Finite Group Databasebeta

← A4×C3⋊#95 #11921355

Subgroups — A4×C3⋊#95 #11921355

Order 1152.

934 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 934 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic3×A4C212yesmaximal
3C22×C3⋊#95C311yesmaximal, characteristic, complemented
4A4×#95—31nomaximal
5C23×C3×A4C2211yescharacteristic
6C2×C3×C4×A4—22no—
7C2×C3×C4×A4C412yescomplemented
8C2×Dic3×A4—22no—
9C2×Dic3×A4—22no—
10C2×Dic3×A4C414yescomplemented
11C3×C3⋊#95—41nomaximal
12C24×C3×C4C2×C311yescharacteristic
13C24×Dic3C2×C312yes—
14C22×C4×A4—21no—
15C22×C4×A4—32no—
16C22×C4×A4D311yescharacteristic
17C2×C3⋊#95—31no—
18C2×C3⋊#95—31no—
19C2×C3⋊#95—32no—
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—
28Dic3×A4—24no—
29C22×#95—31noSylow
30C25×C3C22×C311yescharacteristic
31C23×A4—21no—
32C23×A4C2×D311yescharacteristic
33C23×C3×C4—22no—
34C23×C3×C4—31no—
35C23×C3×C4—32no—
36C23×C3×C4—31no—
37C23×C3×C4—62no—
38C23×C3×C4C3×C412yescomplemented
39C23×Dic3—22no—
40C23×Dic3—22no—
41C23×Dic3—32no—
42C23×Dic3—34no—
43C23×Dic3—32no—
44C23×Dic3—62no—
45C23×Dic3—62no—
46C23×Dic3C3×C414yescomplemented
47C2×C4×A4—24no—
48C2×C4×A4—22no—
49C2×C4×A4—22no—
50C2×C4×A4—34no—
51C2×C4×A4—62no—
52C2×C4×A4—62no—
53C2×C4×A4Dic312yescomplemented
54C3×#95—121no—
55C3⋊#95—32no—
56C3⋊#95—31no—
57C3⋊#95—32no—
58C3⋊#95A411yescharacteristic, direct product factor
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×C4—32no—
71C24×C4C3×D311yescharacteristic
72C2×#95—91no—
73C2×#95—92no—
74C2×#95—91no—
75C24×C3—31no—
76C24×C3—32no—
77C24×C3—31no—
78C24×C3—32no—
79C24×C3—31no—
80C24×C3—31no—
81C24×C3C2×C3×C412yes—
82C24×C3C2×C3×C411yescharacteristic
83C24×C3C3×D411yescharacteristic
84C24×C3C3×D412yes—
85C24×C3C3×Q811yescharacteristic
86C22×A4—21no—
87C22×A4—22no—
88C22×A4—21no—
89C22×A4—21no—
90C22×A4—22no—
91C22×A4Dic611yescharacteristic
92C22×A4C4×D312yes—
93C22×A4D1211yescharacteristic
94C22×A4C2×Dic311yescharacteristic
95C22×A4#6712yes—
96C22×C3×C4—22no—
97C22×C3×C4—32no—
98C22×C3×C4—31no—
99C22×C3×C4—32no—
100C22×C3×C4—32no—
101C22×C3×C4—32no—
102C22×C3×C4—41no—
103C22×C3×C4—62no—
104C22×C3×C4—62no—
105C22×C3×C4—64no—
106C22×C3×C4—64no—
107C22×C3×C4—62no—
108C22×C3×C4—62no—
109C22×C3×C4—62no—
110C22×C3×C4—81no—
111C22×C3×C4—122no—
112C22×C3×C4C2×A411yescharacteristic
113C22×Dic3—24no—
114C22×Dic3—34no—
115C22×Dic3—32no—
116C22×Dic3—34no—
117C22×Dic3—34no—
118C22×Dic3—34no—
119C22×Dic3—62no—
120C22×Dic3—62no—
121C22×Dic3—62no—
122C22×Dic3—62no—
123C22×Dic3—68no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—64no—
131C22×Dic3C2×A412yes—
132C4×A4—24no—
133C4×A4—22no—
134C4×A4—64no—
135C22×C32—42no—
136C22×C32—41no—
137C22×C32—41no—
138C22×C32—42no—
139C22×C32—41no—
140C3×A4#9511yescharacteristic, complemented
141C32×C4—82no—
142C3×Dic3—84no—
143C25C2×C3×D311yescharacteristic
144C23×C4—22no—
145C23×C4—31no—
146C23×C4—31no—
147C23×C4—32no—
148C23×C4—34no—
149C23×C4—62no—
150C23×C4—62no—
151C23×C4—62no—
152C23×C4—92no—
153C23×C4—92no—
154C23×C4—94no—
155C23×C4—182no—
156C23×C4—182no—
157C23×C4C3×Dic312yescomplemented
158#95—31no—
159#95—92no—
160#95—92no—
161#95—91no—
162C23×C3—32no—
163C23×C3—32no—
164C23×C3—32no—
165C23×C3—31no—
166C23×C3—32no—
167C23×C3—32no—
168C23×C3—32no—
169C23×C3—31no—
170C23×C3—31no—
171C23×C3—31no—
172C23×C3—32no—
173C23×C3—32no—
174C23×C3—31no—
175C23×C3—34no—
176C23×C3—32no—
177C23×C3—32no—
178C23×C3—34no—
179C23×C3—32no—
180C23×C3—32no—
181C23×C3—32no—
182C23×C3—31no—
183C23×C3—31no—
184C23×C3—31no—
185C23×C3—31no—
186C23×C3—32no—
187C23×C3—32no—
188C23×C3—31no—
189C23×C3—31no—
190C23×C3—41no—
191C23×C3—81no—
192C23×C3C3×C4211yescharacteristic
193C23×C3C3×C22⋊C412yes—
194C23×C3C3×C22⋊C411yescharacteristic
195C23×C3C3×C4⋊C412yes—
196C23×C3C3×C4⋊C411yescharacteristic
197C23×C3C22×A411yescharacteristic
198C2×A4—21no—
199C2×A4—22no—
200C2×A4—21no—
201C2×A4—22no—
202C2×A4—21no—
203C2×A4C4×Dic311yescharacteristic
204C2×A4Dic3⋊C412yes—
205C2×A4C4⋊Dic311yescharacteristic
206C2×A4(C2×D3)⋊C412yes—
207C2×A4#21711yescharacteristic
208C2×C3×C4—22no—
209C2×C3×C4—32no—
210C2×C3×C4—42no—
211C2×C3×C4—62no—
212C2×C3×C4—64no—
213C2×C3×C4—62no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—62no—
218C2×C3×C4—82no—
219C2×C3×C4—84no—
220C2×C3×C4—82no—
221C2×C3×C4—124no—
222C2×C3×C4—242no—
223C2×C3×C4—242no—
224C2×C3×C4C4×A412yescomplemented
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—34no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—62no—
235C2×Dic3—62no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3C4×A414yescomplemented
239C2×C32—41no—
240C2×C32—42no—
241C2×C32—41no—
242C2×C32—42no—
243C2×C32—41no—
244C24—31no—
245C24—32no—
246C24—32no—
247C24—31no—
248C24—31no—
249C24—31no—
250C24C3×Dic611yescharacteristic
251C24C3×C4×D312yes—
252C24C3×D1211yescharacteristic
253C24C2×C3×Dic311yescharacteristic
254C24C3×#6712yes—
255C22×C4—22no—
256C22×C4—32no—
257C22×C4—32no—
258C22×C4—31no—
259C22×C4—32no—
260C22×C4—32no—
261C22×C4—32no—
262C22×C4—62no—
263C22×C4—62no—
264C22×C4—64no—
265C22×C4—64no—
266C22×C4—62no—
267C22×C4—62no—
268C22×C4—62no—
269C22×C4—64no—
270C22×C4—94no—
271C22×C4—94no—
272C22×C4—94no—
273C22×C4—92no—
274C22×C4—94no—
275C22×C4—182no—
276C22×C4—182no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4—188no—
280C22×C4—184no—
281C22×C4—184no—
282C22×C4—182no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4—182no—
286C22×C4—184no—
287C22×C4D3×A411yescharacteristic
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—31no—
291C22×C3—32no—
292C22×C3—31no—
293C22×C3—34no—
294C22×C3—32no—
295C22×C3—34no—
296C22×C3—32no—
297C22×C3—32no—
298C22×C3—31no—
299C22×C3—32no—
300C22×C3—31no—
301C22×C3—32no—
302C22×C3—32no—
303C22×C3—32no—
304C22×C3—32no—
305C22×C3—32no—
306C22×C3—31no—
307C22×C3—31no—
308C22×C3—32no—
309C22×C3—32no—
310C22×C3—32no—
311C22×C3—31no—
312C22×C3—31no—
313C22×C3—31no—
314C22×C3—32no—
315C22×C3—31no—
316C22×C3—41no—
317C22×C3—42no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3—81no—
322C22×C3—82no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—82no—
326C22×C3C3×#9511yescharacteristic, complemented
327C22×C3C2×C4×A412yes—
328C22×C3C2×C4×A411yescharacteristic
329C22×C3D4×A411yescharacteristic
330C22×C3D4×A412yes—
331C22×C3Q8×A411yescharacteristic
332A4—21no—
333A4C3⋊#9511yescharacteristic, direct product factor
334C3×C4—22no—
335C3×C4—62no—
336C3×C4—82no—
337C3×C4—84no—
338C3×C4—244no—
339Dic3—24no—
340Dic3—64no—
341C32—41noSylow
342C23—31no—
343C23—32no—
344C23—32no—
345C23—32no—
346C23—32no—
347C23—31no—
348C23—32no—
349C23—32no—
350C23—32no—
351C23—31no—
352C23—31no—
353C23—31no—
354C23—32no—
355C23—32no—
356C23—34no—
357C23—32no—
358C23—34no—
359C23—32no—
360C23—31no—
361C23—31no—
362C23—32no—
363C23—32no—
364C23—31no—
365C23—31no—
366C23—31no—
367C23—31no—
368C23—32no—
369C23—32no—
370C23C3×C4×Dic311yescharacteristic
371C23C3×Dic3⋊C412yes—
372C23C3×C4⋊Dic311yescharacteristic
373C23C3×(C2×D3)⋊C412yes—
374C23C3×#21711yescharacteristic
375C23C2×D3×A411yescharacteristic
376C2×C4—22no—
377C2×C4—34no—
378C2×C4—32no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—64no—
382C2×C4—64no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—94no—
389C2×C4—184no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4—184no—
393C2×C4—184no—
394C2×C4—184no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—184no—
398C2×C4—184no—
399C2×C4Dic3×A412yescomplemented
400C2×C3—31no—
401C2×C3—31no—
402C2×C3—32no—
403C2×C3—32no—
404C2×C3—31no—
405C2×C3—31no—
406C2×C3—41no—
407C2×C3—42no—
408C2×C3—41no—
409C2×C3—42no—
410C2×C3—41no—
411C2×C3—81no—
412C2×C3—82no—
413C2×C3—81no—
414C2×C3—82no—
415C2×C3—81no—
416C2×C3C42×A411yescharacteristic
417C2×C3A4×C22⋊C412yes—
418C2×C3A4×C22⋊C411yescharacteristic
419C2×C3A4×C4⋊C412yes—
420C2×C3A4×C4⋊C411yescharacteristic
421C22—31no—
422C22—32no—
423C22—31no—
424C22—32no—
425C22—31no—
426C22—32no—
427C22—34no—
428C22—34no—
429C22—32no—
430C22—32no—
431C22—31no—
432C22—32no—
433C22—31no—
434C22—32no—
435C22—32no—
436C22—32no—
437C22—32no—
438C22—31no—
439C22—31no—
440C22—31no—
441C22—31no—
442C22—32no—
443C22—32no—
444C22—32no—
445C22—32no—
446C22—31no—
447C22—32no—
448C22—31no—
449C22C3×C3⋊#9511yescharacteristic, complemented
450C22A4×Dic611yescharacteristic
451C22C4×D3×A412yes—
452C22A4×D1211yescharacteristic
453C22C2×Dic3×A411yescharacteristic
454C22A4×#6712yes—
455C4—22no—
456C4—64no—
457C4—62no—
458C4—184no—
459C3—41no—
460C3—81no—
461C3A4×#9511yescharacteristic, complemented
462C2—31no—
463C2—31no—
464C2—32no—
465C2—31no—
466C2—32no—
467C2—31no—
468C2C4×Dic3×A411yescharacteristic
469C2A4×Dic3⋊C412yes—
470C2A4×C4⋊Dic311yescharacteristic
471C2A4×(C2×D3)⋊C412yes—
472C2A4×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×A4
commutatorC23×C3C3×C42
FittingC24×C3×C4C2×C3
socle, cosocleC25×C3C22×C3
prime radicalC23×C3×A4C22
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×#95
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C22×C3⋊#95C3semidirect
7. C2×C3×C4×A4C4semidirect
10. C2×Dic3×A4C4semidirect
38. C23×C3×C4C3×C4semidirect
46. C23×Dic3C3×C4semidirect
53. C2×C4×A4Dic3semidirect
58. C3⋊#95A4direct (N × H)
140. C3×A4#95semidirect
157. C23×C4C3×Dic3semidirect
224. C2×C3×C4C4×A4semidirect
238. C2×Dic3C4×A4semidirect
326. C22×C3C3×#95semidirect
333. A4C3⋊#95direct (N × H)
399. C2×C4Dic3×A4semidirect
449. C22C3×C3⋊#95semidirect
461. C3A4×#95semidirect

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×Dic3×A42
C22×C3⋊#953
A4×#953
C3×C3⋊#954