Finite Group Databasebeta

← C127⋊#1304 #30636634

Subgroups — C127⋊#1304 #30636634

Order 16256.

396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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#22549732C212yesmaximal
2#379×C127C211yesmaximal, characteristic
3C2×C22⋊Dic127—22no—
4C2×C22⋊Dic127—22no—
5C2×C22⋊Dic127C414yescomplemented
6C25×C127C2211yescharacteristic
7C2×C22⋊C4×C127—22no—
8C2×C22⋊C4×C127C412yescomplemented
9C22×Dic127—24no—
10C22⋊Dic127—44no—
11C22⋊Dic127—44no—
12C22⋊Dic127—44no—
13C24×C127—42no—
14C24×C127—44no—
15C24×C127C2×C412yes—
16C24×C127C2×C411yescharacteristic
17C24×C127D412yes—
18C24×C127D411yescharacteristic
19C24×C127Q811yescharacteristic
20C22×C4×C127—22no—
21C22⋊C4×C127—44no—
22C22⋊C4×C127—42no—
23C2×Dic127—44no—
24C2×Dic127—44no—
25C2×Dic127—44no—
26C23×C127—22no—
27C23×C127—24no—
28C23×C127—24no—
29C23×C127—24no—
30C23×C127—24no—
31C23×C127—42no—
32C23×C127—42no—
33C23×C127—42no—
34C23×C127—42no—
35C23×C127—41no—
36C23×C127—42no—
37C23×C127—41no—
38C23×C127—416no—
39C23×C127C4211yescharacteristic
40C23×C127C22⋊C412yes—
41C23×C127C22⋊C411yescharacteristic
42C23×C127C4⋊C412yes—
43C23×C127C4⋊C411yescharacteristic
44C2×C4×C127—44no—
45C2×C4×C127—42no—
46C22×C127—22no—
47C22×C127—22no—
48C22×C127—22no—
49C22×C127—22no—
50C22×C127—21no—
51C22×C127—22no—
52C22×C127—22no—
53C22×C127—22no—
54C22×C127—22no—
55C22×C127—21no—
56C22×C127—44no—
57C22×C127—48no—
58C22×C127—48no—
59C22×C127—44no—
60C22×C127—44no—
61C22×C127#9511yescharacteristic
62C22×C127#9914yes—
63C22×C127#9912yes—
64C4×C127—82no—
65Dic127—84no—
66C2×C127—24no—
67C2×C127—22no—
68C2×C127—41no—
69C2×C127—42no—
70C2×C127—41no—
71C2×C127#34212yes—
72C2×C127#34211yescharacteristic
73#1304—1271nomaximal, Sylow
74C127#130411yescharacteristic, complemented, Sylow
75#379—1272no—
76#379D12711yescharacteristic
77C25C2×D12711yescharacteristic
78C2×C22⋊C4—22no—
79C2×C22⋊C4—1274no—
80C2×C22⋊C4—2542no—
81C2×C22⋊C4—2542no—
82C2×C22⋊C4Dic12712yescomplemented
83C24—44no—
84C24—42no—
85C24C4×D12712yes—
86C24C2×Dic12711yescharacteristic
87C24C22⋊D12712yes—
88C24D50811yescharacteristic
89C24Dic25411yescharacteristic
90C22×C4—22no—
91C22×C4—2544no—
92C22⋊C4—44no—
93C22⋊C4—42no—
94C22⋊C4—5084no—
95C22⋊C4—5084no—
96C22⋊C4—5084no—
97C23—24no—
98C23—24no—
99C23—24no—
100C23—22no—
101C23—24no—
102C23—42no—
103C23—42no—
104C23—42no—
105C23—42no—
106C23—41no—
107C23—42no—
108C23—41no—
109C23—416no—
110C23C4×Dic12711yescharacteristic
111C23(C2×D127)⋊C412yes—
112C23C22⋊Dic12711yescharacteristic
113C23Dic127⋊C412yes—
114C23C4⋊Dic12711yescharacteristic
115C2×C4—44no—
116C2×C4—42no—
117C2×C4—5084no—
118C2×C4—5084no—
119C2×C4—5084no—
120C22—22no—
121C22—22no—
122C22—22no—
123C22—22no—
124C22—22no—
125C22—22no—
126C22—22no—
127C22—21no—
128C22—22no—
129C22—21no—
130C22—48no—
131C22—44no—
132C22—44no—
133C22—48no—
134C22—44no—
135C22C127⋊#9511yescharacteristic
136C22#1686112314yes—
137C22#1686112412yes—
138C4—82no—
139C4—10164no—
140C2—22no—
141C2—24no—
142C2—41no—
143C2—42no—
144C2—41no—
145C2#2254964212yes—
146C2#2254964311yescharacteristic
subgroupG/H
centerC22C127⋊#95
commutatorC23×C127C42
FrattiniC25C2×D127
Fitting#379×C127C2
socleC22×C127#95
prime radical, cosocleC25×C127C22
hypercenter#379D127
hypocenterC127#1304
LCSG ▷ C23×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
5. C2×C22⋊Dic127C4semidirect
8. C2×C22⋊C4×C127C4semidirect
74. C127#1304semidirect
82. C2×C22⋊C4Dic127semidirect

Maximal subgroups

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

subgroupindex
#225497322
#379×C1272
#1304127