Finite Group Databasebeta

← #79893

Subgroups — #79893

Order 384.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#5770C212yesmaximal, complemented
2#5751C212yesmaximal, complemented
3C3×#443C211yesmaximal, characteristic, complemented
4#5141C212yesmaximal, complemented
5#4898C212yesmaximal, complemented
6#4826C212yesmaximal, complemented
7#4822C212yesmaximal, complemented
8#4700C211yesmaximal, characteristic, complemented
9#4693C211yesmaximal, characteristic, complemented
10#3291—31nomaximal, Sylow
11#1010C2212yes—
12#1009C2212yescomplemented
13C3×#135C2211yescharacteristic
14C3×#131C2212yescomplemented
15#951C2212yescomplemented
16#949C2212yes—
17#918—22no—
18#916—22no—
19D3×SD16—22no—
20#911—22no—
21#909—22no—
22#909C2212yescomplemented
23#908—22no—
24#908C2212yes—
25#904—22no—
26#904C2211yescharacteristic
27C2×#204—22no—
28C2×#204C2212yescomplemented
29C2×#204C2212yescomplemented
30#901C2212yescomplemented
31#874C2211yescharacteristic
32#869C2211yescharacteristic, complemented
33C3×#108C2211yescharacteristic, complemented
34C3×#104C2212yescomplemented
35C3×C4×C8C2211yescharacteristic, complemented
36#824C2212yescomplemented
37#823C2212yescomplemented
38#819C2211yescharacteristic, complemented
39#805C2212yescomplemented
40#577—32no—
41#577—32no—
42#492—31no—
43#471—32no—
44#471—32no—
45#456—32no—
46#453—32no—
47#443—31no—
48#443D311yescharacteristic, complemented
49C3×#41C2312yes—
50#239—22no—
51D3×Q8—22no—
52#237—22no—
53#237—42no—
54D3×D4—22no—
55D3×D4—42no—
56#235—22no—
57#235—22no—
58#235C2312yes—
59C2×D12—22no—
60C2×D12—41no—
61C2×D12C2312yes—
62C2×Dic6—22no—
63C2×Dic6C2312yes—
64C3×Q16D411yescharacteristic, complemented
65C3×SD16D412yescomplemented
66C3×D8D411yescharacteristic, complemented
67C3×M16—22no—
68C3×M16C2312yes—
69C2×C3×C8—22no—
70C2×C3×C8C2311yescharacteristic
71C2×C3×C8C2311yescharacteristic
72C3×C42C2311yescharacteristic
73#216—22no—
74#215—22no—
75#214—22no—
76#213—22no—
77C4⋊Dic3—41no—
78#208C2312yes—
79Dic12—22no—
80Dic12D411yescharacteristic, complemented
81D24—22no—
82D24D411yescharacteristic, complemented
83#204—22no—
84#204—22no—
85#204—22no—
86#204—22no—
87#204—22no—
88#204—22no—
89#204D412yescomplemented
90ΓL(1,𝔽25)—22no—
91D3×C8—22no—
922−1+4—32no—
93H(5,𝔽2)—32no—
94#137—32no—
95#137—32no—
96#137—62no—
97#137—62no—
98AGL(1,ℤ/8)—32no—
99AGL(1,ℤ/8)—32no—
100AGL(1,ℤ/8)—62no—
101AGL(1,ℤ/8)—62no—
102#135—31no—
103#135—62no—
104#135—62no—
105#135C2×D311yescharacteristic
106C2×SD16—32no—
107C2×SD16—32no—
108C2×SD16—62no—
109C2×SD16—62no—
110#131—32no—
111#131C2×D312yescomplemented
112C4⋊Q8—31no—
113#127—31no—
114#108—31no—
115#108C2×D311yescharacteristic, complemented
116#104—32no—
117#104C2×D312yescomplemented
118#101—32no—
119#100—32no—
120C4×C8C2×D311yescharacteristic, complemented
121C22×D3—22no—
122C22×D3—42no—
123C3×Q8C2×D412yes—
124C3×D4—22no—
125C3×D4C2×D412yes—
126C2×C3×C4—21no—
127C2×C3×C4—22no—
128C2×C3×C4C2411yescharacteristic
129#67—22no—
130#67—42no—
131#67—42no—
132C2×Dic3—22no—
133C2×Dic3—42no—
134D12—22no—
135D12—22no—
136D12—42no—
137D12—82no—
138D12C2×D412yes—
139C4×D3—22no—
140C4×D3—42no—
141C4×D3—42no—
142Dic6—22no—
143Dic6—22no—
144Dic6—42no—
145Dic6C2×D412yes—
146C3×C8—22no—
147C3×C8C2×D411yescharacteristic
148C3×C8C2×D411yescharacteristic
149C3×C8C2×D411yescharacteristic
150C3×C8C2×D411yescharacteristic
151C3⋊C8—22no—
152#41—32no—
153#41—62no—
154#41—62no—
155#41—62no—
156#41—62no—
157#41—122no—
158#41C22×D312yes—
159C2×Q8—32no—
160C2×Q8—62no—
161C2×Q8—62no—
162C2×D4—32no—
163C2×D4—62no—
164C2×D4—62no—
165C2×D4—121no—
166C2×D4—122no—
167Q16—31no—
168Q16—62no—
169Q16—62no—
170Q16D1211yescharacteristic, complemented
171SD16—32no—
172SD16—62no—
173SD16—62no—
174SD16—62no—
175SD16—62no—
176SD16—62no—
177SD16—62no—
178SD16—62no—
179SD16—62no—
180SD16D1212yescomplemented
181D8—31no—
182D8—62no—
183D8—62no—
184D8D1211yescharacteristic, complemented
185M16—22no—
186M16—32no—
187M16—62no—
188M16C22×D312yes—
189C2×C8—22no—
190C2×C8—62no—
191C2×C8C22×D311yescharacteristic
192C2×C8C22×D311yescharacteristic
193C4⋊C4—121no—
194C42C22×D311yescharacteristic
195C22×C3—22no—
196C22×C3H(5,𝔽2)11yescharacteristic
197C2×D3—22no—
198C2×D3—42no—
199C2×D3—82no—
200C2×D3—162no—
201C3×C4—22no—
202C3×C4—22no—
203C3×C4C22×D411yescharacteristic
204C3×C4C22×D411yescharacteristic
205Dic3—22no—
206Dic3—42no—
207C23—62no—
208C23—122no—
209Q8—32no—
210Q8—62no—
211Q8—62no—
212Q8—122no—
213Q8C2×D1212yes—
214D4—22no—
215D4—32no—
216D4—62no—
217D4—62no—
218D4—62no—
219D4—122no—
220D4—122no—
221D4—122no—
222D4—242no—
223D4C2×D1212yes—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—62no—
227C2×C4—62no—
228C2×C4—122no—
229C2×C4—122no—
230C2×C4—122no—
231C2×C4C23×D311yescharacteristic
232C8—22no—
233C8—62no—
234C8C2×D1211yescharacteristic
235C8C2×D1211yescharacteristic
236C8D3×D411yescharacteristic
237C8D3×D411yescharacteristic
238C2×C3—21no—
239C2×C3—42no—
240C2×C3D4211yescharacteristic
241D3—42no—
242D3—82no—
243C22—22no—
244C22—62no—
245C22—122no—
246C22—242no—
247C22—482no—
248C22#100911yescharacteristic
249C4—22no—
250C4—22no—
251C4—62no—
252C4—122no—
253C4C22×D1211yescharacteristic
254C4C2×D3×D411yescharacteristic
255C3#329111yescharacteristic, complemented, Sylow
256C2—21no—
257C2—42no—
258C2—122no—
259C2—242no—
260C2D4×D1211yescharacteristic
subgroupG/H
centerC2D4×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#443C2
socleC2×C3D42
hypercenter#443D3
hypocenterC3#3291
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #5770C2semidirect
2. #5751C2semidirect
3. C3×#443C2semidirect
4. #5141C2semidirect
5. #4898C2semidirect
6. #4826C2semidirect
7. #4822C2semidirect
8. #4700C2semidirect
9. #4693C2semidirect
12. #1009C22semidirect
14. C3×#131C22semidirect
15. #951C22semidirect
22. #909C22semidirect
28. C2×#204C22semidirect
29. C2×#204C22semidirect
30. #901C22semidirect
32. #869C22semidirect
33. C3×#108C22semidirect
34. C3×#104C22semidirect
35. C3×C4×C8C22semidirect
36. #824C22semidirect
37. #823C22semidirect
38. #819C22semidirect
39. #805C22semidirect
48. #443D3semidirect
64. C3×Q16D4semidirect
65. C3×SD16D4semidirect
66. C3×D8D4semidirect
80. Dic12D4semidirect
82. D24D4semidirect
89. #204D4semidirect
111. #131C2×D3semidirect
115. #108C2×D3semidirect
117. #104C2×D3semidirect
120. C4×C8C2×D3semidirect
170. Q16D12semidirect
180. SD16D12semidirect
184. D8D12semidirect
255. C3#3291semidirect

Maximal subgroups

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

subgroupindex
#57702
#57512
C3×#4432
#51412
#48982
#48262
#48222
#47002
#46932
#32913