Finite Group Databasebeta

← D3×#63396 #13141030

Subgroups — D3×#63396 #13141030

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×C9×#41C211yesmaximal, characteristic
2C4×D3×Dic9C211yesmaximal, characteristic, complemented
3D3×#3667C211yesmaximal, characteristic, complemented
4#11720585C211yesmaximal, characteristic, complemented
5C3×#63396C211yesmaximal, characteristic, complemented
6#11720301C211yesmaximal, characteristic, complemented
7#11720300C211yesmaximal, characteristic, complemented
8D3×#837—31nomaximal
9C2×#63396—31nomaximal
10C3×C9×#41C2211yescharacteristic
11C9×#239C411yescharacteristic, complemented
12D3×Q8×C9C411yescharacteristic, complemented
13C9×#237—21no—
14C9×#237C411yescharacteristic, complemented
15D3×D4×C9—21no—
16D3×D4×C9C411yescharacteristic, complemented
17C9×#235—21no—
18C9×#235C2211yescharacteristic
19C2×C4×D3×C9—21no—
20C2×C4×D3×C9C2211yescharacteristic
21C2×D3×Dic9—21no—
22C4×C3⋊Dic9C2211yescharacteristic, complemented
23#88532C2211yescharacteristic, complemented
24C3×C4×Dic9C2211yescharacteristic, complemented
25C3×#3667C2211yescharacteristic, complemented
26Dic3×Dic9—21no—
27#88420—21no—
28D3×C9⋊C8—21no—
29C3×D3×#41D311yescharacteristic
30C4×D3×Dic3—31no—
31D3×#208—31no—
32C2×C9×#41—31no—
33#63664—31no—
34C3×#837—31no—
35#63569—31no—
36#63568—31no—
37C2×C4×Dic9—31no—
38C2×#3667—31no—
39#63396—31no—
40#63396—31no—
41#63396—31no—
42#63396—61no—
43#63396D311yescharacteristic, direct product factor
44C22×D3×C9—21no—
45C22×D3×C9D411yescharacteristic
46C3×Q8×C9C2×C411yescharacteristic, complemented
47C3×D4×C9—21no—
48C3×D4×C9C2×C411yescharacteristic, complemented
49C2×C3×C4×C9—21no—
50C2×C3×C4×C9C2311yescharacteristic
51C2×C3⋊Dic9—21no—
52C9×#67—21no—
53C9×#67—21no—
54C9×#67—21no—
55C2×C9×Dic3—21no—
56C2×C9×Dic3D411yescharacteristic
57C2×C3×Dic9—21no—
58C9×D12—21no—
59C9×D12C2×C411yescharacteristic, complemented
60C4×D3×C9—21no—
61C4×D3×C9—21no—
62C4×D3×C9—21no—
63C4×D3×C9C2×C411yescharacteristic
64C4×D3×C9C2×C411yescharacteristic
65C4×D3×C9D411yescharacteristic
66C4×D3×C9D411yescharacteristic
67C9×Dic6—21no—
68C9×Dic6C2×C411yescharacteristic, complemented
69D3×Dic9—24no—
70C3⋊(C9⋊C8)—21no—
71C3×C9⋊C8—21no—
72C2×#837—91no—
73D3×#104—91no—
74C32×#41C2×D311yescharacteristic
75C3×#239Dic311yescharacteristic
76C3×D3×Q8Dic311yescharacteristic
77C3×#237—21no—
78C3×#237Dic311yescharacteristic
79C3×D3×D4—21no—
80C3×D3×D4Dic311yescharacteristic
81C3×#235—21no—
82C3×#235C2×D311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3C2×D311yescharacteristic
85C2×D3×Dic3—61no—
86C4×C3⋊Dic3—31no—
87#3748—31no—
88C3×C4×Dic3—31no—
89C3×#208—31no—
90Dic32—61no—
91#3711—61no—
92D3×C3⋊C8—61no—
93C9×#41—21no—
94C9×#41—31no—
95C9×#41—31no—
96C9×#41—31no—
97C9×#41—61no—
98C9×#41—61no—
99C9×#41C2×D311yescharacteristic
100C2×Q8×C9—31no—
101C2×D4×C9—31no—
102C2×D4×C9—61no—
103C22×C4×C9—31no—
104C22×C4×C9—61no—
105C22×Dic9—61no—
106C4×Dic9—31no—
107C4×Dic9—61no—
108C4×Dic9—61no—
109C4×Dic9C2×D311yescharacteristic, complemented
110#3667—31no—
111#3667—61no—
112#3667—61no—
113#3667C2×D311yescharacteristic, complemented
114C2×C9⋊C8—61no—
115C22×C3×C9—21no—
116C22×C3×C9C2×D411yescharacteristic
117C2×D3×C9—22no—
118C2×D3×C9—21no—
119C2×D3×C9—42no—
120C2×D3×C9C22⋊C411yescharacteristic
121C2×D3×C9C22⋊C411yescharacteristic
122C3×C4×C9—21no—
123C3×C4×C9C22×C411yescharacteristic
124C3×C4×C9C2×D411yescharacteristic
125C3⋊Dic9—22no—
126C9×Dic3—21no—
127C9×Dic3C22⋊C411yescharacteristic
128C9×Dic3C22⋊C411yescharacteristic
129C3×Dic9—22no—
130C2×C3×#41—31no—
131D3×#41D911yescharacteristic
132C2×C4×Dic3—91no—
133C2×#208—91no—
134D3×M16—91no—
135C42×D3—91no—
136C3×#104—91no—
137#837—31no—
138#837—91no—
139#837—91no—
140#837—91no—
141#837—91no—
142#837—181no—
143#825—91no—
144#805—91no—
145C22×C3×D3—21no—
146C22×C3×D3#6711yescharacteristic
147C32×Q8C2×Dic311yescharacteristic
148C32×D4—21no—
149C32×D4C2×Dic311yescharacteristic
150C2×C32×C4—21no—
151C2×C32×C4C22×D311yescharacteristic
152C2×C3⋊Dic3—61no—
153C3×#67—21no—
154C3×#67—21no—
155C3×#67—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—61no—
158C2×C3×Dic3#6711yescharacteristic
159C3×D12—21no—
160C3×D12C2×Dic311yescharacteristic
161C3×C4×D3—21no—
162C3×C4×D3—21no—
163C3×C4×D3—21no—
164C3×C4×D3C2×Dic311yescharacteristic
165C3×C4×D3C2×Dic311yescharacteristic
166C3×C4×D3#6711yescharacteristic
167C3×C4×D3#6711yescharacteristic
168C3×Dic6—21no—
169C3×Dic6C2×Dic311yescharacteristic
170D3×Dic3—64no—
171C23×C9—31no—
172C23×C9—61no—
173C3⋊(C3⋊C8)—61no—
174C3×C3⋊C8—61no—
175Q8×C9—21no—
176Q8×C9—31no—
177Q8×C9—61no—
178Q8×C9C4×D311yescharacteristic, complemented
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—31no—
182D4×C9—41no—
183D4×C9—61no—
184D4×C9—61no—
185D4×C9—61no—
186D4×C9—61no—
187D4×C9C4×D311yescharacteristic, complemented
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—31no—
191C2×C4×C9—31no—
192C2×C4×C9—31no—
193C2×C4×C9—31no—
194C2×C4×C9—31no—
195C2×C4×C9—41no—
196C2×C4×C9—61no—
197C2×C4×C9—61no—
198C2×C4×C9—61no—
199C2×C4×C9—61no—
200C2×C4×C9C22×D311yescharacteristic
201C2×Dic9—21no—
202C2×Dic9—64no—
203C2×Dic9—61no—
204C2×Dic9—121no—
205C9⋊C8—21no—
206C9⋊C8—61no—
207C9⋊C8—121no—
208C2×#104—271noSylow
209C2×C3×C9—21no—
210C2×C3×C9—41no—
211C2×C3×C9C2×C22⋊C411yescharacteristic
212D3×C9—21no—
213D3×C9—41no—
214D3×C9#10412yescomplemented
215C3×#41—21no—
216C3×#41—31no—
217C3×#41—31no—
218C3×#41—31no—
219C3×#41—61no—
220C3×#41—61no—
221C3×#41C2×D911yescharacteristic
222C3×#41D3211yescharacteristic
223C2×C3×Q8—31no—
224C2×C3×D4—31no—
225C2×C3×D4—61no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C22×Dic3—181no—
229#239Dic911yescharacteristic, complemented
230D3×Q8Dic911yescharacteristic, complemented
231#237—21no—
232#237Dic911yescharacteristic, complemented
233D3×D4—21no—
234D3×D4Dic911yescharacteristic, complemented
235#235—21no—
236#235C2×D911yescharacteristic
237C2×C4×D3—21no—
238C2×C4×D3—181no—
239C2×C4×D3C2×D911yescharacteristic
240C3×M16—91no—
241C3×C42—91no—
242C4×Dic3—31no—
243C4×Dic3—91no—
244C4×Dic3—91no—
245C4×Dic3—181no—
246C4×Dic3—181no—
247C4×Dic3—181no—
248#208—31no—
249#208—91no—
250#208—91no—
251#208—181no—
252#208—181no—
253C2×C3⋊C8—181no—
254ΓL(1,𝔽25)—181no—
255D3×C8—181no—
256C22×C32—21no—
257C22×C32C2×#6711yescharacteristic
258C2×C3×D3—22no—
259C2×C3×D3—21no—
260C2×C3×D3—42no—
261C2×C3×D3#21711yescharacteristic
262C2×C3×D3#21711yescharacteristic
263C32×C4—21no—
264C32×C4C22×Dic311yescharacteristic
265C32×C4C2×#6711yescharacteristic
266C3⋊Dic3—62no—
267C3×Dic3—21no—
268C3×Dic3—62no—
269C3×Dic3#21711yescharacteristic
270C3×Dic3#21711yescharacteristic
271C22×C9—21no—
272C22×C9—21no—
273C22×C9—31no—
274C22×C9—31no—
275C22×C9—41no—
276C22×C9—62no—
277C22×C9—61no—
278C22×C9—122no—
279C22×C9D3×D411yescharacteristic
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—21no—
283C4×C9—31no—
284C4×C9—31no—
285C4×C9—41no—
286C4×C9—61no—
287C4×C9C2×C4×D311yescharacteristic
288C4×C9D3×D411yescharacteristic
289Dic9—22no—
290Dic9—62no—
291Dic9—122no—
292C2×#41—31no—
293C2×M16—271no—
294C2×C42—271no—
295#104—91no—
296#104—271no—
297#104—271no—
298#104—271no—
299C3×C9C2×#10411yescharacteristic, complemented, Sylow
300C23×C3—31no—
301C23×C3—61no—
302C22×D3—21no—
303C22×D3#61111yescharacteristic
304C3×Q8—21no—
305C3×Q8—31no—
306C3×Q8—61no—
307C3×Q8C2×Dic911yescharacteristic, complemented
308C3×Q8D3×Dic311yescharacteristic
309C3×D4—21no—
310C3×D4—21no—
311C3×D4—21no—
312C3×D4—31no—
313C3×D4—41no—
314C3×D4—61no—
315C3×D4—61no—
316C3×D4—61no—
317C3×D4—61no—
318C3×D4C2×Dic911yescharacteristic, complemented
319C3×D4D3×Dic311yescharacteristic
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—31no—
324C2×C3×C4—31no—
325C2×C3×C4—31no—
326C2×C3×C4—31no—
327C2×C3×C4—31no—
328C2×C3×C4—41no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—181no—
334C2×C3×C4C22×D911yescharacteristic
335C2×C3×C4C2×D3211yescharacteristic
336#67—21no—
337#67—21no—
338#67—21no—
339C2×Dic3—21no—
340C2×Dic3—61no—
341C2×Dic3—184no—
342C2×Dic3—181no—
343C2×Dic3—181no—
344C2×Dic3—361no—
345C2×Dic3#61111yescharacteristic
346D12—21no—
347D12C2×Dic911yescharacteristic, complemented
348C4×D3—21no—
349C4×D3—21no—
350C4×D3—21no—
351C4×D3—184no—
352C4×D3C2×Dic911yescharacteristic
353C4×D3C2×Dic911yescharacteristic
354C4×D3#61111yescharacteristic
355C4×D3#61111yescharacteristic
356Dic6—21no—
357Dic6C2×Dic911yescharacteristic, complemented
358C3×C8—181no—
359C3⋊C8—61no—
360C3⋊C8—181no—
361C3⋊C8—181no—
362C3⋊C8—361no—
363C2×C32—21no—
364C2×C32—41no—
365C2×C32C2×#21711yescharacteristic
366C3×D3—21no—
367C3×D3—41no—
368C3×D3#83712yes—
369C2×C9—21no—
370C2×C9—21no—
371C2×C9—32no—
372C2×C9—41no—
373C2×C9—41no—
374C2×C9—61no—
375C2×C9—81no—
376C2×C9—121no—
377C2×C9D3×C22⋊C411yescharacteristic
378#41—31no—
379#41—31no—
380#41—31no—
381#41—61no—
382#41—61no—
383#41D3×D911yescharacteristic
384C2×Q8—31no—
385C2×D4—31no—
386C2×D4—61no—
387C22×C4—31no—
388C22×C4—61no—
389C22×C4—541no—
390M16—91no—
391M16—271no—
392M16—541no—
393C2×C8—541no—
394C42—91no—
395C42—271no—
396C42—541no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—31no—
401C22×C3—31no—
402C22×C3—41no—
403C22×C3—62no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3C2×#61111yescharacteristic
407C22×C3D3×#6711yescharacteristic
408C2×D3—22no—
409C2×D3—21no—
410C2×D3—42no—
411C2×D3#367611yescharacteristic
412C2×D3#367611yescharacteristic
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—31no—
418C3×C4—31no—
419C3×C4—41no—
420C3×C4—61no—
421C3×C4—182no—
422C3×C4C22×Dic911yescharacteristic
423C3×C4C2×#61111yescharacteristic
424C3×C4C2×D3×Dic311yescharacteristic
425C3×C4D3×#6711yescharacteristic
426Dic3—21no—
427Dic3—62no—
428Dic3—182no—
429Dic3—182no—
430Dic3—362no—
431Dic3#367611yescharacteristic
432Dic3#367611yescharacteristic
433C32C2×#83711yescharacteristic
434C9—21no—
435C9D3×#10411yescharacteristic, complemented
436C23—31no—
437C23—61no—
438Q8—31no—
439Q8—61no—
440Q8D3×Dic911yescharacteristic, complemented
441D4—21no—
442D4—31no—
443D4—61no—
444D4—61no—
445D4—61no—
446D4—61no—
447D4D3×Dic911yescharacteristic, complemented
448C2×C4—21no—
449C2×C4—31no—
450C2×C4—31no—
451C2×C4—31no—
452C2×C4—31no—
453C2×C4—31no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—181no—
459C2×C4—544no—
460C2×C4—541no—
461C2×C4C2×D3×D911yescharacteristic
462C8—181no—
463C8—541no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—32no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—61no—
472C2×C3—81no—
473C2×C3—121no—
474C2×C3C2×#367611yescharacteristic
475C2×C3D3×#21711yescharacteristic
476D3—21no—
477D3—41no—
478D3#6339612yesdirect product factor
479C22—21no—
480C22—31no—
481C22—31no—
482C22—62no—
483C22—61no—
484C22—122no—
485C22D3×#61111yescharacteristic
486C4—21no—
487C4—31no—
488C4—31no—
489C4—61no—
490C4—182no—
491C4—542no—
492C4C2×D3×Dic911yescharacteristic
493C4D3×#61111yescharacteristic
494C3—21no—
495C3C2×#6339611yescharacteristic, complemented
496C3D3×#83711yescharacteristic
497C2—21no—
498C2—32no—
499C2—41no—
500C2—61no—
501C2—121no—
502C2D3×#367611yescharacteristic
subgroupG/H
centerC4D3×#611
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC3×C9×#41C22
socleC2×C32C2×#217
prime radicalC3×D3×#41D3
cosocleC2×C3×C4×C9C23
hypercenter#41D3×D9
hypocenterC3×C9C2×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C4×D3×Dic9C2semidirect
3. D3×#3667C2semidirect
4. #11720585C2semidirect
5. C3×#63396C2semidirect
6. #11720301C2semidirect
7. #11720300C2semidirect
11. C9×#239C4semidirect
12. D3×Q8×C9C4semidirect
14. C9×#237C4semidirect
16. D3×D4×C9C4semidirect
22. C4×C3⋊Dic9C22semidirect
23. #88532C22semidirect
24. C3×C4×Dic9C22semidirect
25. C3×#3667C22semidirect
43. #63396D3direct (N × H)
46. C3×Q8×C9C2×C4semidirect
48. C3×D4×C9C2×C4semidirect
59. C9×D12C2×C4semidirect
68. C9×Dic6C2×C4semidirect
109. C4×Dic9C2×D3semidirect
113. #3667C2×D3semidirect
178. Q8×C9C4×D3semidirect
187. D4×C9C4×D3semidirect
214. D3×C9#104semidirect
229. #239Dic9semidirect
230. D3×Q8Dic9semidirect
232. #237Dic9semidirect
234. D3×D4Dic9semidirect
299. C3×C9C2×#104semidirect
307. C3×Q8C2×Dic9semidirect
318. C3×D4C2×Dic9semidirect
347. D12C2×Dic9semidirect
357. Dic6C2×Dic9semidirect
435. C9D3×#104semidirect
440. Q8D3×Dic9semidirect
447. D4D3×Dic9semidirect
478. D3#63396direct (N × H)
495. C3C2×#63396semidirect

Maximal subgroups

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

subgroupindex
D3×C9×#412
C4×D3×Dic92
D3×#36672
#117205852
C3×#633962
#117203012
#117203002
D3×#8373
C2×#633963