Finite Group Databasebeta

← Q8×C3⋊SL(2,ℤ/4) #11923053

Subgroups — Q8×C3⋊SL(2,ℤ/4) #11923053

Order 1152.

842 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C4⋊(C3⋊SL(2,ℤ/4))C213yesmaximal
3C4×C3⋊SL(2,ℤ/4)C213yesmaximal
4Q8×SL(2,ℤ/4)—33nomaximal
5Q8×#217—31nomaximal
6C3×Q8×A4C414yescomplemented
7C2×C3×C4×A4C2213yes—
8C2×C3⋊SL(2,ℤ/4)C2213yes—
9C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
10Q8×C3⋊Dic3—41nomaximal
11C23×C3×Q8D311yescharacteristic
12C2×Q8×A4D313yes—
13C2×Q8×Dic3—31no—
14C2×Q8×Dic3—31no—
15C4⋊SL(2,ℤ/4)—39no—
16C4×SL(2,ℤ/4)—39no—
17#5229—33no—
18#5229—33no—
19#5212—33no—
20C4×#217—33no—
21C22×C3×A4C2311yescharacteristic
22C2×C32×Q8—41no—
23C3×C4×A4C2×C416yes—
24C3⋊SL(2,ℤ/4)—23no—
25C3⋊SL(2,ℤ/4)Q812yesdirect product factor
26C4⋊(C3⋊Dic3)—43no—
27C4×C3⋊Dic3—43no—
28Q8×C22⋊C4—91noSylow
29C22×C3×Q8—31no—
30C22×C3×Q8—34no—
31C22×C3×Q8—33no—
32C22×C3×Q8Dic314yescomplemented
33C23×C3×C4C2×D313yes—
34Q8×A4Dic3112yescomplemented
35C2×C4×A4C2×D319yes—
36C2×SL(2,ℤ/4)—33no—
37C2×SL(2,ℤ/4)—39no—
38C2×#217—31no—
39C2×#217—33no—
40Q8×Dic3—64no—
41Q8×Dic3—63no—
42Q8×Dic3—61no—
43Q8×Dic3—123no—
44C2×C4⋊Dic3—33no—
45C2×C4⋊Dic3—33no—
46C2×C4×Dic3—33no—
47C2×C4×Dic3—33no—
48C3⋊#95—33no—
49C3⋊#95—33no—
50C3⋊#95—36no—
51C2×C3×A4C22×C411yescharacteristic
52C2×C3×A4C2×Q811yescharacteristic
53C2×C3×A4#4111yescharacteristic
54C32×Q8—44no—
55C2×C32×C4—43no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3—43no—
58C23×Q8C3⋊D311yescharacteristic
59C2×C4×Q8—91no—
60C2×C4×Q8—91no—
61#391—93no—
62#391—93no—
63#380—93no—
64C4×C22⋊C4—93no—
65C24×C3C22×D311yescharacteristic
66C22×A4C22×D313yes—
67C2×C3×Q8—34no—
68C2×C3×Q8—34no—
69C2×C3×Q8—312no—
70C2×C3×Q8—33no—
71C2×C3×Q8—43no—
72C2×C3×Q8—61no—
73C2×C3×Q8—66no—
74C2×C3×Q8S411yescharacteristic
75C22×C3×C4—33no—
76C22×C3×C4—33no—
77C22×C3×C4—36no—
78C22×C3×C4C2×Dic316yes—
79C22×Dic3—31no—
80C22×Dic3—31no—
81C22×Dic3—33no—
82C22×Dic3—33no—
83C4×A4C2×Dic3118yes—
84SL(2,ℤ/4)—36no—
85SL(2,ℤ/4)—69no—
86#217—32no—
87#217—32no—
88#217—63no—
89#217—63no—
90C4⋊Dic3—66no—
91C4⋊Dic3—63no—
92C4⋊Dic3—63no—
93C4⋊Dic3—129no—
94C4×Dic3—66no—
95C4×Dic3—63no—
96C4×Dic3—63no—
97C4×Dic3—129no—
98C22×C32—41no—
99C3×A4C4×Q811yescharacteristic, complemented
100C32×C4—46no—
101C3⋊Dic3—42no—
102C3⋊Dic3—83no—
103C22×Q8—31no—
104C22×Q8—33no—
105C22×Q8—34no—
106C22×Q8C3⋊Dic314yescomplemented
107C23×C4C2×C3⋊D313yes—
108C4×Q8—184no—
109C4×Q8—183no—
110C4×Q8—181no—
111C2×C4⋊C4—93no—
112C2×C4⋊C4—93no—
113C2×C22⋊C4—91no—
114C2×C22⋊C4—93no—
115C2×C42—93no—
116C2×C42—93no—
117#95—93no—
118#95—93no—
119#95—96no—
120C23×C3—31no—
121C23×C3—31no—
122C23×C3—31no—
123C23×C3—31no—
124C23×C3D3×Q811yescharacteristic
125C23×C3#23911yescharacteristic
126C23×C3C22×Dic311yescharacteristic
127C2×A4D3×Q813yes—
128C2×A4#23913yes—
129C2×A4C22×Dic313yes—
130C3×Q8—312no—
131C3×Q8—412no—
132C3×Q8—64no—
133C3×Q8SL(2,ℤ/4)14yescomplemented
134C2×C3×C4—33no—
135C2×C3×C4—36no—
136C2×C3×C4—36no—
137C2×C3×C4—36no—
138C2×C3×C4—49no—
139C2×C3×C4—63no—
140C2×C3×C4C2×S413yes—
141C2×Dic3—32no—
142C2×Dic3—32no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—63no—
148C2×Dic3—63no—
149C2×Dic3—63no—
150C2×Dic3—63no—
151C2×Dic3—63no—
152C2×Dic3—63no—
153C2×Dic3—123no—
154C2×Dic3—129no—
155C2×C32—41no—
156C2×C32—41no—
157C2×C32—41no—
158C24C22×C3⋊D311yescharacteristic
159C2×Q8—34no—
160C2×Q8—34no—
161C2×Q8—312no—
162C2×Q8—33no—
163C2×Q8—61no—
164C2×Q8—66no—
165C2×Q8C3⋊S411yescharacteristic
166C22×C4—33no—
167C22×C4—33no—
168C22×C4—36no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—93no—
172C22×C4—93no—
173C22×C4C2×C3⋊Dic316yes—
174C4⋊C4—183no—
175C4⋊C4—186no—
176C4⋊C4—183no—
177C22⋊C4—92no—
178C22⋊C4—92no—
179C22⋊C4—183no—
180C22⋊C4—183no—
181C42—183no—
182C42—186no—
183C42—183no—
184C22×C3—31no—
185C22×C3—31no—
186C22×C3—31no—
187C22×C3—31no—
188C22×C3—31no—
189C22×C3—31no—
190C22×C3—31no—
191C22×C3—31no—
192C22×C3—31no—
193C22×C3—43no—
194C22×C3—61no—
195C22×C3Q8×Dic311yescharacteristic, complemented
196C22×C3C22×S411yescharacteristic
197A4Q8×Dic313yescomplemented
198C3×C4—36no—
199C3×C4—418no—
200C3×C4C2×SL(2,ℤ/4)16yes—
201Dic3—62no—
202Dic3—62no—
203Dic3—126no—
204Dic3—123no—
205Dic3—123no—
206Dic3—249no—
207C32—41noSylow
208C23—31no—
209C23—31no—
210C23—31no—
211C23—31no—
212C23Q8×C3⋊D311yescharacteristic
213C23#383211yescharacteristic
214C23C22×C3⋊Dic311yescharacteristic
215Q8—312no—
216Q8—64no—
217Q8C3⋊SL(2,ℤ/4)14yesdirect product factor
218C2×C4—33no—
219C2×C4—36no—
220C2×C4—36no—
221C2×C4—36no—
222C2×C4—63no—
223C2×C4—92no—
224C2×C4—92no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—183no—
230C2×C4—183no—
231C2×C4—183no—
232C2×C4—183no—
233C2×C4—183no—
234C2×C4—183no—
235C2×C4C2×C3⋊S413yes—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—31no—
239C2×C3—31no—
240C2×C3—43no—
241C2×C3—43no—
242C2×C3—43no—
243C2×C3Q8×S411yescharacteristic
244C2×C3#591911yescharacteristic
245C2×C3C22×SL(2,ℤ/4)11yescharacteristic
246C22—31no—
247C22—31no—
248C22—31no—
249C22—31no—
250C22—31no—
251C22—31no—
252C22—31no—
253C22—31no—
254C22—31no—
255C22—61no—
256C22Q8×C3⋊Dic311yescharacteristic, complemented
257C22C22×C3⋊S411yescharacteristic
258C4—36no—
259C4—182no—
260C4—182no—
261C4—363no—
262C4—363no—
263C4C2×C3⋊SL(2,ℤ/4)16yes—
264C3—43no—
265C3Q8×SL(2,ℤ/4)11yescharacteristic, complemented
266C2—31no—
267C2—31no—
268C2—31no—
269C2—31no—
270C2Q8×C3⋊S411yescharacteristic
271C2#1059658211yescharacteristic
272C2C22×C3⋊SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×Q8D3
socleC24×C3C22×D3
prime radical, cosocleC22×C3×A4C23
hypercenterC2×Q8C3⋊S4
hypocenterC3×A4C4×Q8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
6. C3×Q8×A4C4semidirect
25. C3⋊SL(2,ℤ/4)Q8direct (N × H)
32. C22×C3×Q8Dic3semidirect
34. Q8×A4Dic3semidirect
99. C3×A4C4×Q8semidirect
106. C22×Q8C3⋊Dic3semidirect
133. C3×Q8SL(2,ℤ/4)semidirect
195. C22×C3Q8×Dic3semidirect
197. A4Q8×Dic3semidirect
217. Q8C3⋊SL(2,ℤ/4)direct (N × H)
256. C22Q8×C3⋊Dic3semidirect
265. C3Q8×SL(2,ℤ/4)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C4⋊(C3⋊SL(2,ℤ/4))2
C4×C3⋊SL(2,ℤ/4)2
Q8×SL(2,ℤ/4)3
Q8×#2173
Q8×C3⋊Dic34