Finite Group Databasebeta

← A4×C4⋊Q8 #85593

Subgroups — A4×C4⋊Q8 #85593

Order 384.

384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 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×Q8×A4C212yesmaximal
2A4×C4⋊C4C214yesmaximal
3C42×A4C211yesmaximal, characteristic
4C22×C4⋊Q8C311yesmaximal, characteristic, complemented, Sylow
5Q8×A4—24no—
6C2×C4×A4C2214yes—
7C2×C4×A4C2211yescharacteristic
8C2×C4×A4C2212yes—
9C3×C4⋊Q8—41nomaximal
10C23×Q8C2×C312yes—
11C2×C4⋊Q8—31no—
12C2×C4⋊Q8—31no—
13C2×C4⋊Q8—34no—
14C2×C4⋊Q8—32no—
15C22×C4⋊C4C2×C314yes—
16C22×C42C2×C311yescharacteristic
17C22×A4C2311yescharacteristic
18C2×C3×Q8—42no—
19C4×A4—24no—
20C4×A4D412yes—
21C4×A4Q814yescomplemented
22C3×C4⋊C4—44no—
23C3×C42—41no—
24C22×Q8—24no—
25C22×Q8—32no—
26C22×Q8—34no—
27C22×Q8—32no—
28C22×Q8—64no—
29C23×C4C22×C314yes—
30C23×C4C22×C311yescharacteristic
31C23×C4C22×C312yes—
32C4⋊Q8—38no—
33C4⋊Q8—32no—
34C4⋊Q8—34no—
35C4⋊Q8—32no—
36C4⋊Q8—34no—
37C4⋊Q8—31no—
38C4⋊Q8A411yescharacteristic, direct product factor
39C2×C4⋊C4—34no—
40C2×C4⋊C4—34no—
41C2×C4⋊C4—38no—
42C2×C42—31no—
43C2×C42—32no—
44C2×C42—31no—
45C2×A4C2×D411yescharacteristic
46C2×A4C2×Q812yes—
47C3×Q8—84no—
48C2×C3×C4—42no—
49C2×C3×C4—41no—
50C2×C3×C4—44no—
51C24C23×C311yescharacteristic
52C2×Q8—34no—
53C2×Q8—34no—
54C2×Q8—32no—
55C2×Q8—64no—
56C2×Q8—64no—
57C2×Q8—64no—
58C2×Q8—68no—
59C2×Q8—64no—
60C2×Q8—68no—
61C2×Q8C2×A412yes—
62C22×C4—24no—
63C22×C4—32no—
64C22×C4—31no—
65C22×C4—32no—
66C22×C4—31no—
67C22×C4—34no—
68C22×C4—32no—
69C22×C4—34no—
70C22×C4—34no—
71C22×C4—64no—
72C22×C4C3×D412yes—
73C22×C4C3×Q814yescomplemented
74C4⋊C4—38no—
75C4⋊C4—38no—
76C4⋊C4—34no—
77C4⋊C4C2×A414yes—
78C42—32no—
79C42—31no—
80C42—32no—
81C42C2×A411yescharacteristic
82C22×C3—41no—
83A4C4⋊Q811yescharacteristic, direct product factor
84C3×C4—42no—
85C3×C4—44no—
86C3×C4—84no—
87C23—31no—
88C23—32no—
89C23—31no—
90C23C2×C3×D411yescharacteristic
91C23C2×C3×Q812yes—
92Q8—24no—
93Q8—68no—
94Q8—68no—
95Q8—64no—
96C2×C4—34no—
97C2×C4—32no—
98C2×C4—32no—
99C2×C4—31no—
100C2×C4—32no—
101C2×C4—32no—
102C2×C4—34no—
103C2×C4—34no—
104C2×C4—32no—
105C2×C4—34no—
106C2×C4—34no—
107C2×C4—64no—
108C2×C4—64no—
109C2×C4—64no—
110C2×C4—64no—
111C2×C4C22×A414yes—
112C2×C4C22×A411yescharacteristic
113C2×C4C22×A412yes—
114C2×C3—41no—
115C2×C3—42no—
116C22—31no—
117C22—32no—
118C22—32no—
119C22—31no—
120C22—31no—
121C22—32no—
122C22—32no—
123C22C3×C4⋊Q811yescharacteristic, complemented
124C22C23×A411yescharacteristic
125C4—24no—
126C4—32no—
127C4—34no—
128C4—64no—
129C4D4×A412yes—
130C4Q8×A414yescomplemented
131C3—41noSylow
132C2—31no—
133C2—32no—
134C2—31no—
135C2C2×D4×A411yescharacteristic
136C2C2×Q8×A412yes—
subgroupG/H
center, FrattiniC22C23×A4
commutator, socle, cosocleC24C23×C3
FittingC22×C4⋊Q8C3
prime radicalC22×A4C23
hypercenterC4⋊Q8A4
hypocenterC22C3×C4⋊Q8
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C22×C4⋊Q8C3semidirect
21. C4×A4Q8semidirect
38. C4⋊Q8A4direct (N × H)
73. C22×C4C3×Q8semidirect
83. A4C4⋊Q8direct (N × H)
123. C22C3×C4⋊Q8semidirect
130. C4Q8×A4semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×A42
A4×C4⋊C42
C42×A42
C22×C4⋊Q83
C3×C4⋊Q84