Finite Group Databasebeta

← #2388⋊C3 #73184

Subgroups — #2388⋊C3 #73184

Order 384.

199 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 199 conjugacy classes of subgroups — too many to draw. Only its 21 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#395⋊C3C211yesmaximal, characteristic, complemented
3#393⋊C3C211yesmaximal, characteristic, complemented
4#2388C311yesmaximal, characteristic, complemented, Sylow
5C22⋊SL(2,𝔽3)C2211yescharacteristic
6C2×C4×A4—41nomaximal
7C22×#41C2×C311yescharacteristic, complemented
8C2×C4×D4—31no—
9#395C2×C311yescharacteristic, complemented
10#394—31no—
11#393C2×C311yescharacteristic
12#392—31no—
13C4×C22⋊C4—31no—
14C22×A4—41no—
15#41⋊C3—82no—
16C4×A4—41no—
17C4×A4—41no—
18C2×#41—62no—
19C2×#41—62no—
20C22×Q8C22×C311yescharacteristic
21C22×D4—31no—
22C22×D4—31no—
23C23×C4—31no—
24C23×C4A411yescharacteristic
25C4×D4—62no—
26C4×D4—62no—
27C2×C4⋊C4—31no—
28C2×C22⋊C4—32no—
29C2×C22⋊C4—31no—
30C2×C22⋊C4—31no—
31C2×C42—31no—
32#95—31no—
33#95—31no—
34C2×A4—42no—
35C2×A4—41no—
36C2×C3×C4—161no—
37SL(2,𝔽3)—82no—
38C24—31no—
39C24C2×A411yescharacteristic
40#41—22no—
41#41—62no—
42#41—64no—
43#41—62no—
44#41—62no—
45C2×Q8—62no—
46C2×D4—62no—
47C2×D4—62no—
48C2×D4—62no—
49C2×D4—64no—
50C2×D4—62no—
51C22×C4—32no—
52C22×C4—32no—
53C22×C4—31no—
54C22×C4—31no—
55C22×C4—31no—
56C22×C4—61no—
57C22×C4—62no—
58C22×C4—62no—
59C22×C4—61no—
60C22×C4C2×A411yescharacteristic
61C22×C4C2×A411yescharacteristic
62C4⋊C4—62no—
63C22⋊C4—64no—
64C22⋊C4—62no—
65C22⋊C4—62no—
66C42—61no—
67C42—61no—
68C22×C3—161no—
69A4—41no—
70C3×C4—161no—
71C3×C4—161no—
72C23—32no—
73C23—61no—
74C23—61no—
75C23—62no—
76C23—62no—
77C23—61no—
78C23—61no—
79C23#41⋊C312yescomplemented
80C23C22×A411yescharacteristic
81Q8—22no—
82Q8—62no—
83D4—62no—
84D4—62no—
85D4—68no—
86D4—64no—
87C2×C4—31no—
88C2×C4—31no—
89C2×C4—32no—
90C2×C4—32no—
91C2×C4—41no—
92C2×C4—62no—
93C2×C4—64no—
94C2×C4—61no—
95C2×C4—61no—
96C2×C4—62no—
97C2×C4—61no—
98C2×C4—62no—
99C2×C4—61no—
100C2×C4—62no—
101C2×C4—121no—
102C2×C3—162no—
103C2×C3—161no—
104C22—31no—
105C22—31no—
106C22—41no—
107C22—62no—
108C22—62no—
109C22—62no—
110C22—62no—
111C22—121no—
112C22—122no—
113C22—122no—
114C22C2×#41⋊C311yescharacteristic
115C4—31no—
116C4—41no—
117C4—62no—
118C4—62no—
119C4—121no—
120C4#120⋊C311yescharacteristic
121C3—161noSylow
122C2—31no—
123C2—31no—
124C2—42no—
125C2—122no—
126C2C2×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4#120⋊C3
commutator, cosocle, hypocenterC22×Q8C22×C3
Frattini, socleC23C22×A4
Fitting#2388C3
LCSG ▷ C22×Q8
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #5948C2semidirect
2. #395⋊C3C2semidirect
3. #393⋊C3C2semidirect
4. #2388C3semidirect
7. C22×#41C2×C3semidirect
9. #395C2×C3semidirect
79. C23#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
#59482
#395⋊C32
#393⋊C32
#23883
C2×C4×A44