Finite Group Databasebeta

← #73031

Subgroups — #73031

Order 384.

126 conjugacy classes of subgroups; only the 11 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 11 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#5935C211yesmaximal, characteristic
2#5932C211yesmaximal, characteristic, complemented
3#458⋊C3C211yesmaximal, characteristic, complemented
4#2198—31nomaximal, Sylow
5#997C2211yescharacteristic
6C4×S4—41nomaximal
7#559—31no—
8#458—31no—
9#458D311yescharacteristic, complemented
10#453—31no—
11#353—31no—
12#352—31no—
13#352—31no—
14C2×S4—41no—
15C4×A4—41no—
16SL(2,ℤ/4)—41no—
17SL(2,ℤ/4)—81no—
18GL(2,𝔽3)—81no—
19H(5,𝔽2)C2×D311yescharacteristic
20AGL(1,ℤ/8)—61no—
21#127—31no—
22#124—61no—
23#124—61no—
24#123—31no—
25#123—31no—
26#123—61no—
27#123—61no—
28C4×Q8—61no—
29C4×D4—61no—
30C4×D4—61no—
31#104—61no—
32#100—31no—
33#99—31no—
34#99—31no—
35#99—61no—
36C2×A4—41no—
37C2×A4—81no—
38S4—42no—
39C4×D3—161no—
40SL(2,𝔽3)—81no—
41#41—61no—
42C2×Q8—61no—
43C2×D4—31no—
44C2×D4—31no—
45C2×D4—61no—
46C2×D4—61no—
47C2×D4—61no—
48C22×C4—31no—
49C22×C4—61no—
50C22×C4S411yescharacteristic
51SD16—121no—
52D8—121no—
53M16—61no—
54C4⋊C4—61no—
55C4⋊C4—61no—
56C4⋊C4—61no—
57C4⋊C4—121no—
58C22⋊C4—31no—
59C22⋊C4—31no—
60C22⋊C4—61no—
61C22⋊C4—61no—
62C22⋊C4—61no—
63C22⋊C4—61no—
64C22⋊C4—61no—
65C22⋊C4—61no—
66C22⋊C4—121no—
67C42—31no—
68C42—61no—
69C42—61no—
70C2×D3—161no—
71A4—41no—
72A4—81no—
73C3×C4—161no—
74Dic3—161no—
75C23—21no—
76C23—31no—
77C23—61no—
78C23C2×S411yescharacteristic
79Q8—21no—
80Q8—122no—
81D4—61no—
82D4—121no—
83D4—122no—
84D4—121no—
85D4—122no—
86C2×C4—31no—
87C2×C4—61no—
88C2×C4—61no—
89C2×C4—61no—
90C2×C4—61no—
91C2×C4—61no—
92C2×C4—61no—
93C2×C4—121no—
94C2×C4—121no—
95C2×C4—241no—
96C8—121no—
97C2×C3—161no—
98D3—162no—
99C22—31no—
100C22—41no—
101C22—61no—
102C22—81no—
103C22—121no—
104C22—121no—
105C22—121no—
106C22—121no—
107C4—41no—
108C4—62no—
109C4—61no—
110C4—121no—
111C4—121no—
112C4—121no—
113C4—241no—
114C3—161noSylow
115C2—61no—
116C2—121no—
117C2—241no—
118C2#1020⋊C211yescharacteristic
subgroupG/H
center, socle, hypercenterC2#1020⋊C2
commutator, cosocle, hypocenter#997C22
FrattiniC23C2×S4
Fitting#458D3
prime radical#5935C2
LCSG ▷ #997
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #5932C2semidirect
3. #458⋊C3C2semidirect
9. #458D3semidirect

Maximal subgroups

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

subgroupindex
#59352
#59322
#458⋊C32
#21983
C4×S44