Finite Group Databasebeta

← #2615⋊C3 #73191

Subgroups — #2615⋊C3 #73191

Order 384.

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

normal subgroups only

This group has 197 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, complemented
2#393⋊C3C212yesmaximal, complemented
3#2615C311yesmaximal, characteristic, complemented, Sylow
4C22⋊SL(2,𝔽3)C2211yescharacteristic
5D4×A4—41nomaximal
6C22×#41C2×C311yescharacteristic, complemented
7C2×#121—31no—
8#393C2×C312yescomplemented
9#392—32no—
10#380—31no—
11C22×A4—42no—
12#41⋊C3—82no—
13C4×A4—41no—
14C2×#41—62no—
15C2×#41—62no—
16C22×Q8C22×C311yescharacteristic
17C22×D4—31no—
18C22×D4—32no—
19C22×D4A411yescharacteristic
20C23×C4—31no—
21#121—62no—
22#121—62no—
23C2×C4⋊C4—31no—
24C2×C22⋊C4—32no—
25C2×C22⋊C4—32no—
26#95—32no—
27C2×A4—41no—
28C2×A4—82no—
29C3×D4—161no—
30SL(2,𝔽3)—82no—
31C24—31no—
32C24C2×A412yes—
33#41—22no—
34#41—62no—
35#41—64no—
36#41—62no—
37#41—62no—
38C2×Q8—62no—
39C2×D4—61no—
40C2×D4—62no—
41C2×D4—61no—
42C2×D4—64no—
43C2×D4—64no—
44C2×D4—124no—
45C22×C4—32no—
46C22×C4—32no—
47C22×C4—31no—
48C22×C4—32no—
49C22×C4—62no—
50C22×C4—62no—
51C22×C4C2×A411yescharacteristic
52C4⋊C4—61no—
53C4⋊C4—61no—
54C22⋊C4—64no—
55C22⋊C4—122no—
56C22×C3—162no—
57A4—41no—
58C3×C4—161no—
59C23—22no—
60C23—32no—
61C23—62no—
62C23—61no—
63C23—62no—
64C23—62no—
65C23—62no—
66C23—61no—
67C23C22×A411yescharacteristic
68Q8—22no—
69Q8—62no—
70D4—41no—
71D4—62no—
72D4—62no—
73D4—64no—
74D4—121no—
75D4—128no—
76C2×C4—31no—
77C2×C4—31no—
78C2×C4—32no—
79C2×C4—62no—
80C2×C4—64no—
81C2×C4—62no—
82C2×C4—62no—
83C2×C4—62no—
84C2×C4—64no—
85C2×C3—161no—
86C2×C3—322no—
87C22—31no—
88C22—31no—
89C22—42no—
90C22—62no—
91C22—62no—
92C22—62no—
93C22—122no—
94C22—122no—
95C22—122no—
96C22—122no—
97C222−1+4⋊C311yescharacteristic
98C4—31no—
99C4—62no—
100C4—122no—
101C4#120⋊C311yescharacteristic
102C3—161noSylow
103C2—31no—
104C2—31no—
105C2—82no—
106C2—122no—
107C2C2×#120⋊C311yescharacteristic
subgroupG/H
centerC2C2×#120⋊C3
commutator, cosocle, hypocenterC22×Q8C22×C3
Frattini, socleC23C22×A4
Fitting#2615C3
hypercenterC4#120⋊C3
LCSG ▷ C22×Q8
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #5948C2semidirect
2. #393⋊C3C2semidirect
3. #2615C3semidirect
6. C22×#41C2×C3semidirect
8. #393C2×C3semidirect

Maximal subgroups

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

subgroupindex
#59482
#393⋊C32
#26153
D4×A44