Finite Group Databasebeta

← C3×A4⋊((C3⋊D3)⋊C3) #14519201

Subgroups — C3×A4⋊((C3⋊D3)⋊C3) #14519201

Order 1944.

744 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 64 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
2C3×C3⋊(C3⋊S4)C311yesmaximal, characteristic, complemented
3C32×C3⋊S4—31nomaximal
4A4⋊((C3⋊D3)⋊C3)C313yesmaximal, direct product factor
5C3×(C3⋊S4)⋊C3—32nomaximal
6C3×#638⋊C3—31nomaximal
7C3×C3⋊((C3⋊D3)⋊C3)—41nomaximal
8C33×A4—21no—
9C33×A4D311yescharacteristic, complemented
10C33×A4C2×C311yescharacteristic, complemented
11C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
12C2×C3×(C3⋊D3)⋊C3—31no—
13C3×C22⋊H(3,𝔽3)—21no—
14C3×C22⋊H(3,𝔽3)—22no—
15C3×C22⋊H(3,𝔽3)D312yescomplemented
16A4×H(3,𝔽3)—23no—
17A4×H(3,𝔽3)—23no—
18A4×H(3,𝔽3)—26no—
19A4×H(3,𝔽3)C2×C313yescomplemented
20C3×(C3⋊Dic3)⋊C3—31no—
21C32×H(3,𝔽3)—41noSylow
22C3⋊(C3⋊S4)C3211yescharacteristic, complemented
23C3×C3⋊S4—31no—
24C3×C3⋊S4—33no—
25C3×C3⋊S4—32no—
26C3×C3⋊S4—93no—
27C32×S4—93no—
28C3×#638—31no—
29C32×#67—91no—
30(C3⋊S4)⋊C3—36no—
31#638⋊C3—33no—
32C3×C3⋊(C3⋊D3)—41no—
33C32×C3⋊D3—121no—
34C2×C3×H(3,𝔽3)—31no—
35C3⋊((C3⋊D3)⋊C3)—43no—
36C3×(C3⋊D3)⋊C3—61no—
37C3×(C3⋊D3)⋊C3—122no—
38C22×C33—21no—
39C22×C33C3×D311yescharacteristic, complemented
40C22×C33C3⋊D311yescharacteristic, complemented
41C2×C3×C3⋊D3—31no—
42C2×C32×D3—91no—
43C32×A4—26no—
44C32×A4—21no—
45C32×A4—21no—
46C32×A4—22no—
47C32×A4—23no—
48C32×A4—21no—
49C32×A4—23no—
50C32×A4—22no—
51C32×A4—33no—
52C32×A4—33no—
53C32×A4—63no—
54C32×A4—63no—
55C32×A4—66no—
56C32×A4—63no—
57C32×A4C3×D311yescharacteristic
58C32×A4C3×D313yescomplemented
59C32×A4C3×D312yescomplemented
60C32×A4C2×C3211yescharacteristic, complemented
61C3×C3⋊Dic3—31no—
62C32×Dic3—91no—
63C22×H(3,𝔽3)—23no—
64C22×H(3,𝔽3)C3×D313yescomplemented
65C2×(C3⋊D3)⋊C3—33no—
66C22⋊H(3,𝔽3)—212no—
67C22⋊H(3,𝔽3)—26no—
68C22⋊H(3,𝔽3)—23no—
69C22⋊H(3,𝔽3)—26no—
70C22⋊H(3,𝔽3)—26no—
71C22⋊H(3,𝔽3)C3×D316yescomplemented
72(C3⋊Dic3)⋊C3—33no—
73C34—41no—
74C34—41no—
75C34—81no—
76C3×H(3,𝔽3)—42no—
77C3×H(3,𝔽3)—43no—
78C3×H(3,𝔽3)—86no—
79C3×H(3,𝔽3)—83no—
80C3×H(3,𝔽3)—82no—
81C3×H(3,𝔽3)—81no—
82C3×H(3,𝔽3)—83no—
83C3×H(3,𝔽3)S411yescharacteristic, complemented
84C3⋊S4—31no—
85C3⋊S4—32no—
86C3⋊S4—93no—
87C3×S4—99no—
88C3×S4—93no—
89C3×S4—272no—
90C32×D4—271no—
91#638—31no—
92C3×#67—91no—
93C3×#67—93no—
94C3×#67—271no—
95C2×C33—31no—
96C2×C33—31no—
97C2×C33—61no—
98C3⋊(C3⋊D3)—41no—
99C3×C3⋊D3—61no—
100C3×C3⋊D3—123no—
101C3×C3⋊D3—121no—
102C3×C3⋊D3—122no—
103C3×C3⋊D3—363no—
104C32×D3—181no—
105C32×D3—363no—
106C2×H(3,𝔽3)—33no—
107C2×H(3,𝔽3)—63no—
108(C3⋊D3)⋊C3—63no—
109(C3⋊D3)⋊C3—126no—
110C22×C32—21no—
111C22×C32—23no—
112C22×C32—31no—
113C22×C32—31no—
114C22×C32—61no—
115C22×C32—61no—
116C22×C32—62no—
117C22×C32—61no—
118C22×C32—271no—
119C22×C32C32×D311yescharacteristic, complemented
120C22×C32C3×C3⋊D311yescharacteristic
121C22×C32C3×C3⋊D313yescomplemented
122C2×C3⋊D3—31no—
123C2×C3×D3—93no—
124C2×C3×D3—91no—
125C2×C3×D3—271no—
126C3×A4—21no—
127C3×A4—23no—
128C3×A4—23no—
129C3×A4—22no—
130C3×A4—26no—
131C3×A4—33no—
132C3×A4—32no—
133C3×A4—39no—
134C3×A4—66no—
135C3×A4—69no—
136C3×A4—63no—
137C3×A4—618no—
138C3×A4—62no—
139C3×A4—62no—
140C3×A4—64no—
141C3×A4—61no—
142C3×A4—62no—
143C3×A4—63no—
144C3×A4—69no—
145C3×A4(C3⋊D3)⋊C313yescomplemented
146C3×A4C32×D311yescharacteristic
147C3×A4C32×D312yescomplemented
148C32×C4—271no—
149C3⋊Dic3—31no—
150C3×Dic3—93no—
151C3×Dic3—91no—
152C3×Dic3—271no—
153C33—21no—
154C33—41no—
155C33—41no—
156C33—43no—
157C33—42no—
158C33—83no—
159C33—81no—
160C33—82no—
161C33—86no—
162C33—81no—
163C33—82no—
164C33—81no—
165C33—83no—
166C33—123no—
167C33—123no—
168C33—243no—
169C33—243no—
170C33—243no—
171C33—246no—
172C33C3×S411yescharacteristic, complemented
173C33C3⋊S411yescharacteristic, complemented
174H(3,𝔽3)—23no—
175H(3,𝔽3)—46no—
176H(3,𝔽3)—86no—
177H(3,𝔽3)—86no—
178H(3,𝔽3)—812no—
179H(3,𝔽3)—83no—
180H(3,𝔽3)—86no—
181H(3,𝔽3)C3×S413yescomplemented
182S4—93no—
183S4—272no—
184C3×D4—273no—
185C3×D4—271no—
186#67—91no—
187#67—271no—
188C2×C32—31no—
189C2×C32—31no—
190C2×C32—33no—
191C2×C32—63no—
192C2×C32—61no—
193C2×C32—91no—
194C2×C32—91no—
195C2×C32—181no—
196C2×C32—181no—
197C2×C32—181no—
198C2×C32—182no—
199C2×C32—541no—
200C3⋊D3—61no—
201C3⋊D3—121no—
202C3⋊D3—122no—
203C3⋊D3—363no—
204C3×D3—181no—
205C3×D3—183no—
206C3×D3—363no—
207C3×D3—369no—
208C3×D3—541no—
209C3×D3—1082no—
210C22×C3—21no—
211C22×C3—31no—
212C22×C3—33no—
213C22×C3—61no—
214C22×C3—63no—
215C22×C3—271no—
216C22×C3—273no—
217C22×C3C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
218C22×C3C32×C3⋊D311yescharacteristic
219C2×D3—91no—
220C2×D3—271no—
221A4—23no—
222A4—32no—
223A4—63no—
224A4—62no—
225A4—66no—
226A4C3×(C3⋊D3)⋊C313yescomplemented
227C3×C4—271no—
228C3×C4—273no—
229Dic3—91no—
230Dic3—271no—
231C32—21no—
232C32—23no—
233C32—31no—
234C32—31no—
235C32—41no—
236C32—43no—
237C32—42no—
238C32—61no—
239C32—61no—
240C32—62no—
241C32—61no—
242C32—83no—
243C32—81no—
244C32—86no—
245C32—83no—
246C32—82no—
247C32—123no—
248C32—129no—
249C32—122no—
250C32—242no—
251C32—242no—
252C32—244no—
253C32—243no—
254C32—249no—
255C32—243no—
256C32—249no—
257C32—246no—
258C32—2418no—
259C32—241no—
260C32—242no—
261C32C32×S411yescharacteristic, complemented
262C32C3×C3⋊S411yescharacteristic
263C32C3×C3⋊S413yescomplemented
264D4—271noSylow
265C2×C3—31no—
266C2×C3—31no—
267C2×C3—61no—
268C2×C3—91no—
269C2×C3—93no—
270C2×C3—181no—
271C2×C3—183no—
272C2×C3—543no—
273C2×C3—541no—
274D3—181no—
275D3—363no—
276D3—541no—
277D3—1082no—
278C22—271no—
279C22C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
280C4—271no—
281C3—21no—
282C3—31no—
283C3—33no—
284C3—43no—
285C3—61no—
286C3—63no—
287C3—83no—
288C3—122no—
289C3—243no—
290C3—242no—
291C3—246no—
292C3A4⋊((C3⋊D3)⋊C3)11yescharacteristic, direct product factor
293C3C32×C3⋊S411yescharacteristic
294C2—31no—
295C2—541no—
subgroupG/H
center, hypercenterC3A4⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC32×A4C2×C32
FrattiniC3C32×C3⋊S4
FittingC22×C3×H(3,𝔽3)D3
socleC22×C32C3×C3⋊D3
LCSG ▷ C32×A4
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×A4×H(3,𝔽3)C2semidirect
2. C3×C3⋊(C3⋊S4)C3semidirect
4. A4⋊((C3⋊D3)⋊C3)C3direct (N × H)
9. C33×A4D3semidirect
10. C33×A4C2×C3semidirect
11. C22×C3×H(3,𝔽3)D3semidirect
15. C3×C22⋊H(3,𝔽3)D3semidirect
19. A4×H(3,𝔽3)C2×C3semidirect
22. C3⋊(C3⋊S4)C32semidirect
39. C22×C33C3×D3semidirect
40. C22×C33C3⋊D3semidirect
58. C32×A4C3×D3semidirect
59. C32×A4C3×D3semidirect
60. C32×A4C2×C32semidirect
64. C22×H(3,𝔽3)C3×D3semidirect
71. C22⋊H(3,𝔽3)C3×D3semidirect
83. C3×H(3,𝔽3)S4semidirect
119. C22×C32C32×D3semidirect
121. C22×C32C3×C3⋊D3semidirect
145. C3×A4(C3⋊D3)⋊C3semidirect
147. C3×A4C32×D3semidirect
172. C33C3×S4semidirect
173. C33C3⋊S4semidirect
181. H(3,𝔽3)C3×S4semidirect
217. C22×C3C3⋊((C3⋊D3)⋊C3)semidirect
226. A4C3×(C3⋊D3)⋊C3semidirect
261. C32C32×S4semidirect
263. C32C3×C3⋊S4semidirect
279. C22C3×C3⋊((C3⋊D3)⋊C3)semidirect
292. C3A4⋊((C3⋊D3)⋊C3)direct (N × H)

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
C3×C3⋊(C3⋊S4)3
C32×C3⋊S43
A4⋊((C3⋊D3)⋊C3)3
C3×(C3⋊S4)⋊C33
C3×#638⋊C33
C3×C3⋊((C3⋊D3)⋊C3)4