Finite Group Databasebeta

← C3×C4⋊#994 #11919746

Subgroups — C3×C4⋊#994 #11919746

Order 1152.

908 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 166 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×#994C212yesmaximal, complemented
2C3×C4⋊(#41⋊C3)C214yesmaximal, complemented
3C3×C4×#41⋊C3C211yesmaximal, characteristic, complemented
4C3×#3498C311yesmaximal, characteristic, complemented
5C4⋊#994C313yesmaximal, direct product factor
6C3×#994—24no—
7C2×C3×#41⋊C3C2211yescharacteristic
8C2×C3×#41⋊C3C2214yescomplemented
9C32×C4⋊Q8—41nomaximal
10C3×C4×SL(2,𝔽3)C2212yescomplemented
11C2×C3×H(5,𝔽2)C2×C312yes—
12C2×#994C2×C316yescomplemented
13C3×#550C2×C314yes—
14C3×D42—34no—
15C3×#535—32no—
16C3×#532—31no—
17C2×C3×#127—31no—
18C3×C4×#41C2×C311yescharacteristic
19C4⋊(#41⋊C3)C2×C3112yescomplemented
20C4×#41⋊C3C2×C313yescomplemented
21C2×C32×Q8—42no—
22C3×#41⋊C3—24no—
23C3×#41⋊C3D412yescomplemented
24C2×C3×SL(2,𝔽3)C2311yescharacteristic
25C32×C4⋊C4—44no—
26C32×C42—41no—
27#3498C3211yescharacteristic, complemented, Sylow
28C3×H(5,𝔽2)—24no—
29C3×H(5,𝔽2)—64no—
30C2×C3×#41—32no—
31C2×C3×#41C22×C314yes—
32C2×C3×#41C22×C311yescharacteristic
33C22×C3×D4—34no—
34C22×C3×D4—32no—
35C22×C3×D4—34no—
36#994—212no—
37C2×#41⋊C3C22×C313yes—
38C2×#41⋊C3C22×C3112yescomplemented
39C3×C4⋊Q8—43no—
40C3×C4⋊Q8A411yescharacteristic
41C3×#127—34no—
42C3×#127—32no—
43C3×#127—31no—
44C3×#124—32no—
45C3×#121—34no—
46C3×#121—38no—
47C3×#120—38no—
48C3×C4×Q8C22×C312yes—
49C3×C4×D4—32no—
50C3×C4×D4—34no—
51C3×#117—31no—
52C2×C3×C42—31no—
53C4×SL(2,𝔽3)C22×C316yescomplemented
54C32×Q8—84no—
55C2×C32×C4—41no—
56C2×C32×C4—42no—
57C2×C32×C4—44no—
58C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
59C2×H(5,𝔽2)C2×C3212yes—
60#550C2×C3214yes—
61D42—34no—
62#535—32no—
63#532—31no—
64C2×#127—31no—
65C4×#41C2×C3211yescharacteristic
66C24×C3—34no—
67C3×#41—24no—
68C3×#41—32no—
69C3×#41—64no—
70C3×#41—64no—
71C3×#41—64no—
72C3×#41C3×D412yes—
73C2×C3×Q8—46no—
74C2×C3×Q8C2×A412yes—
75C2×C3×Q8C23×C311yescharacteristic
76C2×C3×D4—31no—
77C2×C3×D4—34no—
78C2×C3×D4—38no—
79C2×C3×D4—34no—
80C2×C3×D4—34no—
81C2×C3×D4—32no—
82C2×C3×D4—64no—
83C2×C3×D4—64no—
84C2×C3×D4—68no—
85C2×C3×D4—68no—
86C2×C3×D4—128no—
87C22×C3×C4—31no—
88C22×C3×C4—32no—
89C22×C3×C4—34no—
90#41⋊C3—212no—
91#41⋊C3C3×D416yescomplemented
92C2×SL(2,𝔽3)C23×C313yes—
93C3×C4⋊C4—32no—
94C3×C4⋊C4—412no—
95C3×C4⋊C4C2×A414yes—
96C3×C22⋊C4—32no—
97C3×C22⋊C4—38no—
98C3×C42—31no—
99C3×C42—32no—
100C3×C42—43no—
101C3×C42C2×A411yescharacteristic
102C22×C32—41no—
103C32×C4—42no—
104C32×C4—44no—
105C32×C4—84no—
106H(5,𝔽2)—24no—
107H(5,𝔽2)—64no—
108C2×#41—32no—
109C2×#41C22×C3214yes—
110C2×#41C22×C3211yescharacteristic
111C22×D4—34no—
112C22×D4—32no—
113C22×D4—34no—
114C4⋊Q8C3×A411yescharacteristic
115#127—34no—
116#127—32no—
117#127—31no—
118#124—32no—
119#121—34no—
120#121—38no—
121#120—38no—
122C4×Q8C22×C3212yes—
123C4×D4—32no—
124C4×D4—34no—
125#117—31no—
126C2×C42—31no—
127C23×C3—31no—
128C23×C3—34no—
129C23×C3—68no—
130C23×C3—128no—
131C3×Q8—24no—
132C3×Q8—31no—
133C3×Q8—812no—
134C3×Q8C2×C3×D411yescharacteristic
135C3×D4—32no—
136C3×D4—32no—
137C3×D4—68no—
138C3×D4—64no—
139C3×D4—64no—
140C3×D4—64no—
141C3×D4—68no—
142C3×D4—128no—
143C2×C3×C4—31no—
144C2×C3×C4—32no—
145C2×C3×C4—32no—
146C2×C3×C4—32no—
147C2×C3×C4—46no—
148C2×C3×C4—43no—
149C2×C3×C4—412no—
150C2×C3×C4—64no—
151C2×C3×C4—64no—
152C2×C3×C4—64no—
153C2×C3×C4C22×A414yes—
154C2×C3×C4C22×A411yescharacteristic
155C2×C3×C4C22×A412yes—
156SL(2,𝔽3)C2×C3×D413yescomplemented
157C2×C32—41no—
158C2×C32—42no—
159C24—34no—
160#41—24no—
161#41—32no—
162#41—64no—
163#41—64no—
164#41—64no—
165#41C32×D412yes—
166C2×Q8C2×C3×A412yes—
167C2×Q8C23×C3211yescharacteristic
168C2×D4—31no—
169C2×D4—34no—
170C2×D4—38no—
171C2×D4—34no—
172C2×D4—34no—
173C2×D4—32no—
174C2×D4—64no—
175C2×D4—64no—
176C2×D4—68no—
177C2×D4—68no—
178C2×D4—128no—
179C22×C4—31no—
180C22×C4—32no—
181C22×C4—34no—
182C4⋊C4—32no—
183C4⋊C4C2×C3×A414yes—
184C22⋊C4—32no—
185C22⋊C4—38no—
186C42—31no—
187C42—32no—
188C42C2×C3×A411yescharacteristic
189C22×C3—32no—
190C22×C3—43no—
191C22×C3—62no—
192C22×C3—64no—
193C22×C3—68no—
194C22×C3—248no—
195C22×C3C23×A411yescharacteristic
196C3×C4—24no—
197C3×C4—31no—
198C3×C4—31no—
199C3×C4—46no—
200C3×C4—412no—
201C3×C4—62no—
202C3×C4—812no—
203C3×C4D4×A412yes—
204C3×C4#99414yescomplemented
205C32—41noSylow
206C23—31no—
207C23—34no—
208C23—68no—
209C23—128no—
210Q8—24no—
211Q8—31no—
212Q8C2×C32×D411yescharacteristic
213D4—32no—
214D4—32no—
215D4—68no—
216D4—64no—
217D4—64no—
218D4—64no—
219D4—68no—
220D4—128no—
221C2×C4—31no—
222C2×C4—32no—
223C2×C4—32no—
224C2×C4—32no—
225C2×C4—64no—
226C2×C4—64no—
227C2×C4—64no—
228C2×C4C22×C3×A414yes—
229C2×C4C22×C3×A411yescharacteristic
230C2×C4C22×C3×A412yes—
231C2×C3—43no—
232C2×C3—46no—
233C2×C3—62no—
234C2×C3—124no—
235C2×C3C2×D4×A411yescharacteristic
236C2×C3C2×#99412yes—
237C22—32no—
238C22—62no—
239C22—64no—
240C22—68no—
241C22—248no—
242C22C23×C3×A411yescharacteristic
243C4—24no—
244C4—31no—
245C4—31no—
246C4—62no—
247C4C3×D4×A412yes—
248C4C3×#99414yescomplemented
249C3—43no—
250C3C4⋊#99411yescharacteristic, direct product factor
251C2—62no—
252C2—124no—
253C2C2×C3×D4×A411yescharacteristic
254C2C2×C3×#99412yes—
subgroupG/H
center, socleC22×C3C23×A4
commutator, cosocleC2×Q8C23×C32
FrattiniC22C23×C3×A4
FittingC3×#3498C3
hypercenterC3×C4⋊Q8A4
hypocenterQ8C2×C32×D4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#994C2semidirect
2. C3×C4⋊(#41⋊C3)C2semidirect
3. C3×C4×#41⋊C3C2semidirect
4. C3×#3498C3semidirect
5. C4⋊#994C3direct (N × H)
8. C2×C3×#41⋊C3C22semidirect
10. C3×C4×SL(2,𝔽3)C22semidirect
12. C2×#994C2×C3semidirect
19. C4⋊(#41⋊C3)C2×C3semidirect
20. C4×#41⋊C3C2×C3semidirect
23. C3×#41⋊C3D4semidirect
27. #3498C32semidirect
38. C2×#41⋊C3C22×C3semidirect
53. C4×SL(2,𝔽3)C22×C3semidirect
58. C3×SL(2,𝔽3)C2×D4semidirect
91. #41⋊C3C3×D4semidirect
156. SL(2,𝔽3)C2×C3×D4semidirect
204. C3×C4#994semidirect
248. C4C3×#994semidirect
250. C3C4⋊#994direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9942
C3×C4⋊(#41⋊C3)2
C3×C4×#41⋊C32
C3×#34983
C4⋊#9943
C32×C4⋊Q84