Finite Group Databasebeta

← C2×#127×D269 #46824155

Subgroups — C2×#127×D269 #46824155

Order 34432.

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×D4×D269C216yesmaximal, complemented
2C2×#22575450C211yesmaximal, characteristic, complemented
3C2×#22575449C216yesmaximal, complemented
4#127×D269C2116yesmaximal, direct product factor
5C2×C42×D269C211yesmaximal, characteristic, complemented
6C2×#127×C269C211yesmaximal, characteristic, complemented
7C24×D269C2214yes—
8C22×D1076C2216yescomplemented
9C22×C22⋊D269C22112yescomplemented
10C2×D4×D269—248no—
11C2×D4×D269C22148yescomplemented
12C22×C4×D269C2213yes—
13#22575450C2218yescomplemented
14#22575449C22148yescomplemented
15C2×C4×Dic269C2213yescomplemented
16C42×D269C2218yescomplemented
17C22×D4×C269C2216yescomplemented
18#127×C269C2218yescomplemented
19C2×C42×C269C2211yescharacteristic, complemented
20C23×D269—248no—
21C23×D269C23116yes—
22C23×D269C2314yes—
23C23×D269C2311yescharacteristic
24C2×D1076—224no—
25C2×D1076C23124yescomplemented
26C2×C22⋊D269—248no—
27C2×C22⋊D269C23148yescomplemented
28D4×D269—2192no—
29C22×Dic269C2313yes—
30C2×C4×D269D4124yescomplemented
31C2×C4×D269C23112yes—
32C4×Dic269C23112yescomplemented
33C24×C269C2314yes—
34C2×D4×C269—224no—
35C2×D4×C269C23124yescomplemented
36C22×C4×C269C2313yes—
37C42×C269C2314yescomplemented
38C22×D269—224no—
39C22×D269—296no—
40C22×D269—464no—
41C22×D269C2×D4112yes—
42C22×D269C2418yes—
43C22×D269C2412yes—
44D1076—248no—
45C22⋊D269—296no—
46C2×Dic269C2×D4112yescomplemented
47C2×Dic269C2416yes—
48C4×D269C2×D4148yescomplemented
49C23×C269—224no—
50C23×C269C2418yes—
51C23×C269C2411yescharacteristic
52D4×C269—248no—
53C2×C4×C269C2×D4112yescomplemented
54C2×C4×C269C2416yes—
55C22×C269—224no—
56C22×C269—416no—
57C22×C269C22×D416yes—
58C22×C269C2511yescharacteristic
59C2×D269—224no—
60C2×D269—416no—
61C2×D269—464no—
62C2×D269#127116yesdirect product factor
63C2×D269C22×D4112yes—
64C4×C269C22×D4112yescomplemented
65Dic269C22×D4112yescomplemented
66C2×C269—48no—
67C2×C269C2×#12714yescomplemented
68C2×C269C23×D413yes—
69D269—48no—
70D269C2×#12718yesdirect product factor
71C269C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—2691nomaximal, Sylow
73C23×D4—2696no—
74C2×#127—2696no—
75C2×#127—26916no—
76C2×#127—2691no—
77C2×#127D26911yescharacteristic, direct product factor
78C22×C42—2691no—
79C25—2694no—
80C22×D4—26912no—
81C22×D4—26948no—
82C22×D4—2696no—
83C22×D4—53848no—
84C22×D4C2×D26916yescomplemented
85C23×C4—2693no—
86#127—26948no—
87#127—2698no—
88#127C2×D26918yesdirect product factor
89C2×C42—2693no—
90C2×C42—2698no—
91C2×C42C2×D26911yescharacteristic, complemented
92C24—2691no—
93C24—26916no—
94C24—2694no—
95C24—53848no—
96C24C22×D26914yes—
97C2×D4—224no—
98C2×D4—26948no—
99C2×D4—26924no—
100C2×D4—538192no—
101C2×D4—53848no—
102C2×D4—53824no—
103C2×D4C22×D269124yescomplemented
104C22×C4—2693no—
105C22×C4—26924no—
106C22×C4—26912no—
107C22×C4C22×D26913yes—
108C42—26912no—
109C42C22×D26914yescomplemented
110C23—224no—
111C23—26912no—
112C23—2692no—
113C23—2698no—
114C23—53896no—
115C23—53824no—
116C23—107664no—
117C23C23×D26918yes—
118C23C23×D26911yescharacteristic
119D4—248no—
120D4—53896no—
121D4—53848no—
122C2×C4—26912no—
123C2×C4—2696no—
124C2×C4—26948no—
125C2×C4D4×D269112yescomplemented
126C2×C4C23×D26916yes—
127C22—224no—
128C22—416no—
129C22—26916no—
130C22—26912no—
131C22—53824no—
132C22—107664no—
133C22—107616no—
134C22C2×D4×D26916yes—
135C22C24×D26911yescharacteristic
136C4—26912no—
137C4C2×D4×D269112yescomplemented
138C2—48no—
139C2—2698no—
140C2—10768no—
141C2#127×D26914yesdirect product factor
142C2C22×D4×D26913yes—
subgroupG/H
centerC23C23×D269
commutator, cosocleC22×C269C25
FrattiniC22C24×D269
FittingC2×#127×C269C2
socleC23×C269C24
hypercenterC2×#127D269
hypocenterC269C22×#127
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D269C2semidirect
2. C2×#22575450C2semidirect
3. C2×#22575449C2semidirect
4. #127×D269C2direct (N × H)
5. C2×C42×D269C2semidirect
6. C2×#127×C269C2semidirect
8. C22×D1076C22semidirect
9. C22×C22⋊D269C22semidirect
11. C2×D4×D269C22semidirect
13. #22575450C22semidirect
14. #22575449C22semidirect
15. C2×C4×Dic269C22semidirect
16. C42×D269C22semidirect
17. C22×D4×C269C22semidirect
18. #127×C269C22semidirect
19. C2×C42×C269C22semidirect
25. C2×D1076C23semidirect
27. C2×C22⋊D269C23semidirect
30. C2×C4×D269D4semidirect
32. C4×Dic269C23semidirect
35. C2×D4×C269C23semidirect
37. C42×C269C23semidirect
46. C2×Dic269C2×D4semidirect
48. C4×D269C2×D4semidirect
53. C2×C4×C269C2×D4semidirect
62. C2×D269#127direct (N × H)
64. C4×C269C22×D4semidirect
65. Dic269C22×D4semidirect
67. C2×C269C2×#127semidirect
70. D269C2×#127direct (N × H)
71. C269C22×#127semidirect
77. C2×#127D269direct (N × H)
84. C22×D4C2×D269semidirect
88. #127C2×D269direct (N × H)
91. C2×C42C2×D269semidirect
103. C2×D4C22×D269semidirect
109. C42C22×D269semidirect
125. C2×C4D4×D269semidirect
137. C4C2×D4×D269semidirect
141. C2#127×D269direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2692
C2×#225754502
C2×#225754492
#127×D2692
C2×C42×D2692
C2×#127×C2692
C22×#127269