Finite Group Databasebeta

← (#66365⋊C2)⋊C3 #14518074

Subgroups — (#66365⋊C2)⋊C3 #14518074

Order 1944.

252 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 28 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
1#11757850C211yesmaximal, characteristic, complemented
2C3×(C3⋊S4)⋊C3—31nomaximal
3C3×((C22⋊C9)⋊C2)⋊C3—31nomaximal
4C3×((C22⋊C9)⋊C2)⋊C3—31nomaximal
5C3×#611⋊C3—31nomaximal
6#66365⋊C2C311yesmaximal, characteristic, complemented
7#4184⋊C3—41nomaximal
8C22×C3×3−1+2D311yescharacteristic, complemented
9C2×C3×AGL(1,ℤ/9)—31no—
10C3×C22⋊H(3,𝔽3)D311yescharacteristic
11C3×#1094D311yescharacteristic, complemented
12C3×#1094D311yescharacteristic, complemented
13C3×3−1+2⋊C4—31no—
14#66365—21no—
15#66365—21no—
16#66365—21no—
17#66365—21no—
18#66365C2×C311yescharacteristic, complemented
19#6910—41noSylow
20C3×C3⋊S4—31no—
21C32×#67—91no—
22(C3⋊S4)⋊C3—31no—
23(C3⋊S4)⋊C3—31no—
24(C3⋊S4)⋊C3—31no—
25C3×(C22⋊C9)⋊C2—31no—
26C3×(C22⋊C9)⋊C2—31no—
27((C22⋊C9)⋊C2)⋊C3—31no—
28((C22⋊C9)⋊C2)⋊C3—31no—
29((C22⋊C9)⋊C2)⋊C3—31no—
30((C22⋊C9)⋊C2)⋊C3—31no—
31((C22⋊C9)⋊C2)⋊C3—31no—
32((C22⋊C9)⋊C2)⋊C3—31no—
33#611⋊C3—31no—
34#611⋊C3—31no—
35#611⋊C3—31no—
36C3×#611—31no—
37C2×C3×3−1+2—31no—
38C3×AGL(1,ℤ/9)—61no—
39C3×AGL(1,ℤ/9)—121no—
40C3×AGL(1,ℤ/9)—121no—
41C3×(C3⋊D3)⋊C3—121no—
42#4184—41no—
43C22×C33C3⋊D311yescharacteristic
44C2×C32×D3—91no—
45C32×A4—31no—
46C32×Dic3—91no—
47C22×3−1+2—21no—
48C22×3−1+2—31no—
49C22×3−1+2—31no—
50C22×3−1+2C3×D311yescharacteristic, complemented
51C22×C3×C9—31no—
52C2×AGL(1,ℤ/9)—31no—
53C2×AGL(1,ℤ/9)—31no—
54C2×AGL(1,ℤ/9)—31no—
55C2×C3×D9—31no—
56C22⋊H(3,𝔽3)—21no—
57C22⋊H(3,𝔽3)—31no—
58C22⋊H(3,𝔽3)—31no—
59C22⋊H(3,𝔽3)C3×D311yescharacteristic
60#1094—21no—
61#1094—31no—
62#1094—31no—
63#1094—31no—
64#1094—31no—
65#1094—31no—
66#1094C3×D311yescharacteristic, complemented
67C3×C22⋊C9—21no—
68C3×C22⋊C9—31no—
69C3×C22⋊C9C3×D311yescharacteristic, complemented
703−1+2⋊C4—31no—
713−1+2⋊C4—31no—
723−1+2⋊C4—31no—
73C3×Dic9—31no—
74C3×3−1+2—41no—
75C3×3−1+2—41no—
76C3×3−1+2S411yescharacteristic, complemented
77C3×H(3,𝔽3)—41no—
78#731—41no—
79#731—81no—
80#731—81no—
81#731—81no—
82#731—81no—
83C3⋊S4—31no—
84C3×S4—271no—
85C32×D4—271no—
86C3×#67—91no—
87C3×#67—91no—
88C3×#67—91no—
89C3×#67—91no—
90(C22⋊C9)⋊C2—31no—
91(C22⋊C9)⋊C2—31no—
92#611—31no—
93C2×C33—31no—
94C3×C3⋊D3—121no—
95C32×D3—181no—
96C2×3−1+2—31no—
97C2×3−1+2—31no—
98C2×3−1+2—31no—
99C2×3−1+2—61no—
100C2×3−1+2—61no—
101C2×3−1+2—61no—
102C2×C3×C9—31no—
103C2×C3×C9—61no—
104AGL(1,ℤ/9)—61no—
105AGL(1,ℤ/9)—61no—
106AGL(1,ℤ/9)—61no—
107AGL(1,ℤ/9)—121no—
108AGL(1,ℤ/9)—121no—
109AGL(1,ℤ/9)—121no—
110AGL(1,ℤ/9)—121no—
111AGL(1,ℤ/9)—121no—
112AGL(1,ℤ/9)—121no—
113(C3⋊D3)⋊C3—121no—
114(C3⋊D3)⋊C3—121no—
115(C3⋊D3)⋊C3—121no—
116C3×D9—61no—
117C3×D9—121no—
118C3×D9—121no—
119C22×C32—91no—
120C22×C32—271no—
121C22×C32#27211yescharacteristic
122C22×C32#27211yescharacteristic
123C22×C32#27211yescharacteristic
124C22×C32C3×C3⋊D311yescharacteristic
125C2×C3×D3—91no—
126C2×C3×D3—91no—
127C2×C3×D3—91no—
128C2×C3×D3—91no—
129C3×A4—31no—
130C3×A4—61no—
131C3×A4—91no—
132C3×A4—181no—
133C32×C4—271no—
134C3×Dic3—91no—
135C3×Dic3—91no—
136C3×Dic3—91no—
137C3×Dic3—91no—
138C22×C9—31no—
139C22×C9—61no—
140C2×D9—31no—
141C22⋊C9—31no—
142C22⋊C9—31no—
143C22⋊C9—61no—
144C22⋊C9—61no—
145Dic9—31no—
146C33—121no—
147C33C3⋊S411yescharacteristic
1483−1+2—21no—
1493−1+2—31no—
1503−1+2—31no—
1513−1+2—41no—
1523−1+2—81no—
1533−1+2—121no—
1543−1+2—121no—
1553−1+2—121no—
1563−1+2—121no—
1573−1+2—121no—
1583−1+2C3×S411yescharacteristic, complemented
159H(3,𝔽3)—41no—
160H(3,𝔽3)—81no—
161H(3,𝔽3)—121no—
162H(3,𝔽3)—121no—
163C3×C9—31no—
164C3×C9—41no—
165C3×C9—81no—
166C3×C9—121no—
167S4—271no—
168C3×D4—271no—
169C3×D4—271no—
170C3×D4—271no—
171C3×D4—271no—
172#67—91no—
173C2×C32—31no—
174C2×C32—31no—
175C2×C32—31no—
176C2×C32—31no—
177C2×C32—91no—
178C2×C32—181no—
179C2×C32—541no—
180C3⋊D3—121no—
181C3×D3—181no—
182C3×D3—181no—
183C3×D3—181no—
184C3×D3—181no—
185C3×D3—1081no—
186C2×C9—31no—
187C2×C9—61no—
188C2×C9—61no—
189C2×C9—61no—
190C2×C9—61no—
191D9—61no—
192D9—121no—
193D9—121no—
194C22×C3—31no—
195C22×C3—31no—
196C22×C3—31no—
197C22×C3—31no—
198C22×C3—271no—
199C22×C3—271no—
200C22×C3—271no—
201C22×C3—271no—
202C22×C3C3×#27211yescharacteristic
203C2×D3—91no—
204A4—91no—
205A4—181no—
206C3×C4—271no—
207C3×C4—271no—
208C3×C4—271no—
209C3×C4—271no—
210Dic3—91no—
211C32—91no—
212C32—121no—
213C32—241no—
214C32—361no—
215C32—721no—
216C32#625811yescharacteristic
217C32#625811yescharacteristic
218C32#625811yescharacteristic
219C32C3×C3⋊S411yescharacteristic
220C9—31no—
221C9—61no—
222C9—121no—
223C9—121no—
224C9—241no—
225C9—241no—
226D4—271noSylow
227C2×C3—31no—
228C2×C3—31no—
229C2×C3—61no—
230C2×C3—91no—
231C2×C3—91no—
232C2×C3—91no—
233C2×C3—541no—
234C2×C3—541no—
235C2×C3—541no—
236C2×C3—541no—
237D3—181no—
238D3—1081no—
239C22—271no—
240C22#4184⋊C311yescharacteristic, complemented
241C4—271no—
242C3—31no—
243C3—31no—
244C3—31no—
245C3—31no—
246C3—361no—
247C3—721no—
248C3C3×#625811yescharacteristic
249C2—31no—
250C2—541no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenter#66365C2×C3
FrattiniC32C3×C3⋊S4
FittingC22×C3×3−1+2D3
socleC22×C3C3×#272
LCSG ▷ #66365
UCSC1

Complements

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

NH ≅ G/Ntype
1. #11757850C2semidirect
6. #66365⋊C2C3semidirect
8. C22×C3×3−1+2D3semidirect
11. C3×#1094D3semidirect
12. C3×#1094D3semidirect
18. #66365C2×C3semidirect
50. C22×3−1+2C3×D3semidirect
66. #1094C3×D3semidirect
69. C3×C22⋊C9C3×D3semidirect
76. C3×3−1+2S4semidirect
158. 3−1+2C3×S4semidirect
240. C22#4184⋊C3semidirect

Maximal subgroups

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

subgroupindex
#117578502
C3×(C3⋊S4)⋊C33
C3×((C22⋊C9)⋊C2)⋊C33
C3×#611⋊C33
#66365⋊C23
#4184⋊C34