Finite Group Databasebeta

← #2616⋊C3 #73192

Subgroups — #2616⋊C3 #73192

Order 384.

171 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 171 conjugacy classes of subgroups — too many to draw. Only its 19 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#5948C211yesmaximal, characteristic
2#395⋊C3C212yesmaximal, complemented
3#2616C311yesmaximal, characteristic, complemented, Sylow
4C22⋊SL(2,𝔽3)C2211yescharacteristic
5Q8×A4—41nomaximal
6C22×#41C2×C311yescharacteristic
7C2×C22⋊Q8—31no—
8#395C2×C312yes—
9#394—32no—
10#380—31no—
11#41⋊C3—82no—
12C4×A4—42no—
13C4×A4—41no—
14C2×#41—62no—
15C2×#41—62no—
16C22×Q8A411yescharacteristic
17C22×Q8C22×C311yescharacteristic
18C22×D4—31no—
19C23×C4—31no—
20C22⋊Q8—62no—
21C22⋊Q8—62no—
22C2×C4⋊C4—31no—
23C2×C4⋊C4—32no—
24C2×C22⋊C4—32no—
25C2×C22⋊C4—32no—
26#95—32no—
27C2×A4—41no—
28C3×Q8—161no—
29SL(2,𝔽3)—82no—
30C24—31no—
31#41—22no—
32#41—62no—
33#41—64no—
34#41—62no—
35#41—62no—
36C2×Q8—62no—
37C2×Q8—61no—
38C2×Q8—61no—
39C2×D4—62no—
40C2×D4—64no—
41C22×C4—32no—
42C22×C4—32no—
43C22×C4—31no—
44C22×C4—32no—
45C22×C4—62no—
46C22×C4—62no—
47C22×C4C2×A411yescharacteristic
48C22×C4C2×A412yes—
49C4⋊C4—61no—
50C4⋊C4—61no—
51C4⋊C4—64no—
52C22⋊C4—64no—
53C22⋊C4—122no—
54A4—41no—
55C3×C4—162no—
56C3×C4—161no—
57C23—32no—
58C23—62no—
59C23—61no—
60C23—62no—
61C23—61no—
62C23C22×A411yescharacteristic
63Q8—22no—
64Q8—41no—
65Q8—62no—
66Q8—121no—
67D4—62no—
68D4—62no—
69D4—64no—
70C2×C4—31no—
71C2×C4—31no—
72C2×C4—32no—
73C2×C4—62no—
74C2×C4—64no—
75C2×C4—62no—
76C2×C4—62no—
77C2×C4—62no—
78C2×C4—62no—
79C2×C4—62no—
80C2×C4—62no—
81C2×C3—161no—
82C22—31no—
83C22—31no—
84C22—62no—
85C22—62no—
86C22—62no—
87C22—122no—
88C22—122no—
89C22#99411yescharacteristic
90C4—31no—
91C4—42no—
92C4—62no—
93C4—122no—
94C4#120⋊C311yescharacteristic
95C3—161noSylow
96C2—31no—
97C2—31no—
98C2—122no—
99C2C2×#120⋊C311yescharacteristic
subgroupG/H
centerC2C2×#120⋊C3
commutator, cosocle, hypocenterC22×Q8C22×C3
Frattini, socleC23C22×A4
Fitting#2616C3
prime radical#5948C2
hypercenterC4#120⋊C3
LCSG ▷ C22×Q8
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #395⋊C3C2semidirect
3. #2616C3semidirect

Maximal subgroups

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

subgroupindex
#59482
#395⋊C32
#26163
Q8×A44