Finite Group Databasebeta

← A4×#830 #11921353

Subgroups — A4×#830 #11921353

Order 1152.

578 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 87 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
2C2×A4×C3⋊C8C212yesmaximal, complemented
3C22×#830C311yesmaximal, characteristic, complemented
4A4×C22⋊C8—31nomaximal
5C23×C3×A4C411yescharacteristic
6C2×C3×C4×A4—22no—
7C2×C3×C4×A4C411yescharacteristic
8C2×C3×C4×A4C2211yescharacteristic
9A4×C3⋊C8—22no—
10C3×#830—41nomaximal
11C24×C3×C4C2×C311yescharacteristic
12C22×C4×A4—21no—
13C22×C4×A4D311yescharacteristic
14C23×C3⋊C8C2×C312yescomplemented
15C2×C8×A4—32no—
16C2×#830—31no—
17C2×#830—31no—
18C2×#830—32no—
19C22×C3×A4—21no—
20C22×C3×A4—21no—
21C22×C3×A4C812yescomplemented
22C22×C3×A4C2×C411yescharacteristic
23C22×C32×C4—41no—
24C3×C4×A4—21no—
25C3×C4×A4D412yes—
26C2×C3×C3⋊C8—42no—
27C22×C22⋊C8—31noSylow
28C25×C3C3×C411yescharacteristic
29C23×A4—21no—
30C23×A4Dic311yescharacteristic
31C23×C3×C4—22no—
32C23×C3×C4—31no—
33C23×C3×C4—31no—
34C23×C3×C4—31no—
35C23×C3×C4—31no—
36C23×C3×C4—62no—
37C23×C3×C4C3×C411yescharacteristic
38C23×C3×C4C22×C311yescharacteristic
39C2×C4×A4—24no—
40C2×C4×A4—22no—
41C2×C4×A4—21no—
42C2×C4×A4—21no—
43C2×C4×A4Dic311yescharacteristic
44C2×C4×A4C2×D311yescharacteristic
45C22×C3⋊C8—22no—
46C22×C3⋊C8—32no—
47C22×C3⋊C8—32no—
48C22×C3⋊C8—62no—
49C8×A4—62no—
50C3×C22⋊C8—121no—
51#830—32no—
52#830—31no—
53#830—32no—
54#830A411yescharacteristic, direct product factor
55C23×C32—41no—
56C2×C3×A4—22no—
57C2×C3×A4C22⋊C411yescharacteristic
58C2×C3×A4C2×C811yescharacteristic
59C2×C3×A4M1611yescharacteristic
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4—82no—
63C3×C3⋊C8—82no—
64C24×C4C3×D311yescharacteristic
65C23×C8—32no—
66C2×C22⋊C8—91no—
67C2×C22⋊C8—92no—
68C2×C22⋊C8—91no—
69C24×C3—21no—
70C24×C3—21no—
71C24×C3—32no—
72C24×C3—31no—
73C24×C3—31no—
74C24×C3—61no—
75C24×C3—61no—
76C24×C3C3×C812yescomplemented
77C24×C3C2×C3×C411yescharacteristic
78C22×A4—22no—
79C22×A4—22no—
80C22×A4—21no—
81C22×A4—21no—
82C22×A4—22no—
83C22×A4—21no—
84C22×A4C3⋊C812yescomplemented
85C22×A4C2×Dic311yescharacteristic
86C22×C3×C4—21no—
87C22×C3×C4—31no—
88C22×C3×C4—32no—
89C22×C3×C4—31no—
90C22×C3×C4—32no—
91C22×C3×C4—31no—
92C22×C3×C4—31no—
93C22×C3×C4—31no—
94C22×C3×C4—31no—
95C22×C3×C4—31no—
96C22×C3×C4—41no—
97C22×C3×C4—62no—
98C22×C3×C4—62no—
99C22×C3×C4—62no—
100C22×C3×C4—62no—
101C22×C3×C4—62no—
102C22×C3×C4—62no—
103C22×C3×C4—62no—
104C22×C3×C4—62no—
105C22×C3×C4—61no—
106C22×C3×C4—81no—
107C22×C3×C4C3×D412yes—
108C22×C3×C4C2×A411yescharacteristic
109C4×A4—22no—
110C4×A4—21no—
111C4×A4—22no—
112C4×A4#6712yes—
113C2×C3×C8—122no—
114C2×C3⋊C8—32no—
115C2×C3⋊C8—62no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—62no—
119C2×C3⋊C8C2×A412yescomplemented
120C22×C32—42no—
121C22×C32—41no—
122C22×C32—81no—
123C22×C32—81no—
124C3×A4C22⋊C811yescharacteristic, complemented
125C32×C4—42no—
126C32×C4—81no—
127C25C3×Dic311yescharacteristic
128C23×C4—22no—
129C23×C4—31no—
130C23×C4—31no—
131C23×C4—31no—
132C23×C4—31no—
133C23×C4—62no—
134C23×C4C3×Dic311yescharacteristic
135C23×C4C2×C3×D311yescharacteristic
136C22×C8—62no—
137C22×C8—92no—
138C22×C8—92no—
139C22×C8—182no—
140C22⋊C8—31no—
141C22⋊C8—92no—
142C22⋊C8—92no—
143C22⋊C8—91no—
144C23×C3—22no—
145C23×C3—31no—
146C23×C3—31no—
147C23×C3—31no—
148C23×C3—31no—
149C23×C3—32no—
150C23×C3—32no—
151C23×C3—32no—
152C23×C3—32no—
153C23×C3—31no—
154C23×C3—41no—
155C23×C3—61no—
156C23×C3—61no—
157C23×C3—61no—
158C23×C3—61no—
159C23×C3—62no—
160C23×C3—61no—
161C23×C3—61no—
162C23×C3—62no—
163C23×C3—62no—
164C23×C3—61no—
165C23×C3—61no—
166C23×C3—64no—
167C23×C3—81no—
168C23×C3C3×C22⋊C411yescharacteristic
169C23×C3C2×C3×C811yescharacteristic
170C23×C3C3×M1611yescharacteristic
171C23×C3C4×A411yescharacteristic
172C2×A4—24no—
173C2×A4—22no—
174C2×A4—21no—
175C2×A4—21no—
176C2×A4—21no—
177C2×A4C2×C3⋊C811yescharacteristic
178C2×A4#20811yescharacteristic
179C2×A4#21711yescharacteristic
180C2×C3×C4—22no—
181C2×C3×C4—32no—
182C2×C3×C4—31no—
183C2×C3×C4—32no—
184C2×C3×C4—32no—
185C2×C3×C4—32no—
186C2×C3×C4—31no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4—62no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4—62no—
193C2×C3×C4—64no—
194C2×C3×C4—62no—
195C2×C3×C4—61no—
196C2×C3×C4—61no—
197C2×C3×C4—82no—
198C2×C3×C4—84no—
199C2×C3×C4—81no—
200C2×C3×C4—81no—
201C2×C3×C4C4×A411yescharacteristic
202C2×C3×C4C22×A411yescharacteristic
203C3×C8—242no—
204C3⋊C8—22no—
205C3⋊C8—62no—
206C2×C32—41no—
207C2×C32—41no—
208C2×C32—41no—
209C2×C32—82no—
210C24—21no—
211C24—21no—
212C24—31no—
213C24—32no—
214C24—31no—
215C24—61no—
216C24—61no—
217C24C3×C3⋊C812yescomplemented
218C24C2×C3×Dic311yescharacteristic
219C22×C4—21no—
220C22×C4—31no—
221C22×C4—32no—
222C22×C4—31no—
223C22×C4—32no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—62no—
230C22×C4—62no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—62no—
234C22×C4—62no—
235C22×C4—62no—
236C22×C4—62no—
237C22×C4—61no—
238C22×C4C3×#6712yes—
239C22×C4D3×A411yescharacteristic
240C2×C8—32no—
241C2×C8—92no—
242C2×C8—182no—
243C2×C8—182no—
244C2×C8—182no—
245C2×C8—182no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—31no—
249C22×C3—31no—
250C22×C3—31no—
251C22×C3—32no—
252C22×C3—31no—
253C22×C3—31no—
254C22×C3—31no—
255C22×C3—31no—
256C22×C3—31no—
257C22×C3—31no—
258C22×C3—32no—
259C22×C3—42no—
260C22×C3—41no—
261C22×C3—62no—
262C22×C3—62no—
263C22×C3—62no—
264C22×C3—62no—
265C22×C3—62no—
266C22×C3—62no—
267C22×C3—62no—
268C22×C3—62no—
269C22×C3—61no—
270C22×C3—61no—
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—82no—
274C22×C3—82no—
275C22×C3—82no—
276C22×C3—81no—
277C22×C3C3×C22⋊C811yescharacteristic, complemented
278C22×C3C8×A412yescomplemented
279C22×C3C2×C4×A411yescharacteristic
280A4—21no—
281A4#83011yescharacteristic, direct product factor
282C3×C4—21no—
283C3×C4—32no—
284C3×C4—42no—
285C3×C4—61no—
286C3×C4—81no—
287C3×C4—82no—
288C3×C4—82no—
289C3×C4D4×A412yes—
290C32—41noSylow
291C23—22no—
292C23—31no—
293C23—31no—
294C23—31no—
295C23—31no—
296C23—32no—
297C23—32no—
298C23—32no—
299C23—32no—
300C23—31no—
301C23—61no—
302C23—61no—
303C23—61no—
304C23—61no—
305C23—62no—
306C23—61no—
307C23—61no—
308C23—62no—
309C23—62no—
310C23—61no—
311C23—61no—
312C23—64no—
313C23C2×C3×C3⋊C811yescharacteristic
314C23C3×#20811yescharacteristic
315C23C3×#21711yescharacteristic
316C23Dic3×A411yescharacteristic
317C2×C4—22no—
318C2×C4—32no—
319C2×C4—31no—
320C2×C4—32no—
321C2×C4—32no—
322C2×C4—32no—
323C2×C4—31no—
324C2×C4—62no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—62no—
328C2×C4—64no—
329C2×C4—62no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4Dic3×A411yescharacteristic
333C2×C4C2×D3×A411yescharacteristic
334C8—62no—
335C8—182no—
336C2×C3—22no—
337C2×C3—31no—
338C2×C3—31no—
339C2×C3—31no—
340C2×C3—31no—
341C2×C3—41no—
342C2×C3—41no—
343C2×C3—41no—
344C2×C3—62no—
345C2×C3—82no—
346C2×C3—84no—
347C2×C3—81no—
348C2×C3—81no—
349C2×C3—81no—
350C2×C3A4×C22⋊C411yescharacteristic
351C2×C3C2×C8×A411yescharacteristic
352C2×C3A4×M1611yescharacteristic
353C22—21no—
354C22—21no—
355C22—31no—
356C22—31no—
357C22—31no—
358C22—32no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—32no—
366C22—62no—
367C22—62no—
368C22—62no—
369C22—62no—
370C22—62no—
371C22—62no—
372C22—62no—
373C22—62no—
374C22—61no—
375C22—61no—
376C22C3×#83011yescharacteristic, complemented
377C22A4×C3⋊C812yescomplemented
378C22C2×Dic3×A411yescharacteristic
379C4—21no—
380C4—32no—
381C4—61no—
382C4A4×#6712yes—
383C3—41no—
384C3—81no—
385C3A4×C22⋊C811yescharacteristic, complemented
386C2—22no—
387C2—31no—
388C2—31no—
389C2—31no—
390C2—31no—
391C2—62no—
392C2C2×A4×C3⋊C811yescharacteristic
393C2A4×#20811yescharacteristic
394C2A4×#21711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC23×C3C2×C3×C8
FittingC24×C3×C4C2×C3
socleC24×C3C2×C3×C4
prime radicalC23×C3×A4C4
cosocleC23×C3×C4C22×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C3×C22⋊C8
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4×C3⋊C8C2semidirect
3. C22×#830C3semidirect
14. C23×C3⋊C8C2×C3semidirect
21. C22×C3×A4C8semidirect
54. #830A4direct (N × H)
76. C24×C3C3×C8semidirect
84. C22×A4C3⋊C8semidirect
119. C2×C3⋊C8C2×A4semidirect
124. C3×A4C22⋊C8semidirect
217. C24C3×C3⋊C8semidirect
277. C22×C3C3×C22⋊C8semidirect
278. C22×C3C8×A4semidirect
281. A4#830direct (N × H)
376. C22C3×#830semidirect
377. C22A4×C3⋊C8semidirect
385. C3A4×C22⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C2×A4×C3⋊C82
C22×#8303
A4×C22⋊C83
C3×#8304