Finite Group Databasebeta

← SL(2,ℤ/8) #67996

Subgroups — SL(2,ℤ/8) #67996

Order 384.

106 conjugacy classes of subgroups; only the 15 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 15 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×#95⋊C3C211yesmaximal, characteristic
2#1294—31nomaximal, Sylow
3C2×SL(2,ℤ/4)—41nomaximal
4#95⋊C3C411yescharacteristic, complemented
5C2×C22⋊C8—31no—
6#380—31no—
7C2×#95D311yescharacteristic
8C22×A4—41no—
9SL(2,ℤ/4)—42no—
10C23×C4—31no—
11C22×C8—61no—
12C2×C4⋊C4—31no—
13C2×C4⋊C4—31no—
14C2×C22⋊C4—61no—
15C22⋊C8—32no—
16C22⋊C8—61no—
17#95—31no—
18#95—61no—
19#95Dic311yescharacteristic, complemented
20C2×A4—41no—
21C2×A4—41no—
22C2×A4—41no—
23C2×Dic3—161no—
24C24S411yescharacteristic
25C22×C4—31no—
26C22×C4—31no—
27C22×C4—31no—
28C22×C4—31no—
29C22×C4—31no—
30C22×C4—31no—
31C22×C4—61no—
32C22×C4—61no—
33C22×C4—121no—
34C22×C4—121no—
35C2×C8—62no—
36C2×C8—121no—
37C2×C8—121no—
38C4⋊C4—121no—
39C4⋊C4—121no—
40C22⋊C4—121no—
41C22⋊C4—121no—
42C22×C3—161no—
43A4—41no—
44Dic3—162no—
45C23—31no—
46C23—31no—
47C23—31no—
48C23—31no—
49C23#22611yescharacteristic
50C23GL(2,𝔽3)11yescharacteristic
51C23SL(2,ℤ/4)11yescharacteristic
52C2×C4—31no—
53C2×C4—31no—
54C2×C4—31no—
55C2×C4—31no—
56C2×C4—61no—
57C2×C4—61no—
58C2×C4—61no—
59C2×C4—61no—
60C2×C4—121no—
61C2×C4—121no—
62C2×C4—121no—
63C2×C4—121no—
64C2×C4—121no—
65C2×C4—121no—
66C2×C4—121no—
67C2×C4—121no—
68C2×C4—121no—
69C2×C4—121no—
70C8—122no—
71C2×C3—161no—
72C2×C3—161no—
73C2×C3—161no—
74C22—31no—
75C22—31no—
76C22—31no—
77C22—31no—
78C22—31no—
79C22—31no—
80C22—31no—
81C22—31no—
82C22—31no—
83C22—61no—
84C22#85711yescharacteristic
85C22#85911yescharacteristic
86C4—61no—
87C4—61no—
88C4—61no—
89C4—61no—
90C4—241no—
91C4—241no—
92C3—161noSylow
93C2—31no—
94C2—31no—
95C2—31no—
96C2—31no—
97C2#462111yescharacteristic
98C2#462211yescharacteristic
99C2#462311yescharacteristic
subgroupG/H
center, hypercenterC22#857
commutator, hypocenter#95⋊C3C4
Frattini, socleC24S4
FittingC2×#95D3
prime radical, cosocleC2×#95⋊C3C2
LCSG ▷ #95⋊C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
4. #95⋊C3C4semidirect
19. #95Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×#95⋊C32
#12943
C2×SL(2,ℤ/4)4