Finite Group Databasebeta

← D3×#907 #10594705

Subgroups — D3×#907 #10594705

Order 576.

563 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#235C211yesmaximal, characteristic
2#64116C211yesmaximal, characteristic, complemented
3C3×#907C211yesmaximal, characteristic, complemented
4C3×D3×M16C211yesmaximal, characteristic, complemented
5#63817C211yesmaximal, characteristic, complemented
6#63815C211yesmaximal, characteristic, complemented
7C2×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#63805C212yesmaximal, complemented
9#63804C212yesmaximal, complemented
10D3×ΓL(1,𝔽25)C212yesmaximal, complemented
11D32×C8C212yesmaximal, complemented
12D3×#131—31nomaximal
13C2×#907—31nomaximal
14#3828C2211yescharacteristic
15C3×#235C2211yescharacteristic
16C2×C3×C4×D3C2211yescharacteristic
17D3×#67C412yes—
18#3804C412yes—
19D3×D12C411yescharacteristic
20C4×D32C2212yes—
21#3799C411yescharacteristic
22#3798C2212yes—
23#3795C411yescharacteristic
24D3×Dic6C411yescharacteristic
25C32×M16C2211yescharacteristic, complemented
26C2×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27#3743C2212yescomplemented
28C8×C3⋊D3C2212yescomplemented
29C3×#208C2211yescharacteristic, complemented
30C2×C3×C3⋊C8C2211yescharacteristic, complemented
31C3×ΓL(1,𝔽25)C2212yescomplemented
32C3×ΓL(1,𝔽25)C2212yescomplemented
33C3×D3×C8C2212yes—
34C3×D3×C8C2212yescomplemented
35#3712C2212yescomplemented
36#3711C2212yescomplemented
37#3710C2212yescomplemented
38D3×C3⋊C8C2211yescharacteristic
39D3×C3⋊C8C2211yescharacteristic
40D3×C3⋊C8C2212yescomplemented
41D3×C3⋊C8C2211yescharacteristic, complemented
42D3×C3⋊C8C2211yescharacteristic, complemented
43D3×#41—31no—
44C2×#235—31no—
45C3×#131—31no—
46C2×C3×M16—31no—
47#948—31no—
48C22×C3⋊C8—31no—
49#907—31no—
50#907—31no—
51#907—31no—
52#907—31no—
53#907—32no—
54#907—32no—
55#907—32no—
56#907—61no—
57#907D311yescharacteristic, direct product factor
58D3×M16—32no—
59D3×M16D311yescharacteristic, complemented
60#901—31no—
61#901—32no—
62C2×ΓL(1,𝔽25)—32no—
63C2×D3×C8—31no—
64C2×D3×C8—32no—
65C2×D3×C8—32no—
66C22×C3×D3C2×C411yescharacteristic
67C2×D32C2×C412yes—
68C2×C32×C4C2311yescharacteristic
69#638C2×C412yes—
70C4⋊(C3⋊D3)C2×C411yescharacteristic
71C4×C3⋊D3C2312yes—
72#634C2×C411yescharacteristic
73C3×#67C2×C412yes—
74C2×C3×Dic3C2×C411yescharacteristic
75C3×D12C2×C411yescharacteristic
76C3×C4×D3C2×C411yescharacteristic
77C3×C4×D3C2×C411yescharacteristic
78C3×C4×D3C2311yescharacteristic
79C3×C4×D3C2311yescharacteristic
80C3×C4×D3C2312yes—
81C3×Dic6C2×C411yescharacteristic
82#627C2×C412yes—
83#626C2×C412yes—
84#626C2×C412yes—
85#625C2×C412yes—
86#624C2×C412yes—
87D3×Dic3C2×C412yes—
88D3×Dic3C2×C412yes—
89C32×C8C2312yes—
90C3⋊(C3⋊C8)C2311yescharacteristic
91C3⋊(C3⋊C8)C2311yescharacteristic
92C3×C3⋊C8C2311yescharacteristic
93C3×C3⋊C8C2311yescharacteristic
94C3×C3⋊C8C2312yes—
95C2×#131—91noSylow
96C3×#41—31no—
97C22×C3×C4—31no—
98C2×#67—32no—
99#239—31no—
100D3×Q8—31no—
101#237—32no—
102#237—31no—
103D3×D4—32no—
104D3×D4—31no—
105#235—31no—
106#235—31no—
107#235—32no—
108#235—31no—
109#235—32no—
110#235—32no—
111#235—31no—
112#235—61no—
113#235C2×D311yescharacteristic
114C2×D12—31no—
115C2×C4×D3—32no—
116C2×C4×D3—32no—
117C2×C4×D3C2×D311yescharacteristic
118C2×Dic6—31no—
119C3×M16—21no—
120C3×M16—31no—
121C3×M16—32no—
122C3×M16—32no—
123C3×M16C2×D311yescharacteristic, complemented
124C3×M16C2×D311yescharacteristic, complemented
125C2×C3×C8—31no—
126C2×C3×C8—32no—
127C2×C3×C8—32no—
128#208—32no—
129#208C2×D311yescharacteristic, complemented
130C2×C3⋊C8—31no—
131C2×C3⋊C8—31no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—31no—
134C2×C3⋊C8—32no—
135C2×C3⋊C8—31no—
136C2×C3⋊C8—31no—
137C2×C3⋊C8—61no—
138C2×C3⋊C8C2×D311yescharacteristic, complemented
139ΓL(1,𝔽25)—32no—
140ΓL(1,𝔽25)—32no—
141ΓL(1,𝔽25)—32no—
142ΓL(1,𝔽25)—32no—
143ΓL(1,𝔽25)—32no—
144ΓL(1,𝔽25)—62no—
145ΓL(1,𝔽25)C2×D312yescomplemented
146ΓL(1,𝔽25)C2×D312yescomplemented
147D3×C8—31no—
148D3×C8—31no—
149D3×C8—31no—
150D3×C8—31no—
151D3×C8—32no—
152D3×C8—32no—
153D3×C8—32no—
154D3×C8—32no—
155D3×C8—32no—
156D3×C8—62no—
157D3×C8C2×D312yes—
158D3×C8C2×D312yescomplemented
159C22×C32C22×C411yescharacteristic
160C2×C3⋊D3C22×C412yes—
161C2×C3×D3—22no—
162C2×C3×D3C22×C412yes—
163C2×C3×D3C22×C411yescharacteristic
164C2×C3×D3C22×C411yescharacteristic
165D32—24no—
166C32×C4C22×C411yescharacteristic
167C32×C4C2411yescharacteristic
168C3⋊Dic3C22×C412yes—
169C3×Dic3C22×C411yescharacteristic
170C3×Dic3C22×C412yes—
171C3×Dic3C22×C411yescharacteristic
172C2×#41—91no—
173#131—31no—
174#131—91no—
175#131—92no—
176#131—92no—
177#131—91no—
178#131—91no—
179C2×M16—31no—
180C2×M16—92no—
181C22×C8—92no—
182C22×C8—91no—
183C23×C3—31no—
184C22×D3—32no—
185C22×D3—32no—
186C22×D3C4×D311yescharacteristic
187C3×Q8—31no—
188C3×D4—32no—
189C3×D4—31no—
190C2×C3×C4—21no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—31no—
194C2×C3×C4—31no—
195C2×C3×C4—31no—
196C2×C3×C4—32no—
197C2×C3×C4C22×D311yescharacteristic
198C2×C3×C4C22×D311yescharacteristic
199#67—32no—
200#67—32no—
201#67—32no—
202#67—32no—
203#67—32no—
204#67—32no—
205#67—62no—
206#67C4×D312yes—
207C2×Dic3—32no—
208C2×Dic3—32no—
209C2×Dic3C4×D311yescharacteristic
210D12—32no—
211D12—32no—
212D12—31no—
213D12—31no—
214D12—61no—
215D12C4×D311yescharacteristic
216C4×D3—32no—
217C4×D3—32no—
218C4×D3—32no—
219C4×D3—32no—
220C4×D3—32no—
221C4×D3—32no—
222C4×D3—62no—
223C4×D3C4×D311yescharacteristic
224C4×D3C4×D311yescharacteristic
225C4×D3C22×D311yescharacteristic
226C4×D3C22×D311yescharacteristic
227C4×D3C22×D312yes—
228Dic6—31no—
229Dic6—31no—
230Dic6—32no—
231Dic6—32no—
232Dic6—61no—
233Dic6C4×D311yescharacteristic
234C3×C8—22no—
235C3×C8—31no—
236C3×C8—31no—
237C3×C8—32no—
238C3×C8C22×D312yes—
239C3×C8C22×D312yes—
240C3⋊C8—31no—
241C3⋊C8—31no—
242C3⋊C8—31no—
243C3⋊C8—31no—
244C3⋊C8—61no—
245C3⋊C8—61no—
246C3⋊C8C22×D311yescharacteristic
247C3⋊C8C22×D312yes—
248C3⋊C8C22×D311yescharacteristic
249C2×C32—21no—
250C2×C32C23×C411yescharacteristic
251C3⋊D3—22no—
252C3×D3—22no—
253C3×D3—21no—
254C3×D3#13112yescomplemented
255#41—31no—
256#41—92no—
257#41—92no—
258#41—91no—
259#41—91no—
260#41—91no—
261C2×Q8—91no—
262C2×D4—91no—
263C2×D4—92no—
264C22×C4—31no—
265C22×C4—92no—
266M16—31no—
267M16—32no—
268M16—32no—
269M16—92no—
270M16—92no—
271M16—92no—
272M16D3211yescharacteristic, complemented
273C2×C8—31no—
274C2×C8—32no—
275C2×C8—32no—
276C2×C8—92no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—91no—
280C2×C8—92no—
281C2×C8—91no—
282C2×C8—91no—
283C2×C8—92no—
284C22×C3—21no—
285C22×C3—31no—
286C22×C3—32no—
287C22×C3—31no—
288C22×C3—62no—
289C22×C3C2×C4×D311yescharacteristic
290C22×C3C2×C4×D311yescharacteristic
291C2×D3—22no—
292C2×D3—32no—
293C2×D3—32no—
294C2×D3—62no—
295C2×D3—64no—
296C2×D3—64no—
297C2×D3C2×C4×D312yes—
298C2×D3C2×C4×D311yescharacteristic
299C2×D3C2×C4×D311yescharacteristic
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—31no—
303C3×C4—32no—
304C3×C4—31no—
305C3×C4C2×C4×D311yescharacteristic
306C3×C4C2×C4×D311yescharacteristic
307C3×C4C23×D311yescharacteristic
308C3×C4C23×D311yescharacteristic
309Dic3—32no—
310Dic3—32no—
311Dic3—62no—
312Dic3C2×C4×D311yescharacteristic
313Dic3C2×C4×D312yes—
314Dic3C2×C4×D311yescharacteristic
315C32C2×#13111yescharacteristic, complemented, Sylow
316C23—31no—
317C23—92no—
318Q8—31no—
319Q8—92no—
320Q8—91no—
321D4—32no—
322D4—31no—
323D4—92no—
324D4—92no—
325D4—92no—
326D4—92no—
327D4—91no—
328C2×C4—31no—
329C2×C4—31no—
330C2×C4—32no—
331C2×C4—31no—
332C2×C4—31no—
333C2×C4—31no—
334C2×C4—92no—
335C2×C4—92no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4C2×D3211yescharacteristic
339C8—31no—
340C8—31no—
341C8—32no—
342C8—91no—
343C8—91no—
344C8C2×D3212yes—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—32no—
349C2×C3—41no—
350C2×C3—62no—
351C2×C3—61no—
352C2×C3C22×C4×D311yescharacteristic
353C2×C3C22×C4×D311yescharacteristic
354D3—21no—
355D3—22no—
356D3—62no—
357D3—62no—
358D3—122no—
359D3#90712yesdirect product factor
360C22—31no—
361C22—31no—
362C22—32no—
363C22—62no—
364C22—92no—
365C22—184no—
366C22C4×D3211yescharacteristic
367C4—31no—
368C4—31no—
369C4—32no—
370C4—92no—
371C4C4×D3211yescharacteristic
372C4C22×D3211yescharacteristic
373C3—21no—
374C3C2×#90711yescharacteristic, complemented
375C3D3×#13111yescharacteristic, complemented
376C2—21no—
377C2—32no—
378C2—61no—
379C2—62no—
380C2—182no—
381C2C2×C4×D3211yescharacteristic
subgroupG/H
center, FrattiniC4C22×D32
commutator, socleC2×C32C23×C4
FittingC32×M16C22
prime radicalD3×#235C2
cosocleC32×C4C24
hypercenterM16D32
hypocenterC32C2×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. #64116C2semidirect
3. C3×#907C2semidirect
4. C3×D3×M16C2semidirect
5. #63817C2semidirect
6. #63815C2semidirect
7. C2×D3×C3⋊C8C2semidirect
8. #63805C2semidirect
9. #63804C2semidirect
10. D3×ΓL(1,𝔽25)C2semidirect
11. D32×C8C2semidirect
25. C32×M16C22semidirect
26. C2×C3⋊(C3⋊C8)C22semidirect
27. #3743C22semidirect
28. C8×C3⋊D3C22semidirect
29. C3×#208C22semidirect
30. C2×C3×C3⋊C8C22semidirect
31. C3×ΓL(1,𝔽25)C22semidirect
32. C3×ΓL(1,𝔽25)C22semidirect
34. C3×D3×C8C22semidirect
35. #3712C22semidirect
36. #3711C22semidirect
37. #3710C22semidirect
40. D3×C3⋊C8C22semidirect
41. D3×C3⋊C8C22semidirect
42. D3×C3⋊C8C22semidirect
57. #907D3direct (N × H)
59. D3×M16D3semidirect
123. C3×M16C2×D3semidirect
124. C3×M16C2×D3semidirect
129. #208C2×D3semidirect
138. C2×C3⋊C8C2×D3semidirect
145. ΓL(1,𝔽25)C2×D3semidirect
146. ΓL(1,𝔽25)C2×D3semidirect
158. D3×C8C2×D3semidirect
254. C3×D3#131semidirect
272. M16D32semidirect
315. C32C2×#131semidirect
359. D3#907direct (N × H)
374. C3C2×#907semidirect
375. C3D3×#131semidirect

Maximal subgroups

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

subgroupindex
D3×#2352
#641162
C3×#9072
C3×D3×M162
#638172
#638152
C2×D3×C3⋊C82
#638052
#638042
D3×ΓL(1,𝔽25)2
D32×C82
D3×#1313
C2×#9073