Finite Group Databasebeta

← C3×A4×(C3⋊D3)⋊C3 #14519238

Subgroups — C3×A4×(C3⋊D3)⋊C3 #14519238

Order 1944.

818 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 110 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×A4×C3⋊D3C311yesmaximal, characteristic, complemented
3C32×D3×A4—31nomaximal
4C22×C3×(C3⋊D3)⋊C3C311yesmaximal, characteristic, complemented
5C3×(C3⋊D3)⋊A4C312yesmaximal, complemented
6A4×(C3⋊D3)⋊C3C319yesmaximal, direct product factor
7C32×(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)—29no—
18A4×H(3,𝔽3)C2×C319yescomplemented
19C32×H(3,𝔽3)—41noSylow
20C22×C3×C3⋊D3C3211yescharacteristic, complemented
21C22×C32×D3—31no—
22C2×C32×A4—91no—
23A4×C3⋊D3C3213yescomplemented
24C3×D3×A4—31no—
25C3×D3×A4—39no—
26C3×D3×A4—32no—
27C3×D3×A4—91no—
28C22×(C3⋊D3)⋊C3C3213yescomplemented
29(C3⋊D3)⋊A4C3216yescomplemented
30C32×C3⋊D3—41no—
31C33×D3—121no—
32C2×C3×H(3,𝔽3)—31no—
33C3×(C3⋊D3)⋊C3—31no—
34C3×(C3⋊D3)⋊C3—42no—
35C3×(C3⋊D3)⋊C3—49no—
36C3×(C3⋊D3)⋊C3A411yescharacteristic, direct product factor
37C22×C33—21no—
38C22×C33C3×D311yescharacteristic, complemented
39C22×C33C2×C3211yescharacteristic, complemented
40C2×C3×C3⋊D3—31no—
41C2×C3×C3⋊D3—31no—
42C2×C32×D3—91no—
43C2×C32×D3—91no—
44C32×A4—21no—
45C32×A4—22no—
46C32×A4—23no—
47C32×A4—29no—
48C32×A4—31no—
49C32×A4—31no—
50C32×A4—63no—
51C32×A4—61no—
52C32×A4—63no—
53C32×A4—62no—
54C32×A4—66no—
55C32×A4—61no—
56C32×A4—61no—
57C32×A4C3×D311yescharacteristic
58C32×A4C3×D319yescomplemented
59C32×A4C3×D312yescomplemented
60C32×A4C2×C3213yescomplemented
61C22×H(3,𝔽3)—23no—
62C22×H(3,𝔽3)C2×C3213yescomplemented
63C2×(C3⋊D3)⋊C3—33no—
64C2×(C3⋊D3)⋊C3—33no—
65C22⋊H(3,𝔽3)—29no—
66C22⋊H(3,𝔽3)—26no—
67C22⋊H(3,𝔽3)—218no—
68C22⋊H(3,𝔽3)C2×C3216yescomplemented
69C34—41no—
70C34—41no—
71C34—81no—
72C3×H(3,𝔽3)—42no—
73C3×H(3,𝔽3)—49no—
74C3×H(3,𝔽3)—89no—
75C3×H(3,𝔽3)—82no—
76C3×H(3,𝔽3)—81no—
77C3×H(3,𝔽3)C2×A411yescharacteristic, complemented
78C23×C32—91no—
79C22×C3⋊D3C3311yescharacteristic, complemented
80C22×C3×D3—31no—
81C22×C3×D3—33no—
82C22×C3×D3—91no—
83C2×C3×A4—92no—
84C2×C3×A4—99no—
85C2×C3×A4—91no—
86D3×A4—33no—
87D3×A4—36no—
88D3×A4—93no—
89C2×C33—31no—
90C2×C33—31no—
91C2×C33—61no—
92C2×C33—361no—
93C3×C3⋊D3—31no—
94C3×C3⋊D3—43no—
95C3×C3⋊D3C3×A411yescharacteristic, complemented
96C32×D3—31no—
97C32×D3—91no—
98C32×D3—122no—
99C32×D3—129no—
100C32×D3—121no—
101C32×D3—361no—
102C2×H(3,𝔽3)—33no—
103C2×H(3,𝔽3)—63no—
104(C3⋊D3)⋊C3—33no—
105(C3⋊D3)⋊C3—46no—
106(C3⋊D3)⋊C3C3×A413yesdirect product factor
107C22×C32—21no—
108C22×C32—23no—
109C22×C32—31no—
110C22×C32—31no—
111C22×C32—61no—
112C22×C32—61no—
113C22×C32—62no—
114C22×C32—61no—
115C22×C32—271no—
116C22×C32—271no—
117C22×C32C32×D311yescharacteristic
118C22×C32C32×D313yescomplemented
119C22×C32C2×C3311yescharacteristic, complemented
120C2×C3⋊D3—31no—
121C2×C3⋊D3—31no—
122C2×C3×D3—93no—
123C2×C3×D3—91no—
124C2×C3×D3—93no—
125C2×C3×D3—91no—
126C2×C3×D3—271no—
127C2×C3×D3—271no—
128C3×A4—21no—
129C3×A4—23no—
130C3×A4—23no—
131C3×A4—26no—
132C3×A4—32no—
133C3×A4—39no—
134C3×A4—33no—
135C3×A4—69no—
136C3×A4—66no—
137C3×A4—618no—
138C3×A4—63no—
139C3×A4—62no—
140C3×A4—62no—
141C3×A4—64no—
142C3×A4—61no—
143C3×A4—62no—
144C3×A4—63no—
145C3×A4—69no—
146C3×A4(C3⋊D3)⋊C311yescharacteristic, direct product factor
147C3×A4C32×D313yes—
148C3×A4C32×D316yescomplemented
149C33—21no—
150C33—41no—
151C33—42no—
152C33—49no—
153C33—43no—
154C33—89no—
155C33—83no—
156C33—82no—
157C33—81no—
158C33—121no—
159C33—121no—
160C33—241no—
161C33—241no—
162C33—241no—
163C33—243no—
164C33—243no—
165C33—246no—
166C33—242no—
167C33D3×A411yescharacteristic, complemented
168C33C2×C3×A411yescharacteristic, complemented
169H(3,𝔽3)—23no—
170H(3,𝔽3)—46no—
171H(3,𝔽3)—86no—
172H(3,𝔽3)—818no—
173H(3,𝔽3)—89no—
174H(3,𝔽3)C2×C3×A413yescomplemented
175C23×C3—93no—
176C23×C3—91no—
177C22×D3—31no—
178C22×D3—91no—
179C2×A4—96no—
180C2×A4—93no—
181C2×C32—31no—
182C2×C32—33no—
183C2×C32—31no—
184C2×C32—63no—
185C2×C32—61no—
186C2×C32—91no—
187C2×C32—91no—
188C2×C32—91no—
189C2×C32—181no—
190C2×C32—181no—
191C2×C32—181no—
192C2×C32—182no—
193C2×C32—271no—
194C2×C32—361no—
195C2×C32—369no—
196C2×C32—362no—
197C3⋊D3—31no—
198C3⋊D3C32×A411yescharacteristic, complemented
199C3×D3—31no—
200C3×D3—33no—
201C3×D3—91no—
202C3×D3—91no—
203C3×D3—93no—
204C3×D3—126no—
205C3×D3—123no—
206C3×D3—271no—
207C3×D3—363no—
208C22×C3—21no—
209C22×C3—31no—
210C22×C3—33no—
211C22×C3—61no—
212C22×C3—63no—
213C22×C3—271no—
214C22×C3—271no—
215C22×C3—273no—
216C22×C3—273no—
217C22×C3C3×(C3⋊D3)⋊C311yescharacteristic, complemented
218C22×C3C33×D311yescharacteristic
219C2×D3—91no—
220C2×D3—91no—
221C2×D3—271no—
222C2×D3—271no—
223A4—23no—
224A4—36no—
225A4—63no—
226A4—66no—
227A4C3×(C3⋊D3)⋊C313yesdirect product factor
228C32—21no—
229C32—23no—
230C32—31no—
231C32—31no—
232C32—41no—
233C32—43no—
234C32—46no—
235C32—61no—
236C32—61no—
237C32—62no—
238C32—61no—
239C32—83no—
240C32—81no—
241C32—86no—
242C32—83no—
243C32—129no—
244C32—123no—
245C32—122no—
246C32—242no—
247C32—242no—
248C32—244no—
249C32—249no—
250C32—243no—
251C32—243no—
252C32—249no—
253C32—246no—
254C32—2418no—
255C32—241no—
256C32—242no—
257C32C3×D3×A411yescharacteristic
258C32C3×D3×A413yescomplemented
259C32C2×C32×A411yescharacteristic, complemented
260C23—91noSylow
261C2×C3—31no—
262C2×C3—31no—
263C2×C3—61no—
264C2×C3—91no—
265C2×C3—93no—
266C2×C3—93no—
267C2×C3—91no—
268C2×C3—181no—
269C2×C3—183no—
270C2×C3—273no—
271C2×C3—271no—
272C2×C3—363no—
273C2×C3—366no—
274D3—31no—
275D3—91no—
276D3—91no—
277D3—271no—
278C22—271no—
279C22—271no—
280C22C32×(C3⋊D3)⋊C311yescharacteristic, complemented
281C3—21no—
282C3—31no—
283C3—33no—
284C3—43no—
285C3—61no—
286C3—63no—
287C3—83no—
288C3—126no—
289C3—243no—
290C3—246no—
291C3A4×(C3⋊D3)⋊C311yescharacteristic, direct product factor
292C3C32×D3×A411yescharacteristic
293C2—31no—
294C2—91no—
295C2—271no—
subgroupG/H
center, hypercenterC3A4×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC22×C32C2×C33
FrattiniC3C32×D3×A4
FittingC22×C3×H(3,𝔽3)C2×C3
socleC22×C32C32×D3
LCSG ▷ C22×C32
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×A4×C3⋊D3C3semidirect
4. C22×C3×(C3⋊D3)⋊C3C3semidirect
5. C3×(C3⋊D3)⋊A4C3semidirect
6. A4×(C3⋊D3)⋊C3C3direct (N × H)
9. C33×A4D3semidirect
10. C33×A4C2×C3semidirect
11. C22×C3×H(3,𝔽3)C2×C3semidirect
16. C3×C22⋊H(3,𝔽3)C2×C3semidirect
18. A4×H(3,𝔽3)C2×C3semidirect
20. C22×C3×C3⋊D3C32semidirect
23. A4×C3⋊D3C32semidirect
28. C22×(C3⋊D3)⋊C3C32semidirect
29. (C3⋊D3)⋊A4C32semidirect
36. C3×(C3⋊D3)⋊C3A4direct (N × H)
38. C22×C33C3×D3semidirect
39. C22×C33C2×C32semidirect
58. C32×A4C3×D3semidirect
59. C32×A4C3×D3semidirect
60. C32×A4C2×C32semidirect
62. C22×H(3,𝔽3)C2×C32semidirect
68. C22⋊H(3,𝔽3)C2×C32semidirect
77. C3×H(3,𝔽3)C2×A4semidirect
79. C22×C3⋊D3C33semidirect
95. C3×C3⋊D3C3×A4semidirect
106. (C3⋊D3)⋊C3C3×A4direct (N × H)
118. C22×C32C32×D3semidirect
119. C22×C32C2×C33semidirect
146. C3×A4(C3⋊D3)⋊C3direct (N × H)
148. C3×A4C32×D3semidirect
167. C33D3×A4semidirect
168. C33C2×C3×A4semidirect
174. H(3,𝔽3)C2×C3×A4semidirect
198. C3⋊D3C32×A4semidirect
217. C22×C3C3×(C3⋊D3)⋊C3semidirect
227. A4C3×(C3⋊D3)⋊C3direct (N × H)
258. C32C3×D3×A4semidirect
259. C32C2×C32×A4semidirect
280. C22C32×(C3⋊D3)⋊C3semidirect
291. C3A4×(C3⋊D3)⋊C3direct (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×A4×C3⋊D33
C32×D3×A43
C22×C3×(C3⋊D3)⋊C33
C3×(C3⋊D3)⋊A43
A4×(C3⋊D3)⋊C33
C32×(C3⋊D3)⋊C34