Finite Group Databasebeta

← C3×D3×C22⋊H(3,𝔽3) #14519246

Subgroups — C3×D3×C22⋊H(3,𝔽3) #14519246

Order 1944.

1088 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C32×C22⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C22×C33×D3C311yesmaximal, characteristic, complemented
3C32×D3×A4C313yesmaximal, complemented
4C2×C3×C22⋊H(3,𝔽3)—31nomaximal
5D3×C22⋊H(3,𝔽3)C319yesmaximal, direct product factor
6C3×D3×H(3,𝔽3)—41nomaximal
7C22×C34C2×C311yescharacteristic, complemented
8C2×C33×D3—31no—
9C2×C33×D3—31no—
10C33×A4C2×C313yescomplemented
11C3×C22⋊H(3,𝔽3)—21no—
12C3×C22⋊H(3,𝔽3)—23no—
13C3×C22⋊H(3,𝔽3)—29no—
14C3×C22⋊H(3,𝔽3)D311yescharacteristic, direct product factor
15C3×C22⋊H(3,𝔽3)C2×C319yescomplemented
16C32×H(3,𝔽3)—41noSylow
17C23×C33—31no—
18C22×C32×D3—33no—
19C22×C32×D3C3211yescharacteristic
20C22×C32×D3C3213yescomplemented
21C2×C32×A4—33no—
22C3×D3×A4—39no—
23C3×D3×A4C3219yescomplemented
24C2×C22⋊H(3,𝔽3)—39no—
25C2×C34—31no—
26C33×D3—31no—
27C33×D3—43no—
28C33×D3A411yescharacteristic, complemented
29C2×C3×H(3,𝔽3)—121no—
30D3×H(3,𝔽3)—49no—
31C22×C33—21no—
32C22×C33—23no—
33C22×C33—33no—
34C22×C33—63no—
35C22×C33—91no—
36C22×C33—91no—
37C22×C33C3×D311yescharacteristic, complemented
38C22×C33C2×C3211yescharacteristic
39C22×C33C2×C3213yescomplemented
40C2×C32×D3—39no—
41C2×C32×D3—39no—
42C2×C32×D3—31no—
43C2×C32×D3—33no—
44C2×C32×D3—31no—
45C2×C32×D3—33no—
46C32×A4—23no—
47C32×A4—29no—
48C32×A4—39no—
49C32×A4—69no—
50C32×A4C3×D313yescomplemented
51C32×A4C2×C3219yescomplemented
52C22⋊H(3,𝔽3)—29no—
53C22⋊H(3,𝔽3)—227no—
54C22⋊H(3,𝔽3)C3×D319yesdirect product factor
55C34—43no—
56C34C2×A411yescharacteristic, complemented
57C3×H(3,𝔽3)—41no—
58C3×H(3,𝔽3)—49no—
59C3×H(3,𝔽3)—89no—
60C3×H(3,𝔽3)—83no—
61C3×H(3,𝔽3)—81no—
62C23×C32—31no—
63C23×C32—33no—
64C23×C32—93no—
65C22×C3×D3—33no—
66C22×C3×D3H(3,𝔽3)13yescomplemented
67C22×C3×D3C3311yescharacteristic
68C2×C3×A4—39no—
69C2×C3×A4—99no—
70D3×A4—39no—
71C2×C33—31no—
72C2×C33—39no—
73C2×C33—31no—
74C2×C33—33no—
75C2×C33—31no—
76C2×C33—61no—
77C2×C33—63no—
78C2×C33—69no—
79C2×C33—91no—
80C2×C33—123no—
81C32×D3—39no—
82C32×D3—31no—
83C32×D3—33no—
84C32×D3—33no—
85C32×D3—49no—
86C32×D3—129no—
87C32×D3C3×A411yescharacteristic
88C32×D3C3×A413yescomplemented
89C2×H(3,𝔽3)—129no—
90C22×C32—23no—
91C22×C32—21no—
92C22×C32—23no—
93C22×C32—33no—
94C22×C32—33no—
95C22×C32—69no—
96C22×C32—63no—
97C22×C32—63no—
98C22×C32—91no—
99C22×C32—93no—
100C22×C32—91no—
101C22×C32—93no—
102C22×C32—99no—
103C22×C32—99no—
104C22×C32C2×H(3,𝔽3)13yescomplemented
105C22×C32C32×D311yescharacteristic
106C22×C32C32×D313yescomplemented
107C22×C32C2×C3311yescharacteristic
108C2×C3×D3—39no—
109C2×C3×D3—39no—
110C2×C3×D3—33no—
111C2×C3×D3—31no—
112C2×C3×D3—33no—
113C2×C3×D3—31no—
114C3×A4—29no—
115C3×A4—39no—
116C3×A4—39no—
117C3×A4—627no—
118C3×A4—69no—
119C3×A4—69no—
120C3×A4C32×D319yescomplemented
121C33—21no—
122C33—23no—
123C33—33no—
124C33—43no—
125C33—49no—
126C33—63no—
127C33—89no—
128C33—83no—
129C33—129no—
130C33—249no—
131C33D3×A411yescharacteristic, complemented
132C33C2×C3×A411yescharacteristic
133C33C2×C3×A413yescomplemented
134H(3,𝔽3)—49no—
135H(3,𝔽3)—827no—
136H(3,𝔽3)—89no—
137C23×C3—33no—
138C23×C3—31no—
139C23×C3—93no—
140C22×D3C3×H(3,𝔽3)11yescharacteristic, complemented
141C2×A4—99no—
142C2×C32—39no—
143C2×C32—31no—
144C2×C32—31no—
145C2×C32—33no—
146C2×C32—39no—
147C2×C32—33no—
148C2×C32—31no—
149C2×C32—33no—
150C2×C32—61no—
151C2×C32—63no—
152C2×C32—63no—
153C2×C32—69no—
154C2×C32—627no—
155C2×C32—69no—
156C2×C32—93no—
157C2×C32—99no—
158C2×C32—91no—
159C2×C32—93no—
160C2×C32—129no—
161C2×C32—369no—
162C3×D3—39no—
163C3×D3—33no—
164C3×D3—31no—
165C3×D3—33no—
166C3×D3—129no—
167C3×D3C22⋊H(3,𝔽3)13yesdirect product factor
168C3×D3C32×A411yescharacteristic
169C22×C3—23no—
170C22×C3—21no—
171C22×C3—33no—
172C22×C3—63no—
173C22×C3—91no—
174C22×C3—93no—
175C22×C3—91no—
176C22×C3—93no—
177C22×C3—99no—
178C22×C3—99no—
179C22×C3D3×H(3,𝔽3)13yescomplemented
180C22×C3C2×C3×H(3,𝔽3)11yescharacteristic, complemented
181C22×C3C33×D311yescharacteristic
182C2×D3—31no—
183C2×D3—31no—
184A4—39no—
185A4—69no—
186C32—21no—
187C32—23no—
188C32—23no—
189C32—33no—
190C32—33no—
191C32—49no—
192C32—63no—
193C32—69no—
194C32—63no—
195C32—89no—
196C32—129no—
197C32—129no—
198C32—249no—
199C32—2427no—
200C32—249no—
201C32C2×C22⋊H(3,𝔽3)13yescomplemented
202C32C3×D3×A411yescharacteristic
203C32C3×D3×A413yescomplemented
204C32C2×C32×A411yescharacteristic
205C23—31noSylow
206C2×C3—39no—
207C2×C3—31no—
208C2×C3—31no—
209C2×C3—33no—
210C2×C3—33no—
211C2×C3—31no—
212C2×C3—63no—
213C2×C3—61no—
214C2×C3—69no—
215C2×C3—93no—
216C2×C3—99no—
217C2×C3—91no—
218C2×C3—93no—
219C2×C3—369no—
220D3—31no—
221D3C3×C22⋊H(3,𝔽3)11yescharacteristic, direct product factor
222C22—91no—
223C22—91no—
224C22C3×D3×H(3,𝔽3)11yescharacteristic, complemented
225C3—23no—
226C3—21no—
227C3—33no—
228C3—63no—
229C3—129no—
230C3—249no—
231C3D3×C22⋊H(3,𝔽3)13yesdirect product factor
232C3C2×C3×C22⋊H(3,𝔽3)11yescharacteristic, complemented
233C3C32×D3×A411yescharacteristic
234C2—31no—
235C2—31no—
236C2—91no—
subgroupG/H
centerC32C3×D3×A4
commutator, cosocleC22×C32C2×C33
FrattiniC3C32×D3×A4
FittingC22×C34C2×C3
socleC22×C33C2×C32
hypercenterC33D3×A4
hypocenterC22×C3C2×C3×H(3,𝔽3)
LCSG ▷ C22×C32 ▷ C22×C3
UCSC1 ◁ C32 ◁ C33

Complements

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

NH ≅ G/Ntype
1. C32×C22⋊H(3,𝔽3)C2semidirect
2. C22×C33×D3C3semidirect
3. C32×D3×A4C3semidirect
5. D3×C22⋊H(3,𝔽3)C3direct (N × H)
7. C22×C34C2×C3semidirect
10. C33×A4C2×C3semidirect
14. C3×C22⋊H(3,𝔽3)D3direct (N × H)
15. C3×C22⋊H(3,𝔽3)C2×C3semidirect
20. C22×C32×D3C32semidirect
23. C3×D3×A4C32semidirect
28. C33×D3A4semidirect
37. C22×C33C3×D3semidirect
39. C22×C33C2×C32semidirect
50. C32×A4C3×D3semidirect
51. C32×A4C2×C32semidirect
54. C22⋊H(3,𝔽3)C3×D3direct (N × H)
56. C34C2×A4semidirect
66. C22×C3×D3H(3,𝔽3)semidirect
88. C32×D3C3×A4semidirect
104. C22×C32C2×H(3,𝔽3)semidirect
106. C22×C32C32×D3semidirect
120. C3×A4C32×D3semidirect
131. C33D3×A4semidirect
133. C33C2×C3×A4semidirect
140. C22×D3C3×H(3,𝔽3)semidirect
167. C3×D3C22⋊H(3,𝔽3)direct (N × H)
179. C22×C3D3×H(3,𝔽3)semidirect
180. C22×C3C2×C3×H(3,𝔽3)semidirect
201. C32C2×C22⋊H(3,𝔽3)semidirect
203. C32C3×D3×A4semidirect
221. D3C3×C22⋊H(3,𝔽3)direct (N × H)
224. C22C3×D3×H(3,𝔽3)semidirect
231. C3D3×C22⋊H(3,𝔽3)direct (N × H)
232. C3C2×C3×C22⋊H(3,𝔽3)semidirect

Maximal subgroups

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

subgroupindex
C32×C22⋊H(3,𝔽3)2
C22×C33×D33
C32×D3×A43
C2×C3×C22⋊H(3,𝔽3)3
D3×C22⋊H(3,𝔽3)3
C3×D3×H(3,𝔽3)4