Finite Group Databasebeta

← SD32×C3⋊D9 #13144210

Subgroups — SD32×C3⋊D9 #13144210

Order 1728.

450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 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
1Q16×C3⋊D9C211yesmaximal, characteristic, complemented
2D8×C3⋊D9C211yesmaximal, characteristic
3C3×C9×SD32C211yesmaximal, characteristic, complemented
4#11720567C211yesmaximal, characteristic, complemented
5#11720564C211yesmaximal, characteristic, complemented
6#11720508C211yesmaximal, characteristic, complemented
7C16×C3⋊D9C211yesmaximal, characteristic, complemented
8C3⋊D3×SD32—31nomaximal
9D9×SD32—33nomaximal
10Q8×C3⋊D9—21no—
11D4×C3⋊D9—21no—
12C3×C9×Q16C2211yescharacteristic, complemented
13C3×C9×D8C2211yescharacteristic
14#88547—21no—
15#88544—21no—
16#88525C2211yescharacteristic
17C8×C3⋊D9C2211yescharacteristic
18#88521C2211yescharacteristic, complemented
19C3×C9×C16C2211yescharacteristic, complemented
20C3⋊(C9⋊C16)C2211yescharacteristic, complemented
21Q16×C3⋊D3—31no—
22D8×C3⋊D3—31no—
23C32×SD32D311yescharacteristic
24#63655—31no—
25#63654—31no—
26#63627—31no—
27C16×C3⋊D3—31no—
28Q16×D9—33no—
29D8×D9—33no—
30C9×SD32D313yescomplemented
31#63387—33no—
32#63386—33no—
33#63359—33no—
34C16×D9—33no—
35C22×C3⋊D9—41no—
36C3×Q8×C9—21no—
37C3×D4×C9—21no—
38#6233—41no—
39C4⋊(C3⋊D9)—21no—
40C4×C3⋊D9—41no—
41C4×C3⋊D9D411yescharacteristic
42#6226—21no—
43#6226—41no—
44C3×C8×C9C2311yescharacteristic
45C3⋊(C9⋊C8)D411yescharacteristic
46D3×SD32—93no—
47D3×SD32—91no—
48Q8×C3⋊D3—61no—
49D4×C3⋊D3—61no—
50C32×Q16C2×D311yescharacteristic
51C32×D8C2×D311yescharacteristic
52#3756—61no—
53#3753—61no—
54#3746—31no—
55#3745—31no—
56C8×C3⋊D3—31no—
57Q8×D9—63no—
58D4×D9—63no—
59C32×C16C2×D311yescharacteristic
60C3⋊(C3⋊C16)—31no—
61C9×Q16C2×D313yescomplemented
62C9×D8C2×D313yes—
63#3674—63no—
64#3673—63no—
65D72—33no—
66C8×D9—33no—
67Dic36—33no—
68C9×C16C2×D313yescomplemented
69C9⋊C16—33no—
70C22×C3×C9—41no—
71C2×C3⋊D9—41no—
72C2×C3⋊D9—82no—
73C2×C3⋊D9D811yescharacteristic
74C3×C4×C9—41no—
75C3×C4×C9C2×D411yescharacteristic
76C3⋊Dic9—41no—
77C3⋊Dic9D811yescharacteristic
78D3×Q16—93no—
79D3×Q16—91no—
80D3×D8—93no—
81D3×D8—91no—
82C3×SD32D913yescomplemented
83C3×SD32C3⋊D311yescharacteristic
84#828—93no—
85#828—91no—
86#827—93no—
87#827—91no—
88#800—93no—
89#800—91no—
90D3×C16—93no—
91D3×C16—91no—
92C22×C3⋊D3—121no—
93C32×Q8—21no—
94C32×D4—21no—
95#638—121no—
96C4⋊(C3⋊D3)—61no—
97C4×C3⋊D3—31no—
98C4×C3⋊D3—121no—
99#634—61no—
100#634—121no—
101C22×D9—123no—
102C32×C8C22×D311yescharacteristic
103C3⋊(C3⋊C8)—31no—
104Q8×C9—23no—
105D4×C9—23no—
106#611—123no—
107D36—63no—
108C4×D9—33no—
109C4×D9—123no—
110Dic18—63no—
111Dic18—123no—
112C8×C9C22×D313yes—
113C9⋊C8—33no—
114C2×SD32—271noSylow
115C2×C3×C9—81no—
116C2×C3×C9C2×D811yescharacteristic
117C3⋊D9—81no—
118C3⋊D9SD3212yesdirect product factor
119D3×Q8—181no—
120D3×Q8—183no—
121D3×D4—181no—
122D3×D4—183no—
123C3×Q16C2×D913yescomplemented
124C3×Q16C2×C3⋊D311yescharacteristic
125C3×D8C2×D913yes—
126C3×D8C2×C3⋊D311yescharacteristic
127#216—181no—
128#216—183no—
129#213—181no—
130#213—183no—
131Dic12—93no—
132Dic12—91no—
133D24—93no—
134D24—91no—
135D3×C8—93no—
136D3×C8—91no—
137C3×C16C2×D913yescomplemented
138C3×C16C2×C3⋊D311yescharacteristic
139C3⋊C16—93no—
140C3⋊C16—91no—
141C22×C32—41no—
142C2×C3⋊D3—31no—
143C2×C3⋊D3—121no—
144C2×C3⋊D3—242no—
145C32×C4—41no—
146C32×C4D3×D411yescharacteristic
147C3⋊Dic3—31no—
148C3⋊Dic3—121no—
149C22×C9—43no—
150C2×D9—33no—
151C2×D9—123no—
152C2×D9—246no—
153C4×C9—43no—
154C4×C9D3×D413yes—
155Dic9—33no—
156Dic9—123no—
157C2×Q16—271no—
158C2×D8—271no—
159SD32—271no—
160SD32—271no—
161SD32—271no—
162SD32C3⋊D911yescharacteristic, direct product factor
163C2×C16—271no—
164C3×C9C2×SD3211yescharacteristic, complemented, Sylow
165C22×D3—361no—
166C22×D3—363no—
167C3×Q8—23no—
168C3×Q8—21no—
169C3×D4—23no—
170C3×D4—21no—
171#67—361no—
172#67—363no—
173D12—183no—
174D12—181no—
175C4×D3—93no—
176C4×D3—91no—
177C4×D3—361no—
178C4×D3—363no—
179Dic6—183no—
180Dic6—181no—
181Dic6—361no—
182Dic6—363no—
183C3×C8C22×D913yes—
184C3×C8C22×C3⋊D311yescharacteristic
185C3⋊C8—93no—
186C3⋊C8—91no—
187C2×C32—81no—
188C2×C32D3×D811yescharacteristic
189C3⋊D3—32no—
190C3⋊D3—241no—
191C2×C9—83no—
192C2×C9D3×D813yes—
193D9—36no—
194D9—243no—
195C2×Q8—541no—
196C2×D4—541no—
197Q16—271no—
198Q16—541no—
199Q16C2×C3⋊D911yescharacteristic, complemented
200D8—271no—
201D8—541no—
202D8C2×C3⋊D911yescharacteristic
203C2×C8—271no—
204C16—271no—
205C16C2×C3⋊D911yescharacteristic, complemented
206C22×C3—41no—
207C22×C3—43no—
208C2×D3—91no—
209C2×D3—93no—
210C2×D3—361no—
211C2×D3—363no—
212C2×D3—722no—
213C2×D3—726no—
214C3×C4—41no—
215C3×C4—43no—
216C3×C4D4×D913yes—
217C3×C4D4×C3⋊D311yescharacteristic
218Dic3—91no—
219Dic3—93no—
220Dic3—361no—
221Dic3—363no—
222C32D3×SD3211yescharacteristic
223C9D3×SD3213yescomplemented
224C23—1081no—
225Q8—21no—
226Q8—541no—
227Q8—1081no—
228D4—21no—
229D4—541no—
230D4—1081no—
231C2×C4—271no—
232C2×C4—1081no—
233C8—271no—
234C8C22×C3⋊D911yescharacteristic
235C2×C3—81no—
236C2×C3—83no—
237C2×C3D8×D913yes—
238C2×C3D8×C3⋊D311yescharacteristic
239D3—92no—
240D3—96no—
241D3—721no—
242D3—723no—
243C22—41no—
244C22—271no—
245C22—1081no—
246C22—2162no—
247C4—41no—
248C4—271no—
249C4—1081no—
250C4D4×C3⋊D911yescharacteristic
251C3D9×SD3213yescomplemented
252C3C3⋊D3×SD3211yescharacteristic
253C2—81no—
254C2—272no—
255C2—2161no—
256C2D8×C3⋊D911yescharacteristic
subgroupG/H
centerC2D8×C3⋊D9
commutator, cosocleC3×C8×C9C23
FrattiniC3×C8C22×C3⋊D3
FittingC3×C9×SD32C2
socleC2×C32D3×D8
prime radicalD8×C3⋊D9C2
hypercenterSD32C3⋊D9
hypocenterC3×C9C2×SD32
LCSG ▷ C3×C8×C9 ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. Q16×C3⋊D9C2semidirect
3. C3×C9×SD32C2semidirect
4. #11720567C2semidirect
5. #11720564C2semidirect
6. #11720508C2semidirect
7. C16×C3⋊D9C2semidirect
12. C3×C9×Q16C22semidirect
18. #88521C22semidirect
19. C3×C9×C16C22semidirect
20. C3⋊(C9⋊C16)C22semidirect
30. C9×SD32D3semidirect
61. C9×Q16C2×D3semidirect
68. C9×C16C2×D3semidirect
82. C3×SD32D9semidirect
118. C3⋊D9SD32direct (N × H)
123. C3×Q16C2×D9semidirect
137. C3×C16C2×D9semidirect
162. SD32C3⋊D9direct (N × H)
164. C3×C9C2×SD32semidirect
199. Q16C2×C3⋊D9semidirect
205. C16C2×C3⋊D9semidirect
223. C9D3×SD32semidirect
251. C3D9×SD32semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊D92
D8×C3⋊D92
C3×C9×SD322
#117205672
#117205642
#117205082
C16×C3⋊D92
C3⋊D3×SD323
D9×SD323