Finite Group Databasebeta

← A4×#875 #11923148

Subgroups — A4×#875 #11923148

Order 1152.

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

normal subgroups only

This group has 910 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×A4×D12C211yesmaximal, characteristic
2C2×A4×Dic6C211yesmaximal, characteristic, complemented
3C3×C42×A4C211yesmaximal, characteristic, complemented
4A4×(C2×D3)⋊C4C214yesmaximal, complemented
5C22×#875C311yesmaximal, characteristic, complemented
6A4×#124—31nomaximal
7C22×D3×A4C2212yes—
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×Dic3×A4C2212yes—
11A4×D12—22no—
12A4×Dic6—22no—
13C3×#875—41nomaximal
14C23×D12C2×C311yescharacteristic
15C23×Dic6C2×C311yescharacteristic, complemented
16C2×Q8×A4—31no—
17C2×D4×A4—31no—
18C22×C3×C42C2×C311yescharacteristic, complemented
19C22×(C2×D3)⋊C4C2×C314yescomplemented
20C2×#875—31no—
21C2×#875—31no—
22C2×#875—31no—
23C2×#875—31no—
24C2×#875—34no—
25A4×C22⋊C4—34no—
26C42×A4—21no—
27C42×A4D311yescharacteristic, complemented
28C22×C3×A4C2311yescharacteristic
29C2×D3×A4—22no—
30C2×D3×A4—24no—
31C2×C3×D12—41no—
32C2×C3×Dic6—41no—
33C3×C4×A4—22no—
34C3×C4×A4D412yes—
35Dic3×A4—22no—
36C32×C42—41no—
37C3×(C2×D3)⋊C4—44no—
38C22×#124—31noSylow
39C24×D3C22×C312yes—
40C23×A4—32no—
41C23×C3×C4C22×C312yes—
42C23×C3×C4C22×C311yescharacteristic
43C23×Dic3C22×C312yes—
44C22×D12—22no—
45C22×D12—31no—
46C22×D12—32no—
47C22×D12—31no—
48C22×D12—62no—
49C22×Dic6—22no—
50C22×Dic6—31no—
51C22×Dic6—31no—
52C22×Dic6—32no—
53C22×Dic6—62no—
54Q8×A4—62no—
55D4×A4—62no—
56C2×C4×A4—22no—
57C2×C4×A4—21no—
58C2×C4×A4—32no—
59C2×C4×A4C2×D312yes—
60C2×C4×A4C2×D311yescharacteristic
61C3×#124—121no—
62C2×C3×C42—31no—
63C2×C3×C42—31no—
64C2×C3×C42—32no—
65C2×(C2×D3)⋊C4—34no—
66C2×(C2×D3)⋊C4—34no—
67C2×(C2×D3)⋊C4—34no—
68C2×(C2×D3)⋊C4—34no—
69#875—32no—
70#875—34no—
71#875—34no—
72#875—34no—
73#875—31no—
74#875—31no—
75#875—31no—
76#875—34no—
77#875A411yescharacteristic, direct product factor
78C22×C3×D3—42no—
79C2×C3×A4C2×D411yescharacteristic
80C2×C3×A4#4112yes—
81D3×A4—42no—
82C2×C32×C4—41no—
83C2×C32×C4—42no—
84C2×C3×Dic3—42no—
85C3×D12—82no—
86C3×Dic6—82no—
87C23×Q8—31no—
88C23×D4—31no—
89C2×#124—91no—
90C2×#124—91no—
91C2×#124—94no—
92C2×#124—91no—
93C2×#124—91no—
94C22×C22⋊C4—34no—
95C22×C42C3×D311yescharacteristic, complemented
96C24×C3C23×C311yescharacteristic
97C23×D3—22no—
98C23×D3—24no—
99C23×D3—32no—
100C23×D3—32no—
101C23×D3—62no—
102C23×D3—64no—
103C22×A4—21no—
104C22×A4—62no—
105C22×A4—64no—
106C22×A4C22×D311yescharacteristic
107C2×C3×Q8—121no—
108C2×C3×D4—121no—
109C22×C3×C4—22no—
110C22×C3×C4—31no—
111C22×C3×C4—31no—
112C22×C3×C4—32no—
113C22×C3×C4—32no—
114C22×C3×C4—32no—
115C22×C3×C4—62no—
116C22×C3×C4C3×D412yes—
117C22×Dic3—22no—
118C22×Dic3—32no—
119C22×Dic3—32no—
120C22×Dic3—62no—
121C2×D12—32no—
122C2×D12—32no—
123C2×D12—31no—
124C2×D12—62no—
125C2×D12—62no—
126C2×D12—64no—
127C2×D12—64no—
128C2×D12—62no—
129C2×D12—62no—
130C2×D12C2×A411yescharacteristic
131C2×Dic6—32no—
132C2×Dic6—31no—
133C2×Dic6—32no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C2×Dic6—62no—
139C2×Dic6—62no—
140C2×Dic6C2×A411yescharacteristic, complemented
141C4×A4—24no—
142C4×A4—22no—
143C4×A4—22no—
144C4×A4—62no—
145C4×A4D1212yes—
146C3×C22⋊C4—124no—
147C3×C42—32no—
148C3×C42—32no—
149C3×C42—31no—
150C3×C42—41no—
151C3×C42—81no—
152C3×C42C2×A411yescharacteristic, complemented
153(C2×D3)⋊C4—38no—
154(C2×D3)⋊C4—34no—
155(C2×D3)⋊C4—34no—
156(C2×D3)⋊C4—34no—
157(C2×D3)⋊C4C2×A414yescomplemented
158C22×C32—41no—
159C2×C3×D3—82no—
160C2×C3×D3—84no—
161C3×A4#12411yescharacteristic, complemented
162C32×C4—42no—
163C32×C4—82no—
164C3×Dic3—82no—
165C25—32no—
166C22×Q8—62no—
167C22×Q8—91no—
168C22×Q8—91no—
169C22×Q8—92no—
170C22×Q8—182no—
171C22×D4—62no—
172C22×D4—91no—
173C22×D4—91no—
174C22×D4—92no—
175C22×D4—182no—
176C23×C4—32no—
177C23×C4C2×C3×D312yes—
178C23×C4C2×C3×D311yescharacteristic
179#124—31no—
180#124—94no—
181#124—91no—
182#124—91no—
183#124—94no—
184#124—94no—
185#124—92no—
186#124—94no—
187#124—91no—
188C2×C22⋊C4—94no—
189C2×C22⋊C4—94no—
190C2×C22⋊C4—94no—
191C2×C22⋊C4—94no—
192C2×C42—31no—
193C2×C42—31no—
194C2×C42—32no—
195C23×C3—31no—
196C23×C3—32no—
197C23×C3—31no—
198C23×C3—122no—
199C23×C3C2×C3×D411yescharacteristic
200C23×C3C3×#4112yes—
201C22×D3—32no—
202C22×D3—42no—
203C22×D3—62no—
204C22×D3—62no—
205C22×D3—64no—
206C22×D3—64no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—64no—
210C22×D3—64no—
211C22×D3—124no—
212C22×D3—122no—
213C22×D3—124no—
214C22×D3C22×A412yes—
215C2×A4—21no—
216C2×A4—22no—
217C2×A4—122no—
218C2×A4C2×D1211yescharacteristic
219C2×A4#23512yes—
220C3×Q8—242no—
221C3×D4—242no—
222C2×C3×C4—32no—
223C2×C3×C4—31no—
224C2×C3×C4—32no—
225C2×C3×C4—32no—
226C2×C3×C4—32no—
227C2×C3×C4—32no—
228C2×C3×C4—41no—
229C2×C3×C4—42no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—62no—
234C2×C3×C4—82no—
235C2×C3×C4—81no—
236C2×C3×C4—122no—
237C2×C3×C4C22×A412yes—
238C2×C3×C4C22×A411yescharacteristic
239C2×Dic3—32no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3C22×A412yes—
245D12—22no—
246D12—64no—
247D12—64no—
248D12—62no—
249Dic6—22no—
250Dic6—64no—
251Dic6—64no—
252Dic6—62no—
253C2×C32—41no—
254C2×C32—42no—
255C3×D3—162no—
256C24—62no—
257C24—64no—
258C24—92no—
259C24—92no—
260C24—182no—
261C24—184no—
262C24C22×C3×D311yescharacteristic
263C2×Q8—31no—
264C2×Q8—92no—
265C2×Q8—92no—
266C2×Q8—91no—
267C2×Q8—182no—
268C2×Q8—182no—
269C2×Q8—182no—
270C2×Q8—184no—
271C2×Q8—182no—
272C2×Q8—184no—
273C2×D4—31no—
274C2×D4—92no—
275C2×D4—92no—
276C2×D4—91no—
277C2×D4—182no—
278C2×D4—182no—
279C2×D4—184no—
280C2×D4—182no—
281C2×D4—184no—
282C2×D4—182no—
283C22×C4—22no—
284C22×C4—31no—
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—32no—
288C22×C4—32no—
289C22×C4—62no—
290C22×C4—62no—
291C22×C4—92no—
292C22×C4—92no—
293C22×C4—182no—
294C22×C4C3×D1212yes—
295C22⋊C4—34no—
296C22⋊C4—94no—
297C22⋊C4—94no—
298C22⋊C4—98no—
299C22⋊C4—94no—
300C42—32no—
301C42—32no—
302C42—31no—
303C42D3×A411yescharacteristic, complemented
304C22×C3—31no—
305C22×C3—32no—
306C22×C3—32no—
307C22×C3—31no—
308C22×C3—31no—
309C22×C3—32no—
310C22×C3—32no—
311C22×C3—41no—
312C22×C3—81no—
313C22×C3—242no—
314C22×C3—244no—
315C22×C3C3×#12411yescharacteristic, complemented
316C22×C3C23×A411yescharacteristic
317C2×D3—22no—
318C2×D3—24no—
319C2×D3—62no—
320C2×D3—64no—
321C2×D3—122no—
322C2×D3—122no—
323C2×D3—124no—
324C2×D3—122no—
325C2×D3—122no—
326C2×D3—124no—
327A4—21no—
328A4#87511yescharacteristic, direct product factor
329C3×C4—22no—
330C3×C4—32no—
331C3×C4—42no—
332C3×C4—62no—
333C3×C4—82no—
334C3×C4—84no—
335C3×C4—82no—
336C3×C4—242no—
337C3×C4D4×A412yes—
338Dic3—22no—
339Dic3—62no—
340C32—41noSylow
341C23—31no—
342C23—32no—
343C23—31no—
344C23—32no—
345C23—92no—
346C23—122no—
347C23—182no—
348C23—182no—
349C23—184no—
350C23—184no—
351C23—182no—
352C23—182no—
353C23—184no—
354C23—184no—
355C23—362no—
356C23—364no—
357C23—364no—
358C23C2×C3×D1211yescharacteristic
359C23C3×#23512yes—
360Q8—62no—
361Q8—184no—
362Q8—184no—
363Q8—182no—
364D4—62no—
365D4—184no—
366D4—184no—
367D4—182no—
368C2×C4—32no—
369C2×C4—31no—
370C2×C4—32no—
371C2×C4—32no—
372C2×C4—32no—
373C2×C4—32no—
374C2×C4—32no—
375C2×C4—62no—
376C2×C4—62no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—92no—
380C2×C4—182no—
381C2×C4—182no—
382C2×C4—182no—
383C2×C4—182no—
384C2×C4C2×D3×A412yes—
385C2×C4C2×D3×A411yescharacteristic
386C2×C3—31no—
387C2×C3—32no—
388C2×C3—31no—
389C2×C3—41no—
390C2×C3—42no—
391C2×C3—81no—
392C2×C3—82no—
393C2×C3—482no—
394C2×C3C2×D4×A411yescharacteristic
395C2×C3A4×#4112yes—
396D3—42no—
397D3—122no—
398C22—31no—
399C22—32no—
400C22—32no—
401C22—31no—
402C22—31no—
403C22—32no—
404C22—32no—
405C22—62no—
406C22—64no—
407C22—182no—
408C22—184no—
409C22—362no—
410C22—362no—
411C22—364no—
412C22—362no—
413C22—362no—
414C22—364no—
415C22C3×#87511yescharacteristic, complemented
416C22C22×D3×A411yescharacteristic
417C4—22no—
418C4—32no—
419C4—62no—
420C4—62no—
421C4—182no—
422C4A4×D1212yes—
423C3—41no—
424C3—81no—
425C3A4×#12411yescharacteristic, complemented
426C2—31no—
427C2—31no—
428C2—32no—
429C2—122no—
430C2—362no—
431C2C2×A4×D1211yescharacteristic
432C2A4×#23512yes—
subgroupG/H
center, FrattiniC22C22×D3×A4
commutator, socle, cosocleC24×C3C23×C3
FittingC22×C3×C42C2×C3
prime radicalC2×A4×D12C2
hypercenterC42D3×A4
hypocenterC22×C3C3×#124
LCSG ▷ C24×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic6C2semidirect
3. C3×C42×A4C2semidirect
4. A4×(C2×D3)⋊C4C2semidirect
5. C22×#875C3semidirect
15. C23×Dic6C2×C3semidirect
18. C22×C3×C42C2×C3semidirect
19. C22×(C2×D3)⋊C4C2×C3semidirect
27. C42×A4D3semidirect
77. #875A4direct (N × H)
95. C22×C42C3×D3semidirect
140. C2×Dic6C2×A4semidirect
152. C3×C42C2×A4semidirect
157. (C2×D3)⋊C4C2×A4semidirect
161. C3×A4#124semidirect
303. C42D3×A4semidirect
315. C22×C3C3×#124semidirect
328. A4#875direct (N × H)
415. C22C3×#875semidirect
425. C3A4×#124semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D122
C2×A4×Dic62
C3×C42×A42
A4×(C2×D3)⋊C42
C22×#8753
A4×#1243
C3×#8754