Finite Group Databasebeta

← C3×C3⋊((C3⋊D3)⋊A4) #14519266

Subgroups — C3×C3⋊((C3⋊D3)⋊A4) #14519266

Order 1944.

968 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 968 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×C3⋊(C3⋊D3)C311yesmaximal, characteristic, complemented
3C3×A4×C3⋊D3—31nomaximal
4C3⋊((C3⋊D3)⋊A4)C313yesmaximal, direct product factor
5C3×(C3⋊D3)⋊A4—33nomaximal
6C3×C3⋊((C3⋊D3)⋊C3)—41nomaximal
7C22×C34C2×C311yescharacteristic, complemented
8C2×C3×C3⋊(C3⋊D3)—31no—
9C2×C3×C3⋊(C3⋊D3)—31no—
10C33×A4—21no—
11C33×A4D311yescharacteristic, complemented
12C3×C22⋊H(3,𝔽3)—23no—
13C3×C22⋊H(3,𝔽3)—23no—
14C3×C22⋊H(3,𝔽3)—29no—
15C3×C22⋊H(3,𝔽3)D313yescomplemented
16C3×C22⋊H(3,𝔽3)C2×C313yescomplemented
17C32×H(3,𝔽3)—41noSylow
18C22×C3⋊(C3⋊D3)C3211yescharacteristic, complemented
19C22×C3×C3⋊D3—31no—
20C22×C3×C3⋊D3—33no—
21C22×C3×C3⋊D3—93no—
22A4×C3⋊D3—33no—
23C3×D3×A4—93no—
24C3×D3×A4—91no—
25(C3⋊D3)⋊A4—39no—
26C2×C34—31no—
27C3×C3⋊(C3⋊D3)—31no—
28C3×C3⋊(C3⋊D3)A411yescharacteristic, complemented
29C32×C3⋊D3—121no—
30C3⋊((C3⋊D3)⋊C3)—43no—
31C3×(C3⋊D3)⋊C3—123no—
32C22×C33—21no—
33C22×C33—23no—
34C22×C33—33no—
35C22×C33—63no—
36C22×C33C3×D311yescharacteristic
37C22×C33C3×D313yescomplemented
38C22×C33C2×C3211yescharacteristic, complemented
39C2×C3⋊(C3⋊D3)—31no—
40C2×C3⋊(C3⋊D3)—31no—
41C2×C3×C3⋊D3—91no—
42C2×C3×C3⋊D3—93no—
43C2×C3×C3⋊D3—99no—
44C2×C3×C3⋊D3—99no—
45C2×C3×C3⋊D3—91no—
46C2×C3×C3⋊D3—93no—
47C32×A4—26no—
48C32×A4—23no—
49C32×A4—21no—
50C32×A4—23no—
51C32×A4—23no—
52C32×A4—33no—
53C32×A4—63no—
54C32×A4—66no—
55C32×A4—63no—
56C32×A4C3×D313yescomplemented
57C32×A4C3⋊D311yescharacteristic, complemented
58C22⋊H(3,𝔽3)—218no—
59C22⋊H(3,𝔽3)—29no—
60C22⋊H(3,𝔽3)—29no—
61C22⋊H(3,𝔽3)C3×D319yescomplemented
62C34—41no—
63C34—81no—
64C34C2×A411yescharacteristic, complemented
65C3×H(3,𝔽3)—43no—
66C3×H(3,𝔽3)—43no—
67C3×H(3,𝔽3)—89no—
68C3×H(3,𝔽3)—83no—
69C3×H(3,𝔽3)—83no—
70C22×C3⋊D3—31no—
71C22×C3⋊D3—33no—
72C22×C3⋊D3—93no—
73C22×C3×D3—93no—
74C22×C3×D3—91no—
75C22×C3×D3—273no—
76C2×C3×A4—271no—
77D3×A4—99no—
78D3×A4—93no—
79C2×C33—31no—
80C2×C33—39no—
81C2×C33—31no—
82C2×C33—33no—
83C2×C33—61no—
84C2×C33—63no—
85C2×C33—69no—
86C3⋊(C3⋊D3)—31no—
87C3⋊(C3⋊D3)C3×A411yescharacteristic, complemented
88C3×C3⋊D3—31no—
89C3×C3⋊D3—33no—
90C3×C3⋊D3—93no—
91C3×C3⋊D3—99no—
92C3×C3⋊D3—91no—
93C3×C3⋊D3—93no—
94C3×C3⋊D3—123no—
95C32×D3—361no—
96C32×D3—363no—
97(C3⋊D3)⋊C3—129no—
98C22×C32—23no—
99C22×C32—21no—
100C22×C32—23no—
101C22×C32—33no—
102C22×C32—33no—
103C22×C32—69no—
104C22×C32—63no—
105C22×C32—63no—
106C22×C32(C3⋊D3)⋊C313yescomplemented
107C22×C32C32×D311yescharacteristic
108C22×C32C32×D313yescomplemented
109C22×C32C3×C3⋊D311yescharacteristic
110C2×C3⋊D3—91no—
111C2×C3⋊D3—93no—
112C2×C3⋊D3—99no—
113C2×C3⋊D3—99no—
114C2×C3⋊D3—93no—
115C2×C3⋊D3—91no—
116C2×C3×D3—273no—
117C2×C3×D3—271no—
118C2×C3×D3—279no—
119C2×C3×D3—279no—
120C2×C3×D3—273no—
121C2×C3×D3—271no—
122C3×A4—23no—
123C3×A4—29no—
124C3×A4—31no—
125C3×A4—39no—
126C3×A4—61no—
127C3×A4—69no—
128C3×A4—62no—
129C3×A4—618no—
130C3×A4—66no—
131C3×A4—69no—
132C3×A4—61no—
133C3×A4—63no—
134C3×A4C3×C3⋊D313yescomplemented
135C33—21no—
136C33—23no—
137C33—33no—
138C33—41no—
139C33—43no—
140C33—63no—
141C33—83no—
142C33—86no—
143C33—83no—
144C33—83no—
145C33—81no—
146C33—123no—
147C33—243no—
148C33—246no—
149C33—243no—
150C33D3×A411yescharacteristic
151C33D3×A413yescomplemented
152C33C2×C3×A411yescharacteristic, complemented
153H(3,𝔽3)—49no—
154H(3,𝔽3)—89no—
155H(3,𝔽3)—818no—
156H(3,𝔽3)—89no—
157C23×C3—271no—
158C22×D3—93no—
159C22×D3—91no—
160C22×D3—273no—
161C2×A4—273no—
162C2×C32—39no—
163C2×C32—31no—
164C2×C32—33no—
165C2×C32—39no—
166C2×C32—33no—
167C2×C32—31no—
168C2×C32—61no—
169C2×C32—63no—
170C2×C32—63no—
171C2×C32—69no—
172C2×C32—627no—
173C2×C32—69no—
174C2×C32—1081no—
175C3⋊D3—31no—
176C3⋊D3—33no—
177C3⋊D3—93no—
178C3⋊D3—99no—
179C3⋊D3—91no—
180C3⋊D3—93no—
181C3×D3—93no—
182C3×D3—91no—
183C3×D3—273no—
184C3×D3—279no—
185C3×D3—273no—
186C3×D3—271no—
187C3×D3—363no—
188C3×D3—369no—
189C22×C3—23no—
190C22×C3—21no—
191C22×C3—33no—
192C22×C3—63no—
193C22×C3—811no—
194C22×C3—811no—
195C22×C3C3×(C3⋊D3)⋊C313yescomplemented
196C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
197C22×C3C32×C3⋊D311yescharacteristic
198C2×D3—271no—
199C2×D3—273no—
200C2×D3—279no—
201C2×D3—279no—
202C2×D3—271no—
203C2×D3—273no—
204A4—33no—
205A4—63no—
206A4—69no—
207C32—21no—
208C32—23no—
209C32—23no—
210C32—33no—
211C32—33no—
212C32—43no—
213C32—63no—
214C32—69no—
215C32—63no—
216C32—89no—
217C32—83no—
218C32—121no—
219C32—129no—
220C32—241no—
221C32—249no—
222C32—2418no—
223C32—242no—
224C32—246no—
225C32—249no—
226C32—241no—
227C32—243no—
228C32(C3⋊D3)⋊A413yescomplemented
229C32C3×D3×A411yescharacteristic
230C32C3×D3×A413yescomplemented
231C32A4×C3⋊D311yescharacteristic
232C23—271noSylow
233C2×C3—39no—
234C2×C3—31no—
235C2×C3—33no—
236C2×C3—31no—
237C2×C3—63no—
238C2×C3—61no—
239C2×C3—69no—
240C2×C3—271no—
241C2×C3—811no—
242C2×C3—1083no—
243D3—91no—
244D3—93no—
245D3—273no—
246D3—279no—
247D3—271no—
248D3—273no—
249C22—811no—
250C22—811no—
251C22C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
252C3—23no—
253C3—21no—
254C3—33no—
255C3—63no—
256C3—123no—
257C3—243no—
258C3—249no—
259C3C3×(C3⋊D3)⋊A413yescomplemented
260C3C3⋊((C3⋊D3)⋊A4)11yescharacteristic, direct product factor
261C3C3×A4×C3⋊D311yescharacteristic
262C2—31no—
263C2—271no—
264C2—811no—
subgroupG/H
center, hypercenterC3C3⋊((C3⋊D3)⋊A4)
commutator, cosocle, hypocenterC22×C33C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C34C2×C3
socleC22×C33C3×D3
LCSG ▷ C22×C33
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C22⋊H(3,𝔽3)C2semidirect
2. C22×C3×C3⋊(C3⋊D3)C3semidirect
4. C3⋊((C3⋊D3)⋊A4)C3direct (N × H)
7. C22×C34C2×C3semidirect
11. C33×A4D3semidirect
15. C3×C22⋊H(3,𝔽3)D3semidirect
16. C3×C22⋊H(3,𝔽3)C2×C3semidirect
18. C22×C3⋊(C3⋊D3)C32semidirect
28. C3×C3⋊(C3⋊D3)A4semidirect
37. C22×C33C3×D3semidirect
38. C22×C33C2×C32semidirect
56. C32×A4C3×D3semidirect
57. C32×A4C3⋊D3semidirect
61. C22⋊H(3,𝔽3)C3×D3semidirect
64. C34C2×A4semidirect
87. C3⋊(C3⋊D3)C3×A4semidirect
106. C22×C32(C3⋊D3)⋊C3semidirect
108. C22×C32C32×D3semidirect
134. C3×A4C3×C3⋊D3semidirect
151. C33D3×A4semidirect
152. C33C2×C3×A4semidirect
195. C22×C3C3×(C3⋊D3)⋊C3semidirect
196. C22×C3C3⋊((C3⋊D3)⋊C3)semidirect
228. C32(C3⋊D3)⋊A4semidirect
230. C32C3×D3×A4semidirect
251. C22C3×C3⋊((C3⋊D3)⋊C3)semidirect
259. C3C3×(C3⋊D3)⋊A4semidirect
260. C3C3⋊((C3⋊D3)⋊A4)direct (N × H)

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×C3×C3⋊(C3⋊D3)3
C3×A4×C3⋊D33
C3⋊((C3⋊D3)⋊A4)3
C3×(C3⋊D3)⋊A43
C3×C3⋊((C3⋊D3)⋊C3)4