Finite Group Databasebeta

← #11923442

Subgroups — #11923442

Order 1152.

121 conjugacy classes of subgroups; only the 8 normal subgroups are shown.

normal subgroups only

This group has 121 conjugacy classes of subgroups — too many to draw. Only its 8 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
1A4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
2C2×A42C411yescharacteristic
3#5936—61no—
4#5432—61no—
5A42C811yescharacteristic, complemented
6C3⋊SL(2,ℤ/4)—81no—
7#1316—91nomaximal, Sylow
8C2×C22⋊A4—21no—
9C23×A4—21no—
10C2×SL(2,ℤ/4)—61no—
11C2×SL(2,ℤ/4)—61no—
12C2×C3×A4—81no—
13#622—161nomaximal
14#379—91no—
15#323—91no—
16#323—91no—
17C22⋊A4—21no—
18C22×A4—21no—
19C22×A4—61no—
20C22×A4—61no—
21SL(2,ℤ/4)—121no—
22SL(2,ℤ/4)—121no—
23SL(2,ℤ/4)—242no—
24SL(2,ℤ/4)—241no—
25#217—241no—
26C3×A4—81no—
27C3⋊Dic3—161no—
28C25#15711yescharacteristic
29C2×C22⋊C4—91no—
30C2×C22⋊C4—91no—
31C2×C22⋊C4—181no—
32C2×C22⋊C4—181no—
33C22⋊C8—181no—
34C22⋊C8—181no—
35C23×C3—81no—
36C2×A4—21no—
37C2×A4—61no—
38C2×A4—61no—
39C2×A4—82no—
40C2×A4—241no—
41C2×Dic3—241no—
42C2×Dic3—241no—
43C2×C32—161no—
44C24—61no—
45C24—61no—
46C24—91no—
47C24—91no—
48C24#62211yescharacteristic, complemented
49C22×C4—91no—
50C22×C4—91no—
51C22×C4—181no—
52C2×C8—361no—
53C2×C8—361no—
54C22⋊C4—361no—
55C22⋊C4—361no—
56C22⋊C4—361no—
57C22⋊C4—361no—
58C22⋊C4—361no—
59C22⋊C4—361no—
60C22×C3—81no—
61C22×C3—241no—
62C22×C3—241no—
63A4—21no—
64A4—82no—
65A4—241no—
66Dic3—481no—
67Dic3—481no—
68Dic3—961no—
69C32—161noSylow
70C23—21no—
71C23—61no—
72C23—61no—
73C23—61no—
74C23—91no—
75C23—91no—
76C23—91no—
77C23—181no—
78C23—181no—
79C23—181no—
80C23—181no—
81C23—361no—
82C2×C4—181no—
83C2×C4—181no—
84C2×C4—361no—
85C2×C4—361no—
86C2×C4—361no—
87C2×C4—361no—
88C2×C4—361no—
89C8—721no—
90C8—721no—
91C2×C3—81no—
92C2×C3—241no—
93C2×C3—241no—
94C2×C3—321no—
95C22—21no—
96C22—61no—
97C22—61no—
98C22—61no—
99C22—91no—
100C22—91no—
101C22—91no—
102C22—181no—
103C22—181no—
104C22—181no—
105C22—181no—
106C22—361no—
107C4—361no—
108C4—361no—
109C4—721no—
110C3—81no—
111C3—321no—
112C2—61no—
113C2—61no—
114C2—91no—
115C2—91no—
116C2#1059677011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#10596770
commutator, hypocenterA42C8
Fitting, socleC25#157
prime radicalC2×A42C4
cosocleA4⋊SL(2,ℤ/4)C2
LCSG ▷ A42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
5. A42C8semidirect
48. C24#622semidirect

Maximal subgroups

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

subgroupindex
A4⋊SL(2,ℤ/4)2
#13169
#62216