Finite Group Databasebeta

← C4⋊#1020 #87504

Subgroups — C4⋊#1020 #87504

Order 384.

435 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 21 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×#1020C212yesmaximal, complemented
2C4×C22⋊A4C211yesmaximal, characteristic, complemented
3#2847—31nomaximal, Sylow
4C2×C22⋊A4C2211yescharacteristic
5#1020—22no—
6C4⋊S4—43nomaximal
7C24×C4D311yescharacteristic, complemented
8C2×#121—33no—
9C2×#120—32no—
10#386—36no—
11#380—33no—
12C22⋊A4D411yescharacteristic, complemented
13C2×S4—46no—
14C4×A4—43no—
15C4×A4—81no—
16C25C2×D311yescharacteristic
17C22×D4—36no—
18C22×D4—31no—
19C23×C4—33no—
20C23×C4—33no—
21C23×C4—61no—
22C23×C4—61no—
23#121—63no—
24#121—63no—
25#121—63no—
26#121—63no—
27#120—66no—
28#120—62no—
29C2×C4⋊C4—33no—
30C2×C22⋊C4—36no—
31C2×C22⋊C4—36no—
32#95—36no—
33C2×A4—43no—
34C2×A4—81no—
35S4—86no—
36D12—161no—
37C24—33no—
38C24—33no—
39C24—32no—
40C24—61no—
41C24—61no—
42C24D1211yescharacteristic, complemented
43C2×D4—63no—
44C2×D4—63no—
45C2×D4—66no—
46C2×D4—66no—
47C2×D4—66no—
48C2×D4—66no—
49C2×D4—66no—
50C2×D4—66no—
51C22×C4—21no—
52C22×C4—31no—
53C22×C4—33no—
54C22×C4—33no—
55C22×C4—33no—
56C22×C4—33no—
57C22×C4—36no—
58C22×C4—66no—
59C22×C4—63no—
60C22×C4—63no—
61C22×C4—61no—
62C22×C4—63no—
63C22×C4S413yescomplemented
64C4⋊C4—63no—
65C4⋊C4—63no—
66C22⋊C4—66no—
67C22⋊C4—66no—
68C22⋊C4—66no—
69C22⋊C4—66no—
70C2×D3—162no—
71A4—43no—
72A4—81no—
73C3×C4—161no—
74C23—21no—
75C23—31no—
76C23—33no—
77C23—33no—
78C23—33no—
79C23—33no—
80C23—33no—
81C23—61no—
82C23—61no—
83C23—63no—
84C23—66no—
85C23—63no—
86C23—63no—
87C23—66no—
88C23—62no—
89C23—66no—
90C23C2×S413yes—
91D4—123no—
92D4—126no—
93D4—126no—
94D4—126no—
95D4—126no—
96D4—121no—
97C2×C4—33no—
98C2×C4—33no—
99C2×C4—33no—
100C2×C4—33no—
101C2×C4—63no—
102C2×C4—66no—
103C2×C4—63no—
104C2×C4—61no—
105C2×C4—61no—
106C2×C4—66no—
107C2×C4—66no—
108C2×C4—66no—
109C2×C3—161no—
110D3—322no—
111C22—21no—
112C22—33no—
113C22—31no—
114C22—33no—
115C22—33no—
116C22—33no—
117C22—33no—
118C22—63no—
119C22—66no—
120C22—63no—
121C22—63no—
122C22—61no—
123C22—61no—
124C22—126no—
125C22—126no—
126C22—122no—
127C22C4⋊S413yescomplemented
128C4—33no—
129C4—61no—
130C4—126no—
131C4#102011yescharacteristic, complemented
132C3—161noSylow
133C2—33no—
134C2—33no—
135C2—61no—
136C2—61no—
137C2—242no—
138C2C2×#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×#1020
commutator, cosocleC2×C22⋊A4C22
FittingC24×C4D3
socleC25C2×D3
hypercenterC4#1020
hypocenterC22⋊A4D4
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×#1020C2semidirect
2. C4×C22⋊A4C2semidirect
7. C24×C4D3semidirect
12. C22⋊A4D4semidirect
42. C24D12semidirect
63. C22×C4S4semidirect
127. C22C4⋊S4semidirect
131. C4#1020semidirect

Maximal subgroups

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

subgroupindex
C2×#10202
C4×C22⋊A42
#28473
C4⋊S44