3⋊D3—181no—
169C3⋊D3—543no—
170C3×D3—541no—
171C3×D3—543no—
172C2×C9—33no—
173C2×C9—63no—
174D9—543no—
175C22×C3—32no—
176C22×C3—31no—
177C22×C3—91no—
178C22×C3—181no—
179C22×C3—183no—
180C22×C3—811no—
181C22×C3#417913yescomplemented
182C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
183C2×D3—273no—
184C2×D3—271no—
185C2×D3—812no—
186C2×D3—811no—
187C3×C4—811no—
188Dic3—273no—
189Dic3—271no—
190Dic3—812no—
191Dic3—811no—
192C32—33no—
193C32—31no—
194C32—61no—
195C32—63no—
196C32—93no—
197C32—183no—
198C32#638⋊C312yes—
199C32#638⋊C311yescharacteristic
200C32C3×#63811yescharacteristic
201C9—33no—
202D4—811noSylow
203C2×C3—23no—
204C2×C3—21no—
205C2×C3—32no—
206C2×C3—31no—
207C2×C3—62no—
208C2×C3—61no—
209C2×C3—91no—
210C2×C3—181no—
211C2×C3—182no—
212C2×C3—186no—
213C2×C3—181no—
214C2×C3—183no—
215C2×C3—1621no—
216C2×C3C2×#417913yes—
217C2×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
218D3—543no—
219D3—541no—
220D3—1622no—
221D3—1621no—
222C22—811no—
223C22C3⋊#417911yescharacteristic, complemented
224C4—811no—
225C3—32no—
226C3—31no—
227C3—91no—
228C3—181no—
229C3—183no—
230C3#1061965013yescomplemented
231C3#1061997711yescharacteristic
232C2—21no—
233C2—1621no—
234C2C2×C3⋊#417911yescharacteristic
subgroupG/H
centerC2C2×C3⋊#4179
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×C3×#732C2
socleC2×C32C2×(C3⋊D3)⋊C3
hypercenterC22C3⋊#4179
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×#732C2semidirect
2. C2×C3⋊#4179C2semidirect
3. C3⋊#66326C2semidirect
4. #10619992C3semidirect
12. C22×C32×C9C2×C3semidirect
13. C2×C3⋊(C3⋊D9)C2×C3semidirect
15. C3⋊(C3⋊Dic9)C2×C3semidirect
18. C22×#732D3semidirect
21. C3×#732D4semidirect
56. C22×C3×C9C3×D3semidirect
69. C32×C9C3×D4semidirect
71. #732#67semidirect
142. C3×C9C3×#67semidirect
181. C22×C3#4179semidirect
223. C22C3⋊#4179semidirect
230. C3#10619650semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7322
C2×C3⋊#41792
C3⋊#663262
#106199923
#106199773
#106196503