Finite Group Databasebeta

← C2×#127×D29 #16832762

Subgroups — C2×#127×D29 #16832762

Order 3712.

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×D29C216yesmaximal, complemented
2C2×#11745236C211yesmaximal, characteristic, complemented
3C2×#11745302C216yesmaximal, complemented
4#127×D29C2116yesmaximal, direct product factor
5C2×C42×D29C211yesmaximal, characteristic, complemented
6C2×C29×#127C211yesmaximal, characteristic, complemented
7C24×D29C2214yes—
8C22×D4×C29C2216yescomplemented
9C22×C22⋊D29C22112yescomplemented
10C2×D4×D29—248no—
11C2×D4×D29C22148yescomplemented
12C22×D116C2216yescomplemented
13C22×C4×D29C2213yes—
14C29×#127C2218yescomplemented
15C2×C42×C29C2211yescharacteristic, complemented
16#11745302C22148yescomplemented
17C2×C4×Dic29C2213yescomplemented
18#11745236C2218yescomplemented
19C42×D29C2218yescomplemented
20C24×C29C2314yes—
21C23×D29—248no—
22C23×D29C2314yes—
23C23×D29C23116yes—
24C23×D29C2311yescharacteristic
25C2×D4×C29—224no—
26C2×D4×C29C23124yescomplemented
27C22×C4×C29C2313yes—
28C2×C22⋊D29—248no—
29C2×C22⋊D29C23148yescomplemented
30C22×Dic29C2313yes—
31D4×D29—2192no—
32C2×D116—224no—
33C2×D116C23124yescomplemented
34C2×C4×D29D4124yescomplemented
35C2×C4×D29C23112yes—
36C42×C29C2314yescomplemented
37C4×Dic29C23112yescomplemented
38C23×C29—224no—
39C23×C29C2418yes—
40C23×C29C2411yescharacteristic
41C22×D29—224no—
42C22×D29—296no—
43C22×D29—464no—
44C22×D29C2×D4112yes—
45C22×D29C2418yes—
46C22×D29C2412yes—
47D4×C29—248no—
48C2×C4×C29C2×D4112yescomplemented
49C2×C4×C29C2416yes—
50C22⋊D29—296no—
51C2×Dic29C2×D4112yescomplemented
52C2×Dic29C2416yes—
53D116—248no—
54C4×D29C2×D4148yescomplemented
55C22×#127—291nomaximal, Sylow
56C22×C29—224no—
57C22×C29—416no—
58C22×C29C22×D416yes—
59C22×C29C2511yescharacteristic
60C2×D29—224no—
61C2×D29—416no—
62C2×D29—464no—
63C2×D29#127116yesdirect product factor
64C2×D29C22×D4112yes—
65C4×C29C22×D4112yescomplemented
66Dic29C22×D4112yescomplemented
67C23×D4—296no—
68C2×#127—296no—
69C2×#127—2916no—
70C2×#127—291no—
71C2×#127D2911yescharacteristic, direct product factor
72C22×C42—291no—
73C2×C29—48no—
74C2×C29C2×#12714yescomplemented
75C2×C29C23×D413yes—
76D29—48no—
77D29C2×#12718yesdirect product factor
78C25—294no—
79C22×D4—2912no—
80C22×D4—2948no—
81C22×D4—296no—
82C22×D4—5848no—
83C22×D4C2×D2916yescomplemented
84C23×C4—293no—
85#127—2948no—
86#127—298no—
87#127C2×D2918yesdirect product factor
88C2×C42—293no—
89C2×C42—298no—
90C2×C42C2×D2911yescharacteristic, complemented
91C29C22×#12711yescharacteristic, complemented, Sylow
92C24—291no—
93C24—2916no—
94C24—294no—
95C24—5848no—
96C24C22×D2914yes—
97C2×D4—224no—
98C2×D4—2948no—
99C2×D4—2924no—
100C2×D4—58192no—
101C2×D4—5848no—
102C2×D4—5824no—
103C2×D4C22×D29124yescomplemented
104C22×C4—293no—
105C22×C4—2924no—
106C22×C4—2912no—
107C22×C4C22×D2913yes—
108C42—2912no—
109C42C22×D2914yescomplemented
110C23—224no—
111C23—2912no—
112C23—292no—
113C23—298no—
114C23—5896no—
115C23—5824no—
116C23—11664no—
117C23C23×D2918yes—
118C23C23×D2911yescharacteristic
119D4—248no—
120D4—5896no—
121D4—5848no—
122C2×C4—2912no—
123C2×C4—296no—
124C2×C4—2948no—
125C2×C4D4×D29112yescomplemented
126C2×C4C23×D2916yes—
127C22—224no—
128C22—416no—
129C22—2916no—
130C22—2912no—
131C22—5824no—
132C22—11664no—
133C22—11616no—
134C22C2×D4×D2916yes—
135C22C24×D2911yescharacteristic
136C4—2912no—
137C4C2×D4×D29112yescomplemented
138C2—48no—
139C2—298no—
140C2—1168no—
141C2#127×D2914yesdirect product factor
142C2C22×D4×D2913yes—
subgroupG/H
centerC23C23×D29
commutator, cosocleC22×C29C25
FrattiniC22C24×D29
FittingC2×C29×#127C2
socleC23×C29C24
hypercenterC2×#127D29
hypocenterC29C22×#127
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×#11745236C2semidirect
3. C2×#11745302C2semidirect
4. #127×D29C2direct (N × H)
5. C2×C42×D29C2semidirect
6. C2×C29×#127C2semidirect
8. C22×D4×C29C22semidirect
9. C22×C22⋊D29C22semidirect
11. C2×D4×D29C22semidirect
12. C22×D116C22semidirect
14. C29×#127C22semidirect
15. C2×C42×C29C22semidirect
16. #11745302C22semidirect
17. C2×C4×Dic29C22semidirect
18. #11745236C22semidirect
19. C42×D29C22semidirect
26. C2×D4×C29C23semidirect
29. C2×C22⋊D29C23semidirect
33. C2×D116C23semidirect
34. C2×C4×D29D4semidirect
36. C42×C29C23semidirect
37. C4×Dic29C23semidirect
48. C2×C4×C29C2×D4semidirect
51. C2×Dic29C2×D4semidirect
54. C4×D29C2×D4semidirect
63. C2×D29#127direct (N × H)
65. C4×C29C22×D4semidirect
66. Dic29C22×D4semidirect
71. C2×#127D29direct (N × H)
74. C2×C29C2×#127semidirect
77. D29C2×#127direct (N × H)
83. C22×D4C2×D29semidirect
87. #127C2×D29direct (N × H)
90. C2×C42C2×D29semidirect
91. C29C22×#127semidirect
103. C2×D4C22×D29semidirect
109. C42C22×D29semidirect
125. C2×C4D4×D29semidirect
137. C4C2×D4×D29semidirect
141. C2#127×D29direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D292
C2×#117452362
C2×#117453022
#127×D292
C2×C42×D292
C2×C29×#1272
C22×#12729