Finite Group Databasebeta

← C4×#16861126 #30638522

Subgroups — C4×#16861126 #30638522

Order 16256.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C2×#16861126C212yesmaximal
2C4×#14523232C212yesmaximal, complemented
3#22549645C212yesmaximal, complemented
4C2×C4×D4×C127C211yesmaximal, characteristic
5C2×#14523232C2214yes—
6#16861126C418yesdirect product factor
7#16861120—22no—
8C4×C127⋊C8—22no—
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127C412yes—
11C4×D4×C127—22no—
12C4×D4×C127—22no—
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C22⋊C4×C127C412yes—
15C2×C42×C127C2211yescharacteristic
16#14523232—24no—
17#14523232C2×C418yescomplemented
18C2×C127⋊C8—24no—
19C24×C127C2×C412yes—
20C2×D4×C127—22no—
21C2×D4×C127—22no—
22C2×D4×C127C2×C414yes—
23C22×C4×C127—22no—
24C22×C4×C127—22no—
25C22×C4×C127—44no—
26C22×C4×C127C2×C411yescharacteristic
27C22×C4×C127C2×C412yes—
28C22×C4×C127C2×C411yescharacteristic
29C22×C4×C127C2311yescharacteristic
30C4⋊C4×C127—22no—
31C22⋊C4×C127—24no—
32C42×C127D412yes—
33C42×C127D412yes—
34C127⋊C8—28no—
35C23×C127—22no—
36C23×C127—22no—
37C23×C127—42no—
38C23×C127—42no—
39C23×C127C4214yes—
40C23×C127C22×C411yescharacteristic
41D4×C127—28no—
42C2×C4×C127—22no—
43C2×C4×C127—22no—
44C2×C4×C127—41no—
45C2×C4×C127—44no—
46C2×C4×C127—44no—
47C2×C4×C127—42no—
48C2×C4×C127C22⋊C412yes—
49C2×C4×C127C22⋊C411yescharacteristic
50C2×C4×C127C22⋊C411yescharacteristic
51C2×C4×C127C22×C412yes—
52C2×C4×C127C2×D412yes—
53C2×C4×C127#4112yes—
54C22×C127—21no—
55C22×C127—21no—
56C22×C127—24no—
57C22×C127—44no—
58C22×C127—44no—
59C22×C127—42no—
60C22×C127—42no—
61C22×C127C2×C4211yescharacteristic
62C22×C127C2×C22⋊C411yescharacteristic
63C22×C127#11711yescharacteristic
64C4×C127—21no—
65C4×C127—22no—
66C4×C127—42no—
67C4×C127#10012yescomplemented
68C4×C127C4×D414yes—
69C2×C127—21no—
70C2×C127—21no—
71C2×C127—44no—
72C2×C127C4×C22⋊C411yescharacteristic
73C2×C127C2×#10011yescharacteristic
74C2×C127#41311yescharacteristic
75C4×#100—1271nomaximal, Sylow
76C127C4×#10011yescharacteristic, complemented, Sylow
77C2×C4×D4D12711yescharacteristic
78C2×#100—1272no—
79C4×M16—1272no—
80#343—1272no—
81C22×D4C2×D12711yescharacteristic
82C23×C4Dic12712yes—
83C2×M16—1274no—
84C4×D4—22no—
85C4×D4—22no—
86C2×C4⋊C4C2×D12711yescharacteristic
87C2×C22⋊C4Dic12712yes—
88C2×C42C2×D12711yescharacteristic
89#100—1278no—
90#97—2542no—
91C4×C8—2542no—
92C24C2×Dic12712yes—
93C2×D4—22no—
94C2×D4—22no—
95C2×D4C4×D12714yes—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—44no—
99C22×C4C2×Dic12711yescharacteristic
100C22×C4C2×Dic12712yes—
101C22×C4C2×Dic12711yescharacteristic
102C22×C4C22×D12711yescharacteristic
103M16—1278no—
104M16—2544no—
105C2×C8—2544no—
106C4⋊C4—22no—
107C22⋊C4—24no—
108C42C22⋊D12712yes—
109C42C22⋊D12712yes—
110C23—22no—
111C23—22no—
112C23—42no—
113C23—42no—
114C23C4×Dic12714yes—
115C23C22×Dic12711yescharacteristic
116D4—28no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—41no—
120C2×C4—44no—
121C2×C4—44no—
122C2×C4—42no—
123C2×C4C22⋊Dic12712yes—
124C2×C4C22⋊Dic12711yescharacteristic
125C2×C4C22⋊Dic12711yescharacteristic
126C2×C4C2×C4×D12712yes—
127C2×C4C2×C22⋊D12712yes—
128C2×C4#1452324812yes—
129C8—2548no—
130C22—21no—
131C22—21no—
132C22—24no—
133C22—44no—
134C22—44no—
135C22—42no—
136C22—42no—
137C22C2×C4×Dic12711yescharacteristic
138C22C2×C22⋊Dic12711yescharacteristic
139C22#1686116811yescharacteristic
140C4—21no—
141C4—22no—
142C4—42no—
143C4#1686112612yesdirect product factor
144C4C4×C22⋊D12714yes—
145C2—21no—
146C2—21no—
147C2—44no—
148C2C4×C22⋊Dic12711yescharacteristic
149C2C2×#1686112611yescharacteristic
150C2#2254986011yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic127
commutatorC22×C127C2×C42
FrattiniC22×C4C22×D127
FittingC2×C4×D4×C127C2
socleC22×C127C2×C22⋊C4
prime radicalC22×D4×C127C22
cosocleC22×C4×C127C23
hypercenterC2×C4×D4D127
hypocenterC127C4×#100
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#14523232C2semidirect
3. #22549645C2semidirect
6. #16861126C4direct (N × H)
17. #14523232C2×C4semidirect
67. C4×C127#100semidirect
76. C127C4×#100semidirect
143. C4#16861126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611262
C4×#145232322
#225496452
C2×C4×D4×C1272
C4×#100127