Finite Group Databasebeta

← #79549

Subgroups — #79549

Order 384.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#908C212yesmaximal, complemented
2#5550C212yesmaximal, complemented
3C3×#436C211yesmaximal, characteristic, complemented
4#5134C212yesmaximal, complemented
5#4844C212yesmaximal, complemented
6#4733C212yesmaximal, complemented
7#4732C212yesmaximal, complemented
8#4696C211yesmaximal, characteristic, complemented
9C4×D24C211yesmaximal, characteristic, complemented
10#3273—31nomaximal, Sylow
11C2×#235C2212yes—
12C22×D12C2212yescomplemented
13C2×C3×M16C2212yescomplemented
14C3×C4×D4C2211yescharacteristic
15#937—22no—
16#930C2212yes—
17#924C2212yescomplemented
18#908—28no—
19C2×Dic12C2211yescharacteristic, complemented
20C2×D24C2212yes—
21C2×D24C2211yescharacteristic
22C2×D24C2211yescharacteristic
23C2×#204C2212yescomplemented
24C2×#204C2212yescomplemented
25#894—22no—
26#884—22no—
27D3×C22⋊C4—22no—
28#875C2212yescomplemented
29C4×D12C2212yescomplemented
30C3×C4⋊C8C2211yescharacteristic, complemented
31C3×C22⋊C8C2212yescomplemented
32C3×C4×C8C2211yescharacteristic, complemented
33#821C2212yescomplemented
34#821C2212yescomplemented
35#818C2211yescharacteristic, complemented
36#816C2212yescomplemented
37C2×AGL(1,ℤ/8)—32no—
38#546—32no—
39#495—31no—
40#468—32no—
41#463—32no—
42#452—32no—
43#447—32no—
44C4×D8—31no—
45#436D311yescharacteristic, complemented
46C23×D3—22no—
47C2×C3×D4D411yescharacteristic
48C22×C3×C4C2312yes—
49C2×#67—22no—
50C2×#67—22no—
51#235—24no—
52#235—42no—
53C2×D12—24no—
54C2×D12—22no—
55C2×D12—42no—
56C2×D12C2312yes—
57C2×D12C2312yes—
58C2×C4×D3—22no—
59C2×C4×D3—22no—
60C2×Dic6C2312yes—
61C3×M16—24no—
62C2×C3×C8C2312yes—
63C2×C3×C8C2311yescharacteristic
64C2×C3×C8C2311yescharacteristic
65C3×C4⋊C4D411yescharacteristic
66C3×C22⋊C4D412yes—
67C3×C42C2311yescharacteristic
68#217—22no—
69(C2×D3)⋊C4—22no—
70(C2×D3)⋊C4—22no—
71(C2×D3)⋊C4—22no—
72(C2×D3)⋊C4—22no—
73C4⋊Dic3C2312yes—
74Dic3⋊C4—22no—
75Dic12—41no—
76D24—24no—
77D24—41no—
78D24D414yescomplemented
79#204—24no—
80#204—24no—
81C2×#41—32no—
82C22×D4—32no—
83AGL(1,ℤ/8)—68no—
84C2×Q16—31no—
85C2×SD16—32no—
86C2×SD16—32no—
87C2×D8—31no—
88C2×D8—32no—
89C2×D8—31no—
90C2×M16C2×D312yescomplemented
91#124—32no—
92#123—62no—
93C22⋊Q8—32no—
94#121—32no—
95#121—62no—
96#120—62no—
97C4×D4—32no—
98C4×D4C2×D311yescharacteristic
99C2×C22⋊C4—62no—
100#107—31no—
101C4⋊C8C2×D311yescharacteristic, complemented
102#103—32no—
103#102—32no—
104#102—32no—
105C22⋊C8C2×D312yescomplemented
106C4×C8C2×D311yescharacteristic, complemented
107C23×C3C2×D412yes—
108C22×D3—22no—
109C22×D3—22no—
110C22×D3—44no—
111C22×D3—44no—
112C22×D3—82no—
113C3×D4—41no—
114C2×C3×C4—22no—
115C2×C3×C4—22no—
116C2×C3×C4C2×D412yes—
117C2×C3×C4C2×D411yescharacteristic
118C2×C3×C4C2×D411yescharacteristic
119C2×C3×C4C2411yescharacteristic
120#67—44no—
121#67—82no—
122C2×Dic3—22no—
123C2×Dic3—22no—
124D12—22no—
125D12—22no—
126D12—22no—
127D12—44no—
128D12C2×D414yes—
129C4×D3—44no—
130C4×D3—82no—
131Dic6—22no—
132Dic6—22no—
133C3×C8—22no—
134C3×C8—21no—
135C3×C8C2×D412yes—
136C24—62no—
137#41—64no—
138#41—122no—
139C2×Q8—32no—
140C2×D4—32no—
141C2×D4—32no—
142C2×D4—64no—
143C2×D4—62no—
144C2×D4—62no—
145C2×D4—62no—
146C2×D4—122no—
147C2×D4D1211yescharacteristic
148C22×C4—62no—
149C22×C4—62no—
150C22×C4C22×D312yes—
151Q16—121no—
152SD16—64no—
153SD16—64no—
154D8—34no—
155D8—64no—
156D8—121no—
157M16—24no—
158C2×C8C22×D311yescharacteristic
159C2×C8C22×D312yes—
160C2×C8C22×D311yescharacteristic
161C4⋊C4—32no—
162C4⋊C4—62no—
163C4⋊C4D1211yescharacteristic
164C22⋊C4—62no—
165C22⋊C4—62no—
166C22⋊C4—62no—
167C22⋊C4—62no—
168C22⋊C4—62no—
169C22⋊C4D1212yes—
170C42C22×D311yescharacteristic
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—22no—
174C22×C3C22×D411yescharacteristic
175C2×D3—24no—
176C2×D3—42no—
177C2×D3—42no—
178C2×D3—42no—
179C2×D3—42no—
180C2×D3—42no—
181C2×D3—88no—
182C3×C4—22no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4C22×D411yescharacteristic
186C3×C4H(5,𝔽2)11yescharacteristic
187Dic3—42no—
188Dic3—42no—
189C23—62no—
190C23—62no—
191C23—124no—
192C23—124no—
193C23—242no—
194C23C2×D1212yes—
195Q8—62no—
196Q8—62no—
197D4—34no—
198D4—41no—
199D4—62no—
200D4—62no—
201D4—62no—
202D4—124no—
203D4—124no—
204D4—242no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—62no—
208C2×C4—62no—
209C2×C4—124no—
210C2×C4—242no—
211C2×C4C2×D1211yescharacteristic
212C2×C4C2×D1211yescharacteristic
213C2×C4C2×D1212yes—
214C2×C4C23×D311yescharacteristic
215C8—22no—
216C8—21no—
217C8D3×D412yes—
218C2×C3—42no—
219C2×C3D4211yescharacteristic
220C2×C3#57511yescharacteristic
221C2×C3#57611yescharacteristic
222D3—44no—
223D3—82no—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—64no—
228C22—122no—
229C22—122no—
230C22—122no—
231C22—122no—
232C22—122no—
233C22—248no—
234C22C22×D1211yescharacteristic
235C4—21no—
236C4—21no—
237C4—22no—
238C4—122no—
239C4—122no—
240C4C2×D3×D411yescharacteristic
241C4#100911yescharacteristic
242C3#327311yescharacteristic, complemented, Sylow
243C2—42no—
244C2—124no—
245C2—242no—
246C2D4×D1211yescharacteristic
247C2#574811yescharacteristic
248C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#436C2
socleC22×C3C22×D4
hypercenter#436D3
hypocenterC3#3273
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#908C2semidirect
2. #5550C2semidirect
3. C3×#436C2semidirect
4. #5134C2semidirect
5. #4844C2semidirect
6. #4733C2semidirect
7. #4732C2semidirect
8. #4696C2semidirect
9. C4×D24C2semidirect
12. C22×D12C22semidirect
13. C2×C3×M16C22semidirect
17. #924C22semidirect
19. C2×Dic12C22semidirect
23. C2×#204C22semidirect
24. C2×#204C22semidirect
28. #875C22semidirect
29. C4×D12C22semidirect
30. C3×C4⋊C8C22semidirect
31. C3×C22⋊C8C22semidirect
32. C3×C4×C8C22semidirect
33. #821C22semidirect
34. #821C22semidirect
35. #818C22semidirect
36. #816C22semidirect
45. #436D3semidirect
78. D24D4semidirect
90. C2×M16C2×D3semidirect
101. C4⋊C8C2×D3semidirect
105. C22⋊C8C2×D3semidirect
106. C4×C8C2×D3semidirect
242. C3#3273semidirect

Maximal subgroups

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

subgroupindex
C2×#9082
#55502
C3×#4362
#51342
#48442
#47332
#47322
#46962
C4×D242
#32733