Finite Group Databasebeta

← C4×Dic3×S4 #11921963

Subgroups — C4×Dic3×S4 #11921963

Order 1152.

1024 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 127 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×C3×C4×S4C211yesmaximal, characteristic
2C2×Dic3×S4C212yesmaximal
3C4×Dic3×A4C211yesmaximal, characteristic, complemented
4C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5Dic3×SL(2,ℤ/4)C212yesmaximal, complemented
6C42×S4—31nomaximal
7C4×D4×Dic3—31nomaximal
8C22×C3×S4C2211yescharacteristic
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11C2×C3⋊SL(2,ℤ/4)C2212yes—
12C2×C3×SL(2,ℤ/4)C2211yescharacteristic
13C3×C4×S4C414yescomplemented
14Dic3×S4C418yesdirect product factor
15C4×D3×Dic3—41nomaximal
16C2×C4×S4—32no—
17C2×C4×S4D311yescharacteristic
18C2×C3×C4×D4—31no—
19C2×D4×Dic3—32no—
20C22×C4×Dic3—31no—
21C22×C4×Dic3D311yescharacteristic, complemented
22C42×A4—31no—
23C4×SL(2,ℤ/4)—31no—
24C4×SL(2,ℤ/4)—32no—
25C4×SL(2,ℤ/4)—61no—
26C4×#217—31no—
27C4×#217—31no—
28Dic3×C4⋊C4—32no—
29Dic3×C22⋊C4—32no—
30Dic3×C22⋊C4—32no—
31C4×C4⋊Dic3—31no—
32C42×Dic3—31no—
33C22×C3×A4C2311yescharacteristic
34C2×C3×S4C2×C414yes—
35C2×C3×S4C2×C412yes—
36C2×C3×C4×D3—41no—
37C3×C4×A4C2×C412yescomplemented
38C2×D3×Dic3—42no—
39Dic3×A4C2×C414yescomplemented
40C3⋊SL(2,ℤ/4)C2×C414yescomplemented
41C3×SL(2,ℤ/4)C2×C412yescomplemented
42C4×C3⋊Dic3—41no—
43C3×C4×Dic3—41no—
44Dic32—42no—
45C42×D4—91noSylow
46C22×S4C2×D311yescharacteristic
47C22×C3×D4—31no—
48C23×C3×C4—31no—
49C23×C3×C4C2×D311yescharacteristic
50C23×Dic3—32no—
51C23×Dic3C2×D312yes—
52C2×C4×A4—21no—
53C2×C4×A4—32no—
54C2×C4×A4C2×D311yescharacteristic
55C2×SL(2,ℤ/4)—32no—
56C2×SL(2,ℤ/4)—62no—
57C2×SL(2,ℤ/4)C2×D311yescharacteristic
58C4×S4—38no—
59C4×S4Dic314yesdirect product factor
60C3×C4×D4—34no—
61C3×C4×D4—34no—
62C2×C3×C4⋊C4—31no—
63C2×C3×C22⋊C4—31no—
64C2×C3×C22⋊C4—31no—
65C2×C3×C42—31no—
66C2×#217—32no—
67C2×#217—32no—
68D4×Dic3—38no—
69D4×Dic3—38no—
70C2×C4⋊Dic3—32no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—31no—
73C2×C4×Dic3—31no—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—31no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3—62no—
81C2×C4×Dic3—61no—
82C42×D3—121no—
83C3⋊#95—32no—
84C3⋊#95—32no—
85C3⋊#95—32no—
86C22×C3×D3—41no—
87C2×C3×A4C22×C412yes—
88C2×C3×A4C22×C411yescharacteristic
89C3×S4C4214yescomplemented
90C2×C32×C4—41no—
91C2×C3⋊Dic3—42no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—42no—
94C3×C4×D3—44no—
95D3×Dic3—48no—
96C2×C4×D4—31no—
97C2×C4×D4—92no—
98C22×C42—31no—
99C22×C42—91no—
100C4×C4⋊C4—91no—
101C4×C4⋊C4—92no—
102C4×C22⋊C4—92no—
103C4×C22⋊C4—92no—
104C4×C22⋊C4—91no—
105C4×C22⋊C4—91no—
106C43—91no—
107C24×C3—31no—
108C24×C3C22×D311yescharacteristic
109C22×A4—21no—
110C22×A4C22×D311yescharacteristic
111C2×S4C4×D314yes—
112C2×S4C2×Dic312yes—
113C2×C3×D4—34no—
114C2×C3×D4—32no—
115C2×C3×D4—34no—
116C2×C3×D4—32no—
117C22×C3×C4—31no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—32no—
121C22×C3×C4—31no—
122C22×C3×C4—31no—
123C22×C3×C4—34no—
124C22×C3×C4—61no—
125C22×C3×C4—62no—
126C22×C3×C4—61no—
127C22×C3×C4C4×D312yescomplemented
128C22×Dic3—32no—
129C22×Dic3—32no—
130C22×Dic3—34no—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—38no—
134C22×Dic3—62no—
135C22×Dic3—64no—
136C22×Dic3—62no—
137C22×Dic3C4×D314yescomplemented
138C2×C4×D3—41no—
139C2×C4×D3—122no—
140C4×A4—22no—
141C4×A4—34no—
142C4×A4C2×Dic312yescomplemented
143SL(2,ℤ/4)—34no—
144SL(2,ℤ/4)—64no—
145SL(2,ℤ/4)C2×Dic312yescomplemented
146C3×C4⋊C4—34no—
147C3×C22⋊C4—34no—
148C3×C22⋊C4—32no—
149C3×C22⋊C4—32no—
150C3×C42—34no—
151C3×C42—121no—
152#217—38no—
153#217—34no—
154#217—34no—
155C4⋊Dic3—38no—
156C4×Dic3—38no—
157C4×Dic3—31no—
158C4×Dic3—32no—
159C4×Dic3—61no—
160C4×Dic3—64no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—62no—
166C4×Dic3—122no—
167C4×Dic3—121no—
168C4×Dic3—241no—
169C4×Dic3S411yescharacteristic, direct product factor
170C22×C32—41no—
171C2×C3×D3—44no—
172C2×C3×D3—42no—
173C3×A4C2×C4211yescharacteristic, complemented
174C32×C4—42no—
175C3⋊Dic3—44no—
176C3×Dic3—42no—
177C3×Dic3—44no—
178C22×D4—31no—
179C23×C4—31no—
180C23×C4—32no—
181C23×C4—92no—
182C23×C4D3211yescharacteristic
183C4×D4—34no—
184C4×D4—34no—
185C4×D4—98no—
186C4×D4—98no—
187C2×C4⋊C4—31no—
188C2×C4⋊C4—92no—
189C2×C22⋊C4—31no—
190C2×C22⋊C4—31no—
191C2×C22⋊C4—92no—
192C2×C22⋊C4—92no—
193C2×C42—31no—
194C2×C42—91no—
195C2×C42—92no—
196C2×C42—92no—
197C2×C42—91no—
198C2×C42—91no—
199C2×C42—92no—
200C2×C42—92no—
201C2×C42—91no—
202C2×C42—181no—
203C2×C42—182no—
204C2×C42—181no—
205#95—92no—
206#95—92no—
207#95—92no—
208C23×C3—31no—
209C23×C3—32no—
210C23×C3—31no—
211C23×C3—34no—
212C23×C3—32no—
213C23×C3—62no—
214C23×C3—61no—
215C23×C3—61no—
216C23×C3C2×C4×D312yes—
217C23×C3C2×C4×D311yescharacteristic
218C22×D3—41no—
219C2×A4—22no—
220C2×A4—21no—
221C2×A4C2×C4×D312yes—
222C2×A4C22×Dic311yescharacteristic
223S4C4×Dic314yesdirect product factor
224C3×D4—34no—
225C3×D4—38no—
226C3×D4—34no—
227C2×C3×C4—34no—
228C2×C3×C4—32no—
229C2×C3×C4—31no—
230C2×C3×C4—32no—
231C2×C3×C4—32no—
232C2×C3×C4—32no—
233C2×C3×C4—32no—
234C2×C3×C4—32no—
235C2×C3×C4—41no—
236C2×C3×C4—61no—
237C2×C3×C4—64no—
238C2×C3×C4—62no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—64no—
242C2×C3×C4—81no—
243C2×C3×C4—122no—
244C2×C3×C4C2×S411yescharacteristic
245C2×Dic3—32no—
246C2×Dic3—34no—
247C2×Dic3—34no—
248C2×Dic3—34no—
249C2×Dic3—34no—
250C2×Dic3—34no—
251C2×Dic3—41no—
252C2×Dic3—62no—
253C2×Dic3—68no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258C2×Dic3—68no—
259C2×Dic3—122no—
260C2×Dic3—242no—
261C2×Dic3C2×S412yes—
262C4×D3—44no—
263C4×D3—128no—
264C2×C32—42no—
265C2×C32—41no—
266C3×D3—44no—
267C24—31no—
268C24C2×D3211yescharacteristic
269C2×D4—32no—
270C2×D4—34no—
271C2×D4—34no—
272C2×D4—32no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—32no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—34no—
280C22×C4—34no—
281C22×C4—61no—
282C22×C4—62no—
283C22×C4—61no—
284C22×C4—92no—
285C22×C4—92no—
286C22×C4—94no—
287C22×C4—92no—
288C22×C4—92no—
289C22×C4—98no—
290C22×C4—182no—
291C22×C4—182no—
292C22×C4—184no—
293C22×C4D3×Dic312yescomplemented
294C4⋊C4—34no—
295C4⋊C4—98no—
296C22⋊C4—34no—
297C22⋊C4—32no—
298C22⋊C4—32no—
299C22⋊C4—98no—
300C22⋊C4—94no—
301C22⋊C4—94no—
302C42—34no—
303C42—31no—
304C42—92no—
305C42—98no—
306C42—91no—
307C42—182no—
308C42—181no—
309C42—181no—
310C42—182no—
311C42—182no—
312C42—184no—
313C42—181no—
314C22×C3—32no—
315C22×C3—31no—
316C22×C3—32no—
317C22×C3—32no—
318C22×C3—31no—
319C22×C3—31no—
320C22×C3—34no—
321C22×C3—41no—
322C22×C3—61no—
323C22×C3—64no—
324C22×C3—62no—
325C22×C3—64no—
326C22×C3—62no—
327C22×C3—81no—
328C22×C3C42×D311yescharacteristic, complemented
329C22×C3C22×S411yescharacteristic
330C2×D3—42no—
331C2×D3—44no—
332A4—21no—
333A4C2×C4×Dic311yescharacteristic, complemented
334C3×C4—34no—
335C3×C4—32no—
336C3×C4—42no—
337C3×C4—62no—
338C3×C4—62no—
339C3×C4—82no—
340C3×C4—124no—
341C3×C4C4×S412yescomplemented
342Dic3—34no—
343Dic3—42no—
344Dic3—64no—
345Dic3—64no—
346Dic3—124no—
347Dic3—244no—
348Dic3C4×S414yesdirect product factor
349C32—41noSylow
350C23—31no—
351C23—31no—
352C23—32no—
353C23—32no—
354C23—34no—
355C23—61no—
356C23—62no—
357C23—61no—
358C23C4×D3212yes—
359C23C2×D3×Dic311yescharacteristic
360D4—38no—
361D4—34no—
362D4—34no—
363C2×C4—32no—
364C2×C4—34no—
365C2×C4—32no—
366C2×C4—31no—
367C2×C4—32no—
368C2×C4—32no—
369C2×C4—32no—
370C2×C4—32no—
371C2×C4—32no—
372C2×C4—61no—
373C2×C4—64no—
374C2×C4—62no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—64no—
378C2×C4—94no—
379C2×C4—94no—
380C2×C4—92no—
381C2×C4—94no—
382C2×C4—94no—
383C2×C4—94no—
384C2×C4—188no—
385C2×C4—182no—
386C2×C4—188no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—182no—
391C2×C4D3×S411yescharacteristic
392C2×C3—32no—
393C2×C3—31no—
394C2×C3—31no—
395C2×C3—42no—
396C2×C3—41no—
397C2×C3—64no—
398C2×C3—82no—
399C2×C3—81no—
400C2×C3C2×C4×S412yes—
401C2×C3C2×C4×S411yescharacteristic
402D3—44no—
403C22—32no—
404C22—31no—
405C22—32no—
406C22—32no—
407C22—31no—
408C22—31no—
409C22—34no—
410C22—61no—
411C22—62no—
412C22—64no—
413C22—64no—
414C22—62no—
415C22C4×D3×Dic311yescharacteristic, complemented
416C22C2×D3×S411yescharacteristic
417C4—34no—
418C4—34no—
419C4—32no—
420C4—62no—
421C4—62no—
422C4—94no—
423C4—184no—
424C4—184no—
425C4Dic3×S412yesdirect product factor
426C3—41no—
427C3—81no—
428C3C42×S411yescharacteristic, complemented
429C2—31no—
430C2—31no—
431C2—32no—
432C2—64no—
433C2C4×D3×S412yes—
434C2C2×Dic3×S411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D3×S4
commutator, hypocenterC3×A4C2×C42
FrattiniC22C2×D3×S4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×C3×S4C22
cosocleC22×C3×A4C23
LCSG ▷ C3×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. C4×Dic3×A4C2semidirect
4. C4×C3⋊SL(2,ℤ/4)C2semidirect
5. Dic3×SL(2,ℤ/4)C2semidirect
13. C3×C4×S4C4semidirect
14. Dic3×S4C4direct (N × H)
21. C22×C4×Dic3D3semidirect
37. C3×C4×A4C2×C4semidirect
39. Dic3×A4C2×C4semidirect
40. C3⋊SL(2,ℤ/4)C2×C4semidirect
41. C3×SL(2,ℤ/4)C2×C4semidirect
59. C4×S4Dic3direct (N × H)
89. C3×S4C42semidirect
127. C22×C3×C4C4×D3semidirect
137. C22×Dic3C4×D3semidirect
142. C4×A4C2×Dic3semidirect
145. SL(2,ℤ/4)C2×Dic3semidirect
169. C4×Dic3S4direct (N × H)
173. C3×A4C2×C42semidirect
223. S4C4×Dic3direct (N × H)
293. C22×C4D3×Dic3semidirect
328. C22×C3C42×D3semidirect
333. A4C2×C4×Dic3semidirect
341. C3×C4C4×S4semidirect
348. Dic3C4×S4direct (N × H)
415. C22C4×D3×Dic3semidirect
425. C4Dic3×S4direct (N × H)
428. C3C42×S4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×S42
C2×Dic3×S42
C4×Dic3×A42
C4×C3⋊SL(2,ℤ/4)2
Dic3×SL(2,ℤ/4)2
C42×S43
C4×D4×Dic33
C4×D3×Dic34