Finite Group Databasebeta

← C3×A4×SD16 #10595553

Subgroups — C3×A4×SD16 #10595553

Order 576.

206 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 56 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×Q8×A4C211yesmaximal, characteristic, complemented
2C3×D4×A4C211yesmaximal, characteristic
3C3×C8×A4C211yesmaximal, characteristic, complemented
4C22×C3×SD16C311yesmaximal, characteristic, complemented
5A4×SD16C313yesmaximal, direct product factor
6C22×C3×A4—21no—
7C3×C4×A4—21no—
8C3×C4×A4C2211yescharacteristic
9C32×SD16—41nomaximal
10C22×C3×Q8C2×C311yescharacteristic, complemented
11C22×C3×D4C2×C311yescharacteristic
12Q8×A4C2×C313yescomplemented
13D4×A4C2×C313yes—
14C2×C3×SD16—31no—
15C2×C3×SD16—31no—
16C2×C3×SD16—31no—
17C2×C3×SD16—31no—
18C22×C3×C8C2×C311yescharacteristic, complemented
19C8×A4C2×C313yescomplemented
20C2×C3×A4—41no—
21C2×C3×A4D411yescharacteristic
22C32×Q8—41no—
23C32×D4—41no—
24C32×C8—41no—
25C22×SD16C3211yescharacteristic, complemented, Sylow
26C24×C3—21no—
27C22×A4—23no—
28C2×C3×Q8—31no—
29C2×C3×Q8—31no—
30C2×C3×Q8—61no—
31C2×C3×D4—31no—
32C2×C3×D4—31no—
33C2×C3×D4—61no—
34C22×C3×C4—21no—
35C22×C3×C4C22×C311yescharacteristic
36C4×A4—23no—
37C4×A4C22×C313yes—
38C3×SD16—32no—
39C3×SD16—31no—
40C3×SD16—31no—
41C3×SD16—31no—
42C3×SD16—43no—
43C3×SD16A411yescharacteristic, direct product factor
44C2×C3×C8—31no—
45C2×C3×C8—31no—
46C22×C32—81no—
47C3×A4SD1611yescharacteristic, direct product factor
48C32×C4—41no—
49C32×C4—81no—
50C22×Q8C2×C3211yescharacteristic, complemented
51C22×D4C2×C3211yescharacteristic
52C2×SD16—31no—
53C2×SD16—31no—
54C2×SD16—31no—
55C2×SD16—31no—
56C22×C8C2×C3211yescharacteristic, complemented
57C23×C3—41no—
58C23×C3—61no—
59C23×C3—61no—
60C23×C3—121no—
61C23×C3C3×D411yescharacteristic
62C2×A4—43no—
63C2×A4C3×D413yes—
64C3×Q8—31no—
65C3×Q8—43no—
66C3×Q8—61no—
67C3×Q8—61no—
68C3×Q8C2×A411yescharacteristic, complemented
69C3×D4—31no—
70C3×D4—43no—
71C3×D4—61no—
72C3×D4—61no—
73C3×D4C2×A411yescharacteristic
74C2×C3×C4—31no—
75C2×C3×C4—31no—
76C2×C3×C4—61no—
77C2×C3×C4—61no—
78C3×C8—31no—
79C3×C8—43no—
80C3×C8C2×A411yescharacteristic, complemented
81C2×C32—41no—
82C2×C32—161no—
83C24—21no—
84C2×Q8—31no—
85C2×Q8—31no—
86C2×Q8—61no—
87C2×D4—31no—
88C2×D4—31no—
89C2×D4—61no—
90C22×C4—21no—
91C22×C4C22×C3211yescharacteristic
92SD16—32no—
93SD16—31no—
94SD16—31no—
95SD16—31no—
96SD16C3×A411yescharacteristic, direct product factor
97C2×C8—31no—
98C2×C8—31no—
99C22×C3—21no—
100C22×C3—31no—
101C22×C3—31no—
102C22×C3—61no—
103C22×C3—83no—
104C22×C3—121no—
105C22×C3—121no—
106C22×C3—121no—
107C22×C3—121no—
108C22×C3C3×SD1611yescharacteristic, complemented
109A4C3×SD1613yesdirect product factor
110C3×C4—21no—
111C3×C4—31no—
112C3×C4—43no—
113C3×C4—61no—
114C3×C4—83no—
115C3×C4C22×A411yescharacteristic
116C32—41noSylow
117C23—41no—
118C23—61no—
119C23—61no—
120C23—121no—
121C23C32×D411yescharacteristic
122Q8—31no—
123Q8—61no—
124Q8—61no—
125Q8C2×C3×A411yescharacteristic, complemented
126D4—31no—
127D4—61no—
128D4—61no—
129D4C2×C3×A411yescharacteristic
130C2×C4—31no—
131C2×C4—31no—
132C2×C4—61no—
133C2×C4—61no—
134C8—31no—
135C8C2×C3×A411yescharacteristic, complemented
136C2×C3—31no—
137C2×C3—31no—
138C2×C3—41no—
139C2×C3—43no—
140C2×C3—121no—
141C2×C3—163no—
142C2×C3D4×A411yescharacteristic
143C22—21no—
144C22—31no—
145C22—31no—
146C22—61no—
147C22—121no—
148C22—121no—
149C22—121no—
150C22—121no—
151C22C32×SD1611yescharacteristic, complemented
152C4—21no—
153C4—31no—
154C4—61no—
155C4C22×C3×A411yescharacteristic
156C3—43no—
157C3A4×SD1611yescharacteristic, direct product factor
158C2—31no—
159C2—31no—
160C2—41no—
161C2—121no—
162C2C3×D4×A411yescharacteristic
subgroupG/H
centerC2×C3D4×A4
commutator, cosocleC22×C4C22×C32
FrattiniC4C22×C3×A4
FittingC22×C3×SD16C3
socleC23×C3C3×D4
prime radicalC3×D4×A4C2
hypercenterC3×SD16A4
hypocenterC22C32×SD16
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

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

NH ≅ G/Ntype
1. C3×Q8×A4C2semidirect
3. C3×C8×A4C2semidirect
4. C22×C3×SD16C3semidirect
5. A4×SD16C3direct (N × H)
10. C22×C3×Q8C2×C3semidirect
12. Q8×A4C2×C3semidirect
18. C22×C3×C8C2×C3semidirect
19. C8×A4C2×C3semidirect
25. C22×SD16C32semidirect
43. C3×SD16A4direct (N × H)
47. C3×A4SD16direct (N × H)
50. C22×Q8C2×C32semidirect
56. C22×C8C2×C32semidirect
68. C3×Q8C2×A4semidirect
80. C3×C8C2×A4semidirect
96. SD16C3×A4direct (N × H)
108. C22×C3C3×SD16semidirect
109. A4C3×SD16direct (N × H)
125. Q8C2×C3×A4semidirect
135. C8C2×C3×A4semidirect
151. C22C32×SD16semidirect
157. C3A4×SD16direct (N × H)

Maximal subgroups

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

subgroupindex
C3×Q8×A42
C3×D4×A42
C3×C8×A42
C22×C3×SD163
A4×SD163
C32×SD164