Finite Group Databasebeta

← #4626⋊C2 #73101

Subgroups — #4626⋊C2 #73101

Order 384.

117 conjugacy classes of subgroups; only the 13 normal subgroups are shown.

normal subgroups only

This group has 117 conjugacy classes of subgroups — too many to draw. Only its 13 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
1#560⋊C3C211yesmaximal, characteristic, complemented
2#857⋊C2C211yesmaximal, characteristic, complemented
3#4626C211yesmaximal, characteristic, complemented
4#2200—31nomaximal, Sylow
5GL(2,ℤ/4)—41nomaximal
6#127⋊C3C2211yescharacteristic
7#126⋊C3—21no—
8#857—21no—
9#560D311yescharacteristic, complemented
10#458—31no—
11B(4,𝔽2)—31no—
12#453—31no—
13#353—31no—
14#352—31no—
15AΣL(1,𝔽16)—31no—
16C22×A4—41no—
17C2×S4—41no—
18SL(2,ℤ/4)—41no—
19C42⋊C3D411yescharacteristic, complemented
20H(5,𝔽2)—31no—
21AGL(1,ℤ/8)—61no—
22#127C2×D311yescharacteristic
23#126—21no—
24#123—31no—
25#123—61no—
26#121—61no—
27#120—31no—
28#120—61no—
29#104—61no—
30#100—31no—
31#99—31no—
32#99—31no—
33#99—61no—
34#99—61no—
35C2×A4—41no—
36C2×A4—81no—
37S4—81no—
38#67—161no—
39C24S411yescharacteristic
40#41—61no—
41#41—121no—
42C2×D4—31no—
43C2×D4—31no—
44C2×D4—61no—
45C2×D4—61no—
46C2×D4—61no—
47C2×D4—121no—
48C2×D4—121no—
49C22×C4—31no—
50SD16—121no—
51D8—121no—
52M16—61no—
53C4⋊C4—61no—
54C4⋊C4—121no—
55C22⋊C4—31no—
56C22⋊C4—31no—
57C22⋊C4—61no—
58C22⋊C4—61no—
59C22⋊C4—61no—
60C22⋊C4—121no—
61C22⋊C4—121no—
62C42#6711yescharacteristic, complemented
63C22×C3—161no—
64C2×D3—161no—
65A4—41no—
66Dic3—161no—
67C23—21no—
68C23—31no—
69C23—61no—
70C23—61no—
71C23—121no—
72C23C2×S411yescharacteristic
73Q8—61no—
74D4—61no—
75D4—121no—
76D4—121no—
77D4—121no—
78D4—121no—
79D4—121no—
80D4—241no—
81D4—241no—
82D4—241no—
83C2×C4—31no—
84C2×C4—61no—
85C2×C4—61no—
86C2×C4—61no—
87C2×C4—121no—
88C2×C4—121no—
89C2×C4—121no—
90C2×C4—121no—
91C8—121no—
92C2×C3—161no—
93C2×C3—321no—
94D3—321no—
95C22—41no—
96C22—61no—
97C22—61no—
98C22—121no—
99C22—121no—
100C22—121no—
101C22—121no—
102C22—241no—
103C22—241no—
104C22GL(2,ℤ/4)11yescharacteristic
105C4—61no—
106C4—121no—
107C4—121no—
108C4—241no—
109C4—241no—
110C3—161noSylow
111C2—31no—
112C2—41no—
113C2—81no—
114C2—121no—
115C2—241no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle#127⋊C3C22
FrattiniC23C2×S4
Fitting#560D3
socleC22GL(2,ℤ/4)
hypocenterC42⋊C3D4
LCSG ▷ #127⋊C3 ▷ C42⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. #560⋊C3C2semidirect
2. #857⋊C2C2semidirect
3. #4626C2semidirect
9. #560D3semidirect
19. C42⋊C3D4semidirect
62. C42#67semidirect

Maximal subgroups

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

subgroupindex
#560⋊C32
#857⋊C22
#46262
#22003
GL(2,ℤ/4)4