Finite Group Databasebeta

← C127×#3025 #30635977

Subgroups — C127×#3025 #30635977

Order 16256.

766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 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
1#585×C127C211yesmaximal, characteristic, complemented
2#525×C127C213yesmaximal, complemented
3#458×C127C214yesmaximal, complemented
4B(4,𝔽2)×C127C214yesmaximal, complemented
5#410×C127C213yesmaximal, complemented
62−1+4×C127—23no—
7H(5,𝔽2)×C127—23no—
8H(5,𝔽2)×C127C2214yes—
9C2×#41×C127—26no—
10C2×#41×C127C2213yes—
11C23×C4×C127C2211yescharacteristic, complemented
12#123×C127C2216yescomplemented
13C22⋊Q8×C127—23no—
14#121×C127—23no—
15#120×C127C2216yescomplemented
16C4×D4×C127—26no—
17#117×C127C2213yescomplemented
18#99×C127C22112yescomplemented
19C24×C127C2311yescharacteristic
20#41×C127—24no—
21#41×C127—212no—
22#41×C127—26no—
23#41×C127—212no—
24#41×C127—26no—
25C2×Q8×C127—26no—
26C2×Q8×C127D413yescomplemented
27C2×D4×C127—26no—
28C2×D4×C127—212no—
29C2×D4×C127—26no—
30C2×D4×C127D413yescomplemented
31C2×D4×C127C2316yes—
32C22×C4×C127—24no—
33C22×C4×C127—23no—
34C22×C4×C127—23no—
35C22×C4×C127D416yescomplemented
36C22×C4×C127C2311yescharacteristic
37C22×C4×C127C2311yescharacteristic
38C4⋊C4×C127—23no—
39C4⋊C4×C127—26no—
40C22⋊C4×C127—26no—
41C22⋊C4×C127—26no—
42C22⋊C4×C127C2316yes—
43C42×C127—23no—
44C23×C127—24no—
45C23×C127—23no—
46C23×C127—42no—
47C23×C127C2×D416yes—
48C23×C127C2411yescharacteristic
49Q8×C127—24no—
50Q8×C127—26no—
51D4×C127—212no—
52D4×C127—212no—
53D4×C127—26no—
54D4×C127—412no—
55C2×C4×C127—212no—
56C2×C4×C127—26no—
57C2×C4×C127—26no—
58C2×C4×C127—26no—
59C2×C4×C127—23no—
60C2×C4×C127—43no—
61C2×C4×C127—41no—
62C2×C4×C127C2×D416yes—
63C2×C4×C127C2×D413yes—
64C2×C4×C127C2×D413yes—
65C22×C127—26no—
66C22×C127—26no—
67C22×C127—41no—
68C22×C127—46no—
69C22×C127—43no—
70C22×C127—41no—
71C22×C127—84no—
72C22×C127C22×D413yes—
73C4×C127—26no—
74C4×C127—46no—
75C4×C127—41no—
76C4×C127#12013yes—
77C4×C127#12011yescharacteristic
78C2×C127—23no—
79C2×C127—42no—
80C2×C127—46no—
81C2×C127C2×#12011yescharacteristic
82#3025C12711yesmaximal, characteristic, direct product factor, Sylow
83C127#302511yescharacteristic, direct product factor, Sylow
84#585C2×C12711yescharacteristic, complemented
85#525C2×C12713yescomplemented
86#458C2×C12714yescomplemented
87B(4,𝔽2)C2×C12714yescomplemented
88#410C2×C12713yescomplemented
892−1+4—23no—
90H(5,𝔽2)—23no—
91H(5,𝔽2)C22×C12714yes—
92C2×#41—26no—
93C2×#41C22×C12713yes—
94C23×C4C22×C12711yescharacteristic, complemented
95#123C22×C12716yescomplemented
96C22⋊Q8—23no—
97#121—23no—
98#120C22×C12716yescomplemented
99C4×D4—26no—
100#117C22×C12713yescomplemented
101#99C22×C127112yescomplemented
102C24C23×C12711yescharacteristic
103#41—24no—
104#41—212no—
105#41—26no—
106#41—212no—
107#41—26no—
108C2×Q8—26no—
109C2×Q8D4×C12713yescomplemented
110C2×D4—26no—
111C2×D4—212no—
112C2×D4—26no—
113C2×D4D4×C12713yescomplemented
114C2×D4C23×C12716yes—
115C22×C4—24no—
116C22×C4—23no—
117C22×C4—23no—
118C22×C4D4×C12716yescomplemented
119C22×C4C23×C12711yescharacteristic
120C22×C4C23×C12711yescharacteristic
121C4⋊C4—23no—
122C4⋊C4—26no—
123C22⋊C4—26no—
124C22⋊C4—26no—
125C22⋊C4C23×C12716yes—
126C42—23no—
127C23—24no—
128C23—23no—
129C23—42no—
130C23C2×D4×C12716yes—
131C23C24×C12711yescharacteristic
132Q8—24no—
133Q8—26no—
134D4—212no—
135D4—212no—
136D4—26no—
137D4—412no—
138C2×C4—212no—
139C2×C4—26no—
140C2×C4—26no—
141C2×C4—26no—
142C2×C4—23no—
143C2×C4—41no—
144C2×C4—43no—
145C2×C4C2×D4×C12716yes—
146C2×C4C2×D4×C12713yes—
147C2×C4C2×D4×C12713yes—
148C22—26no—
149C22—26no—
150C22—41no—
151C22—46no—
152C22—43no—
153C22—41no—
154C22—84no—
155C22C22×D4×C12713yes—
156C4—26no—
157C4—46no—
158C4—41no—
159C4#120×C12711yescharacteristic
160C4#120×C12713yes—
161C2—23no—
162C2—42no—
163C2—46no—
164C2C2×#120×C12711yescharacteristic
subgroupG/H
centerC4×C127#120
commutator, Frattini, cosocleC23C24×C127
socleC2×C127C2×#120
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #585×C127C2semidirect
2. #525×C127C2semidirect
3. #458×C127C2semidirect
4. B(4,𝔽2)×C127C2semidirect
5. #410×C127C2semidirect
11. C23×C4×C127C22semidirect
12. #123×C127C22semidirect
15. #120×C127C22semidirect
17. #117×C127C22semidirect
18. #99×C127C22semidirect
26. C2×Q8×C127D4semidirect
30. C2×D4×C127D4semidirect
35. C22×C4×C127D4semidirect
82. #3025C127direct (N × H)
83. C127#3025direct (N × H)
84. #585C2×C127semidirect
85. #525C2×C127semidirect
86. #458C2×C127semidirect
87. B(4,𝔽2)C2×C127semidirect
88. #410C2×C127semidirect
94. C23×C4C22×C127semidirect
95. #123C22×C127semidirect
98. #120C22×C127semidirect
100. #117C22×C127semidirect
101. #99C22×C127semidirect
109. C2×Q8D4×C127semidirect
113. C2×D4D4×C127semidirect
118. C22×C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
#585×C1272
#525×C1272
#458×C1272
B(4,𝔽2)×C1272
#410×C1272
#3025127