Finite Group Databasebeta

← A4×#940 #11923353

Subgroups — A4×#940 #11923353

Order 1152.

1414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 1414 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×A4C211yesmaximal, characteristic, complemented
2C2×A4×#67C214yesmaximal, complemented
3C2×A4×D12C211yesmaximal, characteristic, complemented
4C4×Dic3×A4C211yesmaximal, characteristic, complemented
5C22×#940C311yesmaximal, characteristic, complemented
6A4×#127—31nomaximal
7C23×C3×A4C2212yes—
8C22×D3×A4C2212yes—
9C3×D4×A4—22no—
10C2×C3×C4×A4C2211yescharacteristic
11A4×#67—28no—
12C2×Dic3×A4C2212yes—
13A4×D12—22no—
14C3×#940—41nomaximal
15C23×C3×D4C2×C311yescharacteristic, complemented
16C23×#67C2×C314yescomplemented
17C23×D12C2×C311yescharacteristic, complemented
18C2×D4×A4—21no—
19C2×D4×A4—34no—
20C2×D4×A4—31no—
21C2×D4×A4D311yescharacteristic, complemented
22C2×#940—31no—
23C2×#940—31no—
24C2×#940—31no—
25C2×#940—34no—
26C2×#940—31no—
27C22×C4×Dic3C2×C311yescharacteristic, complemented
28C42×A4—31no—
29C22×C3×A4—22no—
30C22×C3×A4—24no—
31C22×C3×A4C2311yescharacteristic
32C2×D3×A4—22no—
33C2×D3×A4—24no—
34C2×C32×D4—41no—
35C2×C3×#67—44no—
36C2×C3×D12—41no—
37C3×C4×A4D412yescomplemented
38Dic3×A4D414yescomplemented
39C3×C4×Dic3—41no—
40C22×#127—31noSylow
41C25×C3C22×C312yes—
42C24×D3C22×C312yes—
43C23×A4—22no—
44C23×A4—32no—
45C23×A4C2×D312yes—
46C22×C3×D4—22no—
47C22×C3×D4—31no—
48C22×C3×D4—31no—
49C22×C3×D4—32no—
50C22×C3×D4—62no—
51C23×C3×C4C22×C311yescharacteristic
52C22×#67—28no—
53C22×#67—34no—
54C22×#67—34no—
55C22×#67—34no—
56C22×#67—34no—
57C22×#67—68no—
58C23×Dic3C22×C312yes—
59C22×D12—22no—
60C22×D12—31no—
61C22×D12—32no—
62C22×D12—31no—
63C22×D12—62no—
64D4×A4—24no—
65D4×A4—22no—
66D4×A4—68no—
67D4×A4—62no—
68C2×C4×A4—21no—
69C2×C4×A4—32no—
70C2×C4×A4C2×D311yescharacteristic
71C3×#127—121no—
72#940—34no—
73#940—34no—
74#940—32no—
75#940—34no—
76#940—31no—
77#940—34no—
78#940—31no—
79#940—31no—
80#940A411yescharacteristic, direct product factor
81C2×C4×Dic3—31no—
82C2×C4×Dic3—31no—
83C2×C4×Dic3—32no—
84C23×C32—42no—
85C22×C3×D3—42no—
86C2×C3×A4—42no—
87C2×C3×A4C2×D412yes—
88C2×C3×A4C2×D411yescharacteristic
89D3×A4—42no—
90C32×D4—82no—
91C2×C32×C4—41no—
92C3×#67—88no—
93C2×C3×Dic3—42no—
94C3×D12—82no—
95C23×D4—34no—
96C23×D4—31no—
97C23×D4C3×D311yescharacteristic, complemented
98C2×#127—91no—
99C2×#127—91no—
100C2×#127—91no—
101C2×#127—94no—
102C2×#127—91no—
103C22×C42—31no—
104C24×C3—24no—
105C24×C3—22no—
106C24×C3—32no—
107C24×C3—32no—
108C24×C3—64no—
109C24×C3—62no—
110C24×C3C23×C311yescharacteristic
111C23×D3—22no—
112C23×D3—24no—
113C23×D3—32no—
114C23×D3—32no—
115C23×D3—62no—
116C23×D3—64no—
117C22×A4—24no—
118C22×A4—24no—
119C22×A4—22no—
120C22×A4—21no—
121C22×A4—44no—
122C22×A4—64no—
123C22×A4—62no—
124C22×A4C22×D311yescharacteristic
125C2×C3×D4—32no—
126C2×C3×D4—32no—
127C2×C3×D4—31no—
128C2×C3×D4—41no—
129C2×C3×D4—62no—
130C2×C3×D4—62no—
131C2×C3×D4—64no—
132C2×C3×D4—62no—
133C2×C3×D4—64no—
134C2×C3×D4—62no—
135C2×C3×D4—81no—
136C2×C3×D4—121no—
137C2×C3×D4—124no—
138C2×C3×D4C2×A411yescharacteristic, complemented
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—32no—
142C22×C3×C4C3×D412yescomplemented
143C2×#67—38no—
144C2×#67—34no—
145C2×#67—34no—
146C2×#67—34no—
147C2×#67—68no—
148C2×#67—68no—
149C2×#67—68no—
150C2×#67—68no—
151C2×#67—68no—
152C2×#67—68no—
153C2×#67—68no—
154C2×#67—68no—
155C2×#67C2×A414yescomplemented
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—34no—
159C22×Dic3C3×D414yescomplemented
160C2×D12—32no—
161C2×D12—32no—
162C2×D12—31no—
163C2×D12—62no—
164C2×D12—62no—
165C2×D12—64no—
166C2×D12—64no—
167C2×D12—62no—
168C2×D12—62no—
169C2×D12C2×A411yescharacteristic, complemented
170C4×A4—22no—
171C4×A4—34no—
172C4×A4#6712yescomplemented
173C3×C42—121no—
174C4×Dic3—32no—
175C4×Dic3—31no—
176C4×Dic3—32no—
177C4×Dic3C2×A411yescharacteristic, complemented
178C22×C32—41no—
179C22×C32—82no—
180C22×C32—84no—
181C2×C3×D3—82no—
182C2×C3×D3—84no—
183C3×A4#12711yescharacteristic, complemented
184C32×C4—42no—
185C3×Dic3—44no—
186C25—32no—
187C25C2×C3×D312yes—
188C22×D4—22no—
189C22×D4—31no—
190C22×D4—31no—
191C22×D4—32no—
192C22×D4—62no—
193C22×D4—68no—
194C22×D4—62no—
195C22×D4—91no—
196C22×D4—91no—
197C22×D4—92no—
198C22×D4—94no—
199C22×D4—94no—
200C22×D4—94no—
201C22×D4—94no—
202C22×D4—182no—
203C22×D4—188no—
204C23×C4—32no—
205C23×C4C2×C3×D311yescharacteristic
206#127—31no—
207#127—91no—
208#127—94no—
209#127—91no—
210#127—94no—
211#127—94no—
212#127—94no—
213#127—92no—
214#127—91no—
215C2×C42—91no—
216C2×C42—92no—
217C2×C42—91no—
218C23×C3—32no—
219C23×C3—31no—
220C23×C3—31no—
221C23×C3—32no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3—64no—
225C23×C3—64no—
226C23×C3—62no—
227C23×C3—62no—
228C23×C3—64no—
229C23×C3—64no—
230C23×C3—62no—
231C23×C3—62no—
232C23×C3—82no—
233C23×C3—122no—
234C23×C3—124no—
235C23×C3—122no—
236C23×C3—124no—
237C23×C3C2×C3×D412yes—
238C23×C3C2×C3×D411yescharacteristic
239C23×C3C22×A412yes—
240C22×D3—32no—
241C22×D3—42no—
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—64no—
245C22×D3—64no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—124no—
251C22×D3—122no—
252C22×D3—124no—
253C22×D3C22×A412yes—
254C2×A4—22no—
255C2×A4—21no—
256C2×A4—44no—
257C2×A4—42no—
258C2×A4—122no—
259C2×A4D3×D412yes—
260C2×A4C2×#6711yescharacteristic
261C3×D4—22no—
262C3×D4—64no—
263C3×D4—64no—
264C3×D4—62no—
265C3×D4—82no—
266C3×D4—84no—
267C3×D4—242no—
268C3×D4—248no—
269C2×C3×C4—32no—
270C2×C3×C4—31no—
271C2×C3×C4—32no—
272C2×C3×C4—32no—
273C2×C3×C4—32no—
274C2×C3×C4—41no—
275C2×C3×C4—81no—
276C2×C3×C4—122no—
277C2×C3×C4C22×A411yescharacteristic
278#67—28no—
279#67—68no—
280#67—68no—
281#67—616no—
282#67—68no—
283C2×Dic3—34no—
284C2×Dic3—32no—
285C2×Dic3—34no—
286C2×Dic3—34no—
287C2×Dic3—34no—
288C2×Dic3C22×A412yes—
289D12—22no—
290D12—64no—
291D12—64no—
292D12—62no—
293C2×C32—42no—
294C2×C32—41no—
295C2×C32—162no—
296C3×D3—162no—
297C24—24no—
298C24—22no—
299C24—32no—
300C24—32no—
301C24—62no—
302C24—64no—
303C24—64no—
304C24—62no—
305C24—92no—
306C24—92no—
307C24—182no—
308C24—184no—
309C24C22×C3×D311yescharacteristic
310C2×D4—32no—
311C2×D4—34no—
312C2×D4—32no—
313C2×D4—31no—
314C2×D4—31no—
315C2×D4—62no—
316C2×D4—62no—
317C2×D4—64no—
318C2×D4—62no—
319C2×D4—64no—
320C2×D4—62no—
321C2×D4—92no—
322C2×D4—94no—
323C2×D4—92no—
324C2×D4—94no—
325C2×D4—98no—
326C2×D4—94no—
327C2×D4—91no—
328C2×D4—182no—
329C2×D4—182no—
330C2×D4—184no—
331C2×D4—182no—
332C2×D4—184no—
333C2×D4—182no—
334C2×D4—188no—
335C2×D4—188no—
336C2×D4—188no—
337C2×D4—188no—
338C2×D4—188no—
339C2×D4—188no—
340C2×D4—188no—
341C2×D4—188no—
342C2×D4D3×A411yescharacteristic, complemented
343C22×C4—31no—
344C22×C4—31no—
345C22×C4—32no—
346C22×C4—34no—
347C22×C4—92no—
348C22×C4—92no—
349C22×C4—94no—
350C22×C4C3×#6712yescomplemented
351C42—31no—
352C42—92no—
353C42—92no—
354C42—91no—
355C22×C3—24no—
356C22×C3—22no—
357C22×C3—32no—
358C22×C3—31no—
359C22×C3—32no—
360C22×C3—32no—
361C22×C3—32no—
362C22×C3—31no—
363C22×C3—31no—
364C22×C3—41no—
365C22×C3—64no—
366C22×C3—62no—
367C22×C3—82no—
368C22×C3—84no—
369C22×C3—84no—
370C22×C3—81no—
371C22×C3—122no—
372C22×C3—124no—
373C22×C3—122no—
374C22×C3—122no—
375C22×C3—124no—
376C22×C3—122no—
377C22×C3—164no—
378C22×C3—244no—
379C22×C3—242no—
380C22×C3C3×#12711yescharacteristic, complemented
381C22×C3C23×A411yescharacteristic
382C2×D3—22no—
383C2×D3—24no—
384C2×D3—62no—
385C2×D3—64no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—124no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—124no—
392A4—21no—
393A4#94011yescharacteristic, direct product factor
394C3×C4—32no—
395C3×C4—42no—
396C3×C4—82no—
397C3×C4—124no—
398C3×C4D4×A412yescomplemented
399Dic3—34no—
400Dic3D4×A414yescomplemented
401C32—41noSylow
402C23—31no—
403C23—32no—
404C23—31no—
405C23—32no—
406C23—32no—
407C23—42no—
408C23—62no—
409C23—62no—
410C23—64no—
411C23—64no—
412C23—62no—
413C23—62no—
414C23—64no—
415C23—64no—
416C23—92no—
417C23—124no—
418C23—122no—
419C23—124no—
420C23—122no—
421C23—184no—
422C23—182no—
423C23—184no—
424C23—182no—
425C23—184no—
426C23—182no—
427C23—184no—
428C23—182no—
429C23—364no—
430C23—362no—
431C23—364no—
432C23C3×D3×D412yes—
433C23C2×C3×#6711yescharacteristic
434C23C2×D3×A412yes—
435D4—22no—
436D4—64no—
437D4—68no—
438D4—64no—
439D4—62no—
440D4—62no—
441D4—184no—
442D4—188no—
443D4—184no—
444D4—188no—
445D4—188no—
446D4—1816no—
447D4—182no—
448C2×C4—32no—
449C2×C4—32no—
450C2×C4—31no—
451C2×C4—32no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—94no—
455C2×C4—94no—
456C2×C4—94no—
457C2×C4—92no—
458C2×C4—94no—
459C2×C4C2×D3×A411yescharacteristic
460C2×C3—31no—
461C2×C3—32no—
462C2×C3—31no—
463C2×C3—42no—
464C2×C3—42no—
465C2×C3—41no—
466C2×C3—82no—
467C2×C3—81no—
468C2×C3—122no—
469C2×C3—162no—
470C2×C3—164no—
471C2×C3—482no—
472C2×C3C2×D4×A412yes—
473C2×C3C2×D4×A411yescharacteristic
474D3—42no—
475D3—122no—
476C22—24no—
477C22—22no—
478C22—32no—
479C22—31no—
480C22—32no—
481C22—32no—
482C22—32no—
483C22—31no—
484C22—31no—
485C22—64no—
486C22—64no—
487C22—62no—
488C22—62no—
489C22—122no—
490C22—122no—
491C22—124no—
492C22—122no—
493C22—122no—
494C22—124no—
495C22—184no—
496C22—182no—
497C22—362no—
498C22—364no—
499C22—362no—
500C22—362no—
501C22—364no—
502C22—362no—
503C22C3×#94011yescharacteristic, complemented
504C22C22×D3×A411yescharacteristic
505C4—34no—
506C4—32no—
507C4—94no—
508C4A4×#6712yescomplemented
509C3—41no—
510C3—81no—
511C3A4×#12711yescharacteristic, complemented
512C2—31no—
513C2—32no—
514C2—31no—
515C2—42no—
516C2—122no—
517C2—122no—
518C2—362no—
519C2D3×D4×A412yes—
520C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×D4C2×C3
hypercenterC2×D4D3×A4
hypocenterC22×C3C3×#127
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C2×A4×#67C2semidirect
3. C2×A4×D12C2semidirect
4. C4×Dic3×A4C2semidirect
5. C22×#940C3semidirect
15. C23×C3×D4C2×C3semidirect
16. C23×#67C2×C3semidirect
17. C23×D12C2×C3semidirect
21. C2×D4×A4D3semidirect
27. C22×C4×Dic3C2×C3semidirect
37. C3×C4×A4D4semidirect
38. Dic3×A4D4semidirect
80. #940A4direct (N × H)
97. C23×D4C3×D3semidirect
138. C2×C3×D4C2×A4semidirect
142. C22×C3×C4C3×D4semidirect
155. C2×#67C2×A4semidirect
159. C22×Dic3C3×D4semidirect
169. C2×D12C2×A4semidirect
172. C4×A4#67semidirect
177. C4×Dic3C2×A4semidirect
183. C3×A4#127semidirect
342. C2×D4D3×A4semidirect
350. C22×C4C3×#67semidirect
380. C22×C3C3×#127semidirect
393. A4#940direct (N × H)
398. C3×C4D4×A4semidirect
400. Dic3D4×A4semidirect
503. C22C3×#940semidirect
508. C4A4×#67semidirect
511. C3A4×#127semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C2×A4×#672
C2×A4×D122
C4×Dic3×A42
C22×#9403
A4×#1273
C3×#9404