Finite Group Databasebeta

← C2×D3×#127 #86191

Subgroups — C2×D3×#127 #86191

Order 384.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C22×D3×D4C216yesmaximal, complemented
2C2×C3×#127C211yesmaximal, characteristic, complemented
3C2×#940C216yesmaximal, complemented
4D3×#127C2116yesmaximal, direct product factor
5C2×#874C211yesmaximal, characteristic, complemented
6C2×C42×D3C211yesmaximal, characteristic, complemented
7C22×#127—31nomaximal, Sylow
8C24×D3C2214yes—
9C22×C3×D4C2216yescomplemented
10C22×#67C22112yescomplemented
11C2×D3×D4—248no—
12C2×D3×D4C22148yescomplemented
13C22×D12C2216yescomplemented
14C22×C4×D3C2213yes—
15C3×#127C2218yescomplemented
16C2×C3×C42C2211yescharacteristic, complemented
17#940C22148yescomplemented
18C2×C4×Dic3C2213yescomplemented
19#874C2218yescomplemented
20C42×D3C2218yescomplemented
21C23×D4—36no—
22C2×#127—36no—
23C2×#127—316no—
24C2×#127—31no—
25C2×#127D311yescharacteristic, direct product factor
26C22×C42—31no—
27C24×C3C2314yes—
28C23×D3—248no—
29C23×D3C2314yes—
30C23×D3C23116yes—
31C23×D3C2311yescharacteristic
32C2×C3×D4—224no—
33C2×C3×D4C23124yescomplemented
34C22×C3×C4C2313yes—
35C2×#67—248no—
36C2×#67C23148yescomplemented
37C22×Dic3C2313yes—
38D3×D4—2192no—
39C2×D12—224no—
40C2×D12C23124yescomplemented
41C2×C4×D3D4124yescomplemented
42C2×C4×D3C23112yes—
43C3×C42C2314yescomplemented
44C4×Dic3C23112yescomplemented
45C25—34no—
46C22×D4—312no—
47C22×D4—348no—
48C22×D4—36no—
49C22×D4—648no—
50C22×D4C2×D316yescomplemented
51C23×C4—33no—
52#127—348no—
53#127—38no—
54#127C2×D318yesdirect product factor
55C2×C42—33no—
56C2×C42—38no—
57C2×C42C2×D311yescharacteristic, complemented
58C23×C3—224no—
59C23×C3C2418yes—
60C23×C3C2411yescharacteristic
61C22×D3—224no—
62C22×D3—296no—
63C22×D3—464no—
64C22×D3C2×D4112yes—
65C22×D3C2418yes—
66C22×D3C2412yes—
67C3×D4—248no—
68C2×C3×C4C2×D4112yescomplemented
69C2×C3×C4C2416yes—
70#67—296no—
71C2×Dic3C2×D4112yescomplemented
72C2×Dic3C2416yes—
73D12—248no—
74C4×D3C2×D4148yescomplemented
75C24—31no—
76C24—316no—
77C24—34no—
78C24—648no—
79C24C22×D314yes—
80C2×D4—224no—
81C2×D4—348no—
82C2×D4—324no—
83C2×D4—6192no—
84C2×D4—648no—
85C2×D4—624no—
86C2×D4C22×D3124yescomplemented
87C22×C4—33no—
88C22×C4—324no—
89C22×C4—312no—
90C22×C4C22×D313yes—
91C42—312no—
92C42C22×D314yescomplemented
93C22×C3—224no—
94C22×C3—416no—
95C22×C3C22×D416yes—
96C22×C3C2511yescharacteristic
97C2×D3—224no—
98C2×D3—416no—
99C2×D3—464no—
100C2×D3#127116yesdirect product factor
101C2×D3C22×D4112yes—
102C3×C4C22×D4112yescomplemented
103Dic3C22×D4112yescomplemented
104C23—224no—
105C23—312no—
106C23—32no—
107C23—38no—
108C23—696no—
109C23—624no—
110C23—1264no—
111C23C23×D318yes—
112C23C23×D311yescharacteristic
113D4—248no—
114D4—696no—
115D4—648no—
116C2×C4—312no—
117C2×C4—36no—
118C2×C4—348no—
119C2×C4D3×D4112yescomplemented
120C2×C4C23×D316yes—
121C2×C3—48no—
122C2×C3C2×#12714yescomplemented
123C2×C3C23×D413yes—
124D3—48no—
125D3C2×#12718yesdirect product factor
126C22—224no—
127C22—312no—
128C22—316no—
129C22—416no—
130C22—624no—
131C22—1264no—
132C22—1216no—
133C22C2×D3×D416yes—
134C22C24×D311yescharacteristic
135C4—312no—
136C4C2×D3×D4112yescomplemented
137C3C22×#12711yescharacteristic, complemented, Sylow
138C2—38no—
139C2—48no—
140C2—128no—
141C2D3×#12714yesdirect product factor
142C2C22×D3×D413yes—
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC2×C3×#127C2
socleC23×C3C24
hypercenterC2×#127D3
hypocenterC3C22×#127
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D3×D4C2semidirect
2. C2×C3×#127C2semidirect
3. C2×#940C2semidirect
4. D3×#127C2direct (N × H)
5. C2×#874C2semidirect
6. C2×C42×D3C2semidirect
9. C22×C3×D4C22semidirect
10. C22×#67C22semidirect
12. C2×D3×D4C22semidirect
13. C22×D12C22semidirect
15. C3×#127C22semidirect
16. C2×C3×C42C22semidirect
17. #940C22semidirect
18. C2×C4×Dic3C22semidirect
19. #874C22semidirect
20. C42×D3C22semidirect
25. C2×#127D3direct (N × H)
33. C2×C3×D4C23semidirect
36. C2×#67C23semidirect
40. C2×D12C23semidirect
41. C2×C4×D3D4semidirect
43. C3×C42C23semidirect
44. C4×Dic3C23semidirect
50. C22×D4C2×D3semidirect
54. #127C2×D3direct (N × H)
57. C2×C42C2×D3semidirect
68. C2×C3×C4C2×D4semidirect
71. C2×Dic3C2×D4semidirect
74. C4×D3C2×D4semidirect
86. C2×D4C22×D3semidirect
92. C42C22×D3semidirect
100. C2×D3#127direct (N × H)
102. C3×C4C22×D4semidirect
103. Dic3C22×D4semidirect
119. C2×C4D3×D4semidirect
122. C2×C3C2×#127semidirect
125. D3C2×#127direct (N × H)
136. C4C2×D3×D4semidirect
137. C3C22×#127semidirect
141. C2D3×#127direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D42
C2×C3×#1272
C2×#9402
D3×#1272
C2×#8742
C2×C42×D32
C22×#1273