Finite Group Databasebeta

← S4×C3⋊(D13⋊C3) #72242068

Subgroups — S4×C3⋊(D13⋊C3) #72242068

Order 5616.

326 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 34 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
1#72242049C211yesmaximal, characteristic, complemented
2C3×S4×C13⋊C3C211yesmaximal, characteristic, complemented
3A4×C3⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
4S4×D39C311yesmaximal, characteristic, complemented
5S4×D13⋊C3—31nomaximal
6D4×C3⋊(D13⋊C3)—31nomaximal
7C3×A4×C13⋊C3C2211yescharacteristic, complemented
8D3×C3⋊(D13⋊C3)—41nomaximal
9C3⋊(D13⋊A4)—21no—
10A4×D39C2×C311yescharacteristic, complemented
11C22×C3⋊(D13⋊C3)—31no—
12C22×C3⋊(D13⋊C3)D311yescharacteristic, complemented
13C3⋊(A4⋊D13)C2×C311yescharacteristic, complemented
14C3×C13×S4C2×C311yescharacteristic, complemented
15A4×D13⋊C3—31no—
16A4⋊(D13⋊C3)—31no—
17A4⋊(D13⋊C3)—61no—
18S4×C13⋊C3—21no—
19S4×C13⋊C3D311yescharacteristic, complemented
20C3×D4×C13⋊C3—31no—
21#64625⋊C3—31no—
22#64625⋊C3—31no—
23C4⋊(C3⋊(D13⋊C3))—31no—
24C4×C3⋊(D13⋊C3)—31no—
25C3⋊(C3⋊(D13⋊C3))—41no—
26C3×C3⋊(D13⋊C3)—41no—
27C3×D3×C13⋊C3—41no—
28S4×D13—31no—
29D4×D39—31no—
30D4×D13⋊C3—91no—
31C3×C22⋊(C13⋊C3)—21no—
32C3×A4×C13C22×C311yescharacteristic, complemented
33C22×C3×C13⋊C3—31no—
34C22×C3×C13⋊C3C2×D311yescharacteristic, complemented
35D3×D39—41no—
36C2×C3⋊(D13⋊C3)—31no—
37C2×C3⋊(D13⋊C3)—31no—
38C2×C3⋊(D13⋊C3)—31no—
39C2×C3⋊(D13⋊C3)—61no—
40C2×C3⋊(D13⋊C3)—61no—
41A4×C13⋊C3—21no—
42A4×C13⋊C3—21no—
43A4×C13⋊C3—41no—
44A4×C13⋊C3C2×D311yescharacteristic, complemented
45D3×D13⋊C3—121no—
46C3×C4×C13⋊C3—31no—
47C3⋊(Dic13⋊C3)—31no—
48C3×D3×S4—131nomaximal, Hall
49C32×C13⋊C3—41noHall
50C22×D39—31no—
51C22×D39C3×D311yescharacteristic, complemented
52D13⋊A4—61no—
53A4×D13—31no—
54C22×D13⋊C3—31no—
55C22×D13⋊C3—91no—
56A4⋊D13—31no—
57A4⋊D13—61no—
58C13×S4C3×D311yescharacteristic, complemented
59C3×D4×C13—31no—
60#64625—31no—
61#64625—31no—
62D156—31no—
63C4×D39—31no—
64D4×C13⋊C3—31no—
65D4×C13⋊C3—61no—
66(C22⋊D13)⋊C3—91no—
67(C22⋊D13)⋊C3—91no—
68C4⋊(D13⋊C3)—91no—
69C4×D13⋊C3—91no—
70C3⋊D39—41no—
71C3×D39—41no—
72C3×D3×C13—41no—
73C2×C3×C13⋊C3—31no—
74C2×C3×C13⋊C3—61no—
75C3⋊(D13⋊C3)—31no—
76C3⋊(D13⋊C3)—61no—
77C3⋊(D13⋊C3)—81no—
78C3⋊(D13⋊C3)—121no—
79C3⋊(D13⋊C3)—241no—
80C3⋊(D13⋊C3)S411yescharacteristic, direct product factor
81D3×C13⋊C3—41no—
82D3×C13⋊C3—81no—
83C3×D13⋊C3—121no—
84C3×D3×A4—131no—
85C3×C3⋊S4—131no—
86C32×S4—131no—
87D4×D13—91noHall
88C22×C3×C13—31no—
89C22×C3×C13C2×C3×D311yescharacteristic, complemented
90C2×D39—31no—
91C2×D39—31no—
92C2×D39—31no—
93C2×D39—61no—
94C2×D39—61no—
95C22⋊(C13⋊C3)—21no—
96C22⋊(C13⋊C3)—41no—
97A4×C13—21no—
98A4×C13C2×C3×D311yescharacteristic, complemented
99C22×C13⋊C3—21no—
100C22×C13⋊C3—31no—
101C22×C13⋊C3—61no—
102C22×C13⋊C3D3211yescharacteristic, complemented
103D3×D13—121no—
104C2×D13⋊C3—91no—
105C2×D13⋊C3—91no—
106C2×D13⋊C3—91no—
107C2×D13⋊C3—181no—
108C2×D13⋊C3—181no—
109C3×C4×C13—31no—
110Dic39—31no—
111C4×C13⋊C3—31no—
112C4×C13⋊C3—61no—
113Dic13⋊C3—91no—
114C2×C3×S4—391no—
115D3×S4—131no—
116C3×D3×D4—391no—
117C32×C13—41no—
118C3×C13⋊C3—41no—
119C3×C13⋊C3—81no—
120C3×C13⋊C3—81no—
121C3×C13⋊C3—81no—
122C3×C13⋊C3—161no—
123C3×C13⋊C3C2×S411yescharacteristic, complemented
124C32×A4—131no—
125C3×D32—521no—
126C22×D13—31no—
127C22×D13—91no—
128D4×C13—31no—
129C22⋊D13—91no—
130C22⋊D13—91no—
131D52—91no—
132C4×D13—91no—
133C2×C3×C13—31no—
134C2×C3×C13—61no—
135D39—31no—
136D39—61no—
137D39—121no—
138D39—241no—
139D39C3×S411yescharacteristic, complemented
140C3×D13—121no—
141D3×C13—41no—
142C2×C13⋊C3—31no—
143C2×C13⋊C3—61no—
144C2×C13⋊C3—61no—
145C2×C13⋊C3—121no—
146D13⋊C3—31no—
147D13⋊C3—91no—
148D13⋊C3—181no—
149D13⋊C3—241no—
150C22×C3×D3—131no—
151C22×C3×D3—391no—
152C2×C3×A4—391no—
153D3×A4—131no—
154D3×A4—261no—
155C3⋊S4—131no—
156C3×S4—131no—
157C3×S4—261no—
158C3×S4—391no—
159C3×S4—781no—
160C3×S4D13⋊C311yescharacteristic, complemented
161C32×D4—391no—
162C3×#67—391no—
163C3×#67—391no—
164C3×D12—391no—
165C3×C4×D3—391no—
166C3×C3⋊D3—521no—
167C32×D3—521no—
168C32×D3—521no—
169C22×C13—31no—
170C22×C13C3×D3211yescharacteristic, complemented
171C2×D13—91no—
172C2×D13—91no—
173C2×D13—91no—
174C2×D13—181no—
175C2×D13—181no—
176C4×C13—31no—
177Dic13—91no—
178C2×S4—391no—
179C2×C3×D4—1171no—
180D3×D4—391no—
181C3×C13—41no—
182C3×C13—81no—
183C3×C13C2×C3×S411yescharacteristic, complemented
184C13⋊C3—21no—
185C13⋊C3—81no—
186C13⋊C3—161no—
187C13⋊C3D3×S411yescharacteristic, complemented
188C22×C32—131no—
189C22×C32—391no—
190C2×C3×D3—391no—
191C2×C3×D3—391no—
192C2×C3×D3—391no—
193C2×C3×D3—781no—
194C2×C3×D3—781no—
195C2×C3×D3—1561no—
196C3×A4—131no—
197C3×A4—261no—
198C3×A4—261no—
199C3×A4—261no—
200C3×A4—521no—
201C3×A4C2×D13⋊C311yescharacteristic, complemented
202D32—521no—
203C32×C4—391no—
204C3×Dic3—391no—
205C33—521noSylow
206C2×C13—31no—
207C2×C13—61no—
208D13—31no—
209D13—91no—
210D13—181no—
211C23×C3—391no—
212C23×C3—1171no—
213C22×D3—131no—
214C22×D3—391no—
215C2×A4—391no—
216C2×A4—781no—
217S4—391no—
218S4—781no—
219S4C3⋊(D13⋊C3)11yescharacteristic, direct product factor
220C3×D4—31no—
221C3×D4—391no—
222C3×D4—781no—
223C3×D4—1171no—
224C3×D4—1171no—
225C3×D4—1171no—
226C2×C3×C4—1171no—
227#67—391no—
228#67—391no—
229D12—391no—
230C4×D3—391no—
231C2×C32—391no—
232C2×C32—781no—
233C2×C32—1561no—
234C3⋊D3—521no—
235C3×D3—41no—
236C3×D3—131no—
237C3×D3—391no—
238C3×D3—521no—
239C3×D3—521no—
240C3×D3—3121no—
241C3×D3—781no—
242C3×D3—1041no—
243C3×D3—1041no—
244C3×D3—1561no—
245C2×D4—1171noSylow
246C13C3×D3×S411yescharacteristic, complemented, Sylow
247C22×C3—31no—
248C22×C3—131no—
249C22×C3—261no—
250C22×C3—391no—
251C22×C3—781no—
252C22×C3—1171no—
253C22×C3—1171no—
254C22×C3—1171no—
255C22×C3—2341no—
256C22×C3—2341no—
257C22×C3D3×D13⋊C311yescharacteristic, complemented
258C2×D3—391no—
259C2×D3—391no—
260C2×D3—391no—
261C2×D3—781no—
262C2×D3—781no—
263C2×D3—1561no—
264A4—21no—
265A4—261no—
266A4—521no—
267A4C2×C3⋊(D13⋊C3)11yescharacteristic, complemented
268C3×C4—31no—
269C3×C4—391no—
270C3×C4—781no—
271C3×C4—1171no—
272Dic3—391no—
273C32—41no—
274C32—131no—
275C32—521no—
276C32—1041no—
277C32—1041no—
278C32—1041no—
279C32—2081no—
280C23—391no—
281C23—1171no—
282D4—31no—
283D4—1171no—
284D4—1171no—
285D4—1171no—
286C2×C4—1171no—
287C2×C3—31no—
288C2×C3—61no—
289C2×C3—391no—
290C2×C3—391no—
291C2×C3—3121no—
292C2×C3—781no—
293C2×C3—781no—
294C2×C3—1171no—
295C2×C3—1561no—
296C2×C3—1561no—
297C2×C3—2341no—
298D3—41no—
299D3—131no—
300D3—391no—
301D3—3121no—
302D3—781no—
303D3—1561no—
304C22—31no—
305C22—1171no—
306C22—1171no—
307C22—1171no—
308C22—2341no—
309C22—2341no—
310C22D3×C3⋊(D13⋊C3)11yescharacteristic, complemented
311C4—31no—
312C4—1171no—
313C3—41no—
314C3—81no—
315C3—131no—
316C3—261no—
317C3—1041no—
318C3—2081no—
319C3S4×D13⋊C311yescharacteristic, complemented
320C2—31no—
321C2—61no—
322C2—391no—
323C2—1171no—
324C2—2341no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×A4×C13C22×C3
Fitting, socleC22×C3×C13C2×C3×D3
LCSG ▷ C3×A4×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. #72242049C2semidirect
2. C3×S4×C13⋊C3C2semidirect
3. A4×C3⋊(D13⋊C3)C2semidirect
4. S4×D39C3semidirect
7. C3×A4×C13⋊C3C22semidirect
10. A4×D39C2×C3semidirect
12. C22×C3⋊(D13⋊C3)D3semidirect
13. C3⋊(A4⋊D13)C2×C3semidirect
14. C3×C13×S4C2×C3semidirect
19. S4×C13⋊C3D3semidirect
32. C3×A4×C13C22×C3semidirect
34. C22×C3×C13⋊C3C2×D3semidirect
44. A4×C13⋊C3C2×D3semidirect
51. C22×D39C3×D3semidirect
58. C13×S4C3×D3semidirect
80. C3⋊(D13⋊C3)S4direct (N × H)
89. C22×C3×C13C2×C3×D3semidirect
98. A4×C13C2×C3×D3semidirect
102. C22×C13⋊C3D32semidirect
123. C3×C13⋊C3C2×S4semidirect
139. D39C3×S4semidirect
160. C3×S4D13⋊C3semidirect
170. C22×C13C3×D32semidirect
183. C3×C13C2×C3×S4semidirect
187. C13⋊C3D3×S4semidirect
201. C3×A4C2×D13⋊C3semidirect
219. S4C3⋊(D13⋊C3)direct (N × H)
246. C13C3×D3×S4semidirect
257. C22×C3D3×D13⋊C3semidirect
267. A4C2×C3⋊(D13⋊C3)semidirect
310. C22D3×C3⋊(D13⋊C3)semidirect
319. C3S4×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722420492
C3×S4×C13⋊C32
A4×C3⋊(D13⋊C3)2
S4×D393
S4×D13⋊C33
D4×C3⋊(D13⋊C3)3
D3×C3⋊(D13⋊C3)4
C3×D3×S413