Finite Group Databasebeta

← D3×D96 #11800506

Subgroups — D3×D96 #11800506

Order 1152.

257 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 257 conjugacy classes of subgroups — too many to draw. Only its 60 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
1D3×D48C212yesmaximal, complemented
2#10589314C211yesmaximal, characteristic, complemented
3C3×D96C211yesmaximal, characteristic, complemented
4C3×D3×C32C211yesmaximal, characteristic, complemented
5#10589071C212yesmaximal, complemented
6D3×D32—31nomaximal
7C2×D96—31nomaximal
8D3×D24—22no—
9#63626C2212yescomplemented
10C3×D48C2212yescomplemented
11C3×D3×C16C2211yescharacteristic
12#63546—22no—
13C32×C32C2211yescharacteristic, complemented
14C3×C3⋊C32C2211yescharacteristic, complemented
15D3×D16—32no—
16C2×D48—32no—
17C3×D32—31no—
18C2×C3×C32—31no—
19#4519—32no—
20D96—32no—
21D96—31no—
22D96—31no—
23D96—61no—
24D96D311yescharacteristic, direct product factor
25D3×C32D311yescharacteristic, complemented
26D3×D12—42no—
27#3745—22no—
28C3×D24—22no—
29C3×D3×C8D411yescharacteristic
30#3714—42no—
31C32×C16C2311yescharacteristic
32C3×C3⋊C16D411yescharacteristic
33C2×D32—91noSylow
34D3×D8—62no—
35C2×D24—62no—
36C3×D16—32no—
37C2×C3×C16—31no—
38#826—62no—
39D48—32no—
40D48—32no—
41D48—62no—
42D48—62no—
43D48C2×D312yescomplemented
44D3×C16C2×D311yescharacteristic
45C3×C32—21no—
46C3×C32—31no—
47C3×C32C2×D311yescharacteristic, complemented
48C3×C32C2×D311yescharacteristic, complemented
49C3⋊C32C2×D311yescharacteristic, complemented
50C2×D32—82no—
51C4⋊(C3⋊D3)—42no—
52C3×D12—42no—
53C3×C4×D3D811yescharacteristic
54#626—82no—
55C32×C8C2×D411yescharacteristic
56C3×C3⋊C8D811yescharacteristic
57C2×D16—92no—
58D32—31no—
59D32—92no—
60D32—91no—
61C2×C32—31no—
62D3×D4—122no—
63C2×D12—122no—
64C3×D8—62no—
65C2×C3×C8—31no—
66#213—122no—
67D24—22no—
68D24—62no—
69D24—62no—
70D24—122no—
71D24—122no—
72D3×C8D1211yescharacteristic
73C3×C16—21no—
74C3×C16—31no—
75C3×C16C22×D311yescharacteristic
76C3×C16C22×D311yescharacteristic
77C3⋊C16D1211yescharacteristic
78C2×C3⋊D3—82no—
79C2×C3×D3—82no—
80C2×C3×D3D1611yescharacteristic
81D32—164no—
82C32×C4C2×D811yescharacteristic
83C3×Dic3D1611yescharacteristic
84C2×D8—182no—
85D16—32no—
86D16—92no—
87D16—182no—
88C2×C16—31no—
89C32—31no—
90C32D3211yescharacteristic, complemented
91C22×D3—242no—
92C22×D3—242no—
93C3×D4—122no—
94C2×C3×C4—31no—
95#67—242no—
96D12—42no—
97D12—122no—
98D12—122no—
99D12—242no—
100D12—242no—
101C4×D3D2411yescharacteristic
102C3×C8—21no—
103C3×C8—31no—
104C3×C8C2×D1211yescharacteristic
105C3×C8D3×D411yescharacteristic
106C3⋊C8D2411yescharacteristic
107C2×C32C2×D1611yescharacteristic
108C3⋊D3—162no—
109C3×D3—162no—
110C3×D3D3212yescomplemented
111C2×D4—362no—
112D8—62no—
113D8—182no—
114D8—362no—
115C2×C8—31no—
116C16—31no—
117C16C2×D3211yescharacteristic
118C22×C3—31no—
119C22×C3—242no—
120C2×D3—82no—
121C2×D3—242no—
122C2×D3—242no—
123C2×D3—482no—
124C2×D3—484no—
125C2×D3—484no—
126C2×D3D4811yescharacteristic
127C3×C4—21no—
128C3×C4—31no—
129C3×C4C2×D2411yescharacteristic
130C3×C4D3×D811yescharacteristic
131Dic3D4811yescharacteristic
132C32C2×D3211yescharacteristic, complemented, Sylow
133C23—722no—
134D4—122no—
135D4—362no—
136D4—722no—
137C2×C4—31no—
138C8—31no—
139C8D3×D1211yescharacteristic
140C2×C3—21no—
141C2×C3—32no—
142C2×C3—482no—
143C2×C3C2×D4811yescharacteristic
144C2×C3D3×D1611yescharacteristic
145D3—162no—
146D3—482no—
147D3—482no—
148D3—962no—
149D3D9612yesdirect product factor
150C22—31no—
151C22—242no—
152C22—722no—
153C22—1444no—
154C4—31no—
155C4D3×D2411yescharacteristic
156C3—21no—
157C3C2×D9611yescharacteristic, complemented
158C3D3×D3211yescharacteristic, complemented
159C2—32no—
160C2—482no—
161C2—1442no—
162C2D3×D4811yescharacteristic
subgroupG/H
centerC2D3×D48
commutator, cosocleC32×C16C23
FrattiniC16C2×D32
FittingC32×C32C22
socleC2×C32C2×D16
hypercenterC32D32
hypocenterC32C2×D32
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32

Complements

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

NH ≅ G/Ntype
1. D3×D48C2semidirect
2. #10589314C2semidirect
3. C3×D96C2semidirect
4. C3×D3×C32C2semidirect
5. #10589071C2semidirect
9. #63626C22semidirect
10. C3×D48C22semidirect
13. C32×C32C22semidirect
14. C3×C3⋊C32C22semidirect
24. D96D3direct (N × H)
25. D3×C32D3semidirect
43. D48C2×D3semidirect
47. C3×C32C2×D3semidirect
48. C3×C32C2×D3semidirect
49. C3⋊C32C2×D3semidirect
90. C32D32semidirect
110. C3×D3D32semidirect
132. C32C2×D32semidirect
149. D3D96direct (N × H)
157. C3C2×D96semidirect
158. C3D3×D32semidirect

Maximal subgroups

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

subgroupindex
D3×D482
#105893142
C3×D962
C3×D3×C322
#105890712
D3×D323
C2×D963