Finite Group Databasebeta

← D3×#63474 #13149899

Subgroups — D3×#63474 #13149899

Order 1728.

860 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3699C212yesmaximal, complemented
2#11721791C211yesmaximal, characteristic, complemented
3D3×C9×D8C211yesmaximal, characteristic, complemented
4C3×#63474C211yesmaximal, characteristic, complemented
5#11721178C212yesmaximal, complemented
6#11721177C212yesmaximal, complemented
7D3×#3672C212yesmaximal, complemented
8#11720824C211yesmaximal, characteristic, complemented
9#11720822C211yesmaximal, characteristic, complemented
10D3×C8×D9C211yesmaximal, characteristic, complemented
11D3×Dic36C211yesmaximal, characteristic, complemented
12D3×#912—31nomaximal
13C2×#63474—31nomaximal
14#88742C2212yescomplemented
15D3×D4×C9C2212yes—
16C3×#3699C2212yescomplemented
17D3×#611—22no—
18#88663—22no—
19#88662—22no—
20C2×D3×Dic9—22no—
21C4×D3×D9C2211yescharacteristic
22#88639C2212yescomplemented
23#88638C2212yescomplemented
24D3×Dic18C2212yes—
25C3×C9×D8C2211yescharacteristic, complemented
26#88543C2212yescomplemented
27C8×C3⋊D9C2211yescharacteristic, complemented
28#88521C2211yescharacteristic, complemented
29C9×#213C2212yescomplemented
30C3×#3672C2212yescomplemented
31C9×D24C2211yescharacteristic, complemented
32D3×C8×C9C2211yescharacteristic
33C3×C8×D9C2211yescharacteristic, complemented
34C3×Dic36C2211yescharacteristic, complemented
35#88424C2212yescomplemented
36#88423C2212yescomplemented
37D3×C9⋊C8C2211yescharacteristic
38#88418C2212yescomplemented
39(C3⋊D9)⋊C8C2211yescharacteristic, complemented
40D9×C3⋊C8C2211yescharacteristic, complemented
41D3×#237—32no—
42#64121—31no—
43C3×#912—31no—
44C3×D3×D8D311yescharacteristic
45#63936—32no—
46#63933—32no—
47D3×#214—32no—
48#63810—31no—
49#63807—31no—
50D3×Dic12—31no—
51D32×C8—31no—
52C2×#3699—32no—
53C2×C9×D8—31no—
54C2×#3672—32no—
55#63474—32no—
56#63474—31no—
57#63474—32no—
58#63474—31no—
59#63474—31no—
60#63474—61no—
61#63474D311yescharacteristic, direct product factor
62C2×C8×D9—31no—
63C2×Dic36—31no—
64C22×D3×C9—22no—
65C2×D3×D9D411yescharacteristic
66C3×D4×C9C2312yes—
67#6233—22no—
68C2×C3⋊Dic9—22no—
69C4×C3⋊D9C2311yescharacteristic
70#6226C2312yes—
71C9×#67—22no—
72C3×#611—22no—
73C2×C3×Dic9—22no—
74C9×D12C2312yes—
75C4×D3×C9C2311yescharacteristic
76C3×C4×D9C2311yescharacteristic
77C3×Dic18C2312yes—
78#6195—22no—
79#6194—22no—
80D3×Dic9—22no—
81D3×Dic9—22no—
82D3×Dic9—22no—
83D3×Dic9D411yescharacteristic
84(C3⋊D9)⋊C4D411yescharacteristic
85Dic3×D9D411yescharacteristic
86#6189—22no—
87C3×C8×C9C2311yescharacteristic
88C3⋊(C9⋊C8)C2311yescharacteristic
89C9×C3⋊C8C2311yescharacteristic
90C3×C9⋊C8C2311yescharacteristic
91D3×#135—91no—
92C2×#912—91no—
93#3830—32no—
94C3×#237—32no—
95C3×D3×D4C2×D312yes—
96D3×#67—62no—
97#3805—62no—
98#3804—62no—
99C2×D3×Dic3—62no—
100C4×D32—31no—
101#3796—32no—
102#3795—32no—
103D3×Dic6—32no—
104C32×D8C2×D311yescharacteristic
105#3754—32no—
106#3746—31no—
107C8×C3⋊D3—31no—
108C3×#214—32no—
109C3×#213C2×D312yes—
110C3×Dic12—31no—
111C3×D24C2×D311yescharacteristic
112C3×D3×C8—31no—
113C3×D3×C8C2×D311yescharacteristic
114#3719—32no—
115#3716—32no—
116#3715—32no—
117#3710—31no—
118D3×C3⋊C8—31no—
119D3×C3⋊C8—31no—
120C2×D4×C9—32no—
121C2×#611—62no—
122C22×Dic9—62no—
123#3699—32no—
124#3699—32no—
125#3699—32no—
126#3699—62no—
127#3699—62no—
128#3699—62no—
129#3699C2×D312yescomplemented
130C2×C4×D9—31no—
131C2×Dic18—32no—
132C9×D8—21no—
133C9×D8—32no—
134C9×D8—31no—
135C9×D8C2×D311yescharacteristic, complemented
136C2×C8×C9—31no—
137#3672—32no—
138#3672—32no—
139#3672—32no—
140#3672—62no—
141#3672C2×D312yescomplemented
142C2×C9⋊C8—31no—
143C8×D9—31no—
144C8×D9—31no—
145C8×D9—31no—
146C8×D9—61no—
147C8×D9C2×D311yescharacteristic, complemented
148Dic36—32no—
149Dic36—31no—
150Dic36—61no—
151Dic36C2×D311yescharacteristic, complemented
152C22×C3×C9—22no—
153C2×C3⋊D9C2×D411yescharacteristic
154C2×D3×C9—22no—
155C2×D3×C9—44no—
156C2×D3×C9C2×D411yescharacteristic
157C2×C3×D9C2×D411yescharacteristic
158D3×D9—22no—
159C3×C4×C9C2411yescharacteristic
160C3⋊Dic9—22no—
161C3⋊Dic9C2×D411yescharacteristic
162C9×Dic3C2×D411yescharacteristic
163C3×Dic9—22no—
164C3×Dic9C2×D411yescharacteristic
165D3×#41—92no—
166C2×#237—92no—
167C3×#135—91no—
168C2×C3×D8—31no—
169#950—92no—
170C2×#214—92no—
171#919—91no—
172D3×Q16—91no—
173#916—92no—
174D3×SD16—92no—
175#912—31no—
176#912—91no—
177#912—91no—
178#912—92no—
179#912—92no—
180#912—91no—
181#912—91no—
182#912—181no—
183D3×D8D911yescharacteristic, complemented
184C2×Dic12—91no—
185#904—91no—
186C2×D3×C8—91no—
187C2×D3×C8—91no—
188C22×C3×D3—22no—
189C2×D32—31no—
190C32×D4C22×D312yes—
191#638—62no—
192C2×C3⋊Dic3—62no—
193C4×C3⋊D3—31no—
194#634—32no—
195C3×#67—22no—
196C3×#67—62no—
197C2×C3×Dic3—62no—
198C3×D12C22×D312yes—
199C3×C4×D3—31no—
200C3×C4×D3C22×D311yescharacteristic
201C3×Dic6—32no—
202#627—62no—
203#626—62no—
204#625—62no—
205#624—31no—
206D3×Dic3—31no—
207D3×Dic3—31no—
208D3×Dic3—62no—
209D3×Dic3—62no—
210D3×Dic3—62no—
211C23×C9—62no—
212C22×D9—31no—
213C32×C8C22×D311yescharacteristic
214C3⋊(C3⋊C8)—31no—
215C3×C3⋊C8—31no—
216C3×C3⋊C8C22×D311yescharacteristic
217D4×C9—22no—
218D4×C9—32no—
219D4×C9—62no—
220D4×C9C22×D312yes—
221C2×C4×C9—31no—
222#611—22no—
223#611—62no—
224#611—62no—
225#611—62no—
226#611—122no—
227C2×Dic9—22no—
228C2×Dic9—31no—
229C2×Dic9—62no—
230C2×Dic9—62no—
231C2×Dic9—62no—
232C2×Dic9—62no—
233C2×Dic9—122no—
234C4×D9—31no—
235C4×D9—31no—
236C4×D9—31no—
237C4×D9—61no—
238C4×D9C22×D311yescharacteristic
239Dic18—32no—
240Dic18—62no—
241Dic18—62no—
242Dic18C22×D312yes—
243C8×C9—21no—
244C8×C9—31no—
245C8×C9C22×D311yescharacteristic
246C9⋊C8—31no—
247C9⋊C8—61no—
248C9⋊C8C22×D311yescharacteristic
249C2×#135—271noSylow
250C2×C3×C9—42no—
251C2×C3×C9C22×D411yescharacteristic
252C3⋊D9—21no—
253D3×C9—42no—
254D3×C9#13512yescomplemented
255C3×D9—21no—
256C3×#41—92no—
257C2×C3×D4—32no—
258C2×#67—182no—
259C22×Dic3—182no—
260#239—92no—
261D3×Q8—92no—
262#237—32no—
263#237—92no—
264#237—92no—
265#237—92no—
266#237—92no—
267#237—182no—
268#237—182no—
269#237—182no—
270#237—182no—
271D3×D4—182no—
272D3×D4C2×D912yes—
273#235—92no—
274#235—182no—
275C2×C4×D3—91no—
276C2×C4×D3—91no—
277C2×C4×D3—182no—
278C2×Dic6—92no—
279C3×Q16—91no—
280C3×SD16—92no—
281C3×D8—21no—
282C3×D8—32no—
283C3×D8—31no—
284C3×D8C2×D911yescharacteristic, complemented
285C3×D8D3211yescharacteristic
286C2×C3×C8—31no—
287C2×C3×C8—91no—
288#216—92no—
289#215—92no—
290#214—32no—
291#214—92no—
292#214—92no—
293#214—92no—
294#214—92no—
295#214—182no—
296#213C2×D912yescomplemented
297C2×C3⋊C8—91no—
298C2×C3⋊C8—91no—
299Dic12—31no—
300Dic12—92no—
301Dic12—91no—
302Dic12—91no—
303Dic12—181no—
304D24C2×D911yescharacteristic, complemented
305#204—92no—
306D3×C8—31no—
307D3×C8—91no—
308D3×C8—91no—
309D3×C8—91no—
310D3×C8—91no—
311D3×C8—91no—
312D3×C8—91no—
313D3×C8—181no—
314D3×C8C2×D911yescharacteristic
315C22×C32—22no—
316C2×C3⋊D3—31no—
317C2×C3×D3—22no—
318C2×C3×D3—31no—
319C2×C3×D3—44no—
320C2×C3×D3D3×D411yescharacteristic
321D32—62no—
322C32×C4C23×D311yescharacteristic
323C3⋊Dic3—31no—
324C3⋊Dic3—62no—
325C3×Dic3—31no—
326C3×Dic3—62no—
327C3×Dic3D3×D411yescharacteristic
328C22×C9—22no—
329C22×C9—31no—
330C22×C9—42no—
331C22×C9—62no—
332C22×C9—124no—
333C2×D9—31no—
334C2×D9—61no—
335C2×D9—62no—
336C2×D9D3×D411yescharacteristic
337C4×C9—21no—
338C4×C9—31no—
339C4×C9C23×D311yescharacteristic
340Dic9—22no—
341Dic9—31no—
342Dic9—61no—
343Dic9—62no—
344Dic9—122no—
345Dic9D3×D411yescharacteristic
346C2×#41—272no—
347#135—91no—
348#135—271no—
349#135—272no—
350#135—271no—
351#135—272no—
352#135—271no—
353C2×Q16—271no—
354C2×SD16—272no—
355C2×D8—31no—
356C22×C8—271no—
357C3×C9C2×#13511yescharacteristic, complemented, Sylow
358C23×C3—62no—
359C22×D3—22no—
360C22×D3—91no—
361C22×D3—91no—
362C3×Q8—92no—
363C3×D4—22no—
364C3×D4—32no—
365C3×D4—62no—
366C3×D4—182no—
367C3×D4C22×D912yes—
368C3×D4C2×D3212yes—
369C2×C3×C4—31no—
370C2×C3×C4—91no—
371C2×C3×C4—182no—
372#67—22no—
373#67—62no—
374#67—182no—
375#67—182no—
376#67—182no—
377#67—182no—
378#67—182no—
379#67—362no—
380C2×Dic3—62no—
381C2×Dic3—91no—
382C2×Dic3—91no—
383C2×Dic3—182no—
384C2×Dic3—182no—
385C2×Dic3—182no—
386C2×Dic3—182no—
387C2×Dic3—182no—
388C2×Dic3—362no—
389D12—182no—
390D12C22×D912yes—
391C4×D3—31no—
392C4×D3—91no—
393C4×D3—91no—
394C4×D3—91no—
395C4×D3—91no—
396C4×D3—91no—
397C4×D3—91no—
398C4×D3—181no—
399C4×D3—182no—
400C4×D3—182no—
401C4×D3—182no—
402C4×D3C22×D911yescharacteristic
403Dic6—32no—
404Dic6—92no—
405Dic6—92no—
406Dic6—182no—
407Dic6—182no—
408Dic6—182no—
409C3×C8—21no—
410C3×C8—31no—
411C3×C8—91no—
412C3×C8C22×D911yescharacteristic
413C3×C8C2×D3211yescharacteristic
414C3⋊C8—31no—
415C3⋊C8—91no—
416C3⋊C8—91no—
417C3⋊C8—181no—
418C3⋊C8C22×D911yescharacteristic
419C2×C32—42no—
420C2×C32C2×D3×D411yescharacteristic
421C3⋊D3—61no—
422C3×D3—42no—
423C3×D3—61no—
424C3×D3#91212yes—
425C2×C9—21no—
426C2×C9—32no—
427C2×C9—42no—
428C2×C9—82no—
429C2×C9—122no—
430C2×C9C2×D3×D411yescharacteristic
431D9—21no—
432D9—61no—
433D9—121no—
434#41—92no—
435#41—272no—
436#41—272no—
437#41—272no—
438#41—542no—
439#41—542no—
440C2×Q8—272no—
441C2×D4—32no—
442C2×D4—542no—
443C22×C4—271no—
444C22×C4—542no—
445Q16—91no—
446Q16—272no—
447Q16—271no—
448SD16—92no—
449SD16—272no—
450SD16—272no—
451SD16—272no—
452D8—32no—
453D8—31no—
454D8D3×D911yescharacteristic, complemented
455C2×C8—31no—
456C2×C8—91no—
457C2×C8—271no—
458C2×C8—271no—
459C2×C8—271no—
460C2×C8—271no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—31no—
464C22×C3—42no—
465C22×C3—62no—
466C22×C3—91no—
467C22×C3—124no—
468C2×D3—22no—
469C2×D3—31no—
470C2×D3—44no—
471C2×D3—91no—
472C2×D3—91no—
473C2×D3—181no—
474C2×D3—182no—
475C2×D3—182no—
476C2×D3D4×D911yescharacteristic
477C3×C4—21no—
478C3×C4—31no—
479C3×C4—91no—
480C3×C4—182no—
481C3×C4C23×D911yescharacteristic
482C3×C4C22×D3211yescharacteristic
483Dic3—31no—
484Dic3—62no—
485Dic3—91no—
486Dic3—91no—
487Dic3—181no—
488Dic3—182no—
489Dic3—182no—
490Dic3—362no—
491Dic3D4×D911yescharacteristic
492C32C2×#91211yescharacteristic
493C9—21no—
494C9D3×#13511yescharacteristic, complemented
495C23—62no—
496C23—271no—
497Q8—92no—
498Q8—272no—
499Q8—542no—
500D4—32no—
501D4—62no—
502D4—182no—
503D4—542no—
504D4—542no—
505D4—542no—
506D4C2×D3×D912yes—
507C2×C4—31no—
508C2×C4—91no—
509C2×C4—182no—
510C2×C4—271no—
511C2×C4—271no—
512C2×C4—271no—
513C2×C4—271no—
514C2×C4—542no—
515C2×C4—542no—
516C2×C4—542no—
517C2×C4—542no—
518C8—31no—
519C8—91no—
520C8—271no—
521C8C2×D3×D911yescharacteristic
522C2×C3—21no—
523C2×C3—32no—
524C2×C3—42no—
525C2×C3—42no—
526C2×C3—82no—
527C2×C3—122no—
528C2×C3—181no—
529C2×C3C2×D4×D911yescharacteristic
530C2×C3D32×D411yescharacteristic
531D3—42no—
532D3—61no—
533D3—181no—
534D3—181no—
535D3—361no—
536D3#6347412yesdirect product factor
537C22—22no—
538C22—31no—
539C22—62no—
540C22—91no—
541C22—124no—
542C22—271no—
543C22—542no—
544C4—31no—
545C4—91no—
546C4—182no—
547C4—271no—
548C4—542no—
549C4C22×D3×D911yescharacteristic
550C3—21no—
551C3C2×#6347411yescharacteristic, complemented
552C3D3×#91211yescharacteristic
553C2—32no—
554C2—42no—
555C2—122no—
556C2—181no—
557C2—541no—
558C2D3×D4×D911yescharacteristic
subgroupG/H
centerC2D3×D4×D9
commutator, cosocleC3×C4×C9C24
FrattiniC3×C4C22×D32
FittingC3×C9×D8C22
socleC2×C32C2×D3×D4
hypercenterD8D3×D9
hypocenterC3×C9C2×#135
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. D3×#3699C2semidirect
2. #11721791C2semidirect
3. D3×C9×D8C2semidirect
4. C3×#63474C2semidirect
5. #11721178C2semidirect
6. #11721177C2semidirect
7. D3×#3672C2semidirect
8. #11720824C2semidirect
9. #11720822C2semidirect
10. D3×C8×D9C2semidirect
11. D3×Dic36C2semidirect
14. #88742C22semidirect
16. C3×#3699C22semidirect
22. #88639C22semidirect
23. #88638C22semidirect
25. C3×C9×D8C22semidirect
26. #88543C22semidirect
27. C8×C3⋊D9C22semidirect
28. #88521C22semidirect
29. C9×#213C22semidirect
30. C3×#3672C22semidirect
31. C9×D24C22semidirect
33. C3×C8×D9C22semidirect
34. C3×Dic36C22semidirect
35. #88424C22semidirect
36. #88423C22semidirect
38. #88418C22semidirect
39. (C3⋊D9)⋊C8C22semidirect
40. D9×C3⋊C8C22semidirect
61. #63474D3direct (N × H)
129. #3699C2×D3semidirect
135. C9×D8C2×D3semidirect
141. #3672C2×D3semidirect
147. C8×D9C2×D3semidirect
151. Dic36C2×D3semidirect
183. D3×D8D9semidirect
254. D3×C9#135semidirect
284. C3×D8C2×D9semidirect
296. #213C2×D9semidirect
304. D24C2×D9semidirect
357. C3×C9C2×#135semidirect
454. D8D3×D9semidirect
494. C9D3×#135semidirect
536. D3#63474direct (N × H)
551. C3C2×#63474semidirect

Maximal subgroups

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

subgroupindex
D3×#36992
#117217912
D3×C9×D82
C3×#634742
#117211782
#117211772
D3×#36722
#117208242
#117208222
D3×C8×D92
D3×Dic362
D3×#9123
C2×#634743