Finite Group Databasebeta

← C2×#127×D109 #28376302

Subgroups — C2×#127×D109 #28376302

Order 13952.

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×D109C216yesmaximal, complemented
2C2×#16812696C211yesmaximal, characteristic, complemented
3C2×#16812695C216yesmaximal, complemented
4#127×D109C2116yesmaximal, direct product factor
5C2×C42×D109C211yesmaximal, characteristic, complemented
6C2×#127×C109C211yesmaximal, characteristic, complemented
7C24×D109C2214yes—
8C22×D436C2216yescomplemented
9C22×C22⋊D109C22112yescomplemented
10C2×D4×D109—248no—
11C2×D4×D109C22148yescomplemented
12C22×C4×D109C2213yes—
13#16812696C2218yescomplemented
14#16812695C22148yescomplemented
15C2×C4×Dic109C2213yescomplemented
16C42×D109C2218yescomplemented
17C22×D4×C109C2216yescomplemented
18#127×C109C2218yescomplemented
19C2×C42×C109C2211yescharacteristic, complemented
20C23×D109—248no—
21C23×D109C23116yes—
22C23×D109C2314yes—
23C23×D109C2311yescharacteristic
24C2×D436—224no—
25C2×D436C23124yescomplemented
26C2×C22⋊D109—248no—
27C2×C22⋊D109C23148yescomplemented
28D4×D109—2192no—
29C22×Dic109C2313yes—
30C2×C4×D109D4124yescomplemented
31C2×C4×D109C23112yes—
32C4×Dic109C23112yescomplemented
33C24×C109C2314yes—
34C2×D4×C109—224no—
35C2×D4×C109C23124yescomplemented
36C22×C4×C109C2313yes—
37C42×C109C2314yescomplemented
38C23×C109—224no—
39C23×C109C2418yes—
40C23×C109C2411yescharacteristic
41C22×D109—224no—
42C22×D109—296no—
43C22×D109—464no—
44C22×D109C2×D4112yes—
45C22×D109C2418yes—
46C22×D109C2412yes—
47D4×C109—248no—
48C2×C4×C109C2×D4112yescomplemented
49C2×C4×C109C2416yes—
50C22⋊D109—296no—
51C2×Dic109C2×D4112yescomplemented
52C2×Dic109C2416yes—
53D436—248no—
54C4×D109C2×D4148yescomplemented
55C22×C109—224no—
56C22×C109—416no—
57C22×C109C22×D416yes—
58C22×C109C2511yescharacteristic
59C2×D109—224no—
60C2×D109—416no—
61C2×D109—464no—
62C2×D109#127116yesdirect product factor
63C2×D109C22×D4112yes—
64C4×C109C22×D4112yescomplemented
65Dic109C22×D4112yescomplemented
66C2×C109—48no—
67C2×C109C2×#12714yescomplemented
68C2×C109C23×D413yes—
69D109—48no—
70D109C2×#12718yesdirect product factor
71C22×#127—1091nomaximal, Sylow
72C109C22×#12711yescharacteristic, complemented, Sylow
73C23×D4—1096no—
74C2×#127—1096no—
75C2×#127—10916no—
76C2×#127—1091no—
77C2×#127D10911yescharacteristic, direct product factor
78C22×C42—1091no—
79C25—1094no—
80C22×D4—10912no—
81C22×D4—10948no—
82C22×D4—1096no—
83C22×D4—21848no—
84C22×D4C2×D10916yescomplemented
85C23×C4—1093no—
86#127—10948no—
87#127—1098no—
88#127C2×D10918yesdirect product factor
89C2×C42—1093no—
90C2×C42—1098no—
91C2×C42C2×D10911yescharacteristic, complemented
92C24—1091no—
93C24—10916no—
94C24—1094no—
95C24—21848no—
96C24C22×D10914yes—
97C2×D4—224no—
98C2×D4—10948no—
99C2×D4—10924no—
100C2×D4—218192no—
101C2×D4—21848no—
102C2×D4—21824no—
103C2×D4C22×D109124yescomplemented
104C22×C4—1093no—
105C22×C4—10924no—
106C22×C4—10912no—
107C22×C4C22×D10913yes—
108C42—10912no—
109C42C22×D10914yescomplemented
110C23—224no—
111C23—10912no—
112C23—1092no—
113C23—1098no—
114C23—43664no—
115C23—21896no—
116C23—21824no—
117C23C23×D10918yes—
118C23C23×D10911yescharacteristic
119D4—248no—
120D4—21896no—
121D4—21848no—
122C2×C4—10912no—
123C2×C4—1096no—
124C2×C4—10948no—
125C2×C4D4×D109112yescomplemented
126C2×C4C23×D10916yes—
127C22—224no—
128C22—416no—
129C22—10916no—
130C22—10912no—
131C22—43664no—
132C22—43616no—
133C22—21824no—
134C22C2×D4×D10916yes—
135C22C24×D10911yescharacteristic
136C4—10912no—
137C4C2×D4×D109112yescomplemented
138C2—48no—
139C2—1098no—
140C2—4368no—
141C2#127×D10914yesdirect product factor
142C2C22×D4×D10913yes—
subgroupG/H
centerC23C23×D109
commutator, cosocleC22×C109C25
FrattiniC22C24×D109
FittingC2×#127×C109C2
socleC23×C109C24
hypercenterC2×#127D109
hypocenterC109C22×#127
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D109C2semidirect
2. C2×#16812696C2semidirect
3. C2×#16812695C2semidirect
4. #127×D109C2direct (N × H)
5. C2×C42×D109C2semidirect
6. C2×#127×C109C2semidirect
8. C22×D436C22semidirect
9. C22×C22⋊D109C22semidirect
11. C2×D4×D109C22semidirect
13. #16812696C22semidirect
14. #16812695C22semidirect
15. C2×C4×Dic109C22semidirect
16. C42×D109C22semidirect
17. C22×D4×C109C22semidirect
18. #127×C109C22semidirect
19. C2×C42×C109C22semidirect
25. C2×D436C23semidirect
27. C2×C22⋊D109C23semidirect
30. C2×C4×D109D4semidirect
32. C4×Dic109C23semidirect
35. C2×D4×C109C23semidirect
37. C42×C109C23semidirect
48. C2×C4×C109C2×D4semidirect
51. C2×Dic109C2×D4semidirect
54. C4×D109C2×D4semidirect
62. C2×D109#127direct (N × H)
64. C4×C109C22×D4semidirect
65. Dic109C22×D4semidirect
67. C2×C109C2×#127semidirect
70. D109C2×#127direct (N × H)
72. C109C22×#127semidirect
77. C2×#127D109direct (N × H)
84. C22×D4C2×D109semidirect
88. #127C2×D109direct (N × H)
91. C2×C42C2×D109semidirect
103. C2×D4C22×D109semidirect
109. C42C22×D109semidirect
125. C2×C4D4×D109semidirect
137. C4C2×D4×D109semidirect
141. C2#127×D109direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1092
C2×#168126962
C2×#168126952
#127×D1092
C2×C42×D1092
C2×#127×C1092
C22×#127109