Finite Group Databasebeta

← C3×C8×SL(2,ℤ/4) #11920884

Subgroups — C3×C8×SL(2,ℤ/4) #11920884

Order 1152.

396 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 88 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
2C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×C3×A4⋊C8C211yesmaximal, characteristic
4C8×SL(2,ℤ/4)C311yesmaximal, characteristic, direct product factor
5C3×C8×C22⋊C4—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3×SL(2,ℤ/4)C412yes—
8C3×C8×A4C412yescomplemented
9C3×A4⋊C8C412yescomplemented
10C3×C8×Dic3—41nomaximal
11C23×C3×C8D311yescharacteristic
12C2×C8×A4—21no—
13C2×C8×A4C2×C311yescharacteristic
14C4×SL(2,ℤ/4)C2×C311yescharacteristic
15C2×A4⋊C8C2×C311yescharacteristic
16C2×C3×C22⋊C8—31no—
17C2×C3×C4×C8—31no—
18C2×C3×C4×C8—31no—
19C3×C4×C22⋊C4—31no—
20C3×#336—31no—
21C3×#336—31no—
22C22×C3×A4C2×C411yescharacteristic
23C3×C4×A4C2×C411yescharacteristic
24C3×C4×A4C2×C411yescharacteristic
25C3×SL(2,ℤ/4)C814yesdirect product factor
26C2×C32×C8—41no—
27C3×C4×Dic3—41no—
28C2×C3×C3⋊C8—41no—
29C8×C22⋊C4—31noSylow
30C23×C3×C4C2×D311yescharacteristic
31C2×C4×A4—21no—
32C2×C4×A4C22×C311yescharacteristic
33C2×SL(2,ℤ/4)C3×C412yes—
34C22×C3×C8—31no—
35C22×C3×C8—32no—
36C22×C3×C8—31no—
37C22×C3×C8—31no—
38C22×C3×C8—31no—
39C22×C3×C8Dic312yescomplemented
40C2×C3×C22⋊C4—32no—
41C2×C3×C42—31no—
42C2×C3×C42—31no—
43C8×A4—22no—
44C8×A4C3×C412yescomplemented
45A4⋊C8C3×C412yescomplemented
46C3×C22⋊C8—32no—
47C3×C22⋊C8—32no—
48C3×C4×C8—62no—
49C3×C4×C8—61no—
50C3×C4×C8—61no—
51C3×#95—32no—
52C8×Dic3—41no—
53C2×C3×A4C4211yescharacteristic
54C2×C3×A4C2×C812yes—
55C2×C32×C4—41no—
56C2×C3×Dic3—42no—
57C32×C8—42no—
58C3×C3⋊C8—42no—
59C23×C8C3×D311yescharacteristic
60C2×C22⋊C8—31no—
61C2×C4×C8—31no—
62C2×C4×C8—31no—
63C4×C22⋊C4—31no—
64#336—31no—
65#336—31no—
66C24×C3C4×D311yescharacteristic
67C22×A4—21no—
68C22×A4C2×C3×C411yescharacteristic
69C22×C3×C4—31no—
70C22×C3×C4—31no—
71C22×C3×C4—31no—
72C22×C3×C4—31no—
73C22×C3×C4—32no—
74C22×C3×C4—32no—
75C22×C3×C4C4×D311yescharacteristic
76C22×C3×C4C2×Dic311yescharacteristic
77C4×A4—21no—
78C4×A4—21no—
79C4×A4C2×C3×C411yescharacteristic
80C4×A4C2×C3×C411yescharacteristic
81SL(2,ℤ/4)C3×C814yesdirect product factor
82C2×C3×C8—31no—
83C2×C3×C8—32no—
84C2×C3×C8—32no—
85C2×C3×C8—32no—
86C2×C3×C8—32no—
87C2×C3×C8—32no—
88C2×C3×C8—41no—
89C2×C3×C8—61no—
90C2×C3×C8—61no—
91C2×C3×C8—61no—
92C2×C3×C8—61no—
93C2×C3×C8—61no—
94C2×C3×C8—81no—
95C2×C3×C8S411yescharacteristic
96C3×C22⋊C4—34no—
97C3×C22⋊C4—34no—
98C3×C42—61no—
99C3×C42—61no—
100C3×C42—61no—
101C3×C42—61no—
102C4×Dic3—41no—
103C2×C3⋊C8—41no—
104C22×C32—41no—
105C3×A4C4×C811yescharacteristic, complemented
106C32×C4—41no—
107C32×C4—41no—
108C3×Dic3—44no—
109C23×C4C2×C3×D311yescharacteristic
110C22×C8—31no—
111C22×C8—31no—
112C22×C8—32no—
113C22×C8—31no—
114C22×C8—31no—
115C22×C8C3×Dic312yescomplemented
116C2×C22⋊C4—32no—
117C2×C42—31no—
118C2×C42—31no—
119C22⋊C8—32no—
120C22⋊C8—32no—
121C4×C8—62no—
122C4×C8—61no—
123C4×C8—61no—
124#95—32no—
125C23×C3—31no—
126C23×C3—32no—
127C23×C3—31no—
128C23×C3D3×C812yes—
129C23×C3C4×Dic311yescharacteristic
130C2×A4—22no—
131C2×A4—21no—
132C2×A4C3×C4211yescharacteristic
133C2×A4C2×C3×C812yes—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—34no—
142C2×C3×C4—34no—
143C2×C3×C4—41no—
144C2×C3×C4—61no—
145C2×C3×C4—62no—
146C2×C3×C4—62no—
147C2×C3×C4—62no—
148C2×C3×C4—62no—
149C2×C3×C4—81no—
150C2×C3×C4C2×S411yescharacteristic
151C2×Dic3—42no—
152C3×C8—32no—
153C3×C8—42no—
154C3×C8—62no—
155C3×C8—62no—
156C3×C8—82no—
157C3×C8SL(2,ℤ/4)12yesdirect product factor
158C3⋊C8—42no—
159C2×C32—42no—
160C2×C32—41no—
161C24C3×C4×D311yescharacteristic
162C22×C4—31no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—31no—
166C22×C4—32no—
167C22×C4—32no—
168C22×C4C3×C4×D311yescharacteristic
169C22×C4C2×C3×Dic311yescharacteristic
170C2×C8—31no—
171C2×C8—32no—
172C2×C8—32no—
173C2×C8—32no—
174C2×C8—32no—
175C2×C8—32no—
176C2×C8—61no—
177C2×C8—61no—
178C2×C8—61no—
179C2×C8—61no—
180C2×C8—61no—
181C2×C8C3×S411yescharacteristic
182C22⋊C4—34no—
183C22⋊C4—34no—
184C42—61no—
185C42—61no—
186C42—61no—
187C42—61no—
188C22×C3—32no—
189C22×C3—31no—
190C22×C3—32no—
191C22×C3—32no—
192C22×C3—31no—
193C22×C3—31no—
194C22×C3—41no—
195C22×C3—61no—
196C22×C3—81no—
197C22×C3C8×Dic311yescharacteristic, complemented
198C22×C3C4×S411yescharacteristic
199A4—21no—
200A4C3×C4×C811yescharacteristic, complemented
201C3×C4—31no—
202C3×C4—31no—
203C3×C4—41no—
204C3×C4—41no—
205C3×C4—64no—
206C3×C4—64no—
207C3×C4—81no—
208C3×C4—81no—
209C3×C4C4×S411yescharacteristic
210C3×C4C2×SL(2,ℤ/4)11yescharacteristic
211Dic3—44no—
212C32—41noSylow
213C23—31no—
214C23—32no—
215C23—31no—
216C23C3×D3×C812yes—
217C23C3×C4×Dic311yescharacteristic
218C2×C4—31no—
219C2×C4—31no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—34no—
226C2×C4—34no—
227C2×C4—61no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—62no—
231C2×C4—62no—
232C2×C4C2×C3×S411yescharacteristic
233C8—32no—
234C8—62no—
235C8—62no—
236C8C3×SL(2,ℤ/4)12yesdirect product factor
237C2×C3—32no—
238C2×C3—31no—
239C2×C3—31no—
240C2×C3—42no—
241C2×C3—41no—
242C2×C3—82no—
243C2×C3—81no—
244C2×C3C8×S412yes—
245C2×C3C4×SL(2,ℤ/4)11yescharacteristic
246C22—32no—
247C22—31no—
248C22—32no—
249C22—32no—
250C22—31no—
251C22—31no—
252C22—61no—
253C22C3×C8×Dic311yescharacteristic, complemented
254C22C3×C4×S411yescharacteristic
255C4—31no—
256C4—31no—
257C4—64no—
258C4—64no—
259C4C3×C4×S411yescharacteristic
260C4C2×C3×SL(2,ℤ/4)11yescharacteristic
261C3—41no—
262C3—81no—
263C3C8×SL(2,ℤ/4)11yescharacteristic, direct product factor
264C2—32no—
265C2—31no—
266C2—31no—
267C2C3×C8×S412yes—
268C2C3×C4×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C8S4
commutator, hypocenterA4C3×C4×C8
FrattiniC2×C4C2×C3×S4
FittingC23×C3×C8D3
socleC24×C3C4×D3
prime radicalC22×C3×A4C2×C4
cosocleC2×C4×A4C22×C3
LCSG ▷ A4
UCSC1 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
4. C8×SL(2,ℤ/4)C3direct (N × H)
8. C3×C8×A4C4semidirect
9. C3×A4⋊C8C4semidirect
25. C3×SL(2,ℤ/4)C8direct (N × H)
39. C22×C3×C8Dic3semidirect
44. C8×A4C3×C4semidirect
45. A4⋊C8C3×C4semidirect
81. SL(2,ℤ/4)C3×C8direct (N × H)
105. C3×A4C4×C8semidirect
115. C22×C8C3×Dic3semidirect
157. C3×C8SL(2,ℤ/4)direct (N × H)
197. C22×C3C8×Dic3semidirect
200. A4C3×C4×C8semidirect
236. C8C3×SL(2,ℤ/4)direct (N × H)
253. C22C3×C8×Dic3semidirect
263. C3C8×SL(2,ℤ/4)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C8×A42
C3×C4×SL(2,ℤ/4)2
C2×C3×A4⋊C82
C8×SL(2,ℤ/4)3
C3×C8×C22⋊C43
C3×C8×Dic34