Finite Group Databasebeta

← #73030

Subgroups — #73030

Order 384.

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

normal subgroups only

This group has 134 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#5934C211yesmaximal, characteristic
2#5933C211yesmaximal, characteristic, complemented
3#458⋊C3C211yesmaximal, characteristic, complemented
4#2197—31nomaximal, Sylow
5#997C2211yescharacteristic
6C4×S4—41nomaximal
7#551—31no—
8#458D311yescharacteristic, complemented
9B(4,𝔽2)—31no—
10#455—31no—
11#354—31no—
12#352—31no—
13AΣL(1,𝔽16)—31no—
14C2×S4—41no—
15C2×S4—81no—
16C4×A4—41no—
17SL(2,ℤ/4)—41no—
18#226—81no—
19H(5,𝔽2)C2×D311yescharacteristic
20#137—61no—
21#126—61no—
22#124—31no—
23#123—31no—
24#123—61no—
25C22⋊Q8—61no—
26#120—31no—
27#120—61no—
28C4×D4—61no—
29#117—61no—
30C2×C22⋊C4—61no—
31#104—61no—
32#100—31no—
33#99—31no—
34#99—31no—
35#99—61no—
36C2×A4—41no—
37C2×A4—81no—
38S4—42no—
39S4—82no—
40C4×D3—161no—
41SL(2,𝔽3)—81no—
42C24—31no—
43#41—61no—
44C2×Q8—31no—
45C2×D4—31no—
46C2×D4—61no—
47C2×D4—61no—
48C2×D4—121no—
49C22×C4—61no—
50C22×C4—61no—
51C22×C4S411yescharacteristic, complemented
52Q16—121no—
53SD16—121no—
54M16—61no—
55C4⋊C4—61no—
56C4⋊C4—61no—
57C4⋊C4—61no—
58C4⋊C4—61no—
59C22⋊C4—31no—
60C22⋊C4—31no—
61C22⋊C4—61no—
62C22⋊C4—61no—
63C22⋊C4—61no—
64C22⋊C4—61no—
65C22⋊C4—61no—
66C22⋊C4—61no—
67C22⋊C4—61no—
68C22⋊C4—121no—
69C42—31no—
70C42—61no—
71C2×D3—161no—
72A4—41no—
73A4—81no—
74C3×C4—161no—
75Dic3—161no—
76C23—21no—
77C23—31no—
78C23—61no—
79C23—121no—
80C23—122no—
81C23C2×S411yescharacteristic
82Q8—21no—
83Q8—121no—
84D4—61no—
85D4—121no—
86D4—122no—
87D4—242no—
88C2×C4—31no—
89C2×C4—61no—
90C2×C4—61no—
91C2×C4—61no—
92C2×C4—61no—
93C2×C4—61no—
94C2×C4—61no—
95C2×C4—122no—
96C2×C4—121no—
97C2×C4—241no—
98C8—121no—
99C2×C3—161no—
100D3—162no—
101C22—31no—
102C22—41no—
103C22—62no—
104C22—61no—
105C22—81no—
106C22—121no—
107C22—121no—
108C22—122no—
109C22—121no—
110C22—241no—
111C4—41no—
112C4—61no—
113C4—121no—
114C4—121no—
115C4—121no—
116C4—121no—
117C4—241no—
118C3—161noSylow
119C2—61no—
120C2—121no—
121C2—122no—
122C2#1020⋊C211yescharacteristic
subgroupG/H
center, socle, hypercenterC2#1020⋊C2
commutator, cosocle, hypocenter#997C22
FrattiniC23C2×S4
Fitting#458D3
prime radical#5934C2
LCSG ▷ #997
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #5933C2semidirect
3. #458⋊C3C2semidirect
8. #458D3semidirect
51. C22×C4S4semidirect

Maximal subgroups

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

subgroupindex
#59342
#59332
#458⋊C32
#21973
C4×S44