Finite Group Databasebeta

← C3×D3×A42 #72220696

Subgroups — C3×D3×A42 #72220696

Order 2592.

1189 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 1189 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×A42C211yesmaximal, characteristic, complemented
2C3×D3×C22⋊A4C312yesmaximal, complemented
3C22×C3×D3×A4C312yesmaximal, complemented
4C2×C3×A42—31nomaximal
5D3×A42C319yesmaximal, direct product factor
6C32×D3×A4—42nomaximal
7C32×C22⋊A4C2×C312yescomplemented
8C22×C32×A4C2×C312yescomplemented
9C2×C3×D3×A4—32no—
10C2×C3×D3×A4—32no—
11C3×A42—22no—
12C3×A42—22no—
13C3×A42—29no—
14C3×A42D311yescharacteristic, direct product factor
15C3×A42C2×C319yescomplemented
16C33×A4—42no—
17C24×C3×D3C3211yescharacteristic, complemented
18C2×C3×C22⋊A4—32no—
19C23×C3×A4—32no—
20D3×C22⋊A4C3216yescomplemented
21C22×D3×A4C3216yescomplemented
22C2×A42—39no—
23C22×C32×D3—42no—
24C2×C32×A4—32no—
25C2×C32×A4—122no—
26C3×D3×A4—32no—
27C3×D3×A4—44no—
28C3×D3×A4—418no—
29C3×D3×A4—122no—
30C3×D3×A4A412yesdirect product factor
31C33×D3—161no—
32C24×C32C2×C3211yescharacteristic, complemented
33C23×C3×D3—32no—
34C23×C3×D3—32no—
35C23×C3×D3—91no—
36C23×C3×D3—91no—
37C3×C22⋊A4—22no—
38C3×C22⋊A4—26no—
39C3×C22⋊A4C3×D312yescomplemented
40C3×C22⋊A4C2×C3216yescomplemented
41C22×C3×A4—22no—
42C22×C3×A4—26no—
43C22×C3×A4—92no—
44C22×C3×A4—92no—
45C22×C3×A4C3×D312yescomplemented
46C22×C3×A4C2×C3216yescomplemented
47C2×D3×A4—36no—
48C2×D3×A4—36no—
49A42—218no—
50A42—218no—
51A42C3×D319yesdirect product factor
52C22×C33—42no—
53C2×C32×D3—122no—
54C2×C32×D3—122no—
55C32×A4—42no—
56C32×A4—44no—
57C32×A4—418no—
58C32×A4—84no—
59C32×A4—818no—
60C32×A4—82no—
61C32×A4—82no—
62C32×A4—122no—
63C32×A4C2×A412yescomplemented
64C25×C3—31no—
65C24×D3C3311yescharacteristic, complemented
66C2×C22⋊A4—36no—
67C23×A4—36no—
68C34—161noSylow
69C23×C32—32no—
70C23×C32—91no—
71C23×C32—122no—
72C22×C3×D3—32no—
73C22×C3×D3—32no—
74C22×C3×D3—46no—
75C22×C3×D3—91no—
76C22×C3×D3—92no—
77C22×C3×D3—92no—
78C22×C3×D3—92no—
79C22×C3×D3—92no—
80C22×C3×D3—94no—
81C22×C3×D3—91no—
82C22×C3×D3C3×A412yescomplemented
83C2×C3×A4—32no—
84C2×C3×A4—32no—
85C2×C3×A4—36no—
86C2×C3×A4—66no—
87C2×C3×A4—62no—
88C2×C3×A4—92no—
89C2×C3×A4—1218no—
90C2×C3×A4—124no—
91C2×C3×A4—362no—
92D3×A4—36no—
93D3×A4—412no—
94D3×A4—126no—
95D3×A4C3×A416yesdirect product factor
96C2×C33—122no—
97C2×C33—481no—
98C32×D3—42no—
99C32×D3—122no—
100C32×D3—169no—
101C32×D3—162no—
102C24×C3—21no—
103C24×C3—92no—
104C24×C3—92no—
105C24×C3—271no—
106C24×C3—271no—
107C24×C3C32×D311yescharacteristic, complemented
108C24×C3C2×C3311yescharacteristic, complemented
109C23×D3—32no—
110C23×D3—32no—
111C23×D3—91no—
112C23×D3—91no—
113C22⋊A4—26no—
114C22⋊A4C32×D316yescomplemented
115C22×A4—26no—
116C22×A4—96no—
117C22×A4—96no—
118C22×A4C32×D316yescomplemented
119C22×C32—32no—
120C22×C32—42no—
121C22×C32—46no—
122C22×C32—86no—
123C22×C32—82no—
124C22×C32—91no—
125C22×C32—92no—
126C22×C32—362no—
127C22×C32—362no—
128C22×C32C2×C3×A412yescomplemented
129C2×C3×D3—32no—
130C2×C3×D3—32no—
131C2×C3×D3—91no—
132C2×C3×D3—92no—
133C2×C3×D3—94no—
134C2×C3×D3—91no—
135C2×C3×D3—92no—
136C2×C3×D3—92no—
137C2×C3×D3—126no—
138C2×C3×D3—126no—
139C3×A4—22no—
140C3×A4—26no—
141C3×A4—44no—
142C3×A4—418no—
143C3×A4—412no—
144C3×A4—836no—
145C3×A4—818no—
146C3×A4—812no—
147C3×A4—84no—
148C3×A4—818no—
149C3×A4—122no—
150C3×A4—126no—
151C3×A4—246no—
152C3×A4—242no—
153C3×A4D3×A412yesdirect product factor
154C3×A4C2×C3×A416yescomplemented
155C25—31noSylow
156C33—42no—
157C33—161no—
158C33—169no—
159C33—162no—
160C33—322no—
161C33—329no—
162C33—322no—
163C23×C3—32no—
164C23×C3—32no—
165C23×C3—32no—
166C23×C3—62no—
167C23×C3—91no—
168C23×C3—91no—
169C23×C3—92no—
170C23×C3—92no—
171C23×C3—126no—
172C23×C3—181no—
173C23×C3—272no—
174C23×C3—271no—
175C23×C3—272no—
176C23×C3—272no—
177C23×C3—272no—
178C23×C3—271no—
179C23×C3—274no—
180C22×D3—32no—
181C22×D3—32no—
182C22×D3—91no—
183C22×D3—92no—
184C22×D3—92no—
185C22×D3—92no—
186C22×D3—92no—
187C22×D3—94no—
188C22×D3—91no—
189C22×D3C32×A412yescomplemented
190C2×A4—36no—
191C2×A4—36no—
192C2×A4—66no—
193C2×A4—96no—
194C2×A4—1212no—
195C2×A4—366no—
196C2×C32—32no—
197C2×C32—91no—
198C2×C32—122no—
199C2×C32—122no—
200C2×C32—126no—
201C2×C32—242no—
202C2×C32—246no—
203C2×C32—362no—
204C2×C32—482no—
205C2×C32—489no—
206C3×D3—32no—
207C3×D3—46no—
208C3×D3—91no—
209C3×D3—126no—
210C3×D3—166no—
211C3×D3A4211yescharacteristic, direct product factor
212C24—92no—
213C24—92no—
214C24—271no—
215C24—271no—
216C24C33×D311yescharacteristic, complemented
217C22×C3—22no—
218C22×C3—32no—
219C22×C3—32no—
220C22×C3—46no—
221C22×C3—62no—
222C22×C3—86no—
223C22×C3—91no—
224C22×C3—91no—
225C22×C3—92no—
226C22×C3—92no—
227C22×C3—92no—
228C22×C3—92no—
229C22×C3—181no—
230C22×C3—182no—
231C22×C3—271no—
232C22×C3—272no—
233C22×C3—272no—
234C22×C3—271no—
235C22×C3—274no—
236C22×C3—272no—
237C22×C3—366no—
238C22×C3—366no—
239C22×C3C3×D3×A412yescomplemented
240C22×C3C2×C32×A412yescomplemented
241C2×D3—32no—
242C2×D3—32no—
243C2×D3—91no—
244C2×D3—92no—
245C2×D3—94no—
246C2×D3—91no—
247C2×D3—92no—
248C2×D3—92no—
249A4—26no—
250A4—412no—
251A4—812no—
252A4—126no—
253A4—246no—
254A4C3×D3×A416yesdirect product factor
255C32—42no—
256C32—46no—
257C32—86no—
258C32—82no—
259C32—169no—
260C32—162no—
261C32—166no—
262C32—326no—
263C32—3218no—
264C32—3218no—
265C32—322no—
266C32C2×A4211yescharacteristic, complemented
267C23—32no—
268C23—32no—
269C23—91no—
270C23—92no—
271C23—92no—
272C23—272no—
273C23—271no—
274C23—272no—
275C23—272no—
276C23—272no—
277C23—271no—
278C23—274no—
279C2×C3—32no—
280C2×C3—31no—
281C2×C3—32no—
282C2×C3—62no—
283C2×C3—91no—
284C2×C3—92no—
285C2×C3—91no—
286C2×C3—126no—
287C2×C3—126no—
288C2×C3—181no—
289C2×C3—246no—
290C2×C3—271no—
291C2×C3—366no—
292C2×C3—486no—
293D3—32no—
294D3—91no—
295D3C3×A4211yescharacteristic, direct product factor
296C22—32no—
297C22—91no—
298C22—92no—
299C22—92no—
300C22—92no—
301C22—271no—
302C22—272no—
303C22—272no—
304C22—271no—
305C22—274no—
306C22—272no—
307C22C32×D3×A412yescomplemented
308C3—21no—
309C3—46no—
310C3—86no—
311C3—166no—
312C3—326no—
313C3D3×A4211yescharacteristic, direct product factor
314C3C2×C3×A4211yescharacteristic, complemented
315C2—32no—
316C2—31no—
317C2—91no—
318C2—92no—
319C2—271no—
subgroupG/H
center, hypercenterC3D3×A42
commutator, cosocle, hypocenterC24×C3C2×C33
FrattiniC1G
Fitting, socleC24×C32C2×C32
LCSG ▷ C24×C3
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×A42C2semidirect
2. C3×D3×C22⋊A4C3semidirect
3. C22×C3×D3×A4C3semidirect
5. D3×A42C3direct (N × H)
7. C32×C22⋊A4C2×C3semidirect
8. C22×C32×A4C2×C3semidirect
14. C3×A42D3direct (N × H)
15. C3×A42C2×C3semidirect
17. C24×C3×D3C32semidirect
20. D3×C22⋊A4C32semidirect
21. C22×D3×A4C32semidirect
30. C3×D3×A4A4direct (N × H)
32. C24×C32C2×C32semidirect
39. C3×C22⋊A4C3×D3semidirect
40. C3×C22⋊A4C2×C32semidirect
45. C22×C3×A4C3×D3semidirect
46. C22×C3×A4C2×C32semidirect
51. A42C3×D3direct (N × H)
63. C32×A4C2×A4semidirect
65. C24×D3C33semidirect
82. C22×C3×D3C3×A4semidirect
95. D3×A4C3×A4direct (N × H)
107. C24×C3C32×D3semidirect
108. C24×C3C2×C33semidirect
114. C22⋊A4C32×D3semidirect
118. C22×A4C32×D3semidirect
128. C22×C32C2×C3×A4semidirect
153. C3×A4D3×A4direct (N × H)
154. C3×A4C2×C3×A4semidirect
189. C22×D3C32×A4semidirect
211. C3×D3A42direct (N × H)
216. C24C33×D3semidirect
239. C22×C3C3×D3×A4semidirect
240. C22×C3C2×C32×A4semidirect
254. A4C3×D3×A4direct (N × H)
266. C32C2×A42semidirect
295. D3C3×A42direct (N × H)
307. C22C32×D3×A4semidirect
313. C3D3×A42direct (N × H)
314. C3C2×C3×A42semidirect

Maximal subgroups

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

subgroupindex
C32×A422
C3×D3×C22⋊A43
C22×C3×D3×A43
C2×C3×A423
D3×A423
C32×D3×A44