Finite Group Databasebeta

← C3×#1402 #67962

Subgroups — C3×#1402 #67962

Order 384.

122 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 28 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
1C3×#453C211yesmaximal, characteristic
2C3×#353C211yesmaximal, characteristic, complemented
3C3×#331C211yesmaximal, characteristic, complemented
4#1402C311yesmaximal, characteristic, direct product factor, Sylow
5C3×H(5,𝔽2)C411yescharacteristic, complemented
6C3×AGL(1,ℤ/8)—21no—
7C3×#127C2211yescharacteristic
8C3×C4⋊C8—21no—
9C3×#104—21no—
10C3×#100C411yescharacteristic, complemented
11C3×#99—21no—
12#453C2×C311yescharacteristic
13#353C2×C311yescharacteristic, complemented
14#331C2×C311yescharacteristic, complemented
15C3×#41—21no—
16C3×#41—41no—
17C2×C3×D4—41no—
18C2×C3×D4—41no—
19C2×C3×D4—41no—
20C2×C3×D4C2×C411yescharacteristic
21C2×C3×D4D411yescharacteristic
22C3×SD16—41no—
23C3×D8—41no—
24C3×M16—21no—
25C2×C3×C8—41no—
26C3×C22⋊C4—41no—
27C3×C42D411yescharacteristic
28H(5,𝔽2)C3×C411yescharacteristic, complemented
29AGL(1,ℤ/8)—21no—
30#127C22×C311yescharacteristic
31C4⋊C8—21no—
32#104—21no—
33#100C3×C411yescharacteristic, complemented
34#99—21no—
35C23×C3—21no—
36C23×C3—21no—
37C23×C3—41no—
38C3×Q8—21no—
39C3×D4—21no—
40C3×D4—41no—
41C3×D4—41no—
42C3×D4—42no—
43C3×D4—41no—
44C3×D4—81no—
45C3×D4—81no—
46C2×C3×C4—21no—
47C2×C3×C4—41no—
48C2×C3×C4—41no—
49C2×C3×C4—81no—
50C2×C3×C4C22⋊C411yescharacteristic
51C3×C8—41no—
52C3×C8—81no—
53#41—21no—
54#41—41no—
55C2×D4—41no—
56C2×D4—41no—
57C2×D4—41no—
58C2×D4C2×C3×C411yescharacteristic
59C2×D4C3×D411yescharacteristic
60SD16—41no—
61D8—41no—
62M16—21no—
63C2×C8—41no—
64C22⋊C4—41no—
65C42C3×D411yescharacteristic
66C22×C3—41no—
67C22×C3—41no—
68C22×C3—41no—
69C22×C3—81no—
70C22×C3—81no—
71C22×C3—161no—
72C22×C3#9911yescharacteristic
73C3×C4—21no—
74C3×C4—21no—
75C3×C4—21no—
76C3×C4—41no—
77C3×C4—161no—
78C23—21no—
79C23—21no—
80C23—41no—
81Q8—21no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—42no—
86D4—41no—
87D4—81no—
88D4—81no—
89C2×C4—21no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—81no—
93C2×C4C3×C22⋊C411yescharacteristic
94C8—41no—
95C8—81no—
96C2×C3—21no—
97C2×C3—81no—
98C2×C3—81no—
99C2×C3—81no—
100C2×C3AΣL(1,𝔽16)11yescharacteristic
101C22—41no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—161no—
107C22C3×#9911yescharacteristic
108C4—21no—
109C4—21no—
110C4—21no—
111C4—41no—
112C4—161no—
113C3#140211yescharacteristic, direct product factor, Sylow
114C2—21no—
115C2—81no—
116C2—81no—
117C2—81no—
118C2C3×AΣL(1,𝔽16)11yescharacteristic
subgroupG/H
center, socleC2×C3AΣL(1,𝔽16)
commutatorC2×D4C2×C3×C4
Frattini, cosocle#127C22×C3
prime radicalC3×#453C2
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#353C2semidirect
3. C3×#331C2semidirect
4. #1402C3direct (N × H)
5. C3×H(5,𝔽2)C4semidirect
10. C3×#100C4semidirect
13. #353C2×C3semidirect
14. #331C2×C3semidirect
28. H(5,𝔽2)C3×C4semidirect
33. #100C3×C4semidirect
113. C3#1402direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#4532
C3×#3532
C3×#3312
#14023