Finite Group Databasebeta

← D3×#509 #82034

Subgroups — D3×#509 #82034

Order 384.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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×#135C211yesmaximal, characteristic, complemented
2C2×D3×D8C211yesmaximal, characteristic, complemented
3C3×#509C211yesmaximal, characteristic, complemented
4#5193C211yesmaximal, characteristic, complemented
5#5147C211yesmaximal, characteristic, complemented
6#4914C212yesmaximal, complemented
7D3×SD32C212yesmaximal, complemented
8#4911C212yesmaximal, complemented
9D3×D16C212yesmaximal, complemented
10#4908C211yesmaximal, characteristic, complemented
11D3×M32C211yesmaximal, characteristic, complemented
12C2×#509—31nomaximal, Sylow
13D3×#41—21no—
14C2×D3×D4—21no—
15C3×#135C2211yescharacteristic, complemented
16C2×C3×D8C2211yescharacteristic, complemented
17#950—21no—
18C2×#213—21no—
19#919C2211yescharacteristic, complemented
20D3×Q16C2211yescharacteristic, complemented
21#916—21no—
22D3×SD16—21no—
23#912C2211yescharacteristic, complemented
24D3×D8—21no—
25D3×D8—21no—
26D3×D8C2212yes—
27D3×D8C2212yescomplemented
28D3×D8C2211yescharacteristic, complemented
29#904C2211yescharacteristic, complemented
30C2×D24C2211yescharacteristic, complemented
31C2×D3×C8C2211yescharacteristic
32C3×SD32C2212yescomplemented
33C3×D16C2212yescomplemented
34C3×M32C2211yescharacteristic, complemented
35#828C2212yescomplemented
36#827C2212yescomplemented
37#826C2212yescomplemented
38#826C2212yescomplemented
39#812C2211yescharacteristic, complemented
40#800C2212yescomplemented
41D48C2212yescomplemented
42#798C2212yescomplemented
43D3×C16C2212yescomplemented
44C2×#135—31no—
45C22×D8—31no—
46#509—31no—
47#509—31no—
48#509—32no—
49#509—32no—
50#509—31no—
51#509D311yescharacteristic, direct product factor
52C2×SD32—32no—
53C2×D16—32no—
54C2×M32—31no—
55C23×D3—41no—
56C3×#41—21no—
57C2×C3×D4—21no—
58C2×#67—41no—
59#239—21no—
60D3×Q8—21no—
61#237—21no—
62#237—41no—
63D3×D4—22no—
64D3×D4—22no—
65D3×D4—21no—
66D3×D4—41no—
67D3×D4—41no—
68D3×D4—41no—
69#235—21no—
70#235—41no—
71C2×D12—21no—
72C2×C4×D3—41no—
73C2×C4×D3D411yescharacteristic
74C3×Q16C2311yescharacteristic, complemented
75C3×SD16—21no—
76C3×D8—21no—
77C3×D8C2312yes—
78C3×D8C2311yescharacteristic, complemented
79C2×C3×C8C2311yescharacteristic
80#216—21no—
81#215—21no—
82#214—21no—
83#213—22no—
84#213—22no—
85#213—21no—
86C2×C3⋊C8D411yescharacteristic
87Dic12C2311yescharacteristic, complemented
88D24—21no—
89D24C2312yes—
90D24C2311yescharacteristic, complemented
91#204—21no—
92D3×C8D411yescharacteristic
93D3×C8D411yescharacteristic
94D3×C8C2311yescharacteristic
95D3×C8C2311yescharacteristic
96C3×C16C2312yescomplemented
97C3⋊C16C2312yescomplemented
98C2×#41—61no—
99C22×D4—61no—
100#135—31no—
101#135—31no—
102#135—31no—
103#135—61no—
104#135—61no—
105#135C2×D311yescharacteristic, complemented
106C2×Q16—31no—
107C2×SD16—61no—
108C2×D8—32no—
109C2×D8—32no—
110C2×D8—31no—
111C2×D8—31no—
112C2×D8—61no—
113C2×D8—61no—
114C2×D8—61no—
115C2×D8C2×D311yescharacteristic, complemented
116C22×C8—31no—
117SD32—32no—
118SD32—32no—
119SD32—32no—
120SD32C2×D312yescomplemented
121D16—32no—
122D16—32no—
123D16—32no—
124D16C2×D312yescomplemented
125M32—31no—
126M32—32no—
127M32C2×D311yescharacteristic, complemented
128C2×C16—32no—
129C23×C3—41no—
130C22×D3—41no—
131C22×D3—41no—
132C22×D3—42no—
133C22×D3—42no—
134C22×D3—84no—
135C22×D3D811yescharacteristic
136C3×Q8—21no—
137C3×D4—22no—
138C3×D4—21no—
139C3×D4—41no—
140C3×D4—41no—
141C2×C3×C4—41no—
142C2×C3×C4C2×D411yescharacteristic
143#67—41no—
144#67—41no—
145#67—41no—
146#67—42no—
147#67—42no—
148C2×Dic3—41no—
149C2×Dic3D811yescharacteristic
150D12—21no—
151D12—22no—
152D12—41no—
153D12—41no—
154C4×D3—41no—
155C4×D3—41no—
156C4×D3—41no—
157C4×D3D811yescharacteristic
158C4×D3D811yescharacteristic
159C4×D3C2×D411yescharacteristic
160C4×D3C2×D411yescharacteristic
161Dic6—21no—
162Dic6—41no—
163C3×C8C2×D411yescharacteristic
164C3×C8C2411yescharacteristic
165C3⋊C8C2×D411yescharacteristic
166C3⋊C8C2×D411yescharacteristic
167C24—121no—
168#41—21no—
169#41—61no—
170#41—61no—
171#41—61no—
172#41—121no—
173#41—121no—
174C2×Q8—61no—
175C2×D4—21no—
176C2×D4—62no—
177C2×D4—62no—
178C2×D4—61no—
179C2×D4—61no—
180C2×D4—121no—
181C2×D4—121no—
182C2×D4—121no—
183C2×D4—121no—
184C22×C4—31no—
185C22×C4—121no—
186Q16—31no—
187Q16—61no—
188Q16C22×D311yescharacteristic, complemented
189SD16—21no—
190SD16—61no—
191SD16—61no—
192SD16—61no—
193D8—21no—
194D8—31no—
195D8—32no—
196D8—62no—
197D8—62no—
198D8—61no—
199D8—61no—
200D8C22×D312yes—
201D8C22×D311yescharacteristic, complemented
202C2×C8—31no—
203C2×C8—31no—
204C2×C8—31no—
205C2×C8—31no—
206C2×C8—31no—
207C2×C8C22×D311yescharacteristic
208C16—32no—
209C16C22×D312yescomplemented
210C22×C3—41no—
211C22×C3—42no—
212C22×C3—82no—
213C22×C3C2×D811yescharacteristic
214C2×D3—22no—
215C2×D3—41no—
216C2×D3—42no—
217C2×D3—84no—
218C2×D3—82no—
219C2×D3—82no—
220C2×D3—84no—
221C2×D3C2×D811yescharacteristic
222C2×D3C2×D811yescharacteristic
223C3×C4—41no—
224C3×C4C2×D811yescharacteristic
225C3×C4C22×D411yescharacteristic
226Dic3—41no—
227Dic3C2×D811yescharacteristic
228Dic3C2×D811yescharacteristic
229C23—31no—
230C23—41no—
231C23—121no—
232C23—122no—
233C23—122no—
234C23—121no—
235C23—244no—
236Q8—21no—
237Q8—61no—
238Q8—121no—
239D4—22no—
240D4—21no—
241D4—41no—
242D4—41no—
243D4—62no—
244D4—61no—
245D4—122no—
246D4—122no—
247D4—121no—
248D4—121no—
249D4—121no—
250D4—121no—
251D4—121no—
252C2×C4—31no—
253C2×C4—31no—
254C2×C4—31no—
255C2×C4—31no—
256C2×C4—31no—
257C2×C4—41no—
258C2×C4—121no—
259C2×C4—121no—
260C2×C4—121no—
261C2×C4—121no—
262C2×C4D3×D411yescharacteristic
263C8—31no—
264C8—31no—
265C8D3×D411yescharacteristic
266C8C23×D311yescharacteristic
267C2×C3—21no—
268C2×C3—82no—
269C2×C3—81no—
270C2×C3C22×D811yescharacteristic
271D3—21no—
272D3—81no—
273D3—82no—
274D3#50912yesdirect product factor
275C22—31no—
276C22—31no—
277C22—41no—
278C22—42no—
279C22—62no—
280C22—82no—
281C22—121no—
282C22—122no—
283C22—242no—
284C22—244no—
285C22—242no—
286C22—244no—
287C22D3×D811yescharacteristic
288C4—31no—
289C4—31no—
290C4—41no—
291C4—121no—
292C4D3×D811yescharacteristic
293C4C2×D3×D411yescharacteristic
294C3C2×#50911yescharacteristic, complemented, Sylow
295C2—21no—
296C2—32no—
297C2—61no—
298C2—82no—
299C2—81no—
300C2—242no—
301C2—241no—
302C2C2×D3×D811yescharacteristic
subgroupG/H
centerC2C2×D3×D8
commutator, cosocleC3×C8C24
FrattiniC8C23×D3
FittingC3×#509C2
socleC2×C3C22×D8
hypercenter#509D3
hypocenterC3C2×#509
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. D3×#135C2semidirect
2. C2×D3×D8C2semidirect
3. C3×#509C2semidirect
4. #5193C2semidirect
5. #5147C2semidirect
6. #4914C2semidirect
7. D3×SD32C2semidirect
8. #4911C2semidirect
9. D3×D16C2semidirect
10. #4908C2semidirect
11. D3×M32C2semidirect
15. C3×#135C22semidirect
16. C2×C3×D8C22semidirect
19. #919C22semidirect
20. D3×Q16C22semidirect
23. #912C22semidirect
27. D3×D8C22semidirect
28. D3×D8C22semidirect
29. #904C22semidirect
30. C2×D24C22semidirect
32. C3×SD32C22semidirect
33. C3×D16C22semidirect
34. C3×M32C22semidirect
35. #828C22semidirect
36. #827C22semidirect
37. #826C22semidirect
38. #826C22semidirect
39. #812C22semidirect
40. #800C22semidirect
41. D48C22semidirect
42. #798C22semidirect
43. D3×C16C22semidirect
51. #509D3direct (N × H)
74. C3×Q16C23semidirect
78. C3×D8C23semidirect
87. Dic12C23semidirect
90. D24C23semidirect
96. C3×C16C23semidirect
97. C3⋊C16C23semidirect
105. #135C2×D3semidirect
115. C2×D8C2×D3semidirect
120. SD32C2×D3semidirect
124. D16C2×D3semidirect
127. M32C2×D3semidirect
188. Q16C22×D3semidirect
201. D8C22×D3semidirect
209. C16C22×D3semidirect
274. D3#509direct (N × H)
294. C3C2×#509semidirect

Maximal subgroups

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

subgroupindex
D3×#1352
C2×D3×D82
C3×#5092
#51932
#51472
#49142
D3×SD322
#49112
D3×D162
#49082
D3×M322
C2×#5093