Finite Group Databasebeta

← #2614⋊C3 #73190

Subgroups — #2614⋊C3 #73190

Order 384.

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

normal subgroups only

This group has 172 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
1C2×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic, complemented
2#395⋊C3C211yesmaximal, characteristic, complemented
3#393⋊C3C211yesmaximal, characteristic, complemented
4#2614C311yesmaximal, characteristic, complemented, Sylow
5C22⋊SL(2,𝔽3)C2211yescharacteristic
6D4×A4—41nomaximal
7C23×Q8C2×C311yescharacteristic, complemented
8C2×#123—31no—
9#395—31no—
10#395C2×C311yescharacteristic, complemented
11#393—31no—
12#393C2×C311yescharacteristic, complemented
13#381—31no—
14C22×A4—41no—
15C22×A4—41no—
16C2×SL(2,𝔽3)—82no—
17C4×A4—41no—
18C22×Q8—31no—
19C22×Q8—62no—
20C22×Q8—62no—
21C22×Q8C22×C311yescharacteristic
22C22×D4A411yescharacteristic
23C23×C4—31no—
24#123—62no—
25#123—62no—
26C2×C4⋊C4—31no—
27C2×C4⋊C4—31no—
28C2×C22⋊C4—31no—
29C2×C22⋊C4—31no—
30C2×C22⋊C4—31no—
31#95—31no—
32#95—31no—
33#95—32no—
34C2×A4—41no—
35C2×A4—81no—
36C2×A4—81no—
37C3×D4—161no—
38SL(2,𝔽3)—82no—
39C24C2×A411yescharacteristic
40C24C2×A411yescharacteristic
41C2×Q8—22no—
42C2×Q8—62no—
43C2×Q8—62no—
44C2×Q8—64no—
45C2×Q8—62no—
46C2×Q8—62no—
47C2×Q8—64no—
48C2×Q8—62no—
49C2×D4—61no—
50C2×D4—61no—
51C22×C4—32no—
52C22×C4—32no—
53C22×C4—31no—
54C22×C4—31no—
55C22×C4—31no—
56C22×C4—31no—
57C22×C4—62no—
58C22×C4—62no—
59C22×C4C2×A411yescharacteristic
60C4⋊C4—62no—
61C4⋊C4—62no—
62C22⋊C4—62no—
63C22⋊C4—62no—
64C22⋊C4—61no—
65C22⋊C4—61no—
66C22×C3—161no—
67C22×C3—161no—
68A4—41no—
69C3×C4—161no—
70C23—21no—
71C23—21no—
72C23—31no—
73C23—31no—
74C23—61no—
75C23—61no—
76C23—61no—
77C23C22×A411yescharacteristic
78Q8—22no—
79Q8—62no—
80Q8—62no—
81Q8—62no—
82Q8—64no—
83D4—41no—
84D4—121no—
85C2×C4—32no—
86C2×C4—32no—
87C2×C4—61no—
88C2×C4—62no—
89C2×C4—64no—
90C2×C4—62no—
91C2×C4—62no—
92C2×C4—62no—
93C2×C4—61no—
94C2×C4—61no—
95C2×C4—62no—
96C2×C4—61no—
97C2×C4—61no—
98C2×C3—161no—
99C2×C3—321no—
100C2×C3—321no—
101C22—31no—
102C22—31no—
103C22—31no—
104C22—41no—
105C22—61no—
106C22—61no—
107C22—61no—
108C22—61no—
109C22—121no—
110C22—121no—
111C22#120⋊C311yescharacteristic
112C222−1+4⋊C311yescharacteristic
113C4—41no—
114C4—62no—
115C4—62no—
116C4—121no—
117C4—121no—
118C3—161noSylow
119C2—21no—
120C2—31no—
121C2—31no—
122C2—61no—
123C2—81no—
124C2C2×#120⋊C311yescharacteristic
subgroupG/H
centerC2C2×#120⋊C3
commutator, cosocle, hypocenterC22×Q8C22×C3
Frattini, socleC23C22×A4
Fitting#2614C3
hypercenterC22#120⋊C3
LCSG ▷ C22×Q8
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊SL(2,𝔽3)C2semidirect
2. #395⋊C3C2semidirect
3. #393⋊C3C2semidirect
4. #2614C3semidirect
7. C23×Q8C2×C3semidirect
10. #395C2×C3semidirect
12. #393C2×C3semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊SL(2,𝔽3)2
#395⋊C32
#393⋊C32
#26143
D4×A44