Finite Group Databasebeta

← A4×#947 #11923372

Subgroups — A4×#947 #11923372

Order 1152.

918 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 918 conjugacy classes of subgroups — too many to draw. Only its 99 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×Q8×A4C211yesmaximal, characteristic, complemented
2C2×A4×D12C211yesmaximal, characteristic
3A4×(C2×D3)⋊C4C214yesmaximal, complemented
4C4×Dic3×A4C211yesmaximal, characteristic, complemented
5C22×#947C311yesmaximal, characteristic, complemented
6A4×#124—31nomaximal
7C22×D3×A4C2212yes—
8C3×Q8×A4—22no—
9C2×C3×C4×A4C2212yes—
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2212yes—
12A4×D12—22no—
13C3×#947—41nomaximal
14C23×C3×Q8C2×C311yescharacteristic, complemented
15C23×D12C2×C311yescharacteristic
16C2×Q8×A4—21no—
17C2×Q8×A4D311yescharacteristic, complemented
18C2×D4×A4—31no—
19C2×#947—31no—
20C2×#947—31no—
21C2×#947—34no—
22C2×#947—31no—
23C2×#947—31no—
24C22×(C2×D3)⋊C4C2×C314yescomplemented
25C22×C4×Dic3C2×C311yescharacteristic, complemented
26A4×C22⋊C4—34no—
27C42×A4—31no—
28C22×C3×A4C2311yescharacteristic
29C2×D3×A4—22no—
30C2×D3×A4—24no—
31C2×C32×Q8—41no—
32C2×C3×D12—41no—
33C3×C4×A4—22no—
34C3×C4×A4D412yes—
35Dic3×A4—22no—
36C3×(C2×D3)⋊C4—44no—
37C3×C4×Dic3—41no—
38C22×#124—31noSylow
39C24×D3C22×C312yes—
40C23×A4—32no—
41C22×C3×Q8—22no—
42C22×C3×Q8—31no—
43C22×C3×Q8—32no—
44C22×C3×Q8—31no—
45C22×C3×Q8—62no—
46C23×C3×C4C22×C312yes—
47C23×C3×C4C22×C311yescharacteristic
48C23×Dic3C22×C312yes—
49C22×D12—22no—
50C22×D12—31no—
51C22×D12—32no—
52C22×D12—31no—
53C22×D12—62no—
54Q8×A4—24no—
55Q8×A4—22no—
56D4×A4—62no—
57C2×C4×A4—22no—
58C2×C4×A4—21no—
59C2×C4×A4—32no—
60C2×C4×A4C2×D312yes—
61C2×C4×A4C2×D311yescharacteristic
62C3×#124—121no—
63#947—34no—
64#947—34no—
65#947—32no—
66#947—34no—
67#947—31no—
68#947—31no—
69#947—34no—
70#947—31no—
71#947A411yescharacteristic, direct product factor
72C2×(C2×D3)⋊C4—34no—
73C2×(C2×D3)⋊C4—34no—
74C2×(C2×D3)⋊C4—34no—
75C2×(C2×D3)⋊C4—34no—
76C2×C4×Dic3—31no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—32no—
79C22×C3×D3—42no—
80C2×C3×A4C2×D411yescharacteristic
81C2×C3×A4#4112yes—
82D3×A4—42no—
83C32×Q8—82no—
84C2×C32×C4—41no—
85C2×C32×C4—42no—
86C2×C3×Dic3—42no—
87C3×D12—82no—
88C23×Q8C3×D311yescharacteristic, complemented
89C23×D4—31no—
90C2×#124—91no—
91C2×#124—91no—
92C2×#124—94no—
93C2×#124—91no—
94C2×#124—91no—
95C22×C22⋊C4—34no—
96C22×C42—31no—
97C24×C3C23×C311yescharacteristic
98C23×D3—22no—
99C23×D3—24no—
100C23×D3—32no—
101C23×D3—32no—
102C23×D3—62no—
103C23×D3—64no—
104C22×A4—21no—
105C22×A4—64no—
106C22×A4—62no—
107C22×A4C22×D311yescharacteristic
108C2×C3×Q8—32no—
109C2×C3×Q8—32no—
110C2×C3×Q8—31no—
111C2×C3×Q8—41no—
112C2×C3×Q8—62no—
113C2×C3×Q8—62no—
114C2×C3×Q8—62no—
115C2×C3×Q8—64no—
116C2×C3×Q8—62no—
117C2×C3×Q8—64no—
118C2×C3×Q8—81no—
119C2×C3×Q8C2×A411yescharacteristic, complemented
120C2×C3×D4—121no—
121C22×C3×C4—22no—
122C22×C3×C4—31no—
123C22×C3×C4—31no—
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4—32no—
127C22×C3×C4—62no—
128C22×C3×C4C3×D412yes—
129C22×Dic3—22no—
130C22×Dic3—32no—
131C22×Dic3—32no—
132C22×Dic3—62no—
133C2×D12—32no—
134C2×D12—32no—
135C2×D12—31no—
136C2×D12—62no—
137C2×D12—62no—
138C2×D12—64no—
139C2×D12—64no—
140C2×D12—62no—
141C2×D12—62no—
142C2×D12C2×A411yescharacteristic
143C4×A4—24no—
144C4×A4—22no—
145C4×A4—22no—
146C4×A4—62no—
147C4×A4#6712yes—
148C3×C22⋊C4—124no—
149C3×C42—121no—
150(C2×D3)⋊C4—38no—
151(C2×D3)⋊C4—34no—
152(C2×D3)⋊C4—34no—
153(C2×D3)⋊C4—34no—
154(C2×D3)⋊C4C2×A414yescomplemented
155C4×Dic3—32no—
156C4×Dic3—31no—
157C4×Dic3—32no—
158C4×Dic3C2×A411yescharacteristic, complemented
159C22×C32—41no—
160C2×C3×D3—82no—
161C2×C3×D3—84no—
162C3×A4#12411yescharacteristic, complemented
163C32×C4—42no—
164C32×C4—82no—
165C3×Dic3—82no—
166C25—32no—
167C22×Q8—22no—
168C22×Q8—31no—
169C22×Q8—32no—
170C22×Q8—31no—
171C22×Q8—62no—
172C22×D4—62no—
173C22×D4—91no—
174C22×D4—91no—
175C22×D4—92no—
176C22×D4—182no—
177C23×C4—32no—
178C23×C4C2×C3×D312yes—
179C23×C4C2×C3×D311yescharacteristic
180#124—31no—
181#124—91no—
182#124—94no—
183#124—91no—
184#124—94no—
185#124—94no—
186#124—94no—
187#124—92no—
188#124—91no—
189C2×C22⋊C4—94no—
190C2×C22⋊C4—94no—
191C2×C22⋊C4—94no—
192C2×C22⋊C4—94no—
193C2×C42—91no—
194C2×C42—92no—
195C2×C42—91no—
196C23×C3—32no—
197C23×C3—31no—
198C23×C3—31no—
199C23×C3—122no—
200C23×C3C2×C3×D411yescharacteristic
201C23×C3C3×#4112yes—
202C22×D3—32no—
203C22×D3—42no—
204C22×D3—62no—
205C22×D3—62no—
206C22×D3—64no—
207C22×D3—64no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—64no—
211C22×D3—64no—
212C22×D3—124no—
213C22×D3—122no—
214C22×D3—124no—
215C22×D3C22×A412yes—
216C2×A4—22no—
217C2×A4—21no—
218C2×A4—122no—
219C2×A4#23912yes—
220C2×A4C2×#6711yescharacteristic
221C3×Q8—22no—
222C3×Q8—64no—
223C3×Q8—64no—
224C3×Q8—62no—
225C3×Q8—82no—
226C3×Q8—84no—
227C3×D4—242no—
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—41no—
235C2×C3×C4—42no—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—62no—
239C2×C3×C4—62no—
240C2×C3×C4—82no—
241C2×C3×C4—81no—
242C2×C3×C4—122no—
243C2×C3×C4C22×A412yes—
244C2×C3×C4C22×A411yescharacteristic
245C2×Dic3—32no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3C22×A412yes—
251D12—22no—
252D12—64no—
253D12—64no—
254D12—62no—
255C2×C32—41no—
256C2×C32—42no—
257C3×D3—162no—
258C24—64no—
259C24—62no—
260C24—92no—
261C24—92no—
262C24—182no—
263C24—184no—
264C24C22×C3×D311yescharacteristic
265C2×Q8—32no—
266C2×Q8—32no—
267C2×Q8—31no—
268C2×Q8—62no—
269C2×Q8—62no—
270C2×Q8—62no—
271C2×Q8—64no—
272C2×Q8—62no—
273C2×Q8—64no—
274C2×Q8D3×A411yescharacteristic, complemented
275C2×D4—31no—
276C2×D4—92no—
277C2×D4—92no—
278C2×D4—91no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—184no—
282C2×D4—182no—
283C2×D4—184no—
284C2×D4—182no—
285C22×C4—22no—
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—32no—
291C22×C4—62no—
292C22×C4—62no—
293C22×C4—92no—
294C22×C4—92no—
295C22×C4—182no—
296C22×C4C3×#6712yes—
297C22⋊C4—34no—
298C22⋊C4—94no—
299C22⋊C4—94no—
300C22⋊C4—98no—
301C22⋊C4—94no—
302C42—31no—
303C42—92no—
304C42—92no—
305C42—91no—
306C22×C3—31no—
307C22×C3—32no—
308C22×C3—32no—
309C22×C3—31no—
310C22×C3—31no—
311C22×C3—32no—
312C22×C3—32no—
313C22×C3—41no—
314C22×C3—81no—
315C22×C3—242no—
316C22×C3—244no—
317C22×C3C3×#12411yescharacteristic, complemented
318C22×C3C23×A411yescharacteristic
319C2×D3—22no—
320C2×D3—24no—
321C2×D3—62no—
322C2×D3—64no—
323C2×D3—122no—
324C2×D3—122no—
325C2×D3—124no—
326C2×D3—122no—
327C2×D3—122no—
328C2×D3—124no—
329A4—21no—
330A4#94711yescharacteristic, direct product factor
331C3×C4—22no—
332C3×C4—32no—
333C3×C4—42no—
334C3×C4—62no—
335C3×C4—82no—
336C3×C4—84no—
337C3×C4—82no—
338C3×C4—242no—
339C3×C4D4×A412yes—
340Dic3—22no—
341Dic3—62no—
342C32—41noSylow
343C23—31no—
344C23—32no—
345C23—31no—
346C23—32no—
347C23—92no—
348C23—122no—
349C23—182no—
350C23—182no—
351C23—184no—
352C23—184no—
353C23—182no—
354C23—182no—
355C23—184no—
356C23—184no—
357C23—364no—
358C23—362no—
359C23—364no—
360C23C3×#23912yes—
361C23C2×C3×#6711yescharacteristic
362Q8—22no—
363Q8—64no—
364Q8—64no—
365Q8—62no—
366D4—62no—
367D4—184no—
368D4—184no—
369D4—182no—
370C2×C4—32no—
371C2×C4—31no—
372C2×C4—32no—
373C2×C4—32no—
374C2×C4—32no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—92no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4—182no—
385C2×C4—182no—
386C2×C4C2×D3×A412yes—
387C2×C4C2×D3×A411yescharacteristic
388C2×C3—31no—
389C2×C3—32no—
390C2×C3—31no—
391C2×C3—42no—
392C2×C3—41no—
393C2×C3—82no—
394C2×C3—81no—
395C2×C3—482no—
396C2×C3C2×D4×A411yescharacteristic
397C2×C3A4×#4112yes—
398D3—42no—
399D3—122no—
400C22—32no—
401C22—31no—
402C22—32no—
403C22—32no—
404C22—32no—
405C22—31no—
406C22—31no—
407C22—64no—
408C22—62no—
409C22—184no—
410C22—182no—
411C22—362no—
412C22—362no—
413C22—364no—
414C22—362no—
415C22—362no—
416C22—364no—
417C22C3×#94711yescharacteristic, complemented
418C22C22×D3×A411yescharacteristic
419C4—22no—
420C4—32no—
421C4—62no—
422C4—62no—
423C4—182no—
424C4A4×#6712yes—
425C3—41no—
426C3—81no—
427C3A4×#12411yescharacteristic, complemented
428C2—31no—
429C2—32no—
430C2—31no—
431C2—122no—
432C2—362no—
433C2A4×#23912yes—
434C2C2×A4×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC23×C3×Q8C2×C3
prime radicalC2×A4×D12C2
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×#124
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
3. A4×(C2×D3)⋊C4C2semidirect
4. C4×Dic3×A4C2semidirect
5. C22×#947C3semidirect
14. C23×C3×Q8C2×C3semidirect
17. C2×Q8×A4D3semidirect
24. C22×(C2×D3)⋊C4C2×C3semidirect
25. C22×C4×Dic3C2×C3semidirect
71. #947A4direct (N × H)
88. C23×Q8C3×D3semidirect
119. C2×C3×Q8C2×A4semidirect
154. (C2×D3)⋊C4C2×A4semidirect
158. C4×Dic3C2×A4semidirect
162. C3×A4#124semidirect
274. C2×Q8D3×A4semidirect
317. C22×C3C3×#124semidirect
330. A4#947direct (N × H)
417. C22C3×#947semidirect
427. C3A4×#124semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C2×A4×D122
A4×(C2×D3)⋊C42
C4×Dic3×A42
C22×#9473
A4×#1243
C3×#9474