Finite Group Databasebeta

← C4×#1020 #87503

Subgroups — C4×#1020 #87503

Order 384.

435 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 23 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×#1020C211yesmaximal, characteristic
2C4×C22⋊A4C211yesmaximal, characteristic, complemented
3#5936C211yesmaximal, characteristic, complemented
4C4×#120—31nomaximal, Sylow
5C2×C22⋊A4C2211yescharacteristic
6#1020C412yesdirect product factor
7C4×S4—43nomaximal
8C24×C4D311yescharacteristic, complemented
9C2×#120—31no—
10C2×C4×D4—33no—
11#386—33no—
12#385—33no—
13#379—31no—
14C4×C22⋊C4—33no—
15C22⋊A4C2×C411yescharacteristic, complemented
16C2×S4—43no—
17C4×A4—43no—
18C4×A4—81no—
19SL(2,ℤ/4)—43no—
20C25C2×D311yescharacteristic
21C22×D4—33no—
22C23×C4—33no—
23C23×C4—33no—
24C23×C4—31no—
25C23×C4—61no—
26C23×C4—61no—
27#120—36no—
28#120—32no—
29C4×D4—63no—
30C4×D4—63no—
31C4×D4—63no—
32C4×D4—63no—
33C2×C4⋊C4—33no—
34C2×C22⋊C4—33no—
35C2×C22⋊C4—33no—
36C2×C22⋊C4—33no—
37C2×C22⋊C4—33no—
38C2×C42—33no—
39#95—36no—
40C2×A4—43no—
41C2×A4—81no—
42S4—46no—
43C4×D3—161no—
44C24—33no—
45C24—33no—
46C24—31no—
47C24—61no—
48C24—61no—
49C24C4×D311yescharacteristic, complemented
50C2×D4—36no—
51C2×D4—36no—
52C2×D4—63no—
53C2×D4—63no—
54C2×D4—63no—
55C2×D4—63no—
56C22×C4—21no—
57C22×C4—31no—
58C22×C4—33no—
59C22×C4—33no—
60C22×C4—33no—
61C22×C4—33no—
62C22×C4—33no—
63C22×C4—33no—
64C22×C4—31no—
65C22×C4—66no—
66C22×C4—63no—
67C22×C4—63no—
68C22×C4—63no—
69C22×C4—63no—
70C22×C4—61no—
71C22×C4—63no—
72C22×C4S413yescomplemented
73C4⋊C4—63no—
74C4⋊C4—63no—
75C22⋊C4—36no—
76C22⋊C4—36no—
77C22⋊C4—63no—
78C22⋊C4—63no—
79C22⋊C4—63no—
80C22⋊C4—63no—
81C22⋊C4—63no—
82C22⋊C4—63no—
83C42—63no—
84C42—63no—
85C2×D3—161no—
86A4—43no—
87A4—81no—
88C3×C4—161no—
89Dic3—161no—
90C23—21no—
91C23—31no—
92C23—33no—
93C23—33no—
94C23—33no—
95C23—33no—
96C23—33no—
97C23—32no—
98C23—61no—
99C23—61no—
100C23—63no—
101C23—66no—
102C23—63no—
103C23—63no—
104C23—63no—
105C23—63no—
106C23C2×S413yes—
107D4—66no—
108D4—66no—
109D4—66no—
110D4—66no—
111C2×C4—33no—
112C2×C4—33no—
113C2×C4—33no—
114C2×C4—36no—
115C2×C4—33no—
116C2×C4—63no—
117C2×C4—66no—
118C2×C4—63no—
119C2×C4—63no—
120C2×C4—63no—
121C2×C4—61no—
122C2×C4—61no—
123C2×C4—63no—
124C2×C4—63no—
125C2×C4—66no—
126C2×C4—123no—
127C2×C4—121no—
128C2×C3—161no—
129D3—162no—
130C22—21no—
131C22—33no—
132C22—31no—
133C22—33no—
134C22—33no—
135C22—33no—
136C22—33no—
137C22—63no—
138C22—66no—
139C22—63no—
140C22—63no—
141C22—66no—
142C22—61no—
143C22—61no—
144C22—123no—
145C22—121no—
146C22C4×S413yescomplemented
147C4—33no—
148C4—66no—
149C4—61no—
150C4—123no—
151C4—121no—
152C4#102011yescharacteristic, direct product factor
153C3—161noSylow
154C2—33no—
155C2—33no—
156C2—61no—
157C2—61no—
158C2—122no—
159C2C2×#102011yescharacteristic
subgroupG/H
center, hypercenterC4#1020
commutator, hypocenterC22⋊A4C2×C4
FrattiniC2C2×#1020
FittingC24×C4D3
socleC25C2×D3
prime radicalC2×#1020C2
cosocleC2×C22⋊A4C22
LCSG ▷ C22⋊A4
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊A4C2semidirect
3. #5936C2semidirect
6. #1020C4direct (N × H)
8. C24×C4D3semidirect
15. C22⋊A4C2×C4semidirect
49. C24C4×D3semidirect
72. C22×C4S4semidirect
146. C22C4×S4semidirect
152. C4#1020direct (N × H)

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
#59362
C4×#1203
C4×S44