Finite Group Databasebeta

← A4×#809 #11921256

Subgroups — A4×#809 #11921256

Order 1152.

550 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×A4×C3⋊C8C211yesmaximal, characteristic, complemented
4C22×#809C311yesmaximal, characteristic, complemented
5A4×#102—31nomaximal
6C22×D3×A4—21no—
7C2×C3×C4×A4—21no—
8C2×C3×C4×A4C2211yescharacteristic
9A4×D12—21no—
10A4×D12C412yescomplemented
11A4×C3⋊C8—21no—
12C3×#809—41nomaximal
13C23×D12C2×C311yescharacteristic
14C2×D4×A4—31no—
15C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
16C23×C3⋊C8C2×C311yescharacteristic, complemented
17C2×C8×A4—31no—
18A4×C4⋊C4—21no—
19A4×C4⋊C4D311yescharacteristic, complemented
20C2×#809—31no—
21C2×#809—31no—
22C2×#809—31no—
23C2×#809—31no—
24C22×C3×A4D411yescharacteristic
25C2×D3×A4—22no—
26C2×D3×A4—41no—
27C2×D3×A4—41no—
28C2×C3×D12—41no—
29C3×C4×A4—41no—
30C3×C4×A4C2×C411yescharacteristic
31C3×C4×A4D411yescharacteristic
32C32×C4⋊C4—41no—
33C2×C3×C3⋊C8—41no—
34C22×#102—31noSylow
35C24×D3—21no—
36C23×A4—61no—
37C23×C3×C4—21no—
38C23×C3×C4C22×C311yescharacteristic
39C22×D12—21no—
40C22×D12—31no—
41C22×D12—32no—
42C22×D12—31no—
43C22×D12—61no—
44C22×D12—61no—
45C22×D12C3×C412yescomplemented
46D4×A4—32no—
47D4×A4—61no—
48C2×C4×A4—22no—
49C2×C4×A4—21no—
50C2×C4×A4—21no—
51C2×C4×A4C2×D311yescharacteristic
52C2×C3×C4⋊C4—31no—
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4—61no—
55C22×C3⋊C8—21no—
56C22×C3⋊C8—31no—
57C22×C3⋊C8—31no—
58C22×C3⋊C8—61no—
59C8×A4—61no—
60C3×#102—121no—
61#809—32no—
62#809—31no—
63#809—31no—
64#809—31no—
65#809A411yescharacteristic, direct product factor
66C22×C3×D3—81no—
67C2×C3×A4C22⋊C411yescharacteristic
68C2×C3×A4D811yescharacteristic
69C2×C3×A4SD1611yescharacteristic
70D3×A4—42no—
71C2×C32×C4—41no—
72C2×C32×C4—81no—
73C3×D12—42no—
74C3×D12—81no—
75C3×C3⋊C8—81no—
76C23×D4—31no—
77C23×C8—31no—
78C22×C4⋊C4C3×D311yescharacteristic, complemented
79C2×#102—91no—
80C2×#102—91no—
81C2×#102—91no—
82C2×#102—91no—
83C24×C3C3×D411yescharacteristic
84C23×D3—22no—
85C23×D3—41no—
86C23×D3—41no—
87C23×D3—61no—
88C23×D3—62no—
89C23×D3—61no—
90C23×D3—121no—
91C23×D3—121no—
92C22×A4—21no—
93C22×A4—62no—
94C22×A4—121no—
95C22×A4—121no—
96C22×A4#6711yescharacteristic
97C2×C3×D4—121no—
98C22×C3×C4—31no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—41no—
103C22×C3×C4—61no—
104C22×C3×C4—61no—
105C22×C3×C4—121no—
106C22×C3×C4C2×C3×C411yescharacteristic
107C22×C3×C4C3×D411yescharacteristic
108C2×D12—32no—
109C2×D12—31no—
110C2×D12—32no—
111C2×D12—32no—
112C2×D12—32no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—64no—
118C2×D12—62no—
119C2×D12—61no—
120C2×D12—61no—
121C2×D12—62no—
122C2×D12C2×A411yescharacteristic
123C4×A4—21no—
124C4×A4—21no—
125C4×A4—42no—
126C4×A4—41no—
127C4×A4C4×D311yescharacteristic
128C4×A4D1211yescharacteristic
129C2×C3×C8—121no—
130C3×C4⋊C4—31no—
131C3×C4⋊C4—41no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—81no—
135C3×C4⋊C4C2×A411yescharacteristic, complemented
136C2×C3⋊C8—31no—
137C2×C3⋊C8—61no—
138C2×C3⋊C8—61no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8C2×A411yescharacteristic, complemented
142C22×C32—41no—
143C2×C3×D3—82no—
144C2×C3×D3—161no—
145C2×C3×D3—161no—
146C3×A4#10211yescharacteristic, complemented
147C32×C4—41no—
148C32×C4—41no—
149C32×C4—161no—
150C25—61no—
151C22×D4—32no—
152C22×D4—61no—
153C22×D4—91no—
154C22×D4—91no—
155C22×D4—92no—
156C22×D4—181no—
157C22×D4—181no—
158C23×C4—21no—
159C23×C4C2×C3×D311yescharacteristic
160C22×C8—61no—
161C22×C8—91no—
162C22×C8—91no—
163C22×C8—181no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—61no—
167#102—31no—
168#102—91no—
169#102—91no—
170#102—92no—
171#102—91no—
172C23×C3—31no—
173C23×C3—31no—
174C23×C3—31no—
175C23×C3—31no—
176C23×C3—241no—
177C23×C3C3×C22⋊C411yescharacteristic
178C23×C3C3×D811yescharacteristic
179C23×C3C3×SD1611yescharacteristic
180C22×D3—21no—
181C22×D3—42no—
182C22×D3—62no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—61no—
186C22×D3—62no—
187C22×D3—121no—
188C22×D3—121no—
189C22×D3—121no—
190C22×D3—121no—
191C22×D3—124no—
192C22×D3—122no—
193C22×D3—122no—
194C22×D3—121no—
195C22×D3—121no—
196C22×D3—121no—
197C22×D3—121no—
198C22×D3—122no—
199C2×A4—21no—
200C2×A4—21no—
201C2×A4—21no—
202C2×A4—122no—
203C2×A4(C2×D3)⋊C411yescharacteristic
204C2×A4#21311yescharacteristic
205C2×A4#21511yescharacteristic
206C3×D4—122no—
207C3×D4—241no—
208C2×C3×C4—21no—
209C2×C3×C4—32no—
210C2×C3×C4—31no—
211C2×C3×C4—31no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—41no—
218C2×C3×C4—61no—
219C2×C3×C4—81no—
220C2×C3×C4—82no—
221C2×C3×C4—81no—
222C2×C3×C4—121no—
223C2×C3×C4—121no—
224C2×C3×C4—121no—
225C2×C3×C4—121no—
226C2×C3×C4C22×A411yescharacteristic
227D12—21no—
228D12—32no—
229D12—62no—
230D12—62no—
231D12—62no—
232D12—62no—
233D12—61no—
234D12C4×A412yescomplemented
235C3×C8—241no—
236C3⋊C8—21no—
237C3⋊C8—61no—
238C2×C32—41no—
239C2×C32—41no—
240C2×C32—41no—
241C3×D3—162no—
242C24—62no—
243C24—121no—
244C24—121no—
245C24—181no—
246C24—182no—
247C24—181no—
248C24—361no—
249C24—361no—
250C24C3×#6711yescharacteristic
251C2×D4—31no—
252C2×D4—92no—
253C2×D4—92no—
254C2×D4—92no—
255C2×D4—92no—
256C2×D4—91no—
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C2×D4—184no—
262C2×D4—181no—
263C2×D4—182no—
264C2×D4—181no—
265C2×D4—182no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—41no—
271C22×C4—61no—
272C22×C4—61no—
273C22×C4—121no—
274C22×C4C3×C4×D311yescharacteristic
275C22×C4C3×D1211yescharacteristic
276C2×C8—31no—
277C2×C8—91no—
278C2×C8—181no—
279C2×C8—181no—
280C2×C8—181no—
281C2×C8—181no—
282C4⋊C4—31no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4D3×A411yescharacteristic, complemented
286C22×C3—31no—
287C22×C3—31no—
288C22×C3—31no—
289C22×C3—32no—
290C22×C3—31no—
291C22×C3—31no—
292C22×C3—31no—
293C22×C3—31no—
294C22×C3—31no—
295C22×C3—31no—
296C22×C3—41no—
297C22×C3—81no—
298C22×C3—242no—
299C22×C3—481no—
300C22×C3—481no—
301C22×C3C3×#10211yescharacteristic, complemented
302C22×C3D4×A411yescharacteristic
303C2×D3—22no—
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—62no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—122no—
310C2×D3—122no—
311C2×D3—122no—
312C2×D3—122no—
313C2×D3—121no—
314C2×D3—121no—
315C2×D3—122no—
316C2×D3—122no—
317A4—21no—
318A4#80911yescharacteristic, direct product factor
319C3×C4—31no—
320C3×C4—31no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—81no—
325C3×C4—81no—
326C3×C4—121no—
327C3×C4—161no—
328C3×C4—162no—
329C3×C4C2×C4×A411yescharacteristic
330C3×C4D4×A411yescharacteristic
331C32—41noSylow
332C23—31no—
333C23—31no—
334C23—31no—
335C23—31no—
336C23—61no—
337C23—122no—
338C23—182no—
339C23—182no—
340C23—182no—
341C23—182no—
342C23—181no—
343C23—361no—
344C23—361no—
345C23—361no—
346C23—361no—
347C23—362no—
348C23—362no—
349C23—362no—
350C23—361no—
351C23—361no—
352C23—361no—
353C23—361no—
354C23—364no—
355C23C3×(C2×D3)⋊C411yescharacteristic
356C23C3×#21311yescharacteristic
357C23C3×#21511yescharacteristic
358D4—32no—
359D4—61no—
360D4—92no—
361D4—182no—
362D4—182no—
363D4—182no—
364D4—182no—
365D4—181no—
366C2×C4—21no—
367C2×C4—32no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—61no—
376C2×C4—121no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4C2×D3×A411yescharacteristic
381C8—61no—
382C8—181no—
383C2×C3—31no—
384C2×C3—31no—
385C2×C3—31no—
386C2×C3—31no—
387C2×C3—41no—
388C2×C3—41no—
389C2×C3—41no—
390C2×C3—81no—
391C2×C3—81no—
392C2×C3—81no—
393C2×C3—482no—
394C2×C3A4×C22⋊C411yescharacteristic
395C2×C3A4×D811yescharacteristic
396C2×C3A4×SD1611yescharacteristic
397D3—42no—
398D3—122no—
399C22—31no—
400C22—31no—
401C22—31no—
402C22—32no—
403C22—31no—
404C22—31no—
405C22—31no—
406C22—31no—
407C22—31no—
408C22—31no—
409C22—62no—
410C22—121no—
411C22—121no—
412C22—182no—
413C22—362no—
414C22—362no—
415C22—362no—
416C22—362no—
417C22—362no—
418C22—362no—
419C22—362no—
420C22—362no—
421C22—361no—
422C22—361no—
423C22C3×#80911yescharacteristic, complemented
424C22A4×#6711yescharacteristic
425C4—31no—
426C4—31no—
427C4—41no—
428C4—121no—
429C4C4×D3×A411yescharacteristic
430C4A4×D1211yescharacteristic
431C3—41no—
432C3—81no—
433C3A4×#10211yescharacteristic, complemented
434C2—31no—
435C2—31no—
436C2—31no—
437C2—31no—
438C2—122no—
439C2—362no—
440C2A4×(C2×D3)⋊C411yescharacteristic
441C2A4×#21311yescharacteristic
442C2A4×#21511yescharacteristic
subgroupG/H
centerC22A4×#67
commutatorC22×C3×C4C2×C3×C4
FrattiniC2×C4C2×D3×A4
FittingC22×C3×C4⋊C4C2×C3
socleC24×C3C3×D4
prime radicalC2×A4×D12C2
cosocleC23×C3×C4C22×C3
hypercenterC4⋊C4D3×A4
hypocenterC22×C3C3×#102
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×A4×C4⋊C4C2semidirect
3. C2×A4×C3⋊C8C2semidirect
4. C22×#809C3semidirect
10. A4×D12C4semidirect
15. C22×C3×C4⋊C4C2×C3semidirect
16. C23×C3⋊C8C2×C3semidirect
19. A4×C4⋊C4D3semidirect
45. C22×D12C3×C4semidirect
65. #809A4direct (N × H)
78. C22×C4⋊C4C3×D3semidirect
135. C3×C4⋊C4C2×A4semidirect
141. C2×C3⋊C8C2×A4semidirect
146. C3×A4#102semidirect
234. D12C4×A4semidirect
285. C4⋊C4D3×A4semidirect
301. C22×C3C3×#102semidirect
318. A4#809direct (N × H)
423. C22C3×#809semidirect
433. C3A4×#102semidirect

Maximal subgroups

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

subgroupindex
C2×A4×D122
C3×A4×C4⋊C42
C2×A4×C3⋊C82
C22×#8093
A4×#1023
C3×#8094