Finite Group Databasebeta

← D3×#63384 #13139123

Subgroups — D3×#63384 #13139123

Order 1728.

554 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3697C211yesmaximal, characteristic
2D3×C9×M16C211yesmaximal, characteristic, complemented
3C4×D3×Dic9C211yesmaximal, characteristic, complemented
4#11720558C211yesmaximal, characteristic, complemented
5C3×#63384C211yesmaximal, characteristic, complemented
6#11720292C211yesmaximal, characteristic, complemented
7#11720291C211yesmaximal, characteristic, complemented
8D3×#825—31nomaximal
9C2×#63384—31nomaximal
10#88736C2211yescharacteristic
11C2×C4×D3×C9C2211yescharacteristic
12C3×#3697C2211yescharacteristic
13D3×#611—21no—
14C2×D3×Dic9—21no—
15#88658—21no—
16D3×D36C411yescharacteristic, complemented
17C4×D3×D9—21no—
18#88642C411yescharacteristic, complemented
19#88641C411yescharacteristic, complemented
20#88640—21no—
21D3×Dic18C411yescharacteristic, complemented
22C3×C9×M16C2211yescharacteristic, complemented
23C4×C3⋊Dic9C2211yescharacteristic, complemented
24C3×C4×Dic9C2211yescharacteristic, complemented
25C9×#208C2211yescharacteristic, complemented
26C9×ΓL(1,𝔽25)—21no—
27D3×C8×C9—21no—
28Dic3×Dic9—21no—
29D3×#235—31no—
30C3×D3×M16D311yescharacteristic
31C4×D3×Dic3—31no—
32C2×#3697—31no—
33#63652—31no—
34C3×#825—31no—
35#63570—31no—
36#63568—31no—
37C2×C9×M16—31no—
38C2×C4×Dic9—31no—
39#63384—31no—
40#63384—31no—
41#63384—31no—
42#63384—61no—
43#63384D311yescharacteristic, direct product factor
44C22×D3×C9D411yescharacteristic
45C2×D3×D9—21no—
46C2×C3×C4×C9C2311yescharacteristic
47#6233—21no—
48C2×C3⋊Dic9—21no—
49C4⋊(C3⋊D9)C2×C411yescharacteristic, complemented
50C4×C3⋊D9—21no—
51#6226C2×C411yescharacteristic, complemented
52C3×#611—21no—
53C2×C9×Dic3D411yescharacteristic
54C2×C3×Dic9—21no—
55C4×D3×C9C2×C411yescharacteristic
56C4×D3×C9C2×C411yescharacteristic
57C4×D3×C9D411yescharacteristic
58C4×D3×C9D411yescharacteristic
59C3×D36C2×C411yescharacteristic, complemented
60C3×C4×D9—21no—
61C3×Dic18C2×C411yescharacteristic, complemented
62#6195—21no—
63#6194—21no—
64D3×Dic9—24no—
65D3×Dic9—21no—
66#6192—21no—
67(C3⋊D9)⋊C4—21no—
68Dic3×D9—21no—
69#6189—21no—
70C3×C8×C9—21no—
71C9×C3⋊C8—21no—
72C2×#825—91no—
73D3×#104—91no—
74#3828—31no—
75C3×#235—31no—
76C2×C3×C4×D3C2×D311yescharacteristic
77D3×#67—61no—
78#3804—61no—
79C2×D3×Dic3—61no—
80D3×D12—31no—
81C4×D32—61no—
82#3799—31no—
83#3798—61no—
84#3795—31no—
85D3×Dic6—31no—
86C32×M16C2×D311yescharacteristic
87C4×C3⋊Dic3—31no—
88C3×C4×Dic3—31no—
89C3×#208C2×D311yescharacteristic
90C3×ΓL(1,𝔽25)—21no—
91C3×D3×C8—21no—
92Dic32—61no—
93C22×C4×C9—31no—
94C2×#611—61no—
95C22×Dic9—61no—
96#3697—31no—
97#3697—31no—
98#3697—31no—
99#3697—61no—
100#3697—61no—
101#3697—61no—
102#3697C2×D311yescharacteristic
103C2×D36—31no—
104C2×C4×D9—61no—
105C2×Dic18—31no—
106C9×M16—21no—
107C9×M16—31no—
108C9×M16—61no—
109C9×M16C2×D311yescharacteristic, complemented
110C2×C8×C9—61no—
111C4×Dic9—31no—
112C4×Dic9—61no—
113C4×Dic9—61no—
114C4×Dic9C2×D311yescharacteristic, complemented
115C22×C3×C9C2×D411yescharacteristic
116C2×C3⋊D9—21no—
117C2×D3×C9—22no—
118C2×D3×C9C22⋊C411yescharacteristic
119C2×D3×C9C22⋊C411yescharacteristic
120C2×C3×D9—21no—
121D3×D9—42no—
122C3×C4×C9C22×C411yescharacteristic
123C3×C4×C9C2×D411yescharacteristic
124C3⋊Dic9—22no—
125C3⋊Dic9—21no—
126C9×Dic3C22⋊C411yescharacteristic
127C9×Dic3C22⋊C411yescharacteristic
128C3×Dic9—22no—
129C3×Dic9—21no—
130D3×#41—91no—
131C2×#235—91no—
132C2×C3×M16—31no—
133C2×C4×Dic3—91no—
134D3×M16D911yescharacteristic, complemented
135C42×D3—91no—
136C3×#104—91no—
137#837—91no—
138#825—31no—
139#825—91no—
140#825—91no—
141#825—91no—
142#825—91no—
143#825—181no—
144#805—91no—
145C22×C3×D3D1211yescharacteristic
146C2×D32—61no—
147C2×C32×C4C22×D311yescharacteristic
148#638—61no—
149C2×C3⋊Dic3—61no—
150C4⋊(C3⋊D3)—31no—
151C4×C3⋊D3—61no—
152#634—31no—
153C3×#67—61no—
154C2×C3×Dic3—61no—
155C2×C3×Dic3D1211yescharacteristic
156C3×D12—31no—
157C3×C4×D3—61no—
158C3×C4×D3C4×D311yescharacteristic
159C3×C4×D3C4×D311yescharacteristic
160C3×C4×D3#6711yescharacteristic
161C3×C4×D3#6711yescharacteristic
162C3×Dic6—31no—
163#627—61no—
164#626—61no—
165#626—61no—
166#625—61no—
167#624—61no—
168D3×Dic3—64no—
169D3×Dic3—61no—
170D3×Dic3—61no—
171C23×C9—31no—
172C22×D9—61no—
173C32×C8—21no—
174C3×C3⋊C8—21no—
175C2×C4×C9—21no—
176C2×C4×C9—31no—
177C2×C4×C9—31no—
178C2×C4×C9—31no—
179C2×C4×C9—31no—
180C2×C4×C9—31no—
181C2×C4×C9C22×D311yescharacteristic
182#611—21no—
183#611—61no—
184#611—61no—
185#611—61no—
186#611—121no—
187C2×Dic9—21no—
188C2×Dic9—61no—
189C2×Dic9—64no—
190C2×Dic9—61no—
191C2×Dic9—121no—
192D36—31no—
193D36—61no—
194D36—61no—
195D36C4×D311yescharacteristic, complemented
196C4×D9—21no—
197C4×D9—61no—
198C4×D9—61no—
199C4×D9—61no—
200C4×D9—121no—
201Dic18—31no—
202Dic18—61no—
203Dic18—61no—
204Dic18C4×D311yescharacteristic, complemented
205C8×C9—21no—
206C8×C9—41no—
207C8×C9—61no—
208C2×#104—271noSylow
209C2×C3×C9—21no—
210C2×C3×C9C2×C22⋊C411yescharacteristic
211C3⋊D9—41no—
212D3×C9—21no—
213D3×C9#10412yescomplemented
214C3×D9—41no—
215C3×#41—91no—
216C22×C3×C4—31no—
217C2×#67—181no—
218C22×Dic3—181no—
219#239—91no—
220D3×Q8—91no—
221#237—91no—
222#237—181no—
223D3×D4—91no—
224D3×D4—181no—
225#235—31no—
226#235—91no—
227#235—91no—
228#235—91no—
229#235—91no—
230#235—181no—
231#235—181no—
232#235—181no—
233#235—181no—
234C2×D12—91no—
235C2×C4×D3—181no—
236C2×C4×D3—181no—
237C2×C4×D3—181no—
238C2×C4×D3C2×D911yescharacteristic
239C2×Dic6—91no—
240C3×M16—21no—
241C3×M16—31no—
242C3×M16—61no—
243C3×M16C2×D911yescharacteristic, complemented
244C3×M16D3211yescharacteristic
245C2×C3×C8—61no—
246C3×C42—91no—
247C4×Dic3—31no—
248C4×Dic3—91no—
249C4×Dic3—91no—
250C4×Dic3—181no—
251C4×Dic3—181no—
252C4×Dic3—181no—
253#208C2×D911yescharacteristic, complemented
254ΓL(1,𝔽25)—21no—
255D3×C8—21no—
256C22×C32C2×D1211yescharacteristic
257C2×C3⋊D3—61no—
258C2×C3×D3—22no—
259C2×C3×D3—61no—
260C2×C3×D3(C2×D3)⋊C411yescharacteristic
261C2×C3×D3(C2×D3)⋊C411yescharacteristic
262D32—122no—
263C32×C4C2×C4×D311yescharacteristic
264C32×C4C2×#6711yescharacteristic
265C3⋊Dic3—62no—
266C3⋊Dic3—61no—
267C3×Dic3—62no—
268C3×Dic3—61no—
269C3×Dic3(C2×D3)⋊C411yescharacteristic
270C3×Dic3(C2×D3)⋊C411yescharacteristic
271C22×C9—21no—
272C22×C9—31no—
273C22×C9—31no—
274C22×C9—62no—
275C22×C9D3×D411yescharacteristic
276C2×D9—21no—
277C2×D9—61no—
278C2×D9—121no—
279C2×D9—122no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—31no—
283C4×C9—31no—
284C4×C9C2×C4×D311yescharacteristic
285C4×C9D3×D411yescharacteristic
286Dic9—22no—
287Dic9—21no—
288Dic9—62no—
289Dic9—61no—
290Dic9—121no—
291Dic9—122no—
292C2×#41—271no—
293C2×M16—31no—
294C2×C42—271no—
295#104—91no—
296#104—271no—
297#104—271no—
298#104—271no—
299C3×C9C2×#10411yescharacteristic, complemented, Sylow
300C23×C3—31no—
301C22×D3—181no—
302C22×D3—181no—
303C22×D3D3611yescharacteristic
304C3×Q8—91no—
305C3×D4—91no—
306C3×D4—181no—
307C2×C3×C4—21no—
308C2×C3×C4—31no—
309C2×C3×C4—31no—
310C2×C3×C4—31no—
311C2×C3×C4—31no—
312C2×C3×C4—31no—
313C2×C3×C4—181no—
314C2×C3×C4—181no—
315C2×C3×C4C22×D911yescharacteristic
316C2×C3×C4C2×D3211yescharacteristic
317#67—61no—
318#67—181no—
319#67—181no—
320#67—181no—
321#67—181no—
322#67—181no—
323#67—181no—
324#67—361no—
325C2×Dic3—61no—
326C2×Dic3—181no—
327C2×Dic3—184no—
328C2×Dic3—181no—
329C2×Dic3—181no—
330C2×Dic3—181no—
331C2×Dic3—361no—
332C2×Dic3D3611yescharacteristic
333D12—31no—
334D12—91no—
335D12—91no—
336D12—181no—
337D12—181no—
338D12—181no—
339C4×D3—61no—
340C4×D3—181no—
341C4×D3—181no—
342C4×D3—184no—
343C4×D3—181no—
344C4×D3—181no—
345C4×D3—181no—
346C4×D3—181no—
347C4×D3—361no—
348C4×D3C4×D911yescharacteristic
349C4×D3C4×D911yescharacteristic
350C4×D3#61111yescharacteristic
351C4×D3#61111yescharacteristic
352Dic6—31no—
353Dic6—91no—
354Dic6—91no—
355Dic6—181no—
356Dic6—181no—
357Dic6—181no—
358C3×C8—21no—
359C3×C8—21no—
360C3×C8—41no—
361C3×C8—61no—
362C3⋊C8—21no—
363C2×C32—21no—
364C2×C32C2×(C2×D3)⋊C411yescharacteristic
365C3⋊D3—121no—
366C3×D3—21no—
367C3×D3—121no—
368C3×D3#82512yes—
369C2×C9—21no—
370C2×C9—21no—
371C2×C9—32no—
372C2×C9—41no—
373C2×C9—61no—
374C2×C9D3×C22⋊C411yescharacteristic
375D9—41no—
376D9—121no—
377D9—241no—
378#41—91no—
379#41—271no—
380#41—271no—
381#41—271no—
382#41—541no—
383#41—541no—
384C2×Q8—271no—
385C2×D4—271no—
386C2×D4—541no—
387C22×C4—31no—
388C22×C4—541no—
389C22×C4—541no—
390M16—31no—
391M16—61no—
392M16D3×D911yescharacteristic, complemented
393C2×C8—61no—
394C42—91no—
395C42—271no—
396C42—541no—
397C22×C3—21no—
398C22×C3—31no—
399C22×C3—31no—
400C22×C3—62no—
401C22×C3—181no—
402C22×C3C2×D3611yescharacteristic
403C22×C3D3×D1211yescharacteristic
404C2×D3—22no—
405C2×D3—61no—
406C2×D3—181no—
407C2×D3—181no—
408C2×D3—361no—
409C2×D3—362no—
410C2×D3—362no—
411C2×D3(C2×D9)⋊C411yescharacteristic
412C2×D3(C2×D9)⋊C411yescharacteristic
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—31no—
416C3×C4—31no—
417C3×C4—182no—
418C3×C4—181no—
419C3×C4C2×C4×D911yescharacteristic
420C3×C4C2×#61111yescharacteristic
421C3×C4C4×D3211yescharacteristic
422C3×C4D3×#6711yescharacteristic
423Dic3—62no—
424Dic3—61no—
425Dic3—182no—
426Dic3—182no—
427Dic3—181no—
428Dic3—181no—
429Dic3—361no—
430Dic3—362no—
431Dic3(C2×D9)⋊C411yescharacteristic
432Dic3(C2×D9)⋊C411yescharacteristic
433C32C2×#82511yescharacteristic
434C9—21no—
435C9D3×#10411yescharacteristic, complemented
436C23—31no—
437C23—541no—
438Q8—91no—
439Q8—271no—
440Q8—541no—
441D4—91no—
442D4—181no—
443D4—271no—
444D4—541no—
445D4—541no—
446D4—541no—
447D4—541no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—541no—
456C2×C4—541no—
457C2×C4—541no—
458C2×C4—544no—
459C2×C4—541no—
460C2×C4—541no—
461C2×C4C2×D3×D911yescharacteristic
462C8—21no—
463C8—61no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—32no—
468C2×C3—41no—
469C2×C3—61no—
470C2×C3—361no—
471C2×C3C2×(C2×D9)⋊C411yescharacteristic
472C2×C3D3×(C2×D3)⋊C411yescharacteristic
473D3—21no—
474D3—121no—
475D3—361no—
476D3—361no—
477D3—721no—
478D3#6338412yesdirect product factor
479C22—31no—
480C22—31no—
481C22—62no—
482C22—181no—
483C22—541no—
484C22—1082no—
485C22D3×D3611yescharacteristic
486C4—31no—
487C4—31no—
488C4—182no—
489C4—181no—
490C4—542no—
491C4—541no—
492C4C4×D3×D911yescharacteristic
493C4D3×#61111yescharacteristic
494C3—21no—
495C3C2×#6338411yescharacteristic, complemented
496C3D3×#82511yescharacteristic
497C2—21no—
498C2—32no—
499C2—61no—
500C2—361no—
501C2—1081no—
502C2D3×(C2×D9)⋊C411yescharacteristic
subgroupG/H
centerC4D3×#611
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC3×C9×M16C22
socleC2×C32C2×(C2×D3)⋊C4
prime radicalD3×#3697C2
cosocleC2×C3×C4×C9C23
hypercenterM16D3×D9
hypocenterC3×C9C2×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
2. D3×C9×M16C2semidirect
3. C4×D3×Dic9C2semidirect
4. #11720558C2semidirect
5. C3×#63384C2semidirect
6. #11720292C2semidirect
7. #11720291C2semidirect
16. D3×D36C4semidirect
18. #88642C4semidirect
19. #88641C4semidirect
21. D3×Dic18C4semidirect
22. C3×C9×M16C22semidirect
23. C4×C3⋊Dic9C22semidirect
24. C3×C4×Dic9C22semidirect
25. C9×#208C22semidirect
43. #63384D3direct (N × H)
49. C4⋊(C3⋊D9)C2×C4semidirect
51. #6226C2×C4semidirect
59. C3×D36C2×C4semidirect
61. C3×Dic18C2×C4semidirect
109. C9×M16C2×D3semidirect
114. C4×Dic9C2×D3semidirect
134. D3×M16D9semidirect
195. D36C4×D3semidirect
204. Dic18C4×D3semidirect
213. D3×C9#104semidirect
243. C3×M16C2×D9semidirect
253. #208C2×D9semidirect
299. C3×C9C2×#104semidirect
392. M16D3×D9semidirect
435. C9D3×#104semidirect
478. D3#63384direct (N × H)
495. C3C2×#63384semidirect

Maximal subgroups

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

subgroupindex
D3×#36972
D3×C9×M162
C4×D3×Dic92
#117205582
C3×#633842
#117202922
#117202912
D3×#8253
C2×#633843