Finite Group Databasebeta

← #73029

Subgroups — #73029

Order 384.

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

normal subgroups only

This group has 112 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#5933C211yesmaximal, characteristic
2#5932C211yesmaximal, characteristic
3#458⋊C3C211yesmaximal, characteristic
4#2201—31nomaximal, Sylow
5#997C2211yescharacteristic
6A4⋊Q8—41nomaximal
7#563—31no—
8#458—31no—
9#458D311yescharacteristic
10#455—31no—
11#354—31no—
12#352—31no—
13#352—31no—
14C4×A4—41no—
15SL(2,ℤ/4)—41no—
16SL(2,ℤ/4)—41no—
17SL(2,ℤ/4)—81no—
18#226—81no—
19H(5,𝔽2)C2×D311yescharacteristic
20#137—61no—
21C4⋊Q8—61no—
22#126—61no—
23#126—61no—
24#125—61no—
25#124—31no—
26#123—31no—
27#123—31no—
28#123—61no—
29C22⋊Q8—61no—
30C22⋊Q8—61no—
31#104—61no—
32#100—31no—
33#99—31no—
34#99—31no—
35#99—61no—
36C2×A4—41no—
37C2×A4—81no—
38Dic6—161no—
39SL(2,𝔽3)—81no—
40#41—61no—
41C2×Q8—31no—
42C2×Q8—61no—
43C2×D4—31no—
44C2×D4—61no—
45C22×C4—31no—
46C22×C4S411yescharacteristic
47Q16—121no—
48SD16—121no—
49M16—61no—
50C4⋊C4—61no—
51C4⋊C4—61no—
52C4⋊C4—61no—
53C4⋊C4—61no—
54C4⋊C4—61no—
55C4⋊C4—61no—
56C4⋊C4—61no—
57C4⋊C4—61no—
58C4⋊C4—121no—
59C22⋊C4—31no—
60C22⋊C4—31no—
61C22⋊C4—61no—
62C22⋊C4—61no—
63C22⋊C4—61no—
64C22⋊C4—61no—
65C22⋊C4—61no—
66C22⋊C4—121no—
67C42—31no—
68C42—61no—
69A4—41no—
70A4—81no—
71C3×C4—161no—
72Dic3—161no—
73Dic3—161no—
74C23—21no—
75C23—31no—
76C23C2×S411yescharacteristic
77Q8—21no—
78Q8—121no—
79Q8—241no—
80D4—61no—
81D4—121no—
82C2×C4—31no—
83C2×C4—61no—
84C2×C4—61no—
85C2×C4—61no—
86C2×C4—61no—
87C2×C4—61no—
88C2×C4—61no—
89C2×C4—61no—
90C2×C4—121no—
91C2×C4—121no—
92C8—121no—
93C2×C3—161no—
94C22—31no—
95C22—41no—
96C22—61no—
97C22—81no—
98C22—121no—
99C4—41no—
100C4—61no—
101C4—121no—
102C4—121no—
103C4—121no—
104C4—121no—
105C4—121no—
106C4—241no—
107C3—161noSylow
108C2—61no—
109C2—121no—
110C2#1020⋊C211yescharacteristic
subgroupG/H
center, socle, hypercenterC2#1020⋊C2
commutator, prime radical, cosocle, hypocenter#997C22
FrattiniC23C2×S4
Fitting#458D3
LCSG ▷ #997
UCSC1 ◁ C2

Maximal subgroups

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

subgroupindex
#59332
#59322
#458⋊C32
#22013
A4⋊Q84