Finite Group Databasebeta

← D3×#63365 #13137468

Subgroups — D3×#63365 #13137468

Order 1728.

682 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic
2D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
3D3×#3676C211yesmaximal, characteristic, complemented
4#11720523C211yesmaximal, characteristic, complemented
5C3×#63365C211yesmaximal, characteristic, complemented
6#11720330C211yesmaximal, characteristic, complemented
7#11720329C211yesmaximal, characteristic, complemented
8D3×#806—31nomaximal
9C2×#63365—31nomaximal
10C23×D3×C9C2211yescharacteristic
11C22×D3×D9C411yescharacteristic, complemented
12C2×#6233C2211yescharacteristic
13C2×C3×#611C2211yescharacteristic
14C2×C4×D3×C9—21no—
15D3×#611—21no—
16D3×#611—21no—
17D3×#611—21no—
18D3×#611—21no—
19C2×#6195C411yescharacteristic, complemented
20C2×#6194C411yescharacteristic, complemented
21C2×D3×Dic9—21no—
22C2×D3×Dic9C411yescharacteristic, complemented
23C3×C9×C22⋊C4C2211yescharacteristic, complemented
24#88551C2211yescharacteristic, complemented
25C9×#217C2211yescharacteristic, complemented
26C3×#3676C2211yescharacteristic, complemented
27C9×(C2×D3)⋊C4—21no—
28(C2×D3)⋊Dic9—21no—
29C2×D3×#67—31no—
30C3×D3×C22⋊C4D311yescharacteristic
31D3×#217—31no—
32C22×#611—31no—
33#63633—31no—
34C3×#806—31no—
35#63581—31no—
36#63580—31no—
37C2×C9×C22⋊C4—31no—
38C2×#3676—31no—
39#63365—31no—
40#63365—31no—
41#63365—31no—
42#63365—61no—
43#63365D311yescharacteristic, direct product factor
44C23×C3×C9C2311yescharacteristic
45C22×C3⋊D9C2×C411yescharacteristic, complemented
46C22×D3×C9—42no—
47C22×D3×C9C2×C411yescharacteristic
48C22×D3×C9C2×C411yescharacteristic
49C22×D3×C9D411yescharacteristic
50C22×D3×C9D411yescharacteristic
51C22×D3×C9D411yescharacteristic
52C22×D3×C9D411yescharacteristic
53C22×C3×D9C2×C411yescharacteristic, complemented
54C2×D3×D9—21no—
55C2×D3×D9—21no—
56C2×D3×D9—42no—
57C2×C3×C4×C9—21no—
58#6233—21no—
59#6233—21no—
60C2×C3⋊Dic9—21no—
61C2×C3⋊Dic9C2×C411yescharacteristic, complemented
62C3×#611—21no—
63C3×#611—21no—
64C2×C9×Dic3—21no—
65C2×C3×Dic9—21no—
66C2×C3×Dic9C2×C411yescharacteristic, complemented
67C4×D3×C9—42no—
68#6195—21no—
69#6195—21no—
70#6194—21no—
71#6194—21no—
72D3×Dic9—21no—
73D3×Dic9—21no—
74D3×Dic9—42no—
75C2×#806—91no—
76D3×#99—91no—
77C23×C3×D3C2×D311yescharacteristic
78C22×D32—31no—
79C2×#638—31no—
80C2×C3×#67—31no—
81C2×C3×C4×D3—21no—
82D3×#67—61no—
83D3×#67—61no—
84D3×#67—61no—
85D3×#67—61no—
86C2×#626—31no—
87C2×#625—31no—
88C2×D3×Dic3—31no—
89C2×D3×Dic3—61no—
90C24×C9—31no—
91C23×D9—31no—
92C32×C22⋊C4C2×D311yescharacteristic
93#3757—31no—
94C3×#217—31no—
95C3×#217C2×D311yescharacteristic
96C3×(C2×D3)⋊C4—21no—
97(C2×D3)⋊Dic3—61no—
98C22×C4×C9—61no—
99C2×#611—31no—
100C2×#611—31no—
101C2×#611—31no—
102C2×#611—61no—
103C2×#611—61no—
104C2×#611—61no—
105C2×#611—61no—
106C2×#611—61no—
107C2×#611C2×D311yescharacteristic
108C22×Dic9—31no—
109C22×Dic9—61no—
110C9×C22⋊C4—21no—
111C9×C22⋊C4—31no—
112C9×C22⋊C4—61no—
113C9×C22⋊C4C2×D311yescharacteristic, complemented
114#3676—31no—
115#3676—61no—
116#3676—61no—
117#3676C2×D311yescharacteristic, complemented
118C22×C3×C9—41no—
119C22×C3×C9C22×C411yescharacteristic
120C22×C3×C9C2×D411yescharacteristic
121C22×C3×C9C2×D411yescharacteristic
122C2×C3⋊D9—21no—
123C2×C3⋊D9—41no—
124C2×D3×C9—22no—
125C2×D3×C9—22no—
126C2×D3×C9—22no—
127C2×D3×C9—41no—
128C2×D3×C9—41no—
129C2×D3×C9—41no—
130C2×D3×C9C22⋊C411yescharacteristic
131C2×D3×C9C22⋊C411yescharacteristic
132C2×D3×C9C22⋊C411yescharacteristic
133C2×D3×C9C22⋊C411yescharacteristic
134C2×C3×D9—21no—
135C2×C3×D9—41no—
136D3×D9—42no—
137D3×D9—42no—
138C3×C4×C9—41no—
139C3⋊Dic9—21no—
140C3⋊Dic9—41no—
141C9×Dic3—41no—
142C3×Dic9—21no—
143C3×Dic9—41no—
144C22×#67—91no—
145C2×D3×D4—91no—
146C2×C3×C22⋊C4—31no—
147C2×#217—91no—
148D3×C22⋊C4—91no—
149D3×C22⋊C4D911yescharacteristic, complemented
150C3×#99—91no—
151#834—91no—
152#806—31no—
153#806—91no—
154#806—91no—
155#806—91no—
156#806—91no—
157#806—91no—
158#806—181no—
159C23×C32C22×D311yescharacteristic
160C22×C3⋊D3—31no—
161C22×C3×D3—31no—
162C22×C3×D3—42no—
163C22×C3×D3C4×D311yescharacteristic
164C22×C3×D3C4×D311yescharacteristic
165C22×C3×D3D1211yescharacteristic
166C22×C3×D3D1211yescharacteristic
167C22×C3×D3#6711yescharacteristic
168C22×C3×D3#6711yescharacteristic
169C2×D32—61no—
170C2×D32—61no—
171C2×D32—122no—
172C2×C32×C4—21no—
173#638—61no—
174#638—61no—
175C2×C3⋊Dic3—31no—
176C2×C3⋊Dic3—61no—
177C3×#67—61no—
178C3×#67—61no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—31no—
181C2×C3×Dic3—61no—
182C3×C4×D3—42no—
183#626—61no—
184#626—61no—
185#625—61no—
186#625—61no—
187D3×Dic3—61no—
188D3×Dic3—61no—
189D3×Dic3—122no—
190C23×C9—21no—
191C23×C9—31no—
192C23×C9—31no—
193C23×C9—31no—
194C23×C9—31no—
195C23×C9—31no—
196C23×C9—31no—
197C23×C9—122no—
198C23×C9C22×D311yescharacteristic
199C22×D9—31no—
200C22×D9—61no—
201C22×D9—61no—
202C22×D9—61no—
203C22×D9—122no—
204C22×D9C4×D311yescharacteristic, complemented
205C2×C4×C9—21no—
206C2×C4×C9—41no—
207C2×C4×C9—61no—
208C2×C4×C9—122no—
209#611—21no—
210#611—21no—
211#611—61no—
212#611—61no—
213#611—61no—
214#611—61no—
215#611—61no—
216#611—61no—
217#611—121no—
218#611—121no—
219C2×Dic9—21no—
220C2×Dic9—31no—
221C2×Dic9—61no—
222C2×Dic9—61no—
223C2×Dic9—61no—
224C2×Dic9—61no—
225C2×Dic9—121no—
226C2×Dic9—122no—
227C2×Dic9C4×D311yescharacteristic, complemented
228C2×#99—271noSylow
229C2×C3×C9—21no—
230C2×C3×C9—21no—
231C2×C3×C9—21no—
232C2×C3×C9C2×C22⋊C411yescharacteristic
233C3⋊D9—41no—
234D3×C9—21no—
235D3×C9—21no—
236D3×C9—21no—
237D3×C9#9912yescomplemented
238C3×D9—41no—
239C24×C3—31no—
240C23×D3—91no—
241C23×D3—91no—
242C23×D3C2×D911yescharacteristic
243C2×C3×D4—91no—
244C22×C3×C4—61no—
245C2×#67—31no—
246C2×#67—91no—
247C2×#67—91no—
248C2×#67—91no—
249C2×#67—91no—
250C2×#67—91no—
251C2×#67—181no—
252C2×#67—181no—
253C2×#67—181no—
254C2×#67—181no—
255C2×#67—181no—
256C22×Dic3—91no—
257C22×Dic3—181no—
258D3×D4—181no—
259D3×D4—181no—
260D3×D4—181no—
261D3×D4—181no—
262C2×D12—91no—
263C2×C4×D3—21no—
264C2×C4×D3—91no—
265C2×C4×D3—181no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—31no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—91no—
270C3×C22⋊C4C2×D911yescharacteristic, complemented
271C3×C22⋊C4D3211yescharacteristic
272#217—31no—
273#217—91no—
274#217—91no—
275#217—181no—
276#217—181no—
277#217C2×D911yescharacteristic, complemented
278(C2×D3)⋊C4—21no—
279(C2×D3)⋊C4—181no—
280C22×C32—41no—
281C22×C32C2×C4×D311yescharacteristic
282C22×C32C2×D1211yescharacteristic
283C22×C32C2×#6711yescharacteristic
284C2×C3⋊D3—61no—
285C2×C3⋊D3—121no—
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—61no—
293C2×C3×D3—121no—
294C2×C3×D3(C2×D3)⋊C411yescharacteristic
295C2×C3×D3(C2×D3)⋊C411yescharacteristic
296C2×C3×D3(C2×D3)⋊C411yescharacteristic
297C2×C3×D3(C2×D3)⋊C411yescharacteristic
298D32—122no—
299D32—122no—
300C32×C4—41no—
301C3⋊Dic3—61no—
302C3⋊Dic3—121no—
303C3×Dic3—41no—
304C3×Dic3—61no—
305C3×Dic3—121no—
306C22×C9—21no—
307C22×C9—21no—
308C22×C9—21no—
309C22×C9—31no—
310C22×C9—31no—
311C22×C9—31no—
312C22×C9—31no—
313C22×C9—41no—
314C22×C9—62no—
315C22×C9—62no—
316C22×C9—62no—
317C22×C9—81no—
318C22×C9—121no—
319C22×C9—121no—
320C22×C9—121no—
321C22×C9C2×C4×D311yescharacteristic
322C22×C9D3×D411yescharacteristic
323C22×C9D3×D411yescharacteristic
324C2×D9—21no—
325C2×D9—41no—
326C2×D9—61no—
327C2×D9—121no—
328C2×D9—122no—
329C2×D9—122no—
330C2×D9—121no—
331C2×D9—241no—
332C4×C9—41no—
333C4×C9—81no—
334C4×C9—121no—
335Dic9—21no—
336Dic9—41no—
337Dic9—61no—
338Dic9—121no—
339Dic9—121no—
340Dic9—241no—
341C22×D4—271no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—271no—
344#99—91no—
345#99—271no—
346#99—271no—
347#99—271no—
348C3×C9C2×#9911yescharacteristic, complemented, Sylow
349C23×C3—21no—
350C23×C3—31no—
351C23×C3—31no—
352C23×C3—31no—
353C23×C3—31no—
354C23×C3—31no—
355C23×C3—31no—
356C23×C3—91no—
357C23×C3—122no—
358C23×C3C22×D911yescharacteristic
359C23×C3C2×D3211yescharacteristic
360C22×D3—31no—
361C22×D3—42no—
362C22×D3—91no—
363C22×D3—91no—
364C22×D3—181no—
365C22×D3—181no—
366C22×D3—181no—
367C22×D3—181no—
368C22×D3—181no—
369C22×D3—362no—
370C22×D3—362no—
371C22×D3C4×D911yescharacteristic
372C22×D3C4×D911yescharacteristic
373C22×D3D3611yescharacteristic
374C22×D3D3611yescharacteristic
375C22×D3#61111yescharacteristic
376C22×D3#61111yescharacteristic
377C3×D4—181no—
378C3×D4—181no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—41no—
382C2×C3×C4—61no—
383C2×C3×C4—91no—
384C2×C3×C4—122no—
385C2×C3×C4—181no—
386#67—61no—
387#67—61no—
388#67—181no—
389#67—181no—
390#67—181no—
391#67—181no—
392#67—181no—
393#67—181no—
394#67—181no—
395#67—181no—
396#67—181no—
397#67—181no—
398#67—361no—
399#67—361no—
400C2×Dic3—21no—
401C2×Dic3—31no—
402C2×Dic3—61no—
403C2×Dic3—91no—
404C2×Dic3—91no—
405C2×Dic3—181no—
406C2×Dic3—181no—
407C2×Dic3—181no—
408C2×Dic3—181no—
409C2×Dic3—181no—
410C2×Dic3—361no—
411C2×Dic3—362no—
412D12—181no—
413D12—181no—
414C4×D3—42no—
415C4×D3—181no—
416C4×D3—181no—
417C4×D3—362no—
418C2×C32—21no—
419C2×C32—21no—
420C2×C32—21no—
421C2×C32C2×(C2×D3)⋊C411yescharacteristic
422C3⋊D3—121no—
423C3×D3—21no—
424C3×D3—21no—
425C3×D3—21no—
426C3×D3—121no—
427C3×D3#80612yes—
428C2×C9—21no—
429C2×C9—21no—
430C2×C9—21no—
431C2×C9—21no—
432C2×C9—32no—
433C2×C9—41no—
434C2×C9—41no—
435C2×C9—41no—
436C2×C9—61no—
437C2×C9—61no—
438C2×C9—61no—
439C2×C9D3×C22⋊C411yescharacteristic
440D9—41no—
441D9—121no—
442D9—241no—
443C24—31no—
444C24—271no—
445C2×D4—91no—
446C2×D4—271no—
447C2×D4—271no—
448C2×D4—271no—
449C2×D4—541no—
450C2×D4—541no—
451C2×D4—541no—
452C2×D4—541no—
453C22×C4—61no—
454C22×C4—271no—
455C22×C4—541no—
456C22⋊C4—31no—
457C22⋊C4—61no—
458C22⋊C4—91no—
459C22⋊C4—271no—
460C22⋊C4—541no—
461C22⋊C4D3×D911yescharacteristic, complemented
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—31no—
466C22×C3—31no—
467C22×C3—31no—
468C22×C3—31no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—81no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3—181no—
479C22×C3—361no—
480C22×C3C2×C4×D911yescharacteristic
481C22×C3C2×D3611yescharacteristic
482C22×C3C2×#61111yescharacteristic
483C22×C3C4×D3211yescharacteristic
484C22×C3D3×D1211yescharacteristic
485C22×C3D3×#6711yescharacteristic
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—41no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—61no—
493C2×D3—121no—
494C2×D3—181no—
495C2×D3—181no—
496C2×D3—361no—
497C2×D3—362no—
498C2×D3—362no—
499C2×D3—362no—
500C2×D3—362no—
501C2×D3—361no—
502C2×D3—361no—
503C2×D3—721no—
504C2×D3(C2×D9)⋊C411yescharacteristic
505C2×D3(C2×D9)⋊C411yescharacteristic
506C2×D3(C2×D9)⋊C411yescharacteristic
507C2×D3(C2×D9)⋊C411yescharacteristic
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—81no—
511C3×C4—121no—
512C3×C4—181no—
513C3×C4—361no—
514Dic3—41no—
515Dic3—61no—
516Dic3—121no—
517Dic3—181no—
518Dic3—181no—
519Dic3—361no—
520Dic3—361no—
521Dic3—361no—
522Dic3—721no—
523C32C2×#80611yescharacteristic
524C9—21no—
525C9D3×#9911yescharacteristic, complemented
526C23—31no—
527C23—31no—
528C23—31no—
529C23—31no—
530C23—31no—
531C23—31no—
532C23—91no—
533C23—122no—
534C23—271no—
535C23—541no—
536C23—541no—
537C23—1082no—
538C23C2×D3×D911yescharacteristic
539D4—181no—
540D4—181no—
541D4—541no—
542D4—541no—
543D4—541no—
544D4—541no—
545D4—541no—
546D4—541no—
547C2×C4—21no—
548C2×C4—61no—
549C2×C4—91no—
550C2×C4—122no—
551C2×C4—181no—
552C2×C4—271no—
553C2×C4—541no—
554C2×C4—541no—
555C2×C4—541no—
556C2×C4—1082no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—32no—
565C2×C3—41no—
566C2×C3—41no—
567C2×C3—41no—
568C2×C3—61no—
569C2×C3—61no—
570C2×C3—61no—
571C2×C3—361no—
572C2×C3C2×(C2×D9)⋊C411yescharacteristic
573C2×C3D3×(C2×D3)⋊C411yescharacteristic
574D3—21no—
575D3—21no—
576D3—21no—
577D3—121no—
578D3—361no—
579D3—361no—
580D3—721no—
581D3#6336512yesdirect product factor
582C22—31no—
583C22—31no—
584C22—31no—
585C22—31no—
586C22—41no—
587C22—62no—
588C22—62no—
589C22—62no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—181no—
594C22—361no—
595C22—541no—
596C22—1081no—
597C22—1082no—
598C22—1082no—
599C22C4×D3×D911yescharacteristic
600C22D3×D3611yescharacteristic
601C22D3×#61111yescharacteristic
602C4—41no—
603C4—121no—
604C4—181no—
605C4—361no—
606C4—541no—
607C4—1081no—
608C3—21no—
609C3C2×#6336511yescharacteristic, complemented
610C3D3×#80611yescharacteristic
611C2—21no—
612C2—21no—
613C2—21no—
614C2—32no—
615C2—61no—
616C2—61no—
617C2—61no—
618C2—361no—
619C2—1081no—
620C2D3×(C2×D9)⋊C411yescharacteristic
subgroupG/H
centerC2D3×(C2×D9)⋊C4
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC3×C9×C22⋊C4C22
socleC2×C32C2×(C2×D3)⋊C4
prime radicalC2×D3×#611C2
cosocleC23×C3×C9C23
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#99
LCSG ▷ C22×C3×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. D3×C9×C22⋊C4C2semidirect
3. D3×#3676C2semidirect
4. #11720523C2semidirect
5. C3×#63365C2semidirect
6. #11720330C2semidirect
7. #11720329C2semidirect
11. C22×D3×D9C4semidirect
19. C2×#6195C4semidirect
20. C2×#6194C4semidirect
22. C2×D3×Dic9C4semidirect
23. C3×C9×C22⋊C4C22semidirect
24. #88551C22semidirect
25. C9×#217C22semidirect
26. C3×#3676C22semidirect
43. #63365D3direct (N × H)
45. C22×C3⋊D9C2×C4semidirect
53. C22×C3×D9C2×C4semidirect
61. C2×C3⋊Dic9C2×C4semidirect
66. C2×C3×Dic9C2×C4semidirect
113. C9×C22⋊C4C2×D3semidirect
117. #3676C2×D3semidirect
149. D3×C22⋊C4D9semidirect
204. C22×D9C4×D3semidirect
227. C2×Dic9C4×D3semidirect
237. D3×C9#99semidirect
270. C3×C22⋊C4C2×D9semidirect
277. #217C2×D9semidirect
348. C3×C9C2×#99semidirect
461. C22⋊C4D3×D9semidirect
525. C9D3×#99semidirect
581. D3#63365direct (N × H)
609. C3C2×#63365semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
D3×C9×C22⋊C42
D3×#36762
#117205232
C3×#633652
#117203302
#117203292
D3×#8063
C2×#633653