Finite Group Databasebeta

← C2×#127×D271 #46849634

Subgroups — C2×#127×D271 #46849634

Order 34688.

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×D271C216yesmaximal, complemented
2C2×#22576157C211yesmaximal, characteristic, complemented
3C2×#22576156C216yesmaximal, complemented
4#127×D271C2116yesmaximal, direct product factor
5C2×C42×D271C211yesmaximal, characteristic, complemented
6C2×#127×C271C211yesmaximal, characteristic, complemented
7C24×D271C2214yes—
8C22×D1084C2216yescomplemented
9C22×C22⋊D271C22112yescomplemented
10C2×D4×D271—248no—
11C2×D4×D271C22148yescomplemented
12C22×C4×D271C2213yes—
13#22576157C2218yescomplemented
14#22576156C22148yescomplemented
15C2×C4×Dic271C2213yescomplemented
16C42×D271C2218yescomplemented
17C22×D4×C271C2216yescomplemented
18#127×C271C2218yescomplemented
19C2×C42×C271C2211yescharacteristic, complemented
20C23×D271—248no—
21C23×D271C23116yes—
22C23×D271C2314yes—
23C23×D271C2311yescharacteristic
24C2×D1084—224no—
25C2×D1084C23124yescomplemented
26C2×C22⋊D271—248no—
27C2×C22⋊D271C23148yescomplemented
28D4×D271—2192no—
29C22×Dic271C2313yes—
30C2×C4×D271D4124yescomplemented
31C2×C4×D271C23112yes—
32C4×Dic271C23112yescomplemented
33C24×C271C2314yes—
34C2×D4×C271—224no—
35C2×D4×C271C23124yescomplemented
36C22×C4×C271C2313yes—
37C42×C271C2314yescomplemented
38C22×D271—224no—
39C22×D271—296no—
40C22×D271—464no—
41C22×D271C2×D4112yes—
42C22×D271C2418yes—
43C22×D271C2412yes—
44D1084—248no—
45C22⋊D271—296no—
46C2×Dic271C2×D4112yescomplemented
47C2×Dic271C2416yes—
48C4×D271C2×D4148yescomplemented
49C23×C271—224no—
50C23×C271C2418yes—
51C23×C271C2411yescharacteristic
52D4×C271—248no—
53C2×C4×C271C2×D4112yescomplemented
54C2×C4×C271C2416yes—
55C22×C271—224no—
56C22×C271—416no—
57C22×C271C22×D416yes—
58C22×C271C2511yescharacteristic
59C2×D271—224no—
60C2×D271—416no—
61C2×D271—464no—
62C2×D271#127116yesdirect product factor
63C2×D271C22×D4112yes—
64C4×C271C22×D4112yescomplemented
65Dic271C22×D4112yescomplemented
66C2×C271—48no—
67C2×C271C2×#12714yescomplemented
68C2×C271C23×D413yes—
69D271—48no—
70D271C2×#12718yesdirect product factor
71C271C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—2711nomaximal, Sylow
73C23×D4—2716no—
74C2×#127—2716no—
75C2×#127—27116no—
76C2×#127—2711no—
77C2×#127D27111yescharacteristic, direct product factor
78C22×C42—2711no—
79C25—2714no—
80C22×D4—27112no—
81C22×D4—27148no—
82C22×D4—2716no—
83C22×D4—54248no—
84C22×D4C2×D27116yescomplemented
85C23×C4—2713no—
86#127—27148no—
87#127—2718no—
88#127C2×D27118yesdirect product factor
89C2×C42—2713no—
90C2×C42—2718no—
91C2×C42C2×D27111yescharacteristic, complemented
92C24—2711no—
93C24—27116no—
94C24—2714no—
95C24—54248no—
96C24C22×D27114yes—
97C2×D4—224no—
98C2×D4—27148no—
99C2×D4—27124no—
100C2×D4—542192no—
101C2×D4—54248no—
102C2×D4—54224no—
103C2×D4C22×D271124yescomplemented
104C22×C4—2713no—
105C22×C4—27124no—
106C22×C4—27112no—
107C22×C4C22×D27113yes—
108C42—27112no—
109C42C22×D27114yescomplemented
110C23—224no—
111C23—27112no—
112C23—2712no—
113C23—2718no—
114C23—54296no—
115C23—54224no—
116C23—108464no—
117C23C23×D27118yes—
118C23C23×D27111yescharacteristic
119D4—248no—
120D4—54296no—
121D4—54248no—
122C2×C4—27112no—
123C2×C4—2716no—
124C2×C4—27148no—
125C2×C4D4×D271112yescomplemented
126C2×C4C23×D27116yes—
127C22—224no—
128C22—416no—
129C22—27116no—
130C22—27112no—
131C22—54224no—
132C22—108464no—
133C22—108416no—
134C22C2×D4×D27116yes—
135C22C24×D27111yescharacteristic
136C4—27112no—
137C4C2×D4×D271112yescomplemented
138C2—48no—
139C2—2718no—
140C2—10848no—
141C2#127×D27114yesdirect product factor
142C2C22×D4×D27113yes—
subgroupG/H
centerC23C23×D271
commutator, cosocleC22×C271C25
FrattiniC22C24×D271
FittingC2×#127×C271C2
socleC23×C271C24
hypercenterC2×#127D271
hypocenterC271C22×#127
LCSG ▷ C22×C271 ▷ C271
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D271C2semidirect
2. C2×#22576157C2semidirect
3. C2×#22576156C2semidirect
4. #127×D271C2direct (N × H)
5. C2×C42×D271C2semidirect
6. C2×#127×C271C2semidirect
8. C22×D1084C22semidirect
9. C22×C22⋊D271C22semidirect
11. C2×D4×D271C22semidirect
13. #22576157C22semidirect
14. #22576156C22semidirect
15. C2×C4×Dic271C22semidirect
16. C42×D271C22semidirect
17. C22×D4×C271C22semidirect
18. #127×C271C22semidirect
19. C2×C42×C271C22semidirect
25. C2×D1084C23semidirect
27. C2×C22⋊D271C23semidirect
30. C2×C4×D271D4semidirect
32. C4×Dic271C23semidirect
35. C2×D4×C271C23semidirect
37. C42×C271C23semidirect
46. C2×Dic271C2×D4semidirect
48. C4×D271C2×D4semidirect
53. C2×C4×C271C2×D4semidirect
62. C2×D271#127direct (N × H)
64. C4×C271C22×D4semidirect
65. Dic271C22×D4semidirect
67. C2×C271C2×#127semidirect
70. D271C2×#127direct (N × H)
71. C271C22×#127semidirect
77. C2×#127D271direct (N × H)
84. C22×D4C2×D271semidirect
88. #127C2×D271direct (N × H)
91. C2×C42C2×D271semidirect
103. C2×D4C22×D271semidirect
109. C42C22×D271semidirect
125. C2×C4D4×D271semidirect
137. C4C2×D4×D271semidirect
141. C2#127×D271direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2712
C2×#225761572
C2×#225761562
#127×D2712
C2×C42×D2712
C2×#127×C2712
C22×#127271