Finite Group Databasebeta

← A4×Dic3⋊C8 #11921318

Subgroups — A4×Dic3⋊C8 #11921318

Order 1152.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×C8×A4C211yesmaximal, characteristic
2C4×Dic3×A4C211yesmaximal, characteristic
3C2×A4×C3⋊C8C211yesmaximal, characteristic
4C22×Dic3⋊C8C311yesmaximal, characteristic, complemented
5A4×C4⋊C8—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×Dic3×A4C411yescharacteristic
8C2×Dic3×A4C411yescharacteristic
9C3×C8×A4—21no—
10A4×C3⋊C8—21no—
11C3×Dic3⋊C8—41nomaximal
12C23×C3×C8C2×C311yescharacteristic
13C22×C4×Dic3C2×C311yescharacteristic
14C23×C3⋊C8C2×C311yescharacteristic
15C2×C8×A4—21no—
16C2×C8×A4—31no—
17C2×C8×A4D311yescharacteristic
18C42×A4—31no—
19C2×Dic3⋊C8—31no—
20C2×Dic3⋊C8—31no—
21C2×Dic3⋊C8—31no—
22C2×Dic3⋊C8—31no—
23C22×C3×A4C2×C411yescharacteristic
24C3×C4×A4D411yescharacteristic
25C3×C4×A4Q811yescharacteristic
26Dic3×A4—21no—
27Dic3×A4C812yescomplemented
28C2×C32×C8—41no—
29C3×C4×Dic3—41no—
30C2×C3×C3⋊C8—41no—
31C22×C4⋊C8—31noSylow
32C23×C3×C4C22×C311yescharacteristic
33C23×Dic3C3×C411yescharacteristic
34C23×Dic3C3×C411yescharacteristic
35C2×C4×A4—21no—
36C2×C4×A4—31no—
37C2×C4×A4—31no—
38C2×C4×A4C2×D311yescharacteristic
39C22×C3×C8—21no—
40C22×C3×C8—31no—
41C22×C3×C8—31no—
42C22×C3×C8—61no—
43C2×C4×Dic3—31no—
44C2×C4×Dic3—31no—
45C2×C4×Dic3—31no—
46C2×C4×Dic3—31no—
47C22×C3⋊C8—21no—
48C22×C3⋊C8—31no—
49C22×C3⋊C8—31no—
50C22×C3⋊C8—61no—
51C8×A4—22no—
52C8×A4—21no—
53C8×A4—61no—
54C3×C4⋊C8—121no—
55Dic3⋊C8—32no—
56Dic3⋊C8—31no—
57Dic3⋊C8—31no—
58Dic3⋊C8—31no—
59Dic3⋊C8A411yescharacteristic, direct product factor
60C2×C3×A4C4⋊C411yescharacteristic
61C2×C3×A4C2×C811yescharacteristic
62C2×C3×A4M1611yescharacteristic
63C2×C32×C4—41no—
64C2×C3×Dic3—41no—
65C2×C3×Dic3—41no—
66C32×C8—81no—
67C3×C3⋊C8—81no—
68C23×C8—31no—
69C23×C8C3×D311yescharacteristic
70C22×C42—31no—
71C2×C4⋊C8—91no—
72C2×C4⋊C8—91no—
73C2×C4⋊C8—91no—
74C2×C4⋊C8—91no—
75C24×C3C2×C3×C411yescharacteristic
76C22×A4—21no—
77C22×A4C4×D311yescharacteristic
78C22×C3×C4—31no—
79C22×C3×C4—31no—
80C22×C3×C4—31no—
81C22×C3×C4—31no—
82C22×C3×C4C3×D411yescharacteristic
83C22×C3×C4C3×Q811yescharacteristic
84C22×Dic3—21no—
85C22×Dic3—31no—
86C22×Dic3—31no—
87C22×Dic3—32no—
88C22×Dic3—31no—
89C22×Dic3—31no—
90C22×Dic3—61no—
91C22×Dic3C3×C812yescomplemented
92C4×A4—21no—
93C4×A4—21no—
94C4×A4—32no—
95C4×A4—61no—
96C4×A4Dic611yescharacteristic
97C4×A4#6711yescharacteristic
98C2×C3×C8—31no—
99C2×C3×C8—41no—
100C2×C3×C8—61no—
101C2×C3×C8—61no—
102C2×C3×C8—61no—
103C2×C3×C8—61no—
104C2×C3×C8—81no—
105C2×C3×C8—121no—
106C2×C3×C8C2×A411yescharacteristic
107C3×C42—121no—
108C4×Dic3—32no—
109C4×Dic3—31no—
110C4×Dic3—31no—
111C4×Dic3—31no—
112C4×Dic3C2×A411yescharacteristic
113C2×C3⋊C8—31no—
114C2×C3⋊C8—61no—
115C2×C3⋊C8—61no—
116C2×C3⋊C8—61no—
117C2×C3⋊C8—61no—
118C2×C3⋊C8C2×A411yescharacteristic
119C22×C32—41no—
120C3×A4C4⋊C811yescharacteristic, complemented
121C32×C4—41no—
122C32×C4—41no—
123C3×Dic3—42no—
124C3×Dic3—81no—
125C23×C4—31no—
126C23×C4—31no—
127C23×C4C2×C3×D311yescharacteristic
128C22×C8—21no—
129C22×C8—31no—
130C22×C8—31no—
131C22×C8—61no—
132C22×C8—61no—
133C22×C8—91no—
134C22×C8—91no—
135C22×C8—181no—
136C2×C42—91no—
137C2×C42—91no—
138C2×C42—91no—
139C2×C42—91no—
140C4⋊C8—31no—
141C4⋊C8—91no—
142C4⋊C8—91no—
143C4⋊C8—92no—
144C4⋊C8—91no—
145C23×C3—31no—
146C23×C3—31no—
147C23×C3—31no—
148C23×C3—31no—
149C23×C3C3×C4⋊C411yescharacteristic
150C23×C3C2×C3×C811yescharacteristic
151C23×C3C3×M1611yescharacteristic
152C2×A4—21no—
153C2×A4—21no—
154C2×A4—21no—
155C2×A4D3×C811yescharacteristic
156C2×A4ΓL(1,𝔽25)11yescharacteristic
157C2×A4Dic3⋊C411yescharacteristic
158C2×C3×C4—32no—
159C2×C3×C4—31no—
160C2×C3×C4—31no—
161C2×C3×C4—31no—
162C2×C3×C4—31no—
163C2×C3×C4—31no—
164C2×C3×C4—31no—
165C2×C3×C4—31no—
166C2×C3×C4—41no—
167C2×C3×C4—81no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170C2×C3×C4C22×A411yescharacteristic
171C2×Dic3—32no—
172C2×Dic3—31no—
173C2×Dic3—32no—
174C2×Dic3—32no—
175C2×Dic3—32no—
176C2×Dic3—31no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3C4×A411yescharacteristic
182C2×Dic3C4×A411yescharacteristic
183C3×C8—21no—
184C3×C8—61no—
185C3×C8—81no—
186C3×C8—82no—
187C3×C8—241no—
188C3⋊C8—21no—
189C3⋊C8—61no—
190C2×C32—41no—
191C2×C32—41no—
192C2×C32—41no—
193C24C3×C4×D311yescharacteristic
194C22×C4—31no—
195C22×C4—31no—
196C22×C4—31no—
197C22×C4—31no—
198C22×C4—32no—
199C22×C4—61no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—92no—
204C22×C4—91no—
205C22×C4—181no—
206C22×C4C3×Dic611yescharacteristic
207C22×C4C3×#6711yescharacteristic
208C2×C8—31no—
209C2×C8—31no—
210C2×C8—61no—
211C2×C8—61no—
212C2×C8—61no—
213C2×C8—61no—
214C2×C8—91no—
215C2×C8—181no—
216C2×C8—181no—
217C2×C8—181no—
218C2×C8—181no—
219C2×C8D3×A411yescharacteristic
220C42—31no—
221C42—91no—
222C42—91no—
223C42—92no—
224C42—91no—
225C22×C3—31no—
226C22×C3—31no—
227C22×C3—31no—
228C22×C3—32no—
229C22×C3—31no—
230C22×C3—31no—
231C22×C3—31no—
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—31no—
235C22×C3—41no—
236C22×C3—81no—
237C22×C3C3×C4⋊C811yescharacteristic, complemented
238C22×C3C2×C4×A411yescharacteristic
239A4—21no—
240A4Dic3⋊C811yescharacteristic, direct product factor
241C3×C4—31no—
242C3×C4—31no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—81no—
246C3×C4—81no—
247C3×C4—122no—
248C3×C4—241no—
249C3×C4D4×A411yescharacteristic
250C3×C4Q8×A411yescharacteristic
251Dic3—21no—
252Dic3—32no—
253Dic3—61no—
254Dic3C8×A412yescomplemented
255C32—41noSylow
256C23—31no—
257C23—31no—
258C23—31no—
259C23—31no—
260C23C3×D3×C811yescharacteristic
261C23C3×ΓL(1,𝔽25)11yescharacteristic
262C23C3×Dic3⋊C411yescharacteristic
263C2×C4—32no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—31no—
267C2×C4—31no—
268C2×C4—31no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—31no—
272C2×C4—31no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—91no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—181no—
283C2×C4C2×D3×A411yescharacteristic
284C8—21no—
285C8—61no—
286C8—61no—
287C8—181no—
288C2×C3—31no—
289C2×C3—31no—
290C2×C3—31no—
291C2×C3—31no—
292C2×C3—41no—
293C2×C3—41no—
294C2×C3—41no—
295C2×C3—81no—
296C2×C3—81no—
297C2×C3—81no—
298C2×C3A4×C4⋊C411yescharacteristic
299C2×C3C2×C8×A411yescharacteristic
300C2×C3A4×M1611yescharacteristic
301C22—31no—
302C22—31no—
303C22—31no—
304C22—32no—
305C22—31no—
306C22—31no—
307C22—31no—
308C22—31no—
309C22—31no—
310C22—31no—
311C22C3×Dic3⋊C811yescharacteristic, complemented
312C22C4×D3×A411yescharacteristic
313C4—32no—
314C4—31no—
315C4—31no—
316C4—61no—
317C4—92no—
318C4—181no—
319C4A4×Dic611yescharacteristic
320C4A4×#6711yescharacteristic
321C3—41no—
322C3—81no—
323C3A4×C4⋊C811yescharacteristic, complemented
324C2—31no—
325C2—31no—
326C2—31no—
327C2—31no—
328C2D3×C8×A411yescharacteristic
329C2A4×ΓL(1,𝔽25)11yescharacteristic
330C2A4×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×A4
commutatorC23×C3C2×C3×C8
FittingC23×C3×C8C2×C3
socleC24×C3C2×C3×C4
prime radicalC22×C3×A4C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC2×C8D3×A4
hypocenterC22×C3C3×C4⋊C8
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊C8C3semidirect
27. Dic3×A4C8semidirect
59. Dic3⋊C8A4direct (N × H)
91. C22×Dic3C3×C8semidirect
120. C3×A4C4⋊C8semidirect
237. C22×C3C3×C4⋊C8semidirect
240. A4Dic3⋊C8direct (N × H)
254. Dic3C8×A4semidirect
311. C22C3×Dic3⋊C8semidirect
323. C3A4×C4⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C4×Dic3×A42
C2×A4×C3⋊C82
C22×Dic3⋊C83
A4×C4⋊C83
C3×Dic3⋊C84