Finite Group Databasebeta

← #14516912

Subgroups — #14516912

Order 1944.

264 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 38 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⋊#4179C211yesmaximal, characteristic, complemented
2C2×D3×#732C211yesmaximal, characteristic, complemented
3C3×#66326C211yesmaximal, characteristic, complemented
4#10619880C311yesmaximal, characteristic, complemented
5#6291⋊C3—31nomaximal
6#10619650—31nomaximal
7C2×C3×#732C2211yescharacteristic
8C3⋊#4179—21no—
9D3×#732—21no—
10C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
11C2×C3⋊((C3⋊D3)⋊C3)—31no—
12C2×D3×H(3,𝔽3)—21no—
13C2×D3×H(3,𝔽3)D311yescharacteristic
14C2×C3×D3×C9C2×C311yescharacteristic, complemented
15C3×C3⋊Dic9C2×C311yescharacteristic, complemented
16C3×(C3⋊Dic3)⋊C3—31no—
17C22×#732—31no—
18C2×#4179—31no—
19C2×#4179—61no—
20#66326—21no—
21#66326D311yescharacteristic, complemented
22C3×#732D411yescharacteristic, complemented, Sylow
23#6291—31no—
24C3×#626—91no—
25#6233—31no—
26#638⋊C3—91no—
27#6195—91no—
28C2×C3×H(3,𝔽3)—21no—
29C2×C3×H(3,𝔽3)C2×D311yescharacteristic
30C2×C32×C9C22×C311yescharacteristic
31C3⋊(C3⋊D9)—21no—
32C3⋊((C3⋊D3)⋊C3)—61no—
33D3×H(3,𝔽3)—22no—
34D3×H(3,𝔽3)—21no—
35C3×D3×C9—21no—
36C2×#732—21no—
37C2×#732—21no—
38C2×#732—41no—
39C2×#732—61no—
40C2×#732C2×D311yescharacteristic
41#4179—62no—
42#4179—61no—
43C2×C3⋊(C3⋊D3)—31no—
44C2×C3×C3⋊D3—91no—
45C2×C32×D3—31no—
46C2×C32×D3—61no—
47C2×C32×D3C3×D311yescharacteristic
48C3×C3⋊Dic3—31no—
49C32×Dic3—91no—
50C22×H(3,𝔽3)—31no—
51C22×H(3,𝔽3)—61no—
52C22×C3×C9—31no—
53C2×C3⋊D9—31no—
54C2×C3⋊D9—61no—
55C2×C3⋊D9—91no—
56C2×C3⋊D9—181no—
57C2×(C3⋊D3)⋊C3—91no—
58C2×(C3⋊D3)⋊C3—181no—
59C2×D3×C9—31no—
60C3⋊Dic9C3×D311yescharacteristic, complemented
61(C3⋊Dic3)⋊C3—31no—
62(C3⋊Dic3)⋊C3—61no—
63C3×Dic9—91no—
64C3×H(3,𝔽3)—21no—
65C3×H(3,𝔽3)#6711yescharacteristic
66C32×C9C3×D411yescharacteristic, complemented
67#732—21no—
68#732—21no—
69#732—41no—
70#732D1211yescharacteristic, complemented
71#638—91no—
72C3×#67—271no—
73C3×D12—271no—
74#626—91no—
75#626—271no—
76#611—271no—
77C2×C33—31no—
78C2×C33—61no—
79C2×C33C2×C3×D311yescharacteristic
80C3⋊(C3⋊D3)—61no—
81C3×C3⋊D3—181no—
82C32×D3—21no—
83C32×D3—61no—
84C32×D3—62no—
85C2×H(3,𝔽3)—21no—
86C2×H(3,𝔽3)—21no—
87C2×H(3,𝔽3)—41no—
88C2×H(3,𝔽3)—61no—
89C2×H(3,𝔽3)—62no—
90C2×H(3,𝔽3)—61no—
91C2×H(3,𝔽3)—121no—
92C2×H(3,𝔽3)D3211yescharacteristic
93C2×C3×C9—21no—
94C2×C3×C9—31no—
95C2×C3×C9—61no—
96C2×C3×C9—61no—
97C2×C3×C9C2×C3×D311yescharacteristic
98C3⋊D9—62no—
99C3⋊D9—61no—
100C3⋊D9—181no—
101C3⋊D9—182no—
102(C3⋊D3)⋊C3—182no—
103(C3⋊D3)⋊C3—181no—
104D3×C9—61no—
105C22×C32—31no—
106C22×C32—91no—
107C22×C32—181no—
108C2×C3⋊D3—91no—
109C2×C3⋊D3—91no—
110C2×C3⋊D3—181no—
111C2×C3⋊D3—271no—
112C2×C3⋊D3—541no—
113C2×C3×D3—31no—
114C2×C3×D3—91no—
115C2×C3×D3—181no—
116C2×C3×D3—271no—
117C2×C3×D3—271no—
118C2×C3×D3—541no—
119C2×C3×D3(C3⋊D3)⋊C311yescharacteristic
120C32×C4—271no—
121C3⋊Dic3—31no—
122C3×Dic3—91no—
123C3×Dic3—91no—
124C3×Dic3—181no—
125C3×Dic3—271no—
126C22×C9—91no—
127C2×D9—271no—
128C2×D9—541no—
129Dic9—91no—
130C33—31no—
131C33—61no—
132C33C3×#6711yescharacteristic
133H(3,𝔽3)—21no—
134H(3,𝔽3)—21no—
135H(3,𝔽3)—41no—
136H(3,𝔽3)—61no—
137H(3,𝔽3)—121no—
138H(3,𝔽3)#62611yescharacteristic
139C3×C9—21no—
140C3×C9—31no—
141C3×C9—61no—
142C3×C9C3×D1211yescharacteristic, complemented
143C3×D4—811no—
144#67—271no—
145#67—811no—
146D12—271no—
147C2×C32—21no—
148C2×C32—31no—
149C2×C32—31no—
150C2×C32—61no—
151C2×C32—61no—
152C2×C32—61no—
153C2×C32—61no—
154C2×C32—91no—
155C2×C32—121no—
156C2×C32—181no—
157C2×C32—181no—
158C2×C32—182no—
159C2×C32—181no—
160C2×C32—361no—
161C2×C32C2×(C3⋊D3)⋊C311yescharacteristic
162C2×C32C3×D3211yescharacteristic
163C3⋊D3—181no—
164C3⋊D3—182no—
165C3⋊D3—181no—
166C3⋊D3—541no—
167C3⋊D3—542no—
168C3×D3—21no—
169C3×D3—61no—
170C3×D3—181no—
171C3×D3—182no—
172C3×D3—541no—
173C3×D3—541no—
174C3×D3—542no—
175C2×C9—31no—
176C2×C9—61no—
177C2×C9—181no—
178D9—541no—
179D9—542no—
180C22×C3—31no—
181C22×C3—91no—
182C22×C3—271no—
183C22×C3—541no—
184C22×C3—811no—
185C2×D3—271no—
186C2×D3—271no—
187C2×D3—541no—
188C2×D3—811no—
189C2×D3—1621no—
190C2×D3#417911yescharacteristic, complemented
191C3×C4—271no—
192C3×C4—271no—
193C3×C4—541no—
194Dic3—91no—
195Dic3—271no—
196C32—21no—
197C32—31no—
198C32—31no—
199C32—61no—
200C32—61no—
201C32—61no—
202C32—91no—
203C32—121no—
204C32—181no—
205C32—181no—
206C32—361no—
207C32#638⋊C311yescharacteristic
208C32C3×#62611yescharacteristic
209C9—31no—
210C9—61no—
211D4—811noSylow
212C2×C3—21no—
213C2×C3—31no—
214C2×C3—61no—
215C2×C3—61no—
216C2×C3—91no—
217C2×C3—181no—
218C2×C3—181no—
219C2×C3—181no—
220C2×C3—361no—
221C2×C3—541no—
222C2×C3—542no—
223C2×C3—1621no—
224C2×C3C2×#417911yescharacteristic
225C2×C3D3×(C3⋊D3)⋊C311yescharacteristic
226D3—21no—
227D3—542no—
228D3—541no—
229D3—541no—
230D3—1621no—
231D3—1622no—
232C22—31no—
233C22—811no—
234C4—271no—
235C3—21no—
236C3—31no—
237C3—61no—
238C3—91no—
239C3—181no—
240C3—181no—
241C3—361no—
242C3#1061965011yescharacteristic, complemented
243C3#6291⋊C311yescharacteristic
244C2—61no—
245C2—1621no—
246C2D3×#417911yescharacteristic
subgroupG/H
center, hypercenterC2D3×#4179
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C32C3×D32
FittingC2×C3×#732C22
socleC2×C32C2×(C3⋊D3)⋊C3
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#4179C2semidirect
2. C2×D3×#732C2semidirect
3. C3×#66326C2semidirect
4. #10619880C3semidirect
10. C2×C3⋊(C3⋊D9)C2×C3semidirect
14. C2×C3×D3×C9C2×C3semidirect
15. C3×C3⋊Dic9C2×C3semidirect
21. #66326D3semidirect
22. C3×#732D4semidirect
60. C3⋊Dic9C3×D3semidirect
66. C32×C9C3×D4semidirect
70. #732D12semidirect
142. C3×C9C3×D12semidirect
190. C2×D3#4179semidirect
242. C3#10619650semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#41792
C2×D3×#7322
C3×#663262
#106198803
#6291⋊C33
#106196503