Finite Group Databasebeta

← C3×S4×D13⋊C3 #72242044

Subgroups — C3×S4×D13⋊C3 #72242044

Order 5616.

460 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 62 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⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
2C3×S4×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×A4×D13⋊C3C211yesmaximal, characteristic, complemented
4C3×S4×D13C311yesmaximal, characteristic, complemented
5S4×D13⋊C3C313yesmaximal, direct product factor
6C3×D4×D13⋊C3—31nomaximal
7C3×A4×C13⋊C3C2211yescharacteristic, complemented
8C3×D3×D13⋊C3—41nomaximal
9C3×D13⋊A4—21no—
10C3×A4×D13C2×C311yescharacteristic, complemented
11C22×C3×D13⋊C3—31no—
12C22×C3×D13⋊C3D311yescharacteristic, complemented
13C3×A4⋊D13C2×C311yescharacteristic, complemented
14C3×C13×S4C2×C311yescharacteristic, complemented
15A4×D13⋊C3—23no—
16A4×D13⋊C3C2×C313yescomplemented
17A4⋊(D13⋊C3)C2×C313yescomplemented
18S4×C13⋊C3C2×C313yescomplemented
19C3×D4×C13⋊C3—31no—
20C3×(C22⋊D13)⋊C3—31no—
21C3×(C22⋊D13)⋊C3—31no—
22C3×C4⋊(D13⋊C3)—31no—
23C3×C4×D13⋊C3—31no—
24C3×C3⋊(D13⋊C3)—41no—
25C3×D3×C13⋊C3—41no—
26C32×D13⋊C3—41no—
27S4×D13C3211yescharacteristic, complemented
28C3×D4×D13—31no—
29D4×D13⋊C3—33no—
30C3×C22⋊(C13⋊C3)—21no—
31C3×A4×C13C22×C311yescharacteristic, complemented
32C22×C3×C13⋊C3—31no—
33C22×C3×C13⋊C3C2×D311yescharacteristic, complemented
34C3×D3×D13—41no—
35C2×C3×D13⋊C3—31no—
36C2×C3×D13⋊C3—31no—
37C2×C3×D13⋊C3—31no—
38C2×C3×D13⋊C3—61no—
39C2×C3×D13⋊C3—61no—
40A4×C13⋊C3—23no—
41A4×C13⋊C3C22×C313yescomplemented
42D3×D13⋊C3—43no—
43C3×C4×C13⋊C3—31no—
44C3×Dic13⋊C3—31no—
45C2×C32×S4—131nomaximal, Hall
46C32×C13⋊C3—41noHall
47C22×C3×D13—31no—
48C22×C3×D13C3×D311yescharacteristic, complemented
49D13⋊A4—23no—
50A4×D13—21no—
51A4×D13C2×C3211yescharacteristic, complemented
52C22×D13⋊C3—33no—
53C22×D13⋊C3C3×D313yescomplemented
54A4⋊D13C2×C3211yescharacteristic, complemented
55C13×S4C2×C3211yescharacteristic, complemented
56C3×D4×C13—31no—
57C3×C22⋊D13—31no—
58C3×C22⋊D13—31no—
59C3×D52—31no—
60C3×C4×D13—31no—
61D4×C13⋊C3—33no—
62(C22⋊D13)⋊C3—33no—
63(C22⋊D13)⋊C3—33no—
64C4⋊(D13⋊C3)—33no—
65C4×D13⋊C3—33no—
66C3×D39—41no—
67C3×D3×C13—41no—
68C32×D13—41no—
69C2×C3×C13⋊C3—31no—
70C2×C3×C13⋊C3—61no—
71C3⋊(D13⋊C3)—43no—
72D3×C13⋊C3—43no—
73C3×D13⋊C3—31no—
74C3×D13⋊C3—43no—
75C3×D13⋊C3—61no—
76C3×D13⋊C3—81no—
77C3×D13⋊C3—83no—
78C3×D13⋊C3S411yescharacteristic, direct product factor
79C2×C32×A4—131no—
80C32×S4—131no—
81C32×S4—131no—
82D4×D13—31noHall
83C22×C3×C13—31no—
84C22×C3×C13C2×C3×D311yescharacteristic, complemented
85C2×C3×D13—31no—
86C2×C3×D13—31no—
87C2×C3×D13—31no—
88C2×C3×D13—61no—
89C2×C3×D13—61no—
90C22⋊(C13⋊C3)—23no—
91A4×C13—21no—
92A4×C13C22×C3211yescharacteristic, complemented
93C22×C13⋊C3—33no—
94C22×C13⋊C3C2×C3×D313yescomplemented
95D3×D13—41no—
96C2×D13⋊C3—33no—
97C2×D13⋊C3—33no—
98C2×D13⋊C3—33no—
99C2×D13⋊C3—63no—
100C2×D13⋊C3—63no—
101C3×C4×C13—31no—
102C3×Dic13—31no—
103C4×C13⋊C3—33no—
104Dic13⋊C3—33no—
105C2×C3×S4—133no—
106C2×C3×S4—131no—
107C2×C32×D4—391no—
108C32×C13—41no—
109C3×C13⋊C3—43no—
110C3×C13⋊C3—81no—
111C3×C13⋊C3—83no—
112C3×C13⋊C3C2×S411yescharacteristic, complemented
113C2×C32×D3—521no—
114C32×A4—131no—
115C22×D13—31no—
116C22×D13C32×D311yescharacteristic, complemented
117D4×C13—31no—
118C22⋊D13—31no—
119C22⋊D13—31no—
120D52—31no—
121C4×D13—31no—
122C2×C3×C13—31no—
123C2×C3×C13—61no—
124D39—41no—
125C3×D13—31no—
126C3×D13—41no—
127C3×D13—61no—
128C3×D13—81no—
129C3×D13C3×S411yescharacteristic, complemented
130D3×C13—41no—
131C2×C13⋊C3—33no—
132C2×C13⋊C3—63no—
133D13⋊C3—33no—
134D13⋊C3—63no—
135D13⋊C3—83no—
136D13⋊C3C3×S413yesdirect product factor
137C23×C32—131no—
138C23×C32—391no—
139C2×C3×A4—133no—
140C2×C3×A4—131no—
141C2×C3×A4—263no—
142C2×C3×A4—261no—
143C3×S4—133no—
144C3×S4—131no—
145C3×S4—133no—
146C3×S4D13⋊C311yescharacteristic, direct product factor
147C32×D4—391no—
148C32×D4—391no—
149C32×D4—391no—
150C32×D4—391no—
151C2×C32×C4—391no—
152C2×C33—521no—
153C32×D3—521no—
154C32×D3—521no—
155C22×C13—31no—
156C22×C13C2×C32×D311yescharacteristic, complemented
157C2×D13—31no—
158C2×D13—31no—
159C2×D13—31no—
160C2×D13—61no—
161C2×D13—61no—
162C4×C13—31no—
163Dic13—31no—
164C2×S4—131no—
165C2×C3×D4—391no—
166C2×C3×D4—393no—
167C3×C13—41no—
168C3×C13—81no—
169C3×C13C2×C3×S411yescharacteristic, complemented
170C13⋊C3—83no—
171C13⋊C3C2×C3×S413yescomplemented
172C22×C32—131no—
173C22×C32—391no—
174C22×C32—391no—
175C22×C32—391no—
176C22×C32—391no—
177C22×C32—781no—
178C22×C32—781no—
179C2×C3×D3—521no—
180C2×C3×D3—523no—
181C3×A4—133no—
182C3×A4—263no—
183C3×A4—261no—
184C3×A4C2×D13⋊C311yescharacteristic, complemented
185C32×C4—391no—
186C32×C4—391no—
187C33—521noSylow
188C2×C13—31no—
189C2×C13—61no—
190D13—31no—
191D13—61no—
192D13C32×S411yescharacteristic, complemented
193C23×C3—133no—
194C23×C3—131no—
195C23×C3—391no—
196C23×C3—393no—
197C2×A4—131no—
198C2×A4—261no—
199C2×A4—263no—
200S4—131no—
201S4C3×D13⋊C311yescharacteristic, direct product factor
202C3×D4—31no—
203C3×D4—393no—
204C3×D4—391no—
205C3×D4—391no—
206C3×D4—393no—
207C3×D4—393no—
208C3×D4—393no—
209C3×D4—391no—
210C2×C3×C4—391no—
211C2×C3×C4—393no—
212C2×C32—131no—
213C2×C32—391no—
214C2×C32—391no—
215C2×C32—521no—
216C2×C32—523no—
217C2×C32—781no—
218C2×C32—781no—
219C2×C32—1043no—
220C2×C32—1041no—
221C3×D3—41no—
222C3×D3—523no—
223C3×D3—521no—
224C3×D3—523no—
225C2×D4—391noSylow
226C13C2×C32×S411yescharacteristic, complemented, Sylow
227C22×C3—31no—
228C22×C3—133no—
229C22×C3—393no—
230C22×C3—391no—
231C22×C3—391no—
232C22×C3—391no—
233C22×C3—393no—
234C22×C3—393no—
235C22×C3—393no—
236C22×C3—781no—
237C22×C3—781no—
238C22×C3—783no—
239C22×C3—783no—
240C22×C3D3×D13⋊C311yescharacteristic, complemented
241C2×D3—521no—
242A4—21no—
243A4—263no—
244A4C2×C3×D13⋊C311yescharacteristic, complemented
245C3×C4—31no—
246C3×C4—393no—
247C3×C4—391no—
248C3×C4—393no—
249C32—41no—
250C32—131no—
251C32—523no—
252C32—1043no—
253C32—1041no—
254C23—131no—
255C23—391no—
256D4—31no—
257D4—391no—
258D4—391no—
259D4—391no—
260C2×C4—391no—
261C2×C3—31no—
262C2×C3—61no—
263C2×C3—133no—
264C2×C3—131no—
265C2×C3—393no—
266C2×C3—393no—
267C2×C3—391no—
268C2×C3—521no—
269C2×C3—783no—
270C2×C3—783no—
271C2×C3—781no—
272C2×C3—1041no—
273C2×C3—1043no—
274D3—41no—
275D3—521no—
276C22—31no—
277C22—391no—
278C22—391no—
279C22—391no—
280C22—781no—
281C22—781no—
282C22C3×D3×D13⋊C311yescharacteristic, complemented
283C4—31no—
284C4—391no—
285C3—41no—
286C3—81no—
287C3—133no—
288C3—1043no—
289C3S4×D13⋊C311yescharacteristic, direct product factor
290C2—31no—
291C2—61no—
292C2—131no—
293C2—391no—
294C2—781no—
subgroupG/H
center, hypercenterC3S4×D13⋊C3
commutator, cosocle, hypocenterA4×C13C22×C32
FrattiniC1G
Fitting, socleC22×C3×C13C2×C3×D3
LCSG ▷ A4×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×A4⋊(D13⋊C3)C2semidirect
2. C3×S4×C13⋊C3C2semidirect
3. C3×A4×D13⋊C3C2semidirect
4. C3×S4×D13C3semidirect
5. S4×D13⋊C3C3direct (N × H)
7. C3×A4×C13⋊C3C22semidirect
10. C3×A4×D13C2×C3semidirect
12. C22×C3×D13⋊C3D3semidirect
13. C3×A4⋊D13C2×C3semidirect
14. C3×C13×S4C2×C3semidirect
16. A4×D13⋊C3C2×C3semidirect
17. A4⋊(D13⋊C3)C2×C3semidirect
18. S4×C13⋊C3C2×C3semidirect
27. S4×D13C32semidirect
31. C3×A4×C13C22×C3semidirect
33. C22×C3×C13⋊C3C2×D3semidirect
41. A4×C13⋊C3C22×C3semidirect
48. C22×C3×D13C3×D3semidirect
51. A4×D13C2×C32semidirect
53. C22×D13⋊C3C3×D3semidirect
54. A4⋊D13C2×C32semidirect
55. C13×S4C2×C32semidirect
78. C3×D13⋊C3S4direct (N × H)
84. C22×C3×C13C2×C3×D3semidirect
92. A4×C13C22×C32semidirect
94. C22×C13⋊C3C2×C3×D3semidirect
112. C3×C13⋊C3C2×S4semidirect
116. C22×D13C32×D3semidirect
129. C3×D13C3×S4semidirect
136. D13⋊C3C3×S4direct (N × H)
146. C3×S4D13⋊C3direct (N × H)
156. C22×C13C2×C32×D3semidirect
169. C3×C13C2×C3×S4semidirect
171. C13⋊C3C2×C3×S4semidirect
184. C3×A4C2×D13⋊C3semidirect
192. D13C32×S4semidirect
201. S4C3×D13⋊C3direct (N × H)
226. C13C2×C32×S4semidirect
240. C22×C3D3×D13⋊C3semidirect
244. A4C2×C3×D13⋊C3semidirect
282. C22C3×D3×D13⋊C3semidirect
289. C3S4×D13⋊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⋊(D13⋊C3)2
C3×S4×C13⋊C32
C3×A4×D13⋊C32
C3×S4×D133
S4×D13⋊C33
C3×D4×D13⋊C33
C3×D3×D13⋊C34
C2×C32×S413