Finite Group Databasebeta

← C4×D3×S4 #10596429

Subgroups — C4×D3×S4 #10596429

Order 576.

482 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×D3×S4C211yesmaximal, characteristic
2C4×D3×A4C211yesmaximal, characteristic, complemented
3C4×C3⋊S4C211yesmaximal, characteristic, complemented
4C3×C4×S4C211yesmaximal, characteristic, complemented
5D3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6(C3⋊S4)⋊C4C211yesmaximal, characteristic, complemented
7Dic3×S4C211yesmaximal, characteristic, complemented
8C2×C4×S4—31nomaximal
9C4×D3×D4—31nomaximal
10C2×D3×A4C2211yescharacteristic
11C2×C3⋊S4C2211yescharacteristic
12C2×C3×S4C2211yescharacteristic
13D3×S4C414yesdirect product factor
14C3×C4×A4C2211yescharacteristic, complemented
15C4×D32—41nomaximal
16Dic3×A4C2211yescharacteristic, complemented
17C3⋊SL(2,ℤ/4)C2211yescharacteristic, complemented
18C3×SL(2,ℤ/4)C2211yescharacteristic, complemented
19C22×S4—31no—
20C2×D3×D4—31no—
21C22×C4×D3—31no—
22C22×C4×D3D311yescharacteristic, complemented
23C2×C4×A4—31no—
24C2×SL(2,ℤ/4)—31no—
25C4×S4—31no—
26C4×S4—31no—
27C4×S4—31no—
28C4×S4—61no—
29C4×S4D311yescharacteristic, direct product factor
30C3×C4×D4—31no—
31D4×Dic3—31no—
32C4×#67—31no—
33C4×#67—31no—
34#893—31no—
35D3×C4⋊C4—31no—
36#67⋊C4—31no—
37#67⋊C4—31no—
38D3×C22⋊C4—31no—
39D3×C22⋊C4—31no—
40C4×D12—31no—
41C42×D3—31no—
42C2×C3×A4C2311yescharacteristic
43C2×D32—41no—
44D3×A4C2×C412yescomplemented
45C3⋊S4C2×C412yescomplemented
46C3×S4C2×C412yescomplemented
47C4×C3⋊D3—41no—
48C3×C4×D3—41no—
49C3×C4×D3—41no—
50#624—41no—
51D3×Dic3—41no—
52D3×Dic3—41no—
53C2×C4×D4—91noSylow
54C23×D3—31no—
55C23×D3C2×D311yescharacteristic
56C22×A4—31no—
57C2×S4—31no—
58C2×S4—34no—
59C2×S4—61no—
60C2×S4C2×D311yescharacteristic
61C2×C3×D4—31no—
62C22×C3×C4—31no—
63C22×C3×C4C2×D311yescharacteristic, complemented
64C2×#67—31no—
65C2×#67—31no—
66C22×Dic3—31no—
67C22×Dic3C2×D311yescharacteristic, complemented
68D3×D4—34no—
69D3×D4—34no—
70C2×D12—31no—
71C2×C4×D3—31no—
72C2×C4×D3—31no—
73C2×C4×D3—31no—
74C2×C4×D3—31no—
75C2×C4×D3—31no—
76C2×C4×D3—31no—
77C2×C4×D3—31no—
78C2×C4×D3—31no—
79C2×C4×D3—31no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—121no—
85C4×A4—21no—
86C4×A4—31no—
87C4×A4C2×D311yescharacteristic, complemented
88SL(2,ℤ/4)—31no—
89SL(2,ℤ/4)—61no—
90SL(2,ℤ/4)C2×D311yescharacteristic, complemented
91C3×C4⋊C4—31no—
92C3×C22⋊C4—31no—
93C3×C22⋊C4—31no—
94C3×C42—31no—
95#217—31no—
96#217—31no—
97(C2×D3)⋊C4—31no—
98(C2×D3)⋊C4—31no—
99(C2×D3)⋊C4—31no—
100(C2×D3)⋊C4—31no—
101C4⋊Dic3—31no—
102Dic3⋊C4—31no—
103Dic3⋊C4—31no—
104C4×Dic3—31no—
105C4×Dic3—31no—
106C4×Dic3—31no—
107C2×C3⋊D3—41no—
108C2×C3×D3—41no—
109C2×C3×D3—41no—
110C3×A4C22×C411yescharacteristic, complemented
111D32—44no—
112C32×C4—41no—
113C3⋊Dic3—41no—
114C3×Dic3—41no—
115C3×Dic3—41no—
116C22×D4—91no—
117C23×C4—31no—
118C23×C4—91no—
119C4×D4—31no—
120C4×D4—91no—
121C4×D4—91no—
122C4×D4—91no—
123C4×D4—91no—
124C4×D4—91no—
125C4×D4—91no—
126C4×D4—91no—
127C2×C4⋊C4—91no—
128C2×C22⋊C4—91no—
129C2×C22⋊C4—91no—
130C2×C42—91no—
131C23×C3—31no—
132C23×C3C22×D311yescharacteristic
133C22×D3—31no—
134C22×D3—31no—
135C22×D3—32no—
136C22×D3—31no—
137C22×D3—34no—
138C22×D3—61no—
139C22×D3—62no—
140C22×D3—61no—
141C22×D3—121no—
142C22×D3C4×D312yescomplemented
143C2×A4—21no—
144C2×A4—32no—
145C2×A4C22×D311yescharacteristic
146S4—32no—
147S4—62no—
148S4C4×D312yesdirect product factor
149C3×D4—32no—
150C3×D4—32no—
151C2×C3×C4—31no—
152C2×C3×C4—31no—
153C2×C3×C4—31no—
154C2×C3×C4—31no—
155C2×C3×C4—31no—
156C2×C3×C4—61no—
157C2×C3×C4—61no—
158C2×C3×C4—121no—
159#67—34no—
160#67—32no—
161#67—32no—
162C2×Dic3—31no—
163C2×Dic3—31no—
164C2×Dic3—31no—
165C2×Dic3—31no—
166C2×Dic3—31no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—121no—
170D12—34no—
171C4×D3—34no—
172C4×D3—31no—
173C4×D3—31no—
174C4×D3—31no—
175C4×D3—41no—
176C4×D3—61no—
177C4×D3—61no—
178C4×D3—61no—
179C4×D3—62no—
180C4×D3—61no—
181C4×D3—61no—
182C4×D3—61no—
183C4×D3—61no—
184C4×D3—121no—
185C4×D3—121no—
186C4×D3—121no—
187C4×D3—241no—
188C4×D3S411yescharacteristic, direct product factor
189C2×C32—41no—
190C3⋊D3—42no—
191C3×D3—42no—
192C3×D3—42no—
193C24—31no—
194C24—91no—
195C2×D4—31no—
196C2×D4—91no—
197C2×D4—94no—
198C2×D4—94no—
199C2×D4—91no—
200C2×D4—91no—
201C22×C4—31no—
202C22×C4—31no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—181no—
214C22×C4—181no—
215C22×C4—181no—
216C22×C4—181no—
217C22×C4D3211yescharacteristic, complemented
218C4⋊C4—31no—
219C4⋊C4—91no—
220C4⋊C4—91no—
221C4⋊C4—91no—
222C22⋊C4—31no—
223C22⋊C4—31no—
224C22⋊C4—91no—
225C22⋊C4—91no—
226C22⋊C4—91no—
227C22⋊C4—91no—
228C22⋊C4—91no—
229C22⋊C4—91no—
230C42—31no—
231C42—91no—
232C42—91no—
233C42—91no—
234C22×C3—31no—
235C22×C3—31no—
236C22×C3—32no—
237C22×C3—61no—
238C22×C3—61no—
239C22×C3—121no—
240C22×C3C2×C4×D311yescharacteristic, complemented
241C2×D3—31no—
242C2×D3—32no—
243C2×D3—32no—
244C2×D3—32no—
245C2×D3—32no—
246C2×D3—41no—
247C2×D3—61no—
248C2×D3—64no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—64no—
252C2×D3—124no—
253C2×D3—121no—
254C2×D3—241no—
255C2×D3C2×S411yescharacteristic
256A4—21no—
257A4C2×C4×D311yescharacteristic, complemented
258C3×C4—32no—
259C3×C4—31no—
260C3×C4—41no—
261C3×C4—61no—
262C3×C4—61no—
263C3×C4—81no—
264C3×C4—121no—
265C3×C4C2×S411yescharacteristic, complemented
266Dic3—32no—
267Dic3—31no—
268Dic3—41no—
269Dic3—61no—
270Dic3—61no—
271Dic3—121no—
272Dic3—241no—
273Dic3C2×S411yescharacteristic, complemented
274C32—41noSylow
275C23—31no—
276C23—32no—
277C23—91no—
278C23—91no—
279C23—92no—
280C23—91no—
281C23—94no—
282C23—181no—
283C23—181no—
284C23—182no—
285C23C2×D3211yescharacteristic
286D4—32no—
287D4—32no—
288D4—94no—
289D4—92no—
290D4—94no—
291D4—92no—
292C2×C4—31no—
293C2×C4—31no—
294C2×C4—31no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—31no—
298C2×C4—61no—
299C2×C4—61no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—94no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—181no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—181no—
316C2×C4—182no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C3—31no—
320C2×C3—31no—
321C2×C3—41no—
322C2×C3—62no—
323C2×C3—81no—
324C2×C3—122no—
325C2×C3C22×S411yescharacteristic
326D3—32no—
327D3—42no—
328D3—62no—
329D3—122no—
330D3—242no—
331D3C4×S412yesdirect product factor
332C22—31no—
333C22—31no—
334C22—31no—
335C22—32no—
336C22—61no—
337C22—61no—
338C22—92no—
339C22—92no—
340C22—92no—
341C22—92no—
342C22—91no—
343C22—184no—
344C22—181no—
345C22—181no—
346C22—184no—
347C22—181no—
348C22C4×D3211yescharacteristic, complemented
349C4—32no—
350C4—31no—
351C4—31no—
352C4—61no—
353C4—61no—
354C4—92no—
355C4—91no—
356C4—181no—
357C4—181no—
358C4D3×S411yescharacteristic, direct product factor
359C3—41no—
360C3—81no—
361C3C2×C4×S411yescharacteristic, complemented
362C2—31no—
363C2—31no—
364C2—32no—
365C2—62no—
366C2—92no—
367C2—182no—
368C2C2×D3×S411yescharacteristic
subgroupG/H
center, hypercenterC4D3×S4
commutator, hypocenterC3×A4C22×C4
FrattiniC2C2×D3×S4
FittingC22×C3×C4C2×D3
socleC23×C3C22×D3
prime radicalC2×D3×S4C2
cosocleC2×C3×A4C23
LCSG ▷ C3×A4
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×D3×A4C2semidirect
3. C4×C3⋊S4C2semidirect
4. C3×C4×S4C2semidirect
5. D3×SL(2,ℤ/4)C2semidirect
6. (C3⋊S4)⋊C4C2semidirect
7. Dic3×S4C2semidirect
13. D3×S4C4direct (N × H)
14. C3×C4×A4C22semidirect
16. Dic3×A4C22semidirect
17. C3⋊SL(2,ℤ/4)C22semidirect
18. C3×SL(2,ℤ/4)C22semidirect
22. C22×C4×D3D3semidirect
29. C4×S4D3direct (N × H)
44. D3×A4C2×C4semidirect
45. C3⋊S4C2×C4semidirect
46. C3×S4C2×C4semidirect
63. C22×C3×C4C2×D3semidirect
67. C22×Dic3C2×D3semidirect
87. C4×A4C2×D3semidirect
90. SL(2,ℤ/4)C2×D3semidirect
110. C3×A4C22×C4semidirect
142. C22×D3C4×D3semidirect
148. S4C4×D3direct (N × H)
188. C4×D3S4direct (N × H)
217. C22×C4D32semidirect
240. C22×C3C2×C4×D3semidirect
257. A4C2×C4×D3semidirect
265. C3×C4C2×S4semidirect
273. Dic3C2×S4semidirect
331. D3C4×S4direct (N × H)
348. C22C4×D32semidirect
358. C4D3×S4direct (N × H)
361. C3C2×C4×S4semidirect

Maximal subgroups

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

subgroupindex
C2×D3×S42
C4×D3×A42
C4×C3⋊S42
C3×C4×S42
D3×SL(2,ℤ/4)2
(C3⋊S4)⋊C42
Dic3×S42
C2×C4×S43
C4×D3×D43
C4×D324