Finite Group Databasebeta

← C3×#81791 #11886902

Subgroups — C3×#81791 #11886902

Order 1152.

1033 conjugacy classes of subgroups; only the 234 normal subgroups are shown.

normal subgroups only

This group has 1033 conjugacy classes of subgroups — too many to draw. Only its 234 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
1C3×#5757C214yesmaximal, complemented
2C32×#493C211yesmaximal, characteristic, complemented
3C3×#5160C214yesmaximal, complemented
4C3×#5077C214yesmaximal, complemented
5C3×#4700C212yesmaximal, complemented
6C3×#3292—31nomaximal
7#81791C311yesmaximal, characteristic, direct product factor
8C3×#1004C2214yescomplemented
9C2×C32×D8C2214yescomplemented
10C32×#127C2212yescomplemented
11C3×#932C2218yescomplemented
12C3×#912—24no—
13C3×#911—28no—
14C3×D3×D8—24no—
15C3×#904C2212yes—
16C3×#901C2214yescomplemented
17C32×C4×C8C2211yescharacteristic, complemented
18C3×#833C2214yescomplemented
19C3×#819C2212yescomplemented
20C3×#805C2214yescomplemented
21C3×#576—34no—
22#5757C2×C314yescomplemented
23C3×#493—21no—
24C3×#493D311yescharacteristic, complemented
25C3×#493C2×C311yescharacteristic, complemented
26C3×#472—34no—
27C3×#453—34no—
28C3×#443—32no—
29#5160C2×C314yescomplemented
30#5077C2×C314yescomplemented
31#4700C2×C312yescomplemented
32C2×C32×D4—42no—
33C2×C32×D4C2314yes—
34C2×C3×#67—44no—
35C3×#237—28no—
36C3×D3×D4—28no—
37C3×#235C2314yes—
38C32×D8—24no—
39C32×D8—24no—
40C2×C32×C8C2312yes—
41C32×C42C2311yescharacteristic
42C3×#214—28no—
43C3×#213—28no—
44C3×#208C2314yes—
45C3×Dic12D412yescomplemented
46C3×D24D412yescomplemented
47C3×#204D414yescomplemented
48C3×ΓL(1,𝔽25)—24no—
49C3×D3×C8—24no—
50#3292—31noSylow
51C3×H(5,𝔽2)—34no—
52#1004C22×C314yescomplemented
53C3×AGL(1,ℤ/8)—38no—
54C3×AGL(1,ℤ/8)—68no—
55C3×#135—32no—
56C3×#135—64no—
57C2×C3×D8—24no—
58C2×C3×D8—64no—
59C2×C3×D8C2×D314yescomplemented
60C2×C3×D8C22×C314yescomplemented
61C3×#131—34no—
62C3×#127—22no—
63C3×#127C2×D312yescomplemented
64C3×#127C22×C312yescomplemented
65#932C22×C318yescomplemented
66#912—24no—
67#911—28no—
68D3×D8—24no—
69#904C22×C312yes—
70#901C22×C314yescomplemented
71C3×#108—32no—
72C3×#104—34no—
73C3×#100—34no—
74C3×C4×C8—21no—
75C3×C4×C8C2×D311yescharacteristic, complemented
76C3×C4×C8C22×C311yescharacteristic, complemented
77#833C22×C314yescomplemented
78#819C22×C312yescomplemented
79#805C22×C314yescomplemented
80C23×C32—24no—
81C22×C3×D3—44no—
82C32×D4—28no—
83C32×D4—84no—
84C2×C32×C4—21no—
85C2×C32×C4C2411yescharacteristic
86C3×#67—24no—
87C3×#67—48no—
88C2×C3×Dic3—44no—
89C3×D12C2×D414yes—
90C3×C4×D3—24no—
91C3×Dic6C2×D414yes—
92C32×C8C2×D412yes—
93C32×C8C2×D412yes—
94C3×C3⋊C8—24no—
95#576—34no—
96#493C3×D311yescharacteristic, complemented
97#472—34no—
98#453—34no—
99#443—32no—
100C3×#41—34no—
101C3×#41—68no—
102C2×C3×D4—24no—
103C2×C3×D4—42no—
104C2×C3×D4—42no—
105C2×C3×D4—44no—
106C2×C3×D4—68no—
107C2×C3×D4—124no—
108C2×C3×D4C22×D314yes—
109C2×C3×D4C23×C314yes—
110C2×#67—44no—
111#237—28no—
112D3×D4—28no—
113#235C23×C314yes—
114C3×Q16—32no—
115C3×SD16—34no—
116C3×SD16—68no—
117C3×D8—24no—
118C3×D8—24no—
119C3×D8—24no—
120C3×D8—24no—
121C3×D8—32no—
122C3×D8—44no—
123C3×D8—44no—
124C3×D8—68no—
125C3×M16—34no—
126C3×M16—64no—
127C2×C3×C8—22no—
128C2×C3×C8—64no—
129C2×C3×C8C22×D312yes—
130C2×C3×C8C23×C312yes—
131C3×C42—21no—
132C3×C42C22×D311yescharacteristic
133C3×C42C23×C311yescharacteristic
134#214—28no—
135#213—28no—
136#208C23×C314yes—
137Dic12C3×D412yescomplemented
138D24C3×D412yescomplemented
139#204C3×D414yescomplemented
140ΓL(1,𝔽25)—24no—
141D3×C8—24no—
142C22×C32—44no—
143C22×C32—84no—
144C22×C32H(5,𝔽2)11yescharacteristic
145C2×C3×D3—24no—
146C2×C3×D3—164no—
147C32×C4—22no—
148C32×C4C22×D412yes—
149C3×Dic3—24no—
150H(5,𝔽2)—34no—
151AGL(1,ℤ/8)—38no—
152AGL(1,ℤ/8)—68no—
153#135—32no—
154#135—64no—
155C2×D8—64no—
156C2×D8C2×C3×D314yescomplemented
157#131—34no—
158#127C2×C3×D312yescomplemented
159#108—32no—
160#104—34no—
161#100—34no—
162C4×C8C2×C3×D311yescharacteristic, complemented
163C23×C3—24no—
164C23×C3—24no—
165C23×C3—44no—
166C23×C3—124no—
167C22×D3—44no—
168C3×Q8—34no—
169C3×D4—28no—
170C3×D4—28no—
171C3×D4—34no—
172C3×D4—48no—
173C3×D4—64no—
174C3×D4—84no—
175C3×D4—84no—
176C3×D4—88no—
177C3×D4—128no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—64no—
183C2×C3×C4—124no—
184C2×C3×C4C23×D311yescharacteristic
185C2×C3×C4C24×C311yescharacteristic
186#67—24no—
187#67—48no—
188C2×Dic3—44no—
189D12C2×C3×D414yes—
190C4×D3—24no—
191Dic6C2×C3×D414yes—
192C3×C8—22no—
193C3×C8—22no—
194C3×C8—64no—
195C3×C8D3×D412yes—
196C3×C8D3×D412yes—
197C3×C8C2×C3×D412yes—
198C3×C8C2×C3×D412yes—
199C3⋊C8—24no—
200C2×C32—21no—
201C2×C32—84no—
202C2×C32D4211yescharacteristic
203C3×D3—44no—
204#41—34no—
205#41—68no—
206C2×D4—42no—
207C2×D4—68no—
208C2×D4—124no—
209C2×D4C22×C3×D314yes—
210Q16—32no—
211SD16—34no—
212SD16—68no—
213D8—24no—
214D8—24no—
215D8—32no—
216D8—68no—
217M16—34no—
218M16—64no—
219C2×C8—64no—
220C2×C8C22×C3×D312yes—
221C42C22×C3×D311yescharacteristic
222C22×C3—21no—
223C22×C3—44no—
224C22×C3—44no—
225C22×C3—64no—
226C22×C3—84no—
227C22×C3—84no—
228C22×C3—84no—
229C22×C3—88no—
230C22×C3—484no—
231C22×C3#100411yescharacteristic
232C22×C3C3×H(5,𝔽2)11yescharacteristic
233C2×D3—24no—
234C2×D3—164no—
235C3×C4—24no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—64no—
240C3×C4C2×D3×D412yes—
241C3×C4C22×C3×D412yes—
242Dic3—24no—
243C32#329211yescharacteristic, complemented, Sylow
244C23—24no—
245C23—124no—
246Q8—34no—
247D4—28no—
248D4—34no—
249D4—64no—
250D4—84no—
251D4—128no—
252C2×C4—21no—
253C2×C4—64no—
254C2×C4—124no—
255C2×C4C23×C3×D311yescharacteristic
256C8—64no—
257C8C3×D3×D412yes—
258C8C3×D3×D412yes—
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—84no—
264C2×C3—84no—
265C2×C3—124no—
266C2×C3—164no—
267C2×C3#571711yescharacteristic
268C2×C3C3×D4211yescharacteristic
269D3—44no—
270C22—44no—
271C22—64no—
272C22—84no—
273C22—484no—
274C22C3×#100411yescharacteristic
275C4—22no—
276C4—64no—
277C4C2×C3×D3×D412yes—
278C3—21no—
279C3#8179111yescharacteristic, direct product factor
280C3C3×#329211yescharacteristic, complemented
281C2—21no—
282C2—84no—
283C2—124no—
284C2C3×#571711yescharacteristic
subgroupG/H
centerC2×C3#5717
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#493C2
socleC2×C32D42
hypercenterC3×#493D3
hypocenterC3C3×#3292
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#493

Complements

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

NH ≅ G/Ntype
1. C3×#5757C2semidirect
2. C32×#493C2semidirect
3. C3×#5160C2semidirect
4. C3×#5077C2semidirect
5. C3×#4700C2semidirect
7. #81791C3direct (N × H)
8. C3×#1004C22semidirect
9. C2×C32×D8C22semidirect
10. C32×#127C22semidirect
11. C3×#932C22semidirect
16. C3×#901C22semidirect
17. C32×C4×C8C22semidirect
18. C3×#833C22semidirect
19. C3×#819C22semidirect
20. C3×#805C22semidirect
22. #5757C2×C3semidirect
24. C3×#493D3semidirect
25. C3×#493C2×C3semidirect
29. #5160C2×C3semidirect
30. #5077C2×C3semidirect
31. #4700C2×C3semidirect
45. C3×Dic12D4semidirect
46. C3×D24D4semidirect
47. C3×#204D4semidirect
52. #1004C22×C3semidirect
59. C2×C3×D8C2×D3semidirect
60. C2×C3×D8C22×C3semidirect
63. C3×#127C2×D3semidirect
64. C3×#127C22×C3semidirect
65. #932C22×C3semidirect
70. #901C22×C3semidirect
75. C3×C4×C8C2×D3semidirect
76. C3×C4×C8C22×C3semidirect
77. #833C22×C3semidirect
78. #819C22×C3semidirect
79. #805C22×C3semidirect
96. #493C3×D3semidirect
137. Dic12C3×D4semidirect
138. D24C3×D4semidirect
139. #204C3×D4semidirect
156. C2×D8C2×C3×D3semidirect
158. #127C2×C3×D3semidirect
162. C4×C8C2×C3×D3semidirect
243. C32#3292semidirect
279. C3#81791direct (N × H)
280. C3C3×#3292semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
C32×#4932
C3×#51602
C3×#50772
C3×#47002
C3×#32923
#817913