Finite Group Databasebeta

← SL(2,ℤ/4)⋊C8 #73107

Subgroups — SL(2,ℤ/4)⋊C8 #73107

Order 384.

163 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 163 conjugacy classes of subgroups — too many to draw. Only its 34 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×C8×A4C211yesmaximal, characteristic
2C4×SL(2,ℤ/4)C211yesmaximal, characteristic
3C2×A4⋊C8C211yesmaximal, characteristic
4#1850—31nomaximal, Sylow
5C2×C4×A4C2211yescharacteristic
6C2×SL(2,ℤ/4)C411yescharacteristic
7C2×SL(2,ℤ/4)C411yescharacteristic
8C8×A4—21no—
9A4⋊C8—21no—
10Dic3⋊C8—41nomaximal
11C23×C8D311yescharacteristic
12C2×C4⋊C8—31no—
13C2×C4⋊C8—31no—
14C2×C22⋊C8—31no—
15C4×C22⋊C4—31no—
16#336—31no—
17#336—31no—
18C22×A4C2×C411yescharacteristic
19C4×A4D411yescharacteristic
20C4×A4Q811yescharacteristic
21SL(2,ℤ/4)—21no—
22SL(2,ℤ/4)C812yescomplemented
23C2×C3×C8—41no—
24C4×Dic3—41no—
25C2×C3⋊C8—41no—
26C23×C4C2×D311yescharacteristic
27C22×C8—21no—
28C22×C8—31no—
29C22×C8—31no—
30C22×C8—31no—
31C22×C8—31no—
32C22×C8—61no—
33C2×C22⋊C4—31no—
34C2×C22⋊C4—31no—
35C2×C42—31no—
36C2×C42—31no—
37C4⋊C8—62no—
38C4⋊C8—61no—
39C4⋊C8—61no—
40C22⋊C8—61no—
41C22⋊C8—61no—
42#95—31no—
43#95—31no—
44C2×A4C4⋊C411yescharacteristic
45C2×A4C2×C811yescharacteristic
46C2×A4M1611yescharacteristic
47C2×C3×C4—41no—
48C2×Dic3—41no—
49C2×Dic3—41no—
50C3×C8—81no—
51C3⋊C8—81no—
52C24C4×D311yescharacteristic
53C22×C4—31no—
54C22×C4—31no—
55C22×C4—31no—
56C22×C4—31no—
57C22×C4—31no—
58C22×C4—31no—
59C22×C4—31no—
60C22×C4—31no—
61C22×C4Dic611yescharacteristic
62C22×C4#6711yescharacteristic
63C2×C8—32no—
64C2×C8—31no—
65C2×C8—61no—
66C2×C8—61no—
67C2×C8—61no—
68C2×C8—61no—
69C2×C8—61no—
70C2×C8—61no—
71C2×C8—61no—
72C2×C8—61no—
73C2×C8—61no—
74C2×C8S411yescharacteristic
75C22⋊C4—32no—
76C22⋊C4—32no—
77C22⋊C4—61no—
78C22⋊C4—61no—
79C42—61no—
80C42—61no—
81C42—61no—
82C42—61no—
83C22×C3—41no—
84A4C4⋊C811yescharacteristic, complemented
85C3×C4—41no—
86C3×C4—41no—
87Dic3—42no—
88Dic3—81no—
89C23—31no—
90C23—31no—
91C23—31no—
92C23—31no—
93C23D3×C811yescharacteristic
94C23ΓL(1,𝔽25)11yescharacteristic
95C23Dic3⋊C411yescharacteristic
96C2×C4—31no—
97C2×C4—31no—
98C2×C4—31no—
99C2×C4—31no—
100C2×C4—31no—
101C2×C4—31no—
102C2×C4—31no—
103C2×C4—32no—
104C2×C4—32no—
105C2×C4—61no—
106C2×C4—61no—
107C2×C4—61no—
108C2×C4—61no—
109C2×C4—61no—
110C2×C4—61no—
111C2×C4—61no—
112C2×C4—61no—
113C2×C4—61no—
114C2×C4—61no—
115C2×C4—61no—
116C2×C4C2×S411yescharacteristic
117C8—21no—
118C8—61no—
119C8—121no—
120C8—121no—
121C2×C3—41no—
122C2×C3—41no—
123C2×C3—41no—
124C22—31no—
125C22—31no—
126C22—31no—
127C22—31no—
128C22—31no—
129C22—31no—
130C22—31no—
131C22—31no—
132C22—31no—
133C22—61no—
134C22Dic3⋊C811yescharacteristic, complemented
135C22C4×S411yescharacteristic
136C4—31no—
137C4—31no—
138C4—62no—
139C4—62no—
140C4—121no—
141C4—121no—
142C4A4⋊Q811yescharacteristic
143C4GL(2,ℤ/4)11yescharacteristic
144C3—41noSylow
145C2—31no—
146C2—31no—
147C2—31no—
148C2—31no—
149C2C8×S411yescharacteristic
150C2#540011yescharacteristic
151C2SL(2,ℤ/4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×S4
commutatorC2×A4C2×C8
FittingC23×C8D3
socleC24C4×D3
prime radicalC22×A4C2×C4
cosocleC2×C4×A4C22
hypercenterC2×C8S4
hypocenterA4C4⋊C8
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
22. SL(2,ℤ/4)C8semidirect
84. A4C4⋊C8semidirect
134. C22Dic3⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C8×A42
C4×SL(2,ℤ/4)2
C2×A4⋊C82
#18503
Dic3⋊C84