Finite Group Databasebeta

← C127×#2312 #30635264

Subgroups — C127×#2312 #30635264

Order 16256.

672 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 280 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×C22⋊C4×C127C211yesmaximal, characteristic
2#388×C127C218yesmaximal, complemented
3#380×C127C212yesmaximal, complemented
4#379×C127C212yesmaximal
5C4×C22⋊C4×C127C212yesmaximal, complemented
6C25×C127C2211yescharacteristic
7C23×C4×C127C2211yescharacteristic
8C23×C4×C127C2211yescharacteristic
9C2×C4⋊C4×C127C2214yescomplemented
10C2×C22⋊C4×C127C418yescomplemented
11C2×C22⋊C4×C127C2214yes—
12C2×C22⋊C4×C127C2214yes—
13C2×C22⋊C4×C127C2214yes—
14C2×C22⋊C4×C127C2214yes—
15C2×C42×C127C2214yescomplemented
16#95×C127C2214yescomplemented
17#95×C127C2214yescomplemented
18C24×C127—24no—
19C24×C127—42no—
20C24×C127—42no—
21C24×C127C2×C414yes—
22C24×C127C2312yes—
23C24×C127C2311yescharacteristic
24C22×C4×C127—42no—
25C22×C4×C127—42no—
26C22×C4×C127C2×C414yes—
27C22×C4×C127C2×C414yes—
28C22×C4×C127C2318yes—
29C22×C4×C127C2312yes—
30C22×C4×C127C2312yes—
31C4⋊C4×C127—44no—
32C22⋊C4×C127—28no—
33C22⋊C4×C127—44no—
34C22⋊C4×C127—44no—
35C22⋊C4×C127C2×C4116yes—
36C42×C127—44no—
37C23×C127—22no—
38C23×C127—22no—
39C23×C127—28no—
40C23×C127—24no—
41C23×C127—24no—
42C23×C127—24no—
43C23×C127—44no—
44C23×C127—44no—
45C23×C127—416no—
46C23×C127C22×C414yes—
47C23×C127C22×C412yes—
48C23×C127#4114yes—
49C23×C127C2411yescharacteristic
50C2×C4×C127—24no—
51C2×C4×C127—24no—
52C2×C4×C127—28no—
53C2×C4×C127—28no—
54C2×C4×C127—28no—
55C2×C4×C127—44no—
56C2×C4×C127—44no—
57C2×C4×C127C22×C414yes—
58C2×C4×C127C22×C414yes—
59C22×C127—22no—
60C22×C127—22no—
61C22×C127—28no—
62C22×C127—24no—
63C22×C127—24no—
64C22×C127—24no—
65C22×C127—416no—
66C22×C127—48no—
67C22×C127#11714yes—
68C22×C127C23×C411yescharacteristic
69C22×C127C2×#4112yes—
70C22×C127H(5,𝔽2)12yes—
71C22×C127H(5,𝔽2)12yes—
72C4×C127—24no—
73C4×C127—24no—
74C4×C127—48no—
75C2×C127—24no—
76C2×C127—44no—
77C2×C127C2×#11711yescharacteristic
78C2×C127#51811yescharacteristic
79C2×C127#51811yescharacteristic
80C2×C127#53814yes—
81#2312C12711yesmaximal, characteristic, direct product factor, Sylow
82C127#231211yescharacteristic, direct product factor, Sylow
83C22×C22⋊C4C2×C12711yescharacteristic
84#388C2×C12718yescomplemented
85#380C2×C12712yescomplemented
86#379C2×C12712yes—
87C4×C22⋊C4C2×C12712yescomplemented
88C25C22×C12711yescharacteristic
89C23×C4C22×C12711yescharacteristic
90C23×C4C22×C12711yescharacteristic
91C2×C4⋊C4C22×C12714yescomplemented
92C2×C22⋊C4C4×C12718yescomplemented
93C2×C22⋊C4C22×C12714yes—
94C2×C22⋊C4C22×C12714yes—
95C2×C22⋊C4C22×C12714yes—
96C2×C22⋊C4C22×C12714yes—
97C2×C42C22×C12714yescomplemented
98#95C22×C12714yescomplemented
99#95C22×C12714yescomplemented
100C24—24no—
101C24—42no—
102C24—42no—
103C24C2×C4×C12714yes—
104C24C23×C12712yes—
105C24C23×C12711yescharacteristic
106C22×C4—42no—
107C22×C4—42no—
108C22×C4C2×C4×C12714yes—
109C22×C4C2×C4×C12714yes—
110C22×C4C23×C12718yes—
111C22×C4C23×C12712yes—
112C22×C4C23×C12712yes—
113C4⋊C4—44no—
114C22⋊C4—28no—
115C22⋊C4—44no—
116C22⋊C4—44no—
117C22⋊C4C2×C4×C127116yes—
118C42—44no—
119C23—22no—
120C23—22no—
121C23—28no—
122C23—24no—
123C23—24no—
124C23—24no—
125C23—44no—
126C23—44no—
127C23—416no—
128C23C22×C4×C12714yes—
129C23C22×C4×C12712yes—
130C23#41×C12714yes—
131C23C24×C12711yescharacteristic
132C2×C4—24no—
133C2×C4—24no—
134C2×C4—28no—
135C2×C4—28no—
136C2×C4—28no—
137C2×C4—44no—
138C2×C4—44no—
139C2×C4C22×C4×C12714yes—
140C2×C4C22×C4×C12714yes—
141C22—22no—
142C22—22no—
143C22—28no—
144C22—24no—
145C22—24no—
146C22—24no—
147C22—416no—
148C22—48no—
149C22#117×C12714yes—
150C22C23×C4×C12711yescharacteristic
151C22C2×#41×C12712yes—
152C22H(5,𝔽2)×C12712yes—
153C22H(5,𝔽2)×C12712yes—
154C4—24no—
155C4—24no—
156C4—48no—
157C2—24no—
158C2—44no—
159C2C2×#117×C12711yescharacteristic
160C2#518×C12711yescharacteristic
161C2#518×C12711yescharacteristic
162C2#538×C12714yes—
subgroupG/H
center, socleC23×C127C24
commutatorC22C23×C4×C127
Frattini, cosocleC23C24×C127
prime radicalC25×C127C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #388×C127C2semidirect
3. #380×C127C2semidirect
5. C4×C22⋊C4×C127C2semidirect
9. C2×C4⋊C4×C127C22semidirect
10. C2×C22⋊C4×C127C4semidirect
15. C2×C42×C127C22semidirect
16. #95×C127C22semidirect
17. #95×C127C22semidirect
81. #2312C127direct (N × H)
82. C127#2312direct (N × H)
84. #388C2×C127semidirect
85. #380C2×C127semidirect
87. C4×C22⋊C4C2×C127semidirect
91. C2×C4⋊C4C22×C127semidirect
92. C2×C22⋊C4C4×C127semidirect
97. C2×C42C22×C127semidirect
98. #95C22×C127semidirect
99. #95C22×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×C1272
#388×C1272
#380×C1272
#379×C1272
C4×C22⋊C4×C1272
#2312127