Finite Group Databasebeta

← C3×#10591422 #13158428

Subgroups — C3×#10591422 #13158428

Order 1728.

672 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#938C211yesmaximal, characteristic
2C3×#63841C211yesmaximal, characteristic, complemented
3C3×#63659C211yesmaximal, characteristic, complemented
4C32×#832C211yesmaximal, characteristic, complemented
5C3×#63576C211yesmaximal, characteristic, complemented
6C3×#63573C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5035—31nomaximal
9C3×#4779—31nomaximal
10#10591422C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic
12C2×C32×#67—21no—
13C2×C32×C4×D3C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
16C32×#217—21no—
17C32×C4⋊Dic3C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C2×C32×C3⋊C8C2211yescharacteristic
20C3×(C2×D3)⋊Dic3—21no—
21C3×Dic32—21no—
22C32×#121—31no—
23C3×#938—21no—
24C3×#938D311yescharacteristic
25C3×#938C2×C311yescharacteristic
26C3×#926—31no—
27C3×#892—31no—
28#63841C2×C311yescharacteristic, complemented
29C32×#102—31no—
30#63659C2×C311yescharacteristic, complemented
31C3×#832—21no—
32C3×#832—31no—
33C3×#832—31no—
34C3×#832—61no—
35C3×#832D311yescharacteristic, complemented
36C3×#832C2×C311yescharacteristic, complemented
37C3×#830—31no—
38C3×(C2×D3)⋊C8—31no—
39C3×#817—31no—
40C3×#808—31no—
41C3×#807—31no—
42C3×#807—31no—
43#63576C2×C311yescharacteristic, complemented
44#63573C2×C311yescharacteristic, complemented
45(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
46C23×C33—21no—
47C22×C32×D3D411yescharacteristic
48C33×D4—21no—
49C33×D4—21no—
50C2×C33×C4C2311yescharacteristic
51C2×C3×C3⋊Dic3—21no—
52C32×#67—42no—
53C2×C32×Dic3—21no—
54C2×C32×Dic3—21no—
55C2×C32×Dic3D411yescharacteristic
56C32×C4×D3—21no—
57C32×C4×D3—21no—
58C3×C3⋊(C3⋊C8)—21no—
59C32×C3⋊C8—21no—
60C3×#482—91no—
61#5035—31no—
62#4779—31no—
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C2×C32×D4—21no—
66C2×C32×D4—41no—
67C2×C32×D4—61no—
68C2×C32×D4C2×D311yescharacteristic
69C2×C32×D4C2×D311yescharacteristic
70C2×C32×D4C22×C311yescharacteristic
71C22×C32×C4—31no—
72C2×C3×#67—22no—
73C2×C3×#67—21no—
74C2×C3×#67—21no—
75C2×C3×C4×D3—21no—
76C2×C3×C4×D3C2×D311yescharacteristic
77C2×C3×C4×D3C22×C311yescharacteristic
78C2×C32×C8—31no—
79C32×C4⋊C4—31no—
80C32×C4⋊C4—31no—
81C32×C22⋊C4—61no—
82C4⋊(C3⋊Dic3)C22×C311yescharacteristic
83C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
84C3×#217—22no—
85C3×#217—21no—
86C3×#217—21no—
87C3×#217—61no—
88C3×(C2×D3)⋊C4—61no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—31no—
92C3×C4⋊Dic3—31no—
93C3×C4⋊Dic3—61no—
94C3×C4⋊Dic3C2×D311yescharacteristic
95C3×C4⋊Dic3C2×D311yescharacteristic
96C3×C4⋊Dic3C22×C311yescharacteristic
97C3×C4⋊Dic3C22×C311yescharacteristic
98C3×C4×Dic3—61no—
99C3×C4×Dic3—61no—
100C2×C3×C3⋊C8—21no—
101C2×C3×C3⋊C8—31no—
102C2×C3×C3⋊C8—31no—
103C2×C3×C3⋊C8—61no—
104C2×C3×C3⋊C8C2×D311yescharacteristic
105C2×C3×C3⋊C8C22×C311yescharacteristic
106(C2×D3)⋊Dic3—21no—
107Dic32—21no—
108C22×C33—41no—
109C22×C33—41no—
110C22×C33—41no—
111C22×C33C2×D411yescharacteristic
112C2×C32×D3—21no—
113C2×C32×D3—21no—
114C2×C32×D3—21no—
115C33×C4#4111yescharacteristic
116C33×C4#4111yescharacteristic
117C3×C3⋊Dic3—41no—
118C32×Dic3—21no—
119C32×Dic3—41no—
120C32×Dic3—41no—
121C3×#121—31no—
122C3×#121—31no—
123C3×#121—61no—
124C3×#117—91no—
125#938C3×D311yescharacteristic
126#926—31no—
127#892—31no—
128C3×#107—91no—
129C3×#106—91no—
130C3×#102—31no—
131C3×#102—31no—
132C3×#102—61no—
133C3×#102—91no—
134C3×C22⋊C8—91no—
135#832—31no—
136#832—31no—
137#832—61no—
138#832C3×D311yescharacteristic, complemented
139#830—31no—
140(C2×D3)⋊C8—31no—
141#817—31no—
142#808—31no—
143#807—31no—
144#807—31no—
145C23×C32—21no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32—31no—
150C23×C32—41no—
151C23×C32—41no—
152C23×C32—42no—
153C22×C3×D3—21no—
154C22×C3×D3#6711yescharacteristic
155C22×C3×D3C3×D411yescharacteristic
156C32×D4—21no—
157C32×D4—21no—
158C32×D4—22no—
159C32×D4—22no—
160C32×D4—21no—
161C32×D4—21no—
162C32×D4—21no—
163C32×D4—21no—
164C32×D4—41no—
165C32×D4—41no—
166C32×D4—41no—
167C32×D4—41no—
168C32×D4—42no—
169C32×D4—42no—
170C32×D4—122no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—31no—
175C2×C32×C4—41no—
176C2×C32×C4—61no—
177C2×C32×C4—61no—
178C2×C32×C4—61no—
179C2×C32×C4—61no—
180C2×C32×C4C22×D311yescharacteristic
181C2×C32×C4C22×D311yescharacteristic
182C2×C32×C4C23×C311yescharacteristic
183C2×C3⋊Dic3—21no—
184C3×#67—44no—
185C3×#67—42no—
186C3×#67—42no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3—61no—
195C2×C3×Dic3—61no—
196C2×C3×Dic3—121no—
197C2×C3×Dic3#6711yescharacteristic
198C2×C3×Dic3C3×D411yescharacteristic
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201C3×C4×D3—21no—
202C3×C4×D3—21no—
203C3×C4×D3—41no—
204C3×C4×D3—41no—
205C32×C8—61no—
206C3⋊(C3⋊C8)—21no—
207C3×C3⋊C8—21no—
208C3×C3⋊C8—21no—
209C3×C3⋊C8—41no—
210C3×C3⋊C8—61no—
211C3×C3⋊C8—61no—
212C3×C3⋊C8—121no—
213#482—91noSylow
214C2×C33—81no—
215C2×C33#12311yescharacteristic
216C2×C33#13511yescharacteristic
217C2×C33AGL(1,ℤ/8)11yescharacteristic
218C32×D3—41no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—41no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—62no—
226C2×C3×D4D3211yescharacteristic
227C2×C3×D4C2×C3×D311yescharacteristic
228C2×C3×D4C2×C3×D311yescharacteristic
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—61no—
232C2×#67—21no—
233C2×C4×D3C2×C3×D311yescharacteristic
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8—61no—
237C2×C3×C8—91no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—91no—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—62no—
248C3×C22⋊C4—181no—
249C3×C42—181no—
250#217—21no—
251#217—61no—
252(C2×D3)⋊C4—61no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3C2×C3×D311yescharacteristic
257C4⋊Dic3C2×C3×D311yescharacteristic
258C4×Dic3—61no—
259C4×Dic3—61no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8C2×C3×D311yescharacteristic
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32—41no—
268C22×C32—42no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—44no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—61no—
284C22×C32—61no—
285C22×C32—61no—
286C22×C32—81no—
287C22×C32—81no—
288C22×C32—81no—
289C22×C32—81no—
290C22×C32—82no—
291C22×C32—82no—
292C22×C32D3×D411yescharacteristic
293C22×C32C2×#6711yescharacteristic
294C22×C32C2×C3×D411yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—21no—
297C2×C3×D3—21no—
298C2×C3×D3—21no—
299C2×C3×D3—21no—
300C2×C3×D3—21no—
301C2×C3×D3—21no—
302C2×C3×D3—41no—
303C2×C3×D3—41no—
304C32×C4—21no—
305C32×C4—21no—
306C32×C4—21no—
307C32×C4—21no—
308C32×C4—21no—
309C32×C4—21no—
310C32×C4—41no—
311C32×C4—41no—
312C32×C4—61no—
313C32×C4—121no—
314C32×C4—121no—
315C32×C4#23511yescharacteristic
316C32×C4#23711yescharacteristic
317C32×C4#23711yescharacteristic
318C32×C4#23711yescharacteristic
319C32×C4C3×#4111yescharacteristic
320C32×C4C3×#4111yescharacteristic
321C3⋊Dic3—41no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C3×Dic3—41no—
328C3×Dic3—41no—
329C3×Dic3—41no—
330C3×Dic3—81no—
331C3×Dic3—121no—
332C3×Dic3—121no—
333C3×Dic3—241no—
334#121—31no—
335#117—91no—
336#107—91no—
337#106—91no—
338#102—31no—
339#102—91no—
340C22⋊C8—91no—
341C33#48211yescharacteristic, complemented, Sylow
342C23×C3—22no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—31no—
347C23×C3—31no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—42no—
351C23×C3—61no—
352C22×D3C3×#6711yescharacteristic
353C3×D4—22no—
354C3×D4—22no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—21no—
360C3×D4—21no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—41no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—124no—
368C3×D4—122no—
369C3×D4—122no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—41no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4—181no—
390C2×C3×C4C2×D3211yescharacteristic
391C2×C3×C4C22×C3×D311yescharacteristic
392C2×C3×C4C22×C3×D311yescharacteristic
393#67—42no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—121no—
399C2×Dic3C3×#6711yescharacteristic
400C4×D3—21no—
401C4×D3—21no—
402C3×C8—61no—
403C3×C8—61no—
404C3×C8—121no—
405C3×C8—181no—
406C3⋊C8—21no—
407C3⋊C8—61no—
408C3⋊C8—61no—
409C3⋊C8—121no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32—21no—
418C2×C32—21no—
419C2×C32—41no—
420C2×C32—41no—
421C2×C32—41no—
422C2×C32—82no—
423C2×C32—82no—
424C2×C32—82no—
425C2×C32—84no—
426C2×C32—81no—
427C2×C32—81no—
428C2×C32—81no—
429C2×C32—121no—
430C2×C32#88311yescharacteristic
431C2×C32#91111yescharacteristic
432C2×C32#91611yescharacteristic
433C2×C32#93211yescharacteristic
434C2×C32#93511yescharacteristic
435C2×C32#95011yescharacteristic
436C2×C32C3×#12311yescharacteristic
437C2×C32C3×#13511yescharacteristic
438C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
439C3×D3—42no—
440C3×D3—41no—
441C3×D3—41no—
442C2×D4—61no—
443C2×D4C3×D3211yescharacteristic
444C22×C4—31no—
445C2×C8—31no—
446C2×C8—91no—
447C4⋊C4—31no—
448C4⋊C4—31no—
449C4⋊C4—91no—
450C22⋊C4—61no—
451C22⋊C4—181no—
452C42—181no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—44no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—62no—
473C22×C3—61no—
474C22×C3—61no—
475C22×C3—61no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3—61no—
479C22×C3—81no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—82no—
484C22×C3—82no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3D3×#6711yescharacteristic
488C22×C3C3×D3×D411yescharacteristic
489C22×C3C2×C3×#6711yescharacteristic
490C2×D3—21no—
491C2×D3—21no—
492C2×D3—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—61no—
502C3×C4—61no—
503C3×C4—121no—
504C3×C4—122no—
505C3×C4—121no—
506C3×C4—121no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4—241no—
510C3×C4—361no—
511C3×C4#380411yescharacteristic
512C3×C4#380511yescharacteristic
513C3×C4C3×#23511yescharacteristic
514C3×C4C3×#23711yescharacteristic
515C3×C4C3×#23711yescharacteristic
516C3×C4C3×#23711yescharacteristic
517Dic3—21no—
518Dic3—41no—
519Dic3—41no—
520Dic3—121no—
521Dic3—121no—
522Dic3—241no—
523C32—21no—
524C32—21no—
525C32—21no—
526C32—41no—
527C32#477911yescharacteristic, complemented
528C32#503511yescharacteristic, complemented
529C32C3×#48211yescharacteristic, complemented
530C23—21no—
531C23—31no—
532D4—21no—
533D4—21no—
534D4—122no—
535C2×C4—31no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—181no—
541C2×C4C2×C3×D3211yescharacteristic
542C8—61no—
543C8—181no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—82no—
557C2×C3—82no—
558C2×C3—82no—
559C2×C3—84no—
560C2×C3—81no—
561C2×C3—81no—
562C2×C3—81no—
563C2×C3—122no—
564C2×C3—121no—
565C2×C3—121no—
566C2×C3#6393211yescharacteristic
567C2×C3#6393511yescharacteristic
568C2×C3#6396911yescharacteristic
569C2×C3C3×#88311yescharacteristic
570C2×C3C3×#91111yescharacteristic
571C2×C3C3×#91611yescharacteristic
572C2×C3C3×#93211yescharacteristic
573C2×C3C3×#93511yescharacteristic
574C2×C3C3×#95011yescharacteristic
575D3—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—61no—
580C22—61no—
581C22—61no—
582C22C3×D3×#6711yescharacteristic
583C4—61no—
584C4—121no—
585C4—121no—
586C4—361no—
587C4C3×#380411yescharacteristic
588C4C3×#380511yescharacteristic
589C3—21no—
590C3—21no—
591C3—21no—
592C3—41no—
593C3#1059142211yescharacteristic, direct product factor
594C3C3×#477911yescharacteristic, complemented
595C3C3×#503511yescharacteristic, complemented
596C2—81no—
597C2—121no—
598C2C3×#6393211yescharacteristic
599C2C3×#6393511yescharacteristic
600C2C3×#6396911yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC32×#938C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C3×#63841C2semidirect
3. C3×#63659C2semidirect
4. C32×#832C2semidirect
5. C3×#63576C2semidirect
6. C3×#63573C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591422C3direct (N × H)
28. #63841C2×C3semidirect
30. #63659C2×C3semidirect
35. C3×#832D3semidirect
36. C3×#832C2×C3semidirect
43. #63576C2×C3semidirect
44. #63573C2×C3semidirect
45. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
138. #832C3×D3semidirect
341. C33#482semidirect
527. C32#4779semidirect
528. C32#5035semidirect
529. C32C3×#482semidirect
593. C3#10591422direct (N × H)
594. C3C3×#4779semidirect
595. C3C3×#5035semidirect

Maximal subgroups

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

subgroupindex
C32×#9382
C3×#638412
C3×#636592
C32×#8322
C3×#635762
C3×#635732
C3×(C2×D3)⋊(C3⋊C8)2
C3×#50353
C3×#47793
#105914223