Finite Group Databasebeta

← A4×C3⋊((C3⋊D3)⋊C3) #14519254

Subgroups — A4×C3⋊((C3⋊D3)⋊C3) #14519254

Order 1944.

785 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×A4×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2A4×C3⋊(C3⋊D3)C311yesmaximal, characteristic, complemented
3C3×A4×C3⋊D3—31nomaximal
4C22×C3⋊((C3⋊D3)⋊C3)C311yesmaximal, characteristic, complemented
5C3⋊((C3⋊D3)⋊A4)C312yesmaximal, complemented
6A4×(C3⋊D3)⋊C3—33nomaximal
7C3×C3⋊((C3⋊D3)⋊C3)—41nomaximal
8C33×A4—21no—
9C33×A4D311yescharacteristic, complemented
10C33×A4C2×C311yescharacteristic, complemented
11C22×C3×H(3,𝔽3)C2×C311yescharacteristic, complemented
12C2×C3⋊((C3⋊D3)⋊C3)—31no—
13C2×C3⋊((C3⋊D3)⋊C3)—31no—
14C3×C22⋊H(3,𝔽3)—21no—
15C3×C22⋊H(3,𝔽3)—22no—
16C3×C22⋊H(3,𝔽3)C2×C312yescomplemented
17A4×H(3,𝔽3)—23no—
18A4×H(3,𝔽3)—23no—
19A4×H(3,𝔽3)—26no—
20A4×H(3,𝔽3)D313yescomplemented
21C32×H(3,𝔽3)—41noSylow
22C22×C3⋊(C3⋊D3)C3211yescharacteristic, complemented
23C22×C3×C3⋊D3—31no—
24A4×C3⋊D3—31no—
25A4×C3⋊D3—32no—
26A4×C3⋊D3—33no—
27A4×C3⋊D3—93no—
28C3×D3×A4—93no—
29C3×D3×A4—91no—
30C22×(C3⋊D3)⋊C3—33no—
31(C3⋊D3)⋊A4—36no—
32C3×C3⋊(C3⋊D3)—41no—
33C32×C3⋊D3—121no—
34C2×C3×H(3,𝔽3)—31no—
35C3⋊((C3⋊D3)⋊C3)—31no—
36C3⋊((C3⋊D3)⋊C3)—42no—
37C3⋊((C3⋊D3)⋊C3)A411yescharacteristic, direct product factor
38C3×(C3⋊D3)⋊C3—123no—
39C22×C33—21no—
40C22×C33C3×D311yescharacteristic, complemented
41C22×C33C2×C3211yescharacteristic, complemented
42C2×C3⋊(C3⋊D3)—31no—
43C2×C3⋊(C3⋊D3)—31no—
44C2×C3×C3⋊D3—91no—
45C2×C3×C3⋊D3—91no—
46C32×A4—26no—
47C32×A4—21no—
48C32×A4—22no—
49C32×A4—23no—
50C32×A4—21no—
51C32×A4—21no—
52C32×A4—23no—
53C32×A4—22no—
54C32×A4—33no—
55C32×A4—33no—
56C32×A4—63no—
57C32×A4—66no—
58C32×A4—63no—
59C32×A4—63no—
60C32×A4C3×D311yescharacteristic
61C32×A4C3×D312yescomplemented
62C32×A4C3×D313yescomplemented
63C32×A4C3⋊D311yescharacteristic, complemented
64C22×H(3,𝔽3)—23no—
65C22×H(3,𝔽3)C3×D313yescomplemented
66C2×(C3⋊D3)⋊C3—93no—
67C2×(C3⋊D3)⋊C3—93no—
68C22⋊H(3,𝔽3)—212no—
69C22⋊H(3,𝔽3)—26no—
70C22⋊H(3,𝔽3)—26no—
71C22⋊H(3,𝔽3)—23no—
72C22⋊H(3,𝔽3)—26no—
73C22⋊H(3,𝔽3)C3×D316yescomplemented
74C34—41no—
75C34—41no—
76C34—81no—
77C3×H(3,𝔽3)—42no—
78C3×H(3,𝔽3)—43no—
79C3×H(3,𝔽3)—86no—
80C3×H(3,𝔽3)—83no—
81C3×H(3,𝔽3)—82no—
82C3×H(3,𝔽3)—81no—
83C3×H(3,𝔽3)—83no—
84C3×H(3,𝔽3)C2×A411yescharacteristic, complemented
85C22×C3⋊D3—31no—
86C22×C3⋊D3—33no—
87C22×C3⋊D3—93no—
88C22×C3×D3—93no—
89C22×C3×D3—91no—
90C2×C3×A4—271no—
91D3×A4—96no—
92D3×A4—93no—
93D3×A4—91no—
94D3×A4—92no—
95D3×A4—273no—
96C2×C33—31no—
97C2×C33—31no—
98C2×C33—61no—
99C3⋊(C3⋊D3)—31no—
100C3⋊(C3⋊D3)C3×A411yescharacteristic, complemented
101C3×C3⋊D3—31no—
102C3×C3⋊D3—91no—
103C3×C3⋊D3—122no—
104C3×C3⋊D3—121no—
105C3×C3⋊D3—123no—
106C3×C3⋊D3—363no—
107C32×D3—361no—
108C32×D3—363no—
109C2×H(3,𝔽3)—33no—
110C2×H(3,𝔽3)—63no—
111(C3⋊D3)⋊C3—33no—
112(C3⋊D3)⋊C3—93no—
113(C3⋊D3)⋊C3—126no—
114C22×C32—21no—
115C22×C32—23no—
116C22×C32—33no—
117C22×C32—33no—
118C22×C32—63no—
119C22×C32C32×D311yescharacteristic
120C22×C32C32×D313yescomplemented
121C22×C32C3×C3⋊D311yescharacteristic, complemented
122C2×C3⋊D3—91no—
123C2×C3⋊D3—91no—
124C2×C3⋊D3—93no—
125C2×C3⋊D3—93no—
126C2×C3⋊D3—273no—
127C2×C3⋊D3—273no—
128C2×C3×D3—271no—
129C2×C3×D3—273no—
130C2×C3×D3—271no—
131C2×C3×D3—273no—
132C3×A4—23no—
133C3×A4—21no—
134C3×A4—22no—
135C3×A4—23no—
136C3×A4—26no—
137C3×A4—31no—
138C3×A4—36no—
139C3×A4—33no—
140C3×A4—61no—
141C3×A4—66no—
142C3×A4—63no—
143C3×A4—69no—
144C3×A4—618no—
145C3×A4—62no—
146C3×A4—66no—
147C3×A4—63no—
148C3×A4—63no—
149C3×A4—66no—
150C3×A4—61no—
151C3×A4—63no—
152C3×A4(C3⋊D3)⋊C313yescomplemented
153C3×A4C3×C3⋊D311yescharacteristic
154C3×A4C3×C3⋊D312yescomplemented
155C33—21no—
156C33—41no—
157C33—41no—
158C33—42no—
159C33—43no—
160C33—83no—
161C33—81no—
162C33—82no—
163C33—86no—
164C33—82no—
165C33—81no—
166C33—83no—
167C33—81no—
168C33—123no—
169C33—123no—
170C33—243no—
171C33—243no—
172C33—243no—
173C33—246no—
174C33D3×A411yescharacteristic, complemented
175C33C2×C3×A411yescharacteristic, complemented
176H(3,𝔽3)—23no—
177H(3,𝔽3)—46no—
178H(3,𝔽3)—86no—
179H(3,𝔽3)—86no—
180H(3,𝔽3)—812no—
181H(3,𝔽3)—86no—
182H(3,𝔽3)—83no—
183H(3,𝔽3)D3×A413yescomplemented
184C23×C3—271no—
185C22×D3—93no—
186C22×D3—91no—
187C22×D3—273no—
188C2×A4—272no—
189C2×A4—271no—
190C2×C32—31no—
191C2×C32—33no—
192C2×C32—31no—
193C2×C32—63no—
194C2×C32—61no—
195C2×C32—93no—
196C2×C32—93no—
197C2×C32—183no—
198C2×C32—1081no—
199C3⋊D3—31no—
200C3⋊D3—33no—
201C3⋊D3—93no—
202C3⋊D3—91no—
203C3⋊D3—93no—
204C3⋊D3—273no—
205C3×D3—93no—
206C3×D3—91no—
207C3×D3—273no—
208C3×D3—271no—
209C3×D3—362no—
210C3×D3—361no—
211C3×D3—363no—
212C3×D3—366no—
213C3×D3—1083no—
214C22×C3—33no—
215C22×C3—31no—
216C22×C3—61no—
217C22×C3—63no—
218C22×C3—811no—
219C22×C3—811no—
220C22×C3C3×(C3⋊D3)⋊C313yescomplemented
221C22×C3C32×C3⋊D311yescharacteristic
222C2×D3—271no—
223C2×D3—273no—
224C2×D3—271no—
225C2×D3—273no—
226C2×D3—813no—
227C2×D3—813no—
228A4—23no—
229A4—21no—
230A4—32no—
231A4—62no—
232A4—63no—
233A4—66no—
234A4C3⋊((C3⋊D3)⋊C3)11yescharacteristic, direct product factor
235C32—21no—
236C32—23no—
237C32—33no—
238C32—33no—
239C32—41no—
240C32—43no—
241C32—42no—
242C32—63no—
243C32—81no—
244C32—83no—
245C32—86no—
246C32—82no—
247C32—83no—
248C32—121no—
249C32—123no—
250C32—126no—
251C32—241no—
252C32—243no—
253C32—249no—
254C32—243no—
255C32—241no—
256C32—243no—
257C32—246no—
258C32—242no—
259C32—246no—
260C32—2418no—
261C32—243no—
262C32—246no—
263C32C3×D3×A411yescharacteristic
264C32C3×D3×A413yescomplemented
265C32A4×C3⋊D311yescharacteristic, complemented
266C23—271noSylow
267C2×C3—31no—
268C2×C3—33no—
269C2×C3—93no—
270C2×C3—91no—
271C2×C3—181no—
272C2×C3—183no—
273C2×C3—271no—
274C2×C3—811no—
275C2×C3—1081no—
276C2×C3—1082no—
277D3—91no—
278D3—93no—
279D3—273no—
280D3—271no—
281D3—273no—
282D3—813no—
283C22—811no—
284C22—811no—
285C22C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
286C3—33no—
287C3—31no—
288C3—41no—
289C3—61no—
290C3—63no—
291C3—81no—
292C3—83no—
293C3—122no—
294C3—242no—
295C3—243no—
296C3—246no—
297C3A4×(C3⋊D3)⋊C313yescomplemented
298C3C3×A4×C3⋊D311yescharacteristic
299C2—31no—
300C2—271no—
301C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC22×C33C2×C32
FrattiniC3C3×A4×C3⋊D3
FittingC22×C3×H(3,𝔽3)C2×C3
socleC22×C32C32×D3
LCSG ▷ C22×C33
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×A4×H(3,𝔽3)C2semidirect
2. A4×C3⋊(C3⋊D3)C3semidirect
4. C22×C3⋊((C3⋊D3)⋊C3)C3semidirect
5. C3⋊((C3⋊D3)⋊A4)C3semidirect
9. C33×A4D3semidirect
10. C33×A4C2×C3semidirect
11. C22×C3×H(3,𝔽3)C2×C3semidirect
16. C3×C22⋊H(3,𝔽3)C2×C3semidirect
20. A4×H(3,𝔽3)D3semidirect
22. C22×C3⋊(C3⋊D3)C32semidirect
37. C3⋊((C3⋊D3)⋊C3)A4direct (N × H)
40. C22×C33C3×D3semidirect
41. C22×C33C2×C32semidirect
61. C32×A4C3×D3semidirect
62. C32×A4C3×D3semidirect
63. C32×A4C3⋊D3semidirect
65. C22×H(3,𝔽3)C3×D3semidirect
73. C22⋊H(3,𝔽3)C3×D3semidirect
84. C3×H(3,𝔽3)C2×A4semidirect
100. C3⋊(C3⋊D3)C3×A4semidirect
120. C22×C32C32×D3semidirect
121. C22×C32C3×C3⋊D3semidirect
152. C3×A4(C3⋊D3)⋊C3semidirect
154. C3×A4C3×C3⋊D3semidirect
174. C33D3×A4semidirect
175. C33C2×C3×A4semidirect
183. H(3,𝔽3)D3×A4semidirect
220. C22×C3C3×(C3⋊D3)⋊C3semidirect
234. A4C3⋊((C3⋊D3)⋊C3)direct (N × H)
264. C32C3×D3×A4semidirect
265. C32A4×C3⋊D3semidirect
285. C22C3×C3⋊((C3⋊D3)⋊C3)semidirect
297. C3A4×(C3⋊D3)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×A4×H(3,𝔽3)2
A4×C3⋊(C3⋊D3)3
C3×A4×C3⋊D33
C22×C3⋊((C3⋊D3)⋊C3)3
C3⋊((C3⋊D3)⋊A4)3
A4×(C3⋊D3)⋊C33
C3×C3⋊((C3⋊D3)⋊C3)4