Finite Group Databasebeta

← D3×C9×SD16 #11721545

Subgroups — D3×C9×SD16 #11721545

Order 864.

224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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×Q8×C9C211yesmaximal, characteristic, complemented
2D3×D4×C9C211yesmaximal, characteristic
3C3×C9×SD16C211yesmaximal, characteristic, complemented
4C9×#215C211yesmaximal, characteristic, complemented
5C9×#214C211yesmaximal, characteristic, complemented
6C9×#204C211yesmaximal, characteristic, complemented
7D3×C8×C9C211yesmaximal, characteristic, complemented
8C3×D3×SD16C311yesmaximal, characteristic
9C2×C9×SD16—31nomaximal
10C22×D3×C9—21no—
11C3×Q8×C9C2211yescharacteristic, complemented
12C3×D4×C9C2211yescharacteristic
13C9×#67—21no—
14C9×D12C2211yescharacteristic
15C4×D3×C9—21no—
16C4×D3×C9C2211yescharacteristic
17C9×Dic6—21no—
18C9×Dic6C2211yescharacteristic, complemented
19C3×C8×C9C2211yescharacteristic, complemented
20C9×C3⋊C8C2211yescharacteristic, complemented
21C3×D3×Q8C2×C311yescharacteristic
22C3×D3×D4C2×C311yescharacteristic
23C32×SD16C2×C311yescharacteristic
24C3×#215C2×C311yescharacteristic
25C3×#214C2×C311yescharacteristic
26C3×#204C2×C311yescharacteristic
27C3×D3×C8C2×C311yescharacteristic
28C2×Q8×C9—31no—
29C2×D4×C9—31no—
30C9×SD16—21no—
31C9×SD16—31no—
32C9×SD16—31no—
33C9×SD16—31no—
34C9×SD16D311yescharacteristic, direct product factor
35C2×C8×C9—31no—
36C22×C3×C9—21no—
37C2×D3×C9—21no—
38C2×D3×C9—42no—
39C2×D3×C9D411yescharacteristic
40C3×C4×C9—21no—
41C3×C4×C9C2311yescharacteristic
42C9×Dic3—21no—
43C9×Dic3D411yescharacteristic
44C2×C3×SD16—31no—
45D3×SD16C911yescharacteristic, direct product factor
46C22×C3×D3—21no—
47C32×Q8C22×C311yescharacteristic
48C32×D4C22×C311yescharacteristic
49C3×#67—21no—
50C3×D12C22×C311yescharacteristic
51C3×C4×D3—21no—
52C3×C4×D3C22×C311yescharacteristic
53C3×Dic6—21no—
54C3×Dic6C22×C311yescharacteristic
55C23×C9—61no—
56C32×C8C22×C311yescharacteristic
57C3×C3⋊C8C22×C311yescharacteristic
58Q8×C9—21no—
59Q8×C9—31no—
60Q8×C9—61no—
61Q8×C9C2×D311yescharacteristic, complemented
62D4×C9—21no—
63D4×C9—31no—
64D4×C9—61no—
65D4×C9C2×D311yescharacteristic
66C2×C4×C9—31no—
67C2×C4×C9—61no—
68C8×C9—21no—
69C8×C9—31no—
70C8×C9C2×D311yescharacteristic, complemented
71C2×C3×C9—41no—
72C2×C3×C9C2×D411yescharacteristic
73D3×C9—41no—
74D3×C9SD1612yesdirect product factor
75C2×C3×Q8—31no—
76C2×C3×D4—31no—
77D3×Q8C2×C911yescharacteristic, complemented
78D3×D4C2×C911yescharacteristic
79C3×SD16—21no—
80C3×SD16—31no—
81C3×SD16—31no—
82C3×SD16—31no—
83C3×SD16C2×C911yescharacteristic, complemented
84C3×SD16C3×D311yescharacteristic
85C2×C3×C8—31no—
86#215C2×C911yescharacteristic, complemented
87#214C2×C911yescharacteristic, complemented
88#204C2×C911yescharacteristic, complemented
89D3×C8C2×C911yescharacteristic, complemented
90C22×C32—21no—
91C2×C3×D3—21no—
92C2×C3×D3—42no—
93C2×C3×D3C3×D411yescharacteristic
94C32×C4—21no—
95C32×C4C23×C311yescharacteristic
96C3×Dic3—21no—
97C3×Dic3C3×D411yescharacteristic
98C22×C9—21no—
99C22×C9—31no—
100C22×C9—41no—
101C22×C9—61no—
102C22×C9—122no—
103C4×C9—21no—
104C4×C9—21no—
105C4×C9—31no—
106C4×C9—41no—
107C4×C9—61no—
108C4×C9C22×D311yescharacteristic
109C2×SD16—31noSylow
110C3×C9C2×SD1611yescharacteristic, complemented, Sylow
111C23×C3—61no—
112C22×D3—21no—
113C3×Q8—21no—
114C3×Q8—31no—
115C3×Q8—61no—
116C3×Q8C22×C911yescharacteristic, complemented
117C3×Q8C2×C3×D311yescharacteristic
118C3×D4—21no—
119C3×D4—31no—
120C3×D4—61no—
121C3×D4C22×C911yescharacteristic
122C3×D4C2×C3×D311yescharacteristic
123C2×C3×C4—31no—
124C2×C3×C4—61no—
125#67—21no—
126D12C22×C911yescharacteristic
127C4×D3—21no—
128C4×D3C22×C911yescharacteristic
129Dic6—21no—
130Dic6C22×C911yescharacteristic, complemented
131C3×C8—21no—
132C3×C8—31no—
133C3×C8C22×C911yescharacteristic, complemented
134C3×C8C2×C3×D311yescharacteristic
135C3⋊C8C22×C911yescharacteristic, complemented
136C2×C32—41no—
137C2×C32C2×C3×D411yescharacteristic
138C3×D3—41no—
139C3×D3C3×SD1612yes—
140C2×C9—21no—
141C2×C9—32no—
142C2×C9—41no—
143C2×C9—81no—
144C2×C9—121no—
145C2×C9D3×D411yescharacteristic
146C2×Q8—31no—
147C2×D4—31no—
148SD16—31no—
149SD16—31no—
150SD16—31no—
151SD16D3×C911yescharacteristic, direct product factor
152C2×C8—31no—
153C22×C3—21no—
154C22×C3—21no—
155C22×C3—31no—
156C22×C3—41no—
157C22×C3—61no—
158C22×C3—122no—
159C2×D3—21no—
160C2×D3—42no—
161C2×D3D4×C911yescharacteristic
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—31no—
166C3×C4—41no—
167C3×C4—61no—
168C3×C4C23×C911yescharacteristic
169C3×C4C22×C3×D311yescharacteristic
170Dic3—21no—
171Dic3D4×C911yescharacteristic
172C32C2×C3×SD1611yescharacteristic
173C9—21no—
174C9D3×SD1611yescharacteristic, direct product factor
175C23—61no—
176Q8—31no—
177Q8—61no—
178Q8C2×D3×C911yescharacteristic, complemented
179D4—31no—
180D4—61no—
181D4C2×D3×C911yescharacteristic
182C2×C4—31no—
183C2×C4—61no—
184C8—31no—
185C8C2×D3×C911yescharacteristic, complemented
186C2×C3—21no—
187C2×C3—32no—
188C2×C3—41no—
189C2×C3—41no—
190C2×C3—81no—
191C2×C3—121no—
192C2×C3C2×D4×C911yescharacteristic
193C2×C3C3×D3×D411yescharacteristic
194D3—41no—
195D3C9×SD1612yesdirect product factor
196C22—21no—
197C22—31no—
198C22—61no—
199C22—122no—
200C4—21no—
201C4—31no—
202C4—61no—
203C4C22×D3×C911yescharacteristic
204C3—21no—
205C3C2×C9×SD1611yescharacteristic, complemented
206C3C3×D3×SD1611yescharacteristic
207C2—32no—
208C2—41no—
209C2—121no—
210C2D3×D4×C911yescharacteristic
subgroupG/H
centerC2×C9D3×D4
commutatorC3×C4C23×C9
FrattiniC3×C4C22×C3×D3
FittingC3×C9×SD16C2
socleC2×C32C2×C3×D4
prime radicalC3×D3×D4C2×C3
cosocleC32×C4C23×C3
hypercenterC9×SD16D3
hypocenterC3C2×C9×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C9 ◁ C4×C9 ◁ C9×SD16

Complements

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

NH ≅ G/Ntype
1. D3×Q8×C9C2semidirect
3. C3×C9×SD16C2semidirect
4. C9×#215C2semidirect
5. C9×#214C2semidirect
6. C9×#204C2semidirect
7. D3×C8×C9C2semidirect
11. C3×Q8×C9C22semidirect
18. C9×Dic6C22semidirect
19. C3×C8×C9C22semidirect
20. C9×C3⋊C8C22semidirect
34. C9×SD16D3direct (N × H)
45. D3×SD16C9direct (N × H)
61. Q8×C9C2×D3semidirect
70. C8×C9C2×D3semidirect
74. D3×C9SD16direct (N × H)
77. D3×Q8C2×C9semidirect
83. C3×SD16C2×C9semidirect
86. #215C2×C9semidirect
87. #214C2×C9semidirect
88. #204C2×C9semidirect
89. D3×C8C2×C9semidirect
110. C3×C9C2×SD16semidirect
116. C3×Q8C22×C9semidirect
130. Dic6C22×C9semidirect
133. C3×C8C22×C9semidirect
135. C3⋊C8C22×C9semidirect
151. SD16D3×C9direct (N × H)
174. C9D3×SD16direct (N × H)
178. Q8C2×D3×C9semidirect
185. C8C2×D3×C9semidirect
195. D3C9×SD16direct (N × H)
205. C3C2×C9×SD16semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×C92
D3×D4×C92
C3×C9×SD162
C9×#2152
C9×#2142
C9×#2042
D3×C8×C92
C3×D3×SD163
C2×C9×SD163