Finite Group Databasebeta

← Q8×Dic3×A4 #11923365

Subgroups — Q8×Dic3×A4 #11923365

Order 1152.

826 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 826 conjugacy classes of subgroups — too many to draw. Only its 153 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×Q8×A4C211yesmaximal, characteristic
2A4×C4⋊Dic3C213yesmaximal
3C4×Dic3×A4C213yesmaximal
4C22×Q8×Dic3C311yesmaximal, characteristic, complemented
5C4×Q8×A4—31nomaximal
6C3×Q8×A4C414yescomplemented
7C2×C3×C4×A4C2213yes—
8C2×Dic3×A4C2213yes—
9C2×Dic3×A4C2211yescharacteristic
10C3×Q8×Dic3—41nomaximal
11C23×C3×Q8C2×C311yescharacteristic
12C2×Q8×A4—21no—
13C2×Q8×A4D311yescharacteristic
14C2×Q8×Dic3—31no—
15C2×Q8×Dic3—33no—
16C2×Q8×Dic3—33no—
17C2×Q8×Dic3—31no—
18C22×C4⋊Dic3C2×C313yes—
19C22×C4×Dic3C2×C313yes—
20A4×C4⋊C4—33no—
21C42×A4—33no—
22C22×C3×A4C2311yescharacteristic
23C2×C32×Q8—41no—
24C3×C4×A4C2×C416yes—
25Dic3×A4—23no—
26Dic3×A4Q812yesdirect product factor
27C3×C4⋊Dic3—43no—
28C3×C4×Dic3—43no—
29C22×C4×Q8—31noSylow
30C22×C3×Q8—34no—
31C22×C3×Q8—33no—
32C22×C3×Q8—31no—
33C22×C3×Q8C3×C414yescomplemented
34C23×C3×C4C22×C313yes—
35C23×Dic3C22×C313yes—
36C23×Dic3C22×C311yescharacteristic
37Q8×A4—24no—
38Q8×A4Dic314yesdirect product factor
39C2×C4×A4—23no—
40C2×C4×A4—31no—
41C2×C4×A4—33no—
42C2×C4×A4C2×D313yes—
43C3×C4×Q8—121no—
44Q8×Dic3—36no—
45Q8×Dic3—36no—
46Q8×Dic3—32no—
47Q8×Dic3—31no—
48Q8×Dic3—33no—
49Q8×Dic3—33no—
50Q8×Dic3A411yescharacteristic, direct product factor
51C2×C4⋊Dic3—33no—
52C2×C4⋊Dic3—33no—
53C2×C4⋊Dic3—36no—
54C2×C4×Dic3—33no—
55C2×C4×Dic3—33no—
56C2×C4×Dic3—33no—
57C2×C4×Dic3—33no—
58C2×C3×A4C22×C411yescharacteristic
59C2×C3×A4C2×Q811yescharacteristic
60C2×C3×A4#4111yescharacteristic
61C32×Q8—44no—
62C2×C32×C4—43no—
63C2×C3×Dic3—41no—
64C2×C3×Dic3—43no—
65C23×Q8C3×D311yescharacteristic
66C2×C4×Q8—91no—
67C2×C4×Q8—93no—
68C2×C4×Q8—93no—
69C2×C4×Q8—91no—
70C22×C4⋊C4—33no—
71C22×C42—33no—
72C24×C3C23×C311yescharacteristic
73C22×A4—21no—
74C22×A4C22×D311yescharacteristic
75C2×C3×Q8—312no—
76C2×C3×Q8—32no—
77C2×C3×Q8—312no—
78C2×C3×Q8—34no—
79C2×C3×Q8—34no—
80C2×C3×Q8—33no—
81C2×C3×Q8—41no—
82C2×C3×Q8—81no—
83C2×C3×Q8C2×A411yescharacteristic
84C22×C3×C4—33no—
85C22×C3×C4—33no—
86C22×C3×C4—36no—
87C22×C3×C4C2×C3×C416yes—
88C22×Dic3—23no—
89C22×Dic3—31no—
90C22×Dic3—31no—
91C22×Dic3—32no—
92C22×Dic3—33no—
93C22×Dic3—33no—
94C22×Dic3—63no—
95C22×Dic3C3×Q812yescomplemented
96C4×A4—26no—
97C4×A4—32no—
98C4×A4—63no—
99C4×A4C2×Dic316yes—
100C3×C4⋊C4—123no—
101C3×C42—123no—
102C4⋊Dic3—36no—
103C4⋊Dic3—33no—
104C4⋊Dic3—36no—
105C4⋊Dic3C2×A413yes—
106C4×Dic3—36no—
107C4×Dic3—33no—
108C4×Dic3—33no—
109C4×Dic3—33no—
110C4×Dic3C2×A413yes—
111C22×C32—41no—
112C3×A4C4×Q811yescharacteristic, complemented
113C32×C4—46no—
114C3×Dic3—42no—
115C3×Dic3—83no—
116C22×Q8—33no—
117C22×Q8—34no—
118C22×Q8—31no—
119C22×Q8C3×Dic314yescomplemented
120C23×C4—31no—
121C23×C4—33no—
122C23×C4C2×C3×D313yes—
123C4×Q8—31no—
124C4×Q8—93no—
125C4×Q8—93no—
126C4×Q8—92no—
127C4×Q8—96no—
128C4×Q8—96no—
129C4×Q8—91no—
130C2×C4⋊C4—93no—
131C2×C4⋊C4—96no—
132C2×C4⋊C4—93no—
133C2×C42—93no—
134C2×C42—93no—
135C2×C42—93no—
136C2×C42—93no—
137C23×C3—31no—
138C23×C3—31no—
139C23×C3—31no—
140C23×C3—31no—
141C23×C3C22×C3×C411yescharacteristic
142C23×C3C2×C3×Q811yescharacteristic
143C23×C3C3×#4111yescharacteristic
144C2×A4—21no—
145C2×A4—21no—
146C2×A4—21no—
147C2×A4D3×Q811yescharacteristic
148C2×A4#23911yescharacteristic
149C2×A4C22×Dic311yescharacteristic
150C3×Q8—38no—
151C3×Q8—312no—
152C3×Q8—44no—
153C3×Q8—84no—
154C3×Q8C4×A414yescomplemented
155C2×C3×C4—36no—
156C2×C3×C4—33no—
157C2×C3×C4—36no—
158C2×C3×C4—36no—
159C2×C3×C4—36no—
160C2×C3×C4—43no—
161C2×C3×C4—83no—
162C2×C3×C4—121no—
163C2×C3×C4—123no—
164C2×C3×C4C22×A413yes—
165C2×Dic3—32no—
166C2×Dic3—31no—
167C2×Dic3—32no—
168C2×Dic3—32no—
169C2×Dic3—32no—
170C2×Dic3—33no—
171C2×Dic3—63no—
172C2×Dic3—63no—
173C2×Dic3—63no—
174C2×Dic3—63no—
175C2×Dic3C22×A413yes—
176C2×Dic3C22×A411yescharacteristic
177C2×C32—41no—
178C2×C32—41no—
179C2×C32—41no—
180C24C22×C3×D311yescharacteristic
181C2×Q8—312no—
182C2×Q8—32no—
183C2×Q8—312no—
184C2×Q8—34no—
185C2×Q8—34no—
186C2×Q8—33no—
187C2×Q8D3×A411yescharacteristic
188C22×C4—33no—
189C22×C4—33no—
190C22×C4—36no—
191C22×C4—32no—
192C22×C4—63no—
193C22×C4—91no—
194C22×C4—93no—
195C22×C4—91no—
196C22×C4—92no—
197C22×C4—93no—
198C22×C4—183no—
199C22×C4C2×C3×Dic316yes—
200C4⋊C4—33no—
201C4⋊C4—96no—
202C4⋊C4—96no—
203C4⋊C4—93no—
204C42—33no—
205C42—93no—
206C42—93no—
207C42—96no—
208C42—93no—
209C22×C3—31no—
210C22×C3—31no—
211C22×C3—31no—
212C22×C3—32no—
213C22×C3—31no—
214C22×C3—31no—
215C22×C3—31no—
216C22×C3—31no—
217C22×C3—31no—
218C22×C3—31no—
219C22×C3—41no—
220C22×C3—81no—
221C22×C3C3×C4×Q811yescharacteristic, complemented
222C22×C3C23×A411yescharacteristic
223A4—21no—
224A4Q8×Dic311yescharacteristic, direct product factor
225C3×C4—36no—
226C3×C4—46no—
227C3×C4—86no—
228C3×C4—122no—
229C3×C4—243no—
230C3×C4C2×C4×A416yes—
231Dic3—23no—
232Dic3—32no—
233Dic3—63no—
234Dic3Q8×A412yesdirect product factor
235C32—41noSylow
236C23—31no—
237C23—31no—
238C23—31no—
239C23—31no—
240C23C3×D3×Q811yescharacteristic
241C23C3×#23911yescharacteristic
242C23C22×C3×Dic311yescharacteristic
243Q8—38no—
244Q8—312no—
245Q8Dic3×A414yesdirect product factor
246C2×C4—36no—
247C2×C4—31no—
248C2×C4—33no—
249C2×C4—36no—
250C2×C4—36no—
251C2×C4—36no—
252C2×C4—33no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—92no—
258C2×C4—93no—
259C2×C4—183no—
260C2×C4—183no—
261C2×C4—183no—
262C2×C4—183no—
263C2×C4C2×D3×A413yes—
264C2×C3—31no—
265C2×C3—31no—
266C2×C3—31no—
267C2×C3—31no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—41no—
271C2×C3—81no—
272C2×C3—81no—
273C2×C3—81no—
274C2×C3C22×C4×A411yescharacteristic
275C2×C3C2×Q8×A411yescharacteristic
276C2×C3A4×#4111yescharacteristic
277C22—31no—
278C22—31no—
279C22—31no—
280C22—32no—
281C22—31no—
282C22—31no—
283C22—31no—
284C22—31no—
285C22—31no—
286C22—31no—
287C22C3×Q8×Dic311yescharacteristic, complemented
288C22C22×D3×A411yescharacteristic
289C4—32no—
290C4—36no—
291C4—63no—
292C4—92no—
293C4—183no—
294C4C2×Dic3×A416yes—
295C3—41no—
296C3—81no—
297C3C4×Q8×A411yescharacteristic, complemented
298C2—31no—
299C2—31no—
300C2—31no—
301C2—31no—
302C2D3×Q8×A411yescharacteristic
303C2A4×#23911yescharacteristic
304C2C22×Dic3×A411yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×A4
commutatorC23×C3C22×C3×C4
FittingC23×C3×Q8C2×C3
socle, cosocleC24×C3C23×C3
prime radicalC22×C3×A4C23
hypercenterC2×Q8D3×A4
hypocenterC22×C3C3×C4×Q8
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. C22×Q8×Dic3C3semidirect
6. C3×Q8×A4C4semidirect
26. Dic3×A4Q8direct (N × H)
33. C22×C3×Q8C3×C4semidirect
38. Q8×A4Dic3direct (N × H)
50. Q8×Dic3A4direct (N × H)
95. C22×Dic3C3×Q8semidirect
112. C3×A4C4×Q8semidirect
119. C22×Q8C3×Dic3semidirect
154. C3×Q8C4×A4semidirect
221. C22×C3C3×C4×Q8semidirect
224. A4Q8×Dic3direct (N × H)
234. Dic3Q8×A4direct (N × H)
245. Q8Dic3×A4direct (N × H)
287. C22C3×Q8×Dic3semidirect
297. C3C4×Q8×A4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
A4×C4⋊Dic32
C4×Dic3×A42
C22×Q8×Dic33
C4×Q8×A43
C3×Q8×Dic34