Finite Group Databasebeta

← D8×D12 #79605

Subgroups — D8×D12 #79605

Order 384.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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×D3×D8C212yesmaximal, complemented
2D4×D12C212yesmaximal, complemented
3C3×C4×D8C211yesmaximal, characteristic, complemented
4#5015C212yesmaximal, complemented
5#4883C212yesmaximal, complemented
6#4773C214yesmaximal, complemented
7#4695C211yesmaximal, characteristic, complemented
8C8×D12C211yesmaximal, characteristic, complemented
9D4×D8—31nomaximal, Sylow
10C2×D3×D4C2214yescomplemented
11C22×D12—22no—
12C2×C3×D8C2211yescharacteristic
13C3×C4×D4C2212yescomplemented
14C2×#213C2214yescomplemented
15#930—22no—
16D3×D8—28no—
17C2×D24C2212yescomplemented
18C2×D24C2212yescomplemented
19C2×D3×C8C2212yescomplemented
20#895C2214yescomplemented
21#882—24no—
22#874C2212yescomplemented
23C4×D12C2211yescharacteristic
24C3×#107C2211yescharacteristic, complemented
25C3×#102C2212yescomplemented
26C3×C4×C8C2211yescharacteristic, complemented
27(C2×D3)⋊C8C2212yescomplemented
28#809C2214yescomplemented
29C4⋊(C3⋊C8)C2211yescharacteristic, complemented
30C22×D8—32no—
31D42—32no—
32#493—31no—
33#466—32no—
34#459—32no—
35#447—34no—
36C4×D8D311yescharacteristic, complemented
37C8×D4—31no—
38C23×D3—24no—
39C2×C3×D4C2312yes—
40C22×C3×C4—22no—
41C2×#67—24no—
42D3×D4—28no—
43D3×D4—44no—
44C2×D12—24no—
45C2×D12—22no—
46C2×D12—22no—
47C2×D12—48no—
48C2×D12D411yescharacteristic
49C2×D12C2314yes—
50C2×C4×D3C2312yes—
51C3×D8D414yescomplemented
52C2×C3×C8C2311yescharacteristic
53C2×C3×C8C2311yescharacteristic
54C3×C4⋊C4C2312yes—
55C3×C22⋊C4—22no—
56C3×C42C2311yescharacteristic
57#213—28no—
58(C2×D3)⋊C4—24no—
59(C2×D3)⋊C4D412yes—
60C4⋊Dic3D411yescharacteristic
61C2×C3⋊C8C2312yes—
62D24—24no—
63D24—42no—
64D3×C8—24no—
65C22×D4—34no—
66C22×D4—62no—
67C2×D8—34no—
68C2×D8—32no—
69C2×D8—32no—
70C2×D8—68no—
71C2×D8C2×D311yescharacteristic
72C22×C8—32no—
73#127—32no—
74#121—34no—
75#121—62no—
76#120—64no—
77C4×D4—31no—
78C4×D4C2×D312yescomplemented
79#107C2×D311yescharacteristic, complemented
80C4⋊C8—31no—
81#102—34no—
82#102C2×D312yescomplemented
83C22⋊C8—32no—
84C4×C8C2×D311yescharacteristic, complemented
85C23×C3—22no—
86C22×D3—24no—
87C22×D3—48no—
88C22×D3—48no—
89C22×D3—84no—
90C22×D3C2×D412yes—
91C3×D4—22no—
92C3×D4C2×D414yescomplemented
93C2×C3×C4—22no—
94C2×C3×C4—44no—
95C2×C3×C4C2×D411yescharacteristic
96C2×C3×C4C2×D411yescharacteristic
97C2×C3×C4C2411yescharacteristic
98#67—48no—
99C2×Dic3C2×D412yes—
100D12—24no—
101D12—24no—
102D12—48no—
103D12—44no—
104D12—82no—
105D12D814yesdirect product factor
106C4×D3—22no—
107C4×D3—22no—
108C3×C8—21no—
109C3×C8C2×D412yescomplemented
110C3⋊C8—22no—
111C24—64no—
112C2×D4—31no—
113C2×D4—34no—
114C2×D4—64no—
115C2×D4—64no—
116C2×D4—68no—
117C2×D4—62no—
118C2×D4—62no—
119C2×D4—128no—
120C2×D4—124no—
121C2×D4C22×D312yes—
122C22×C4—22no—
123C22×C4—32no—
124D8—68no—
125D8—64no—
126D8—122no—
127D8D1214yesdirect product factor
128C2×C8—32no—
129C2×C8—64no—
130C2×C8C22×D311yescharacteristic
131C2×C8C22×D311yescharacteristic
132C4⋊C4—31no—
133C4⋊C4C22×D312yes—
134C22⋊C4—22no—
135C22⋊C4—32no—
136C22⋊C4—64no—
137C42C22×D311yescharacteristic
138C22×C3—24no—
139C22×C3—42no—
140C22×C3—42no—
141C22×C3C22×D411yescharacteristic
142C2×D3—22no—
143C2×D3—22no—
144C2×D3—44no—
145C2×D3—44no—
146C2×D3—44no—
147C2×D3—816no—
148C2×D3C2×D814yescomplemented
149C3×C4—21no—
150C3×C4—42no—
151C3×C4C2×D812yescomplemented
152C3×C4C22×D411yescharacteristic
153C3×C4H(5,𝔽2)11yescharacteristic
154Dic3—22no—
155C23—22no—
156C23—32no—
157C23—64no—
158C23—128no—
159C23—128no—
160C23—244no—
161D4—22no—
162D4—34no—
163D4—64no—
164D4—64no—
165D4—128no—
166D4—128no—
167D4—124no—
168D4—242no—
169D4C2×D1214yescomplemented
170C2×C4—22no—
171C2×C4—32no—
172C2×C4—44no—
173C2×C4—62no—
174C2×C4—62no—
175C2×C4D3×D411yescharacteristic
176C2×C4D3×D411yescharacteristic
177C2×C4C23×D311yescharacteristic
178C8—21no—
179C8—62no—
180C8C2×D1212yescomplemented
181C2×C3—44no—
182C2×C3D4211yescharacteristic
183C2×C3C22×D811yescharacteristic
184C2×C3#57611yescharacteristic
185D3—24no—
186D3—84no—
187C22—24no—
188C22—34no—
189C22—42no—
190C22—42no—
191C22—62no—
192C22—62no—
193C22—124no—
194C22—124no—
195C22—124no—
196C22—2416no—
197C22C2×D3×D411yescharacteristic
198C4—21no—
199C4—42no—
200C4—62no—
201C4D3×D812yescomplemented
202C4C22×D1211yescharacteristic
203C4#100911yescharacteristic
204C3D4×D811yescharacteristic, complemented, Sylow
205C2—44no—
206C2—64no—
207C2—244no—
208C2D4×D1211yescharacteristic
209C2C2×D3×D811yescharacteristic
210C2#576911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C4×D8C2
socleC22×C3C22×D4
hypercenterC4×D8D3
hypocenterC3D4×D8
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D3×D8C2semidirect
2. D4×D12C2semidirect
3. C3×C4×D8C2semidirect
4. #5015C2semidirect
5. #4883C2semidirect
6. #4773C2semidirect
7. #4695C2semidirect
8. C8×D12C2semidirect
10. C2×D3×D4C22semidirect
13. C3×C4×D4C22semidirect
14. C2×#213C22semidirect
17. C2×D24C22semidirect
18. C2×D24C22semidirect
19. C2×D3×C8C22semidirect
20. #895C22semidirect
22. #874C22semidirect
24. C3×#107C22semidirect
25. C3×#102C22semidirect
26. C3×C4×C8C22semidirect
27. (C2×D3)⋊C8C22semidirect
28. #809C22semidirect
29. C4⋊(C3⋊C8)C22semidirect
36. C4×D8D3semidirect
51. C3×D8D4semidirect
78. C4×D4C2×D3semidirect
79. #107C2×D3semidirect
82. #102C2×D3semidirect
84. C4×C8C2×D3semidirect
92. C3×D4C2×D4semidirect
105. D12D8direct (N × H)
109. C3×C8C2×D4semidirect
127. D8D12direct (N × H)
148. C2×D3C2×D8semidirect
151. C3×C4C2×D8semidirect
169. D4C2×D12semidirect
180. C8C2×D12semidirect
201. C4D3×D8semidirect
204. C3D4×D8semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D82
D4×D122
C3×C4×D82
#50152
#48832
#47732
#46952
C8×D122
D4×D83