Finite Group Databasebeta

← C3×A4⋊#95 #11920920

Subgroups — C3×A4⋊#95 #11920920

Order 1152.

876 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C22×C3×SL(2,ℤ/4)C212yesmaximal
3A4⋊#95C311yesmaximal, characteristic, direct product factor
4C3×C22⋊#95—31nomaximal
5C23×C3×A4C2211yescharacteristic
6C2×C3×C4×A4—22no—
7C2×C3×C4×A4C412yescomplemented
8C2×C3×SL(2,ℤ/4)—22no—
9C2×C3×SL(2,ℤ/4)—22no—
10C2×C3×SL(2,ℤ/4)C414yescomplemented
11C3×C3⋊#95—41nomaximal
12C24×C3×C4D311yescharacteristic
13C22×C4×A4—21no—
14C22×C4×A4C2×C311yescharacteristic
15C22×SL(2,ℤ/4)C2×C312yes—
16C22×C3×C22⋊C4—32no—
17C2×C3×#95—32no—
18C2×C3×#95—31no—
19C2×C3×#95—31no—
20C22×C3×A4C2×C412yes—
21C22×C3×A4C2×C411yescharacteristic
22C22×C3×A4D411yescharacteristic
23C22×C3×A4D412yes—
24C22×C3×A4Q811yescharacteristic
25C22×C32×C4—41no—
26C22×C3×Dic3—42no—
27C3×C4×A4—22no—
28C3×SL(2,ℤ/4)—24no—
29C22⋊#95—31noSylow
30C25×C3C2×D311yescharacteristic
31C23×A4—21no—
32C23×A4C22×C311yescharacteristic
33C23×C3×C4—22no—
34C23×C3×C4—31no—
35C23×C3×C4—31no—
36C23×C3×C4—32no—
37C23×C3×C4—32no—
38C23×C3×C4—32no—
39C23×C3×C4—62no—
40C23×C3×C4Dic312yescomplemented
41C2×C4×A4—24no—
42C2×C4×A4—22no—
43C2×C4×A4—22no—
44C2×C4×A4C3×C412yescomplemented
45C2×SL(2,ℤ/4)—22no—
46C2×SL(2,ℤ/4)—22no—
47C2×SL(2,ℤ/4)C3×C414yescomplemented
48C2×C3×C22⋊C4—34no—
49C2×C3×C22⋊C4—34no—
50C2×C3×C22⋊C4—62no—
51C2×C3×C22⋊C4—62no—
52C2×C3×C22⋊C4—62no—
53C2×C3×C22⋊C4—62no—
54C3×#95—64no—
55C3×#95—61no—
56C3×#95—62no—
57C3×#95—61no—
58C3⋊#95—41no—
59C23×C32—41no—
60C2×C3×A4C4211yescharacteristic
61C2×C3×A4C22⋊C412yes—
62C2×C3×A4C22⋊C411yescharacteristic
63C2×C3×A4C4⋊C412yes—
64C2×C3×A4C4⋊C411yescharacteristic
65C2×C32×C4—42no—
66C2×C32×C4—82no—
67C2×C3×Dic3—44no—
68C2×C3×Dic3—82no—
69C2×C3×Dic3—82no—
70C24×C4C3×D311yescharacteristic
71C22×C22⋊C4—32no—
72C2×#95—32no—
73C2×#95—31no—
74C2×#95—31no—
75C24×C3—31no—
76C24×C3—31no—
77C24×C3—32no—
78C24×C3—31no—
79C24×C3—32no—
80C24×C3—31no—
81C24×C3Dic611yescharacteristic
82C24×C3C4×D312yes—
83C24×C3D1211yescharacteristic
84C24×C3C2×Dic311yescharacteristic
85C24×C3#6712yes—
86C22×A4—21no—
87C22×A4—22no—
88C22×A4—21no—
89C22×A4—21no—
90C22×A4—22no—
91C22×A4C2×C3×C412yes—
92C22×A4C2×C3×C411yescharacteristic
93C22×A4C3×D411yescharacteristic
94C22×A4C3×D412yes—
95C22×A4C3×Q811yescharacteristic
96C22×C3×C4—22no—
97C22×C3×C4—32no—
98C22×C3×C4—34no—
99C22×C3×C4—31no—
100C22×C3×C4—32no—
101C22×C3×C4—32no—
102C22×C3×C4—34no—
103C22×C3×C4—34no—
104C22×C3×C4—41no—
105C22×C3×C4—62no—
106C22×C3×C4—62no—
107C22×C3×C4—61no—
108C22×C3×C4—62no—
109C22×C3×C4—64no—
110C22×C3×C4—64no—
111C22×C3×C4—62no—
112C22×C3×C4—62no—
113C22×C3×C4—62no—
114C22×C3×C4—62no—
115C22×C3×C4—62no—
116C22×C3×C4—62no—
117C22×C3×C4—62no—
118C22×C3×C4—62no—
119C22×C3×C4—62no—
120C22×C3×C4—62no—
121C22×C3×C4—62no—
122C22×C3×C4—62no—
123C22×C3×C4—62no—
124C22×C3×C4—81no—
125C22×C3×C4S411yescharacteristic
126C22×Dic3—42no—
127C4×A4—24no—
128C4×A4—22no—
129SL(2,ℤ/4)—24no—
130C3×C22⋊C4—64no—
131C3×C22⋊C4—64no—
132C3×C22⋊C4—64no—
133C3×C22⋊C4—64no—
134C22×C32—41no—
135C22×C32—42no—
136C22×C32—41no—
137C22×C32—41no—
138C22×C32—42no—
139C3×A4#9511yescharacteristic, complemented
140C32×C4—82no—
141C3×Dic3—84no—
142C25C2×C3×D311yescharacteristic
143C23×C4—22no—
144C23×C4—31no—
145C23×C4—31no—
146C23×C4—32no—
147C23×C4—32no—
148C23×C4—32no—
149C23×C4—62no—
150C23×C4C3×Dic312yescomplemented
151C2×C22⋊C4—34no—
152C2×C22⋊C4—34no—
153C2×C22⋊C4—62no—
154C2×C22⋊C4—62no—
155C2×C22⋊C4—62no—
156C2×C22⋊C4—62no—
157#95—64no—
158#95—61no—
159#95—62no—
160#95—61no—
161C23×C3—31no—
162C23×C3—31no—
163C23×C3—32no—
164C23×C3—32no—
165C23×C3—31no—
166C23×C3—31no—
167C23×C3—31no—
168C23×C3—31no—
169C23×C3—32no—
170C23×C3—32no—
171C23×C3—32no—
172C23×C3—32no—
173C23×C3—32no—
174C23×C3—31no—
175C23×C3—32no—
176C23×C3—31no—
177C23×C3—32no—
178C23×C3—32no—
179C23×C3—32no—
180C23×C3—31no—
181C23×C3—31no—
182C23×C3—31no—
183C23×C3—32no—
184C23×C3—41no—
185C23×C3—61no—
186C23×C3—61no—
187C23×C3—62no—
188C23×C3—61no—
189C23×C3—62no—
190C23×C3—81no—
191C23×C3C4×Dic311yescharacteristic
192C23×C3Dic3⋊C412yes—
193C23×C3C4⋊Dic311yescharacteristic
194C23×C3(C2×D3)⋊C412yes—
195C23×C3#21711yescharacteristic
196C23×C3C2×S411yescharacteristic
197C2×A4—21no—
198C2×A4—22no—
199C2×A4—21no—
200C2×A4—22no—
201C2×A4—21no—
202C2×A4C3×C4211yescharacteristic
203C2×A4C3×C22⋊C412yes—
204C2×A4C3×C22⋊C411yescharacteristic
205C2×A4C3×C4⋊C412yes—
206C2×A4C3×C4⋊C411yescharacteristic
207C2×C3×C4—22no—
208C2×C3×C4—34no—
209C2×C3×C4—32no—
210C2×C3×C4—42no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4—64no—
220C2×C3×C4—64no—
221C2×C3×C4—64no—
222C2×C3×C4—64no—
223C2×C3×C4—82no—
224C2×C3×C4—84no—
225C2×C3×C4—82no—
226C2×C3×C4—122no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230C2×C3×C4—122no—
231C2×C3×C4—122no—
232C2×C3×C4—122no—
233C2×C3×C4—122no—
234C2×C3×C4SL(2,ℤ/4)12yescomplemented
235C2×Dic3—44no—
236C2×Dic3—82no—
237C2×Dic3—82no—
238C2×C32—41no—
239C2×C32—42no—
240C2×C32—41no—
241C2×C32—42no—
242C2×C32—41no—
243C24—31no—
244C24—32no—
245C24—31no—
246C24—32no—
247C24—31no—
248C24—31no—
249C24C3×Dic611yescharacteristic
250C24C3×C4×D312yes—
251C24C3×D1211yescharacteristic
252C24C2×C3×Dic311yescharacteristic
253C24C3×#6712yes—
254C22×C4—22no—
255C22×C4—32no—
256C22×C4—34no—
257C22×C4—31no—
258C22×C4—32no—
259C22×C4—32no—
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—62no—
263C22×C4—62no—
264C22×C4—61no—
265C22×C4—62no—
266C22×C4—64no—
267C22×C4—64no—
268C22×C4—62no—
269C22×C4—62no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—62no—
280C22×C4—62no—
281C22×C4C3×S411yescharacteristic
282C22⋊C4—64no—
283C22⋊C4—64no—
284C22⋊C4—64no—
285C22⋊C4—64no—
286C22×C3—31no—
287C22×C3—32no—
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—31no—
291C22×C3—32no—
292C22×C3—31no—
293C22×C3—31no—
294C22×C3—32no—
295C22×C3—32no—
296C22×C3—32no—
297C22×C3—32no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—31no—
301C22×C3—31no—
302C22×C3—32no—
303C22×C3—32no—
304C22×C3—32no—
305C22×C3—32no—
306C22×C3—31no—
307C22×C3—32no—
308C22×C3—31no—
309C22×C3—41no—
310C22×C3—42no—
311C22×C3—41no—
312C22×C3—42no—
313C22×C3—41no—
314C22×C3—61no—
315C22×C3—62no—
316C22×C3—62no—
317C22×C3—61no—
318C22×C3—61no—
319C22×C3—81no—
320C22×C3—82no—
321C22×C3—81no—
322C22×C3—82no—
323C22×C3—81no—
324C22×C3C3⋊#9511yescharacteristic, complemented
325C22×C3A4⋊Q811yescharacteristic
326C22×C3C4×S412yes—
327C22×C3C4⋊S411yescharacteristic
328C22×C3C2×SL(2,ℤ/4)11yescharacteristic
329C22×C3GL(2,ℤ/4)12yes—
330A4—21no—
331A4C3×#9511yescharacteristic, complemented
332C3×C4—22no—
333C3×C4—62no—
334C3×C4—82no—
335C3×C4—84no—
336C3×C4—124no—
337C3×C4—124no—
338Dic3—84no—
339C32—41noSylow
340C23—31no—
341C23—31no—
342C23—32no—
343C23—32no—
344C23—31no—
345C23—31no—
346C23—32no—
347C23—32no—
348C23—31no—
349C23—31no—
350C23—32no—
351C23—32no—
352C23—32no—
353C23—31no—
354C23—32no—
355C23—31no—
356C23—32no—
357C23—32no—
358C23—32no—
359C23—31no—
360C23—31no—
361C23—31no—
362C23—32no—
363C23—61no—
364C23—61no—
365C23—62no—
366C23—61no—
367C23—62no—
368C23C3×C4×Dic311yescharacteristic
369C23C3×Dic3⋊C412yes—
370C23C3×C4⋊Dic311yescharacteristic
371C23C3×(C2×D3)⋊C412yes—
372C23C3×#21711yescharacteristic
373C23C2×C3×S411yescharacteristic
374C2×C4—22no—
375C2×C4—34no—
376C2×C4—32no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—64no—
380C2×C4—64no—
381C2×C4—62no—
382C2×C4—62no—
383C2×C4—64no—
384C2×C4—64no—
385C2×C4—64no—
386C2×C4—64no—
387C2×C4—64no—
388C2×C4—64no—
389C2×C4—122no—
390C2×C4—122no—
391C2×C4—122no—
392C2×C4—122no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4—122no—
396C2×C4—122no—
397C2×C4C3×SL(2,ℤ/4)12yescomplemented
398C2×C3—32no—
399C2×C3—31no—
400C2×C3—31no—
401C2×C3—32no—
402C2×C3—31no—
403C2×C3—31no—
404C2×C3—41no—
405C2×C3—42no—
406C2×C3—41no—
407C2×C3—42no—
408C2×C3—41no—
409C2×C3—81no—
410C2×C3—82no—
411C2×C3—81no—
412C2×C3—82no—
413C2×C3—81no—
414C2×C3C4×SL(2,ℤ/4)11yescharacteristic
415C2×C3SL(2,ℤ/4)⋊C412yes—
416C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
417C2×C3(C2×S4)⋊C412yes—
418C2×C3#543211yescharacteristic
419C22—31no—
420C22—32no—
421C22—31no—
422C22—32no—
423C22—31no—
424C22—32no—
425C22—31no—
426C22—31no—
427C22—32no—
428C22—32no—
429C22—32no—
430C22—32no—
431C22—31no—
432C22—31no—
433C22—31no—
434C22—31no—
435C22—32no—
436C22—32no—
437C22—32no—
438C22—32no—
439C22—31no—
440C22—32no—
441C22—31no—
442C22—61no—
443C22—62no—
444C22—62no—
445C22—61no—
446C22—61no—
447C22C3×C3⋊#9511yescharacteristic, complemented
448C22C3×A4⋊Q811yescharacteristic
449C22C3×C4×S412yes—
450C22C3×C4⋊S411yescharacteristic
451C22C2×C3×SL(2,ℤ/4)11yescharacteristic
452C22C3×GL(2,ℤ/4)12yes—
453C4—22no—
454C4—62no—
455C4—124no—
456C4—124no—
457C3—41no—
458C3—81no—
459C3A4⋊#9511yescharacteristic, direct product factor
460C2—32no—
461C2—31no—
462C2—31no—
463C2—32no—
464C2—31no—
465C2—31no—
466C2C3×C4×SL(2,ℤ/4)11yescharacteristic
467C2C3×SL(2,ℤ/4)⋊C412yes—
468C2C3×C4⋊SL(2,ℤ/4)11yescharacteristic
469C2C3×(C2×S4)⋊C412yes—
470C2C3×#543211yescharacteristic
subgroupG/H
centerC23×C3C2×S4
commutatorC2×A4C3×C42
FrattiniC23C2×C3×S4
FittingC24×C3×C4D3
socleC25×C3C2×D3
prime radicalC23×C3×A4C22
cosocleC23×A4C22×C3
hypercenterC22×C3×C4S4
hypocenterA4C3×#95
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
3. A4⋊#95C3direct (N × H)
7. C2×C3×C4×A4C4semidirect
10. C2×C3×SL(2,ℤ/4)C4semidirect
40. C23×C3×C4Dic3semidirect
44. C2×C4×A4C3×C4semidirect
47. C2×SL(2,ℤ/4)C3×C4semidirect
139. C3×A4#95semidirect
150. C23×C4C3×Dic3semidirect
234. C2×C3×C4SL(2,ℤ/4)semidirect
324. C22×C3C3⋊#95semidirect
331. A4C3×#95semidirect
397. C2×C4C3×SL(2,ℤ/4)semidirect
447. C22C3×C3⋊#95semidirect
459. C3A4⋊#95direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C22×C3×SL(2,ℤ/4)2
A4⋊#953
C3×C22⋊#953
C3×C3⋊#954