Finite Group Databasebeta

← D3×#471 #80928

Subgroups — D3×#471 #80928

Order 384.

468 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#137C211yesmaximal, characteristic, complemented
2D3×AGL(1,ℤ/8)C211yesmaximal, characteristic
3C2×D3×SD16C211yesmaximal, characteristic, complemented
4D3×#131C211yesmaximal, characteristic, complemented
5C3×#471C211yesmaximal, characteristic, complemented
6#5203C211yesmaximal, characteristic, complemented
7#5200C211yesmaximal, characteristic, complemented
8#5177C211yesmaximal, characteristic, complemented
9#5141C211yesmaximal, characteristic, complemented
10#4898C211yesmaximal, characteristic, complemented
11D3×#108C211yesmaximal, characteristic, complemented
12#4754C211yesmaximal, characteristic, complemented
13D3×#101C211yesmaximal, characteristic, complemented
14#4748C211yesmaximal, characteristic, complemented
15D3×#100C211yesmaximal, characteristic, complemented
16C2×#471—31nomaximal, Sylow
17D3×#41C2211yescharacteristic
18C2×D3×Q8C2211yescharacteristic
19C2×D3×D4C2211yescharacteristic
20C3×#137C2211yescharacteristic, complemented
21C3×AGL(1,ℤ/8)C2211yescharacteristic
22C2×C3×SD16C2211yescharacteristic, complemented
23C3×#131C2211yescharacteristic, complemented
24#951C2211yescharacteristic, complemented
25#949C2211yescharacteristic
26#948C2211yescharacteristic, complemented
27#942C2211yescharacteristic, complemented
28C2×#215C2211yescharacteristic, complemented
29C2×#214C2211yescharacteristic, complemented
30#932C2211yescharacteristic
31#918—21no—
32D3×Q16—21no—
33#915—21no—
34#914—21no—
35D3×SD16—21no—
36D3×SD16—21no—
37D3×SD16—21no—
38D3×SD16—21no—
39D3×SD16—21no—
40D3×SD16—21no—
41#911—21no—
42D3×D8—21no—
43#909C2211yescharacteristic, complemented
44#908C2211yescharacteristic
45#907—21no—
46#907C2211yescharacteristic, complemented
47D3×M16—21no—
48D3×M16C2211yescharacteristic
49D3×M16C2211yescharacteristic
50D3×M16C2211yescharacteristic
51C2×#204C2211yescharacteristic, complemented
52#901—21no—
53#901C2211yescharacteristic, complemented
54C2×D3×C8—21no—
55C2×D3×C8C2211yescharacteristic
56C3×#108C2211yescharacteristic, complemented
57C3×#101C2211yescharacteristic, complemented
58C3×#100C2211yescharacteristic, complemented
59#836C2211yescharacteristic, complemented
60#833C2211yescharacteristic, complemented
61#824C2211yescharacteristic, complemented
62#824C2211yescharacteristic, complemented
63#823C2211yescharacteristic, complemented
64#823C2211yescharacteristic, complemented
65#822C2211yescharacteristic, complemented
66#822C2211yescharacteristic, complemented
67#819C2211yescharacteristic, complemented
68C2×#137—31no—
69C2×AGL(1,ℤ/8)—31no—
70C22×SD16—31no—
71C2×#131—31no—
72#471—31no—
73#471—31no—
74#471—31no—
75#471—31no—
76#471—31no—
77#471—31no—
78#471—31no—
79#471D311yescharacteristic, direct product factor
80C2×#108—31no—
81C2×#101—31no—
82C2×#100—31no—
83C23×D3—21no—
84C3×#41C2311yescharacteristic
85C2×C3×Q8C2311yescharacteristic
86C2×C3×D4C2311yescharacteristic
87C2×#67—21no—
88#239D411yescharacteristic
89D3×Q8—21no—
90D3×Q8—21no—
91D3×Q8—21no—
92D3×Q8—21no—
93D3×Q8D411yescharacteristic
94#237—21no—
95#237D411yescharacteristic
96D3×D4—21no—
97D3×D4—21no—
98D3×D4—21no—
99D3×D4—21no—
100D3×D4—21no—
101D3×D4D411yescharacteristic
102#235—21no—
103#235C2311yescharacteristic
104C2×D12C2311yescharacteristic
105C2×C4×D3—21no—
106C2×C4×D3—21no—
107C2×C4×D3C2311yescharacteristic
108C2×Dic6—21no—
109C2×Dic6C2311yescharacteristic
110C3×Q16—21no—
111C3×SD16—21no—
112C3×SD16—21no—
113C3×SD16—21no—
114C3×SD16—21no—
115C3×D8—21no—
116C3×M16—21no—
117C3×M16C2311yescharacteristic
118C3×M16C2311yescharacteristic
119C3×M16C2311yescharacteristic
120C2×C3×C8—21no—
121C2×C3×C8C2311yescharacteristic
122#216—21no—
123#216—21no—
124#215—21no—
125#215—21no—
126#215—21no—
127#215—21no—
128#214—21no—
129#214—21no—
130#214—21no—
131#214—21no—
132#213—21no—
133#213—21no—
134#208—21no—
135#208C2311yescharacteristic
136#208C2311yescharacteristic
137#208C2311yescharacteristic
138C2×C3⋊C8—21no—
139C2×C3⋊C8C2311yescharacteristic
140Dic12—21no—
141D24—21no—
142#204—21no—
143#204—21no—
144#204—21no—
145#204—21no—
146ΓL(1,𝔽25)—21no—
147ΓL(1,𝔽25)—21no—
148ΓL(1,𝔽25)—21no—
149ΓL(1,𝔽25)—21no—
150ΓL(1,𝔽25)—21no—
151D3×C8—21no—
152D3×C8—21no—
153D3×C8—21no—
154D3×C8—21no—
155D3×C8—21no—
156D3×C8D411yescharacteristic
157D3×C8D411yescharacteristic
158D3×C8D411yescharacteristic
159D3×C8D411yescharacteristic
160C2×#41—31no—
161C22×Q8—31no—
162C22×D4—31no—
163#137—31no—
164#137—31no—
165#137—31no—
166#137—61no—
167#137—61no—
168#137C2×D311yescharacteristic, complemented
169AGL(1,ℤ/8)—31no—
170AGL(1,ℤ/8)—31no—
171AGL(1,ℤ/8)—31no—
172AGL(1,ℤ/8)—61no—
173AGL(1,ℤ/8)—61no—
174AGL(1,ℤ/8)C2×D311yescharacteristic
175C2×Q16—61no—
176C2×SD16—31no—
177C2×SD16—31no—
178C2×SD16—31no—
179C2×SD16—61no—
180C2×SD16—61no—
181C2×SD16—61no—
182C2×SD16—61no—
183C2×SD16—61no—
184C2×SD16—61no—
185C2×SD16C2×D311yescharacteristic, complemented
186C2×D8—61no—
187#131—31no—
188#131—31no—
189#131—31no—
190#131—61no—
191#131—61no—
192#131C2×D311yescharacteristic, complemented
193C2×M16—31no—
194C2×M16—31no—
195C2×M16—31no—
196C2×M16—61no—
197C22×C8—31no—
198C22×C8—61no—
199#108—31no—
200#108—31no—
201#108—31no—
202#108C2×D311yescharacteristic, complemented
203#101—31no—
204#101—31no—
205#101—31no—
206#101C2×D311yescharacteristic, complemented
207#100—31no—
208#100—31no—
209#100—31no—
210#100C2×D311yescharacteristic, complemented
211C23×C3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—82no—
217C22×D3#4111yescharacteristic
218C3×Q8—21no—
219C3×Q8—21no—
220C3×Q8C2×D411yescharacteristic
221C3×D4—21no—
222C3×D4—21no—
223C3×D4—21no—
224C3×D4C2×D411yescharacteristic
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4C2411yescharacteristic
228#67—21no—
229#67—21no—
230#67—21no—
231#67—41no—
232#67—41no—
233C2×Dic3—21no—
234C2×Dic3—21no—
235C2×Dic3#4111yescharacteristic
236D12—21no—
237D12—21no—
238D12—21no—
239D12C2×D411yescharacteristic
240C4×D3—21no—
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—41no—
244C4×D3—41no—
245C4×D3C2×D411yescharacteristic
246C4×D3C2×D411yescharacteristic
247C4×D3C2×D411yescharacteristic
248C4×D3C2×D411yescharacteristic
249Dic6—21no—
250Dic6—21no—
251Dic6—21no—
252Dic6—41no—
253Dic6—41no—
254Dic6C2×D411yescharacteristic
255C3×C8—21no—
256C3×C8—21no—
257C3×C8—21no—
258C3×C8C2×D411yescharacteristic
259C3×C8C2×D411yescharacteristic
260C3⋊C8—21no—
261C3⋊C8—21no—
262C3⋊C8—21no—
263C3⋊C8C2×D411yescharacteristic
264C3⋊C8C2×D411yescharacteristic
265C24—61no—
266#41—31no—
267#41—31no—
268#41—31no—
269#41—61no—
270#41—61no—
271#41C22×D311yescharacteristic
272C2×Q8—31no—
273C2×Q8—31no—
274C2×Q8—61no—
275C2×Q8—61no—
276C2×Q8—61no—
277C2×Q8—61no—
278C2×Q8—61no—
279C2×Q8C22×D311yescharacteristic
280C2×D4—31no—
281C2×D4—31no—
282C2×D4—61no—
283C2×D4—61no—
284C2×D4—61no—
285C2×D4—61no—
286C2×D4—61no—
287C2×D4—61no—
288C2×D4C22×D311yescharacteristic
289C22×C4—31no—
290C22×C4—61no—
291C22×C4—61no—
292Q16—21no—
293Q16—61no—
294Q16—61no—
295Q16—61no—
296SD16—21no—
297SD16—21no—
298SD16—21no—
299SD16—21no—
300SD16—61no—
301SD16—61no—
302SD16—61no—
303SD16—61no—
304SD16—61no—
305SD16—61no—
306SD16—61no—
307SD16—61no—
308SD16—61no—
309SD16—61no—
310SD16—61no—
311SD16—61no—
312D8—21no—
313D8—61no—
314D8—61no—
315D8—61no—
316M16—21no—
317M16—31no—
318M16—31no—
319M16—31no—
320M16—61no—
321M16—61no—
322M16—61no—
323M16—61no—
324M16—61no—
325M16—61no—
326M16C22×D311yescharacteristic
327M16C22×D311yescharacteristic
328M16C22×D311yescharacteristic
329C2×C8—21no—
330C2×C8—31no—
331C2×C8—31no—
332C2×C8—31no—
333C2×C8—31no—
334C2×C8—31no—
335C2×C8—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—61no—
340C2×C8—61no—
341C2×C8C22×D311yescharacteristic
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—81no—
345C22×C3C2×#4111yescharacteristic
346C2×D3—22no—
347C2×D3—21no—
348C2×D3—42no—
349C2×D3—41no—
350C2×D3—82no—
351C2×D3—82no—
352C2×D3—81no—
353C2×D3#12111yescharacteristic
354C2×D3#12111yescharacteristic
355C3×C4—21no—
356C3×C4—41no—
357C3×C4C22×D411yescharacteristic
358C3×C4C22×D411yescharacteristic
359Dic3—21no—
360Dic3—41no—
361Dic3#12111yescharacteristic
362Dic3#12111yescharacteristic
363C23—21no—
364C23—31no—
365C23—61no—
366C23—61no—
367C23—121no—
368C23—121no—
369C23—242no—
370Q8—21no—
371Q8—21no—
372Q8—31no—
373Q8—61no—
374Q8—61no—
375Q8—61no—
376Q8—121no—
377Q8—121no—
378Q8D3×D411yescharacteristic
379D4—21no—
380D4—21no—
381D4—21no—
382D4—31no—
383D4—61no—
384D4—61no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—61no—
389D4—121no—
390D4—121no—
391D4D3×D411yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4C23×D311yescharacteristic
407C8—21no—
408C8—21no—
409C8—21no—
410C8—31no—
411C8—31no—
412C8—61no—
413C8—61no—
414C8—61no—
415C8D3×D411yescharacteristic
416C8D3×D411yescharacteristic
417C2×C3—21no—
418C2×C3—41no—
419C2×C3—81no—
420C2×C3C2×#12111yescharacteristic
421D3—21no—
422D3—41no—
423D3—81no—
424D3#47112yesdirect product factor
425C22—21no—
426C22—31no—
427C22—31no—
428C22—41no—
429C22—62no—
430C22—61no—
431C22—81no—
432C22—122no—
433C22—121no—
434C22—241no—
435C22—242no—
436C22—242no—
437C22D3×#4111yescharacteristic
438C4—21no—
439C4—31no—
440C4—31no—
441C4—41no—
442C4—61no—
443C4—121no—
444C4C2×D3×D411yescharacteristic
445C4C2×D3×D411yescharacteristic
446C3C2×#47111yescharacteristic, complemented, Sylow
447C2—21no—
448C2—32no—
449C2—41no—
450C2—61no—
451C2—81no—
452C2—121no—
453C2—241no—
454C2D3×#12111yescharacteristic
subgroupG/H
centerC2D3×#121
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#471C2
socleC2×C3C2×#121
prime radicalD3×AGL(1,ℤ/8)C2
hypercenter#471D3
hypocenterC3C2×#471
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. D3×#137C2semidirect
3. C2×D3×SD16C2semidirect
4. D3×#131C2semidirect
5. C3×#471C2semidirect
6. #5203C2semidirect
7. #5200C2semidirect
8. #5177C2semidirect
9. #5141C2semidirect
10. #4898C2semidirect
11. D3×#108C2semidirect
12. #4754C2semidirect
13. D3×#101C2semidirect
14. #4748C2semidirect
15. D3×#100C2semidirect
20. C3×#137C22semidirect
22. C2×C3×SD16C22semidirect
23. C3×#131C22semidirect
24. #951C22semidirect
26. #948C22semidirect
27. #942C22semidirect
28. C2×#215C22semidirect
29. C2×#214C22semidirect
43. #909C22semidirect
46. #907C22semidirect
51. C2×#204C22semidirect
53. #901C22semidirect
56. C3×#108C22semidirect
57. C3×#101C22semidirect
58. C3×#100C22semidirect
59. #836C22semidirect
60. #833C22semidirect
61. #824C22semidirect
62. #824C22semidirect
63. #823C22semidirect
64. #823C22semidirect
65. #822C22semidirect
66. #822C22semidirect
67. #819C22semidirect
79. #471D3direct (N × H)
168. #137C2×D3semidirect
185. C2×SD16C2×D3semidirect
192. #131C2×D3semidirect
202. #108C2×D3semidirect
206. #101C2×D3semidirect
210. #100C2×D3semidirect
424. D3#471direct (N × H)
446. C3C2×#471semidirect

Maximal subgroups

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

subgroupindex
D3×#1372
D3×AGL(1,ℤ/8)2
C2×D3×SD162
D3×#1312
C3×#4712
#52032
#52002
#51772
#51412
#48982
D3×#1082
#47542
D3×#1012
#47482
D3×#1002
C2×#4713