Finite Group Databasebeta

← A4×#907 #11923306

Subgroups — A4×#907 #11923306

Order 1152.

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

normal subgroups only

This group has 728 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
1A4×#235C211yesmaximal, characteristic
2C3×A4×M16C211yesmaximal, characteristic, complemented
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4A4×ΓL(1,𝔽25)C212yesmaximal, complemented
5D3×C8×A4C212yesmaximal, complemented
6C22×#907C311yesmaximal, characteristic, complemented
7A4×#131—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9A4×#67C412yes—
10A4×D12C411yescharacteristic
11C4×D3×A4C2212yes—
12A4×Dic6C411yescharacteristic
13C3×#907—41nomaximal
14C3×C8×A4C2212yes—
15A4×C3⋊C8C2211yescharacteristic
16A4×C3⋊C8C2211yescharacteristic
17C22×#235C2×C311yescharacteristic
18A4×#41—31no—
19C22×C3×M16C2×C311yescharacteristic, complemented
20C23×C3⋊C8C2×C311yescharacteristic, complemented
21C2×#907—31no—
22C2×#907—32no—
23C2×#907—32no—
24C2×#907—31no—
25C2×#907—31no—
26C2×#907—31no—
27C22×ΓL(1,𝔽25)C2×C312yescomplemented
28C22×D3×C8C2×C312yescomplemented
29A4×M16—21no—
30A4×M16—32no—
31A4×M16D311yescharacteristic, complemented
32C2×C8×A4—31no—
33C2×C8×A4—32no—
34C22×C3×A4C2×C411yescharacteristic
35C2×D3×A4C2×C412yes—
36C3×#235—41no—
37C3×C4×A4C2×C411yescharacteristic
38C3×C4×A4C2311yescharacteristic
39Dic3×A4C2×C412yes—
40C32×M16—41no—
41C2×C3×C3⋊C8—41no—
42C3×ΓL(1,𝔽25)—42no—
43C3×D3×C8—42no—
44C22×#131—31noSylow
45C23×C3×C4C22×C311yescharacteristic
46C22×#67C3×C412yes—
47C2×#235—31no—
48C2×#235—31no—
49C2×#235—31no—
50C2×#235—32no—
51C2×#235—32no—
52C2×#235—31no—
53C22×D12C3×C411yescharacteristic
54C22×C4×D3C22×C312yes—
55C22×Dic6C3×C411yescharacteristic
56Q8×A4—31no—
57D4×A4—32no—
58D4×A4—31no—
59C2×C4×A4—21no—
60C2×C4×A4—32no—
61C2×C4×A4C2×D311yescharacteristic
62C3×#131—121no—
63C2×C3×M16—31no—
64C2×C3×M16—32no—
65C2×C3×M16—31no—
66C22×C3×C8C22×C312yes—
67C22×C3⋊C8—31no—
68C22×C3⋊C8—31no—
69C22×C3⋊C8—31no—
70C22×C3⋊C8—31no—
71C22×C3⋊C8C22×C311yescharacteristic
72C22×C3⋊C8C22×C311yescharacteristic
73#907—32no—
74#907—32no—
75#907—34no—
76#907—34no—
77#907—32no—
78#907—31no—
79#907—31no—
80#907—31no—
81#907—32no—
82#907—32no—
83#907A411yescharacteristic, direct product factor
84C2×ΓL(1,𝔽25)—32no—
85C2×ΓL(1,𝔽25)—32no—
86C2×ΓL(1,𝔽25)—32no—
87C2×ΓL(1,𝔽25)—32no—
88C2×D3×C8—32no—
89C2×D3×C8—32no—
90C2×D3×C8—32no—
91C2×D3×C8—32no—
92C8×A4—22no—
93C8×A4—31no—
94C8×A4—31no—
95C8×A4C2×D312yes—
96C2×C3×A4—21no—
97C2×C3×A4C22×C411yescharacteristic
98D3×A4—22no—
99C2×C32×C4—41no—
100C3×#67—42no—
101C3×D12—41no—
102C3×C4×D3—42no—
103C3×Dic6—41no—
104C32×C8—42no—
105C3×C3⋊C8—41no—
106C3×C3⋊C8—41no—
107C22×#41—31no—
108C2×#131—91no—
109C2×#131—92no—
110C2×#131—91no—
111C2×#131—91no—
112C2×#131—92no—
113C2×#131—91no—
114C22×M16—32no—
115C22×M16C3×D311yescharacteristic, complemented
116C23×C8—31no—
117C23×C8—32no—
118C24×C3C2×C3×C411yescharacteristic
119C23×D3C2×C3×C412yes—
120C22×A4—21no—
121C22×A4—32no—
122C22×A4C4×D311yescharacteristic
123C3×#41—121no—
124C22×C3×C4—31no—
125C22×C3×C4—31no—
126C22×C3×C4—31no—
127C22×C3×C4—31no—
128C22×C3×C4C2×C3×C411yescharacteristic
129C22×C3×C4C23×C311yescharacteristic
130C2×#67—32no—
131C2×#67—32no—
132C2×#67—32no—
133C2×#67—32no—
134C22×Dic3C2×C3×C412yes—
135#235—32no—
136#235—32no—
137#235—34no—
138#235—32no—
139#235—34no—
140#235—31no—
141#235—32no—
142#235—31no—
143#235—32no—
144#235—31no—
145#235C2×A411yescharacteristic
146C2×D12—31no—
147C2×D12—32no—
148C2×D12—31no—
149C2×C4×D3—32no—
150C2×C4×D3—32no—
151C2×C4×D3—32no—
152C2×C4×D3—32no—
153C2×Dic6—31no—
154C2×Dic6—31no—
155C2×Dic6—32no—
156C4×A4—21no—
157C4×A4—21no—
158C4×A4—32no—
159C4×A4C4×D311yescharacteristic
160C4×A4C22×D311yescharacteristic
161C3×M16—32no—
162C3×M16—31no—
163C3×M16—32no—
164C3×M16—41no—
165C3×M16—81no—
166C3×M16—122no—
167C3×M16C2×A411yescharacteristic, complemented
168C2×C3×C8—32no—
169C2×C3×C8—32no—
170C2×C3×C8—122no—
171C2×C3×C8—121no—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—31no—
174C2×C3⋊C8—31no—
175C2×C3⋊C8—31no—
176C2×C3⋊C8—31no—
177C2×C3⋊C8—31no—
178C2×C3⋊C8—31no—
179C2×C3⋊C8—31no—
180C2×C3⋊C8C2×A411yescharacteristic, complemented
181ΓL(1,𝔽25)—34no—
182ΓL(1,𝔽25)—32no—
183ΓL(1,𝔽25)—32no—
184ΓL(1,𝔽25)—32no—
185ΓL(1,𝔽25)C2×A412yescomplemented
186D3×C8—34no—
187D3×C8—32no—
188D3×C8—32no—
189D3×C8—32no—
190D3×C8C2×A412yescomplemented
191C22×C32—41no—
192C2×C3×D3—42no—
193C3×A4#13111yescharacteristic, complemented
194C32×C4—41no—
195C32×C4—41no—
196C3×Dic3—42no—
197C2×#41—91no—
198C2×#41—91no—
199C2×#41—92no—
200C2×#41—91no—
201C2×#41—92no—
202C2×#41—91no—
203C22×Q8—31no—
204C22×D4—32no—
205C22×D4—31no—
206C23×C4—32no—
207C23×C4C2×C3×D311yescharacteristic
208#131—31no—
209#131—91no—
210#131—92no—
211#131—92no—
212#131—91no—
213#131—92no—
214#131—94no—
215#131—92no—
216#131—92no—
217#131—94no—
218#131—91no—
219C2×M16—31no—
220C2×M16—32no—
221C2×M16—31no—
222C2×M16—92no—
223C2×M16—92no—
224C2×M16—92no—
225C2×M16—92no—
226C22×C8—31no—
227C22×C8—31no—
228C22×C8—92no—
229C22×C8—91no—
230C22×C8—92no—
231C22×C8—92no—
232C22×C8—92no—
233C22×C8—91no—
234C22×C8—91no—
235C22×C8—91no—
236C22×C8C2×C3×D312yes—
237C23×C3—21no—
238C23×C3—31no—
239C23×C3—31no—
240C23×C3—61no—
241C23×C3C22×C3×C411yescharacteristic
242C22×D3—22no—
243C22×D3—32no—
244C22×D3—32no—
245C22×D3—62no—
246C2×A4—21no—
247C2×A4—21no—
248C2×A4—41no—
249C2×A4—62no—
250C2×A4C2×C4×D311yescharacteristic
251C3×Q8—121no—
252C3×D4—121no—
253C3×D4—122no—
254C2×C3×C4—32no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—41no—
263C2×C3×C4—81no—
264C2×C3×C4—122no—
265C2×C3×C4C22×A411yescharacteristic
266#67—34no—
267#67—32no—
268#67—32no—
269#67—32no—
270#67C4×A412yes—
271C2×Dic3—32no—
272C2×Dic3—32no—
273D12—32no—
274D12—32no—
275D12—31no—
276D12C4×A411yescharacteristic
277C4×D3—34no—
278C4×D3—32no—
279C4×D3—32no—
280C4×D3—32no—
281C4×D3C22×A412yes—
282Dic6—32no—
283Dic6—31no—
284Dic6—32no—
285Dic6C4×A411yescharacteristic
286C3×C8—32no—
287C3×C8—42no—
288C3×C8—82no—
289C3×C8—121no—
290C3×C8—121no—
291C3×C8C22×A412yes—
292C3⋊C8—31no—
293C3⋊C8—31no—
294C3⋊C8C22×A411yescharacteristic
295C3⋊C8C22×A411yescharacteristic
296C2×C32—41no—
297C2×C32—81no—
298C3×D3—82no—
299C24—32no—
300C24C3×C4×D311yescharacteristic
301#41—31no—
302#41—92no—
303#41—92no—
304#41—91no—
305#41—91no—
306#41—92no—
307#41—94no—
308#41—94no—
309#41—92no—
310#41—92no—
311#41—91no—
312C2×Q8—91no—
313C2×Q8—91no—
314C2×Q8—92no—
315C2×D4—91no—
316C2×D4—91no—
317C2×D4—92no—
318C2×D4—92no—
319C2×D4—92no—
320C2×D4—92no—
321C2×D4—92no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—32no—
327C22×C4—92no—
328C22×C4—92no—
329C22×C4—92no—
330C22×C4—92no—
331C22×C4C3×C4×D311yescharacteristic
332C22×C4C22×C3×D311yescharacteristic
333M16—32no—
334M16—31no—
335M16—32no—
336M16—32no—
337M16—92no—
338M16—92no—
339M16—94no—
340M16—92no—
341M16D3×A411yescharacteristic, complemented
342C2×C8—31no—
343C2×C8—32no—
344C2×C8—32no—
345C2×C8—32no—
346C2×C8—92no—
347C2×C8—91no—
348C2×C8—91no—
349C2×C8—92no—
350C2×C8—91no—
351C2×C8—91no—
352C2×C8—94no—
353C2×C8—92no—
354C2×C8—91no—
355C2×C8—92no—
356C2×C8—91no—
357C2×C8—91no—
358C22×C3—31no—
359C22×C3—31no—
360C22×C3—31no—
361C22×C3—41no—
362C22×C3—61no—
363C22×C3—61no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—81no—
367C22×C3—122no—
368C22×C3C3×#13111yescharacteristic, complemented
369C22×C3C2×C4×A411yescharacteristic
370C2×D3—32no—
371C2×D3—62no—
372C2×D3—62no—
373C2×D3—62no—
374C2×D3—62no—
375C2×D3C2×C4×A412yes—
376A4—21no—
377A4#90711yescharacteristic, direct product factor
378C3×C4—31no—
379C3×C4—31no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—81no—
383C3×C4—81no—
384C3×C4—122no—
385C3×C4C2×C4×A411yescharacteristic
386C3×C4C23×A411yescharacteristic
387Dic3—32no—
388Dic3C2×C4×A412yes—
389C32—41noSylow
390C23—21no—
391C23—31no—
392C23—31no—
393C23—61no—
394C23—62no—
395C23—92no—
396C23—92no—
397C23—182no—
398C23C2×C3×C4×D311yescharacteristic
399Q8—31no—
400Q8—92no—
401Q8—92no—
402Q8—91no—
403D4—32no—
404D4—31no—
405D4—92no—
406D4—92no—
407D4—92no—
408D4—92no—
409D4—94no—
410D4—92no—
411D4—91no—
412C2×C4—32no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—32no—
418C2×C4—31no—
419C2×C4—31no—
420C2×C4—31no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—94no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4C2×D3×A411yescharacteristic
428C8—31no—
429C8—32no—
430C8—31no—
431C8—91no—
432C8—91no—
433C8C2×D3×A412yes—
434C2×C3—21no—
435C2×C3—31no—
436C2×C3—31no—
437C2×C3—41no—
438C2×C3—61no—
439C2×C3—81no—
440C2×C3—81no—
441C2×C3—161no—
442C2×C3—242no—
443C2×C3C22×C4×A411yescharacteristic
444D3—22no—
445D3—62no—
446C22—31no—
447C22—31no—
448C22—31no—
449C22—32no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—61no—
454C22—92no—
455C22—182no—
456C22—182no—
457C22—182no—
458C22—182no—
459C22C3×#90711yescharacteristic, complemented
460C22C4×D3×A411yescharacteristic
461C4—31no—
462C4—31no—
463C4—32no—
464C4—92no—
465C4C4×D3×A411yescharacteristic
466C4C22×D3×A411yescharacteristic
467C3—41no—
468C3—81no—
469C3A4×#13111yescharacteristic, complemented
470C2—21no—
471C2—31no—
472C2—31no—
473C2—61no—
474C2—62no—
475C2—182no—
476C2C2×C4×D3×A411yescharacteristic
subgroupG/H
center, FrattiniC4C22×D3×A4
commutator, socleC23×C3C22×C3×C4
FittingC22×C3×M16C2×C3
prime radicalA4×#235C2
cosocleC22×C3×C4C23×C3
hypercenterM16D3×A4
hypocenterC22×C3C3×#131
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. C3×A4×M16C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. A4×ΓL(1,𝔽25)C2semidirect
5. D3×C8×A4C2semidirect
6. C22×#907C3semidirect
19. C22×C3×M16C2×C3semidirect
20. C23×C3⋊C8C2×C3semidirect
27. C22×ΓL(1,𝔽25)C2×C3semidirect
28. C22×D3×C8C2×C3semidirect
31. A4×M16D3semidirect
83. #907A4direct (N × H)
115. C22×M16C3×D3semidirect
167. C3×M16C2×A4semidirect
180. C2×C3⋊C8C2×A4semidirect
185. ΓL(1,𝔽25)C2×A4semidirect
190. D3×C8C2×A4semidirect
193. C3×A4#131semidirect
341. M16D3×A4semidirect
368. C22×C3C3×#131semidirect
377. A4#907direct (N × H)
459. C22C3×#907semidirect
469. C3A4×#131semidirect

Maximal subgroups

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

subgroupindex
A4×#2352
C3×A4×M162
C2×A4×C3⋊C82
A4×ΓL(1,𝔽25)2
D3×C8×A42
C22×#9073
A4×#1313
C3×#9074