Finite Group Databasebeta

← C3×#10591487 #13158499

Subgroups — C3×#10591487 #13158499

Order 1728.

734 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#940C211yesmaximal, characteristic
2C3×#63918C211yesmaximal, characteristic, complemented
3C3×#63659C211yesmaximal, characteristic, complemented
4C32×#832C211yesmaximal, characteristic, complemented
5C3×#63563C211yesmaximal, characteristic, complemented
6C3×#63562C211yesmaximal, characteristic, complemented
7C3×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#5070—31nomaximal
9C3×#4760—31nomaximal
10#10591487C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic
12C2×C32×#67—21no—
13C2×C32×#67—21no—
14C2×C32×D12C2211yescharacteristic
15C2×C3×#627—21no—
16C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
18C32×C4⋊Dic3C2211yescharacteristic
19C32×C4×Dic3C2211yescharacteristic
20C2×C32×C3⋊C8C2211yescharacteristic
21C3×Dic3⋊Dic3—21no—
22C32×#127—31no—
23C3×#940—21no—
24C3×#940D311yescharacteristic
25C3×#940C2×C311yescharacteristic
26C3×#888—31no—
27C3×#869—31no—
28#63918C2×C311yescharacteristic, complemented
29C32×#102—31no—
30#63659C2×C311yescharacteristic, complemented
31C3×#832—21no—
32C3×#832—31no—
33C3×#832—31no—
34C3×#832—31no—
35C3×#832—31no—
36C3×#832—61no—
37C3×#832D311yescharacteristic, complemented
38C3×#832C2×C311yescharacteristic, complemented
39C3×#821—31no—
40C3×C8×Dic3—31no—
41C3×#809—31no—
42C3×C4×C3⋊C8—31no—
43#63563C2×C311yescharacteristic, complemented
44#63562C2×C311yescharacteristic, complemented
45Dic3×C3⋊C8C2×C311yescharacteristic, complemented
46C23×C33—21no—
47C22×C32×D3—21no—
48C33×D4—21no—
49C33×D4—21no—
50C2×C33×C4C2311yescharacteristic
51C2×C3×C3⋊Dic3—21no—
52C32×#67—42no—
53C32×#67—42no—
54C2×C32×Dic3—21no—
55C2×C32×Dic3D411yescharacteristic
56C2×C32×Dic3D411yescharacteristic
57C32×D12—21no—
58C32×D12—21no—
59C3×#627—42no—
60C3×C3⋊(C3⋊C8)—21no—
61C32×C3⋊C8—21no—
62C3×#486—91no—
63#5070—31no—
64#4760—31no—
65C2×C32×D4—21no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4—31no—
69C2×C32×D4—41no—
70C2×C32×D4—61no—
71C2×C32×D4—61no—
72C2×C32×D4C2×D311yescharacteristic
73C2×C32×D4C2×D311yescharacteristic
74C2×C32×D4C22×C311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C2×C3×#67—21no—
78C2×C3×#67—21no—
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C2×C3×D12—21no—
82C2×C3×D12C2×D311yescharacteristic
83C2×C3×D12C22×C311yescharacteristic
84C2×C3×Dic6—61no—
85C2×C3×Dic6—61no—
86C2×#627—21no—
87C2×C32×C8—31no—
88C32×C4⋊C4—31no—
89C32×C42—31no—
90C4⋊(C3⋊Dic3)C22×C311yescharacteristic
91C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—31no—
94C3×C4⋊Dic3—31no—
95C3×C4⋊Dic3—61no—
96C3×C4⋊Dic3—61no—
97C3×C4⋊Dic3C2×D311yescharacteristic
98C3×C4⋊Dic3C22×C311yescharacteristic
99C3×Dic3⋊C4—61no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3C2×D311yescharacteristic
102C3×C4×Dic3C22×C311yescharacteristic
103C2×C3×C3⋊C8—21no—
104C2×C3×C3⋊C8—31no—
105C2×C3×C3⋊C8—31no—
106C2×C3×C3⋊C8—61no—
107C2×C3×C3⋊C8C2×D311yescharacteristic
108C2×C3×C3⋊C8C22×C311yescharacteristic
109Dic3⋊Dic3—21no—
110C22×C33—41no—
111C22×C33—41no—
112C22×C33—41no—
113C22×C33C2×D411yescharacteristic
114C2×C32×D3—41no—
115C2×C32×D3—41no—
116C2×C32×D3—41no—
117C33×C4#4111yescharacteristic
118C33×C4#4111yescharacteristic
119C3×C3⋊Dic3—41no—
120C32×Dic3—41no—
121C32×Dic3D812yes—
122C32×Dic3SD1612yes—
123C3×C4⋊Q8—91no—
124C3×#127—31no—
125C3×#127—31no—
126C3×#127—61no—
127#940C3×D311yescharacteristic
128#888—31no—
129#869—31no—
130C3×#102—31no—
131C3×#102—31no—
132C3×#102—61no—
133C3×#102—91no—
134C3×#102—91no—
135C3×#102—91no—
136C3×C4×C8—91no—
137#832—31no—
138#832—31no—
139#832—31no—
140#832—31no—
141#832—61no—
142#832C3×D311yescharacteristic, complemented
143#821—31no—
144C8×Dic3—31no—
145#809—31no—
146C4×C3⋊C8—31no—
147C23×C32—21no—
148C23×C32—22no—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—41no—
152C23×C32—41no—
153C23×C32—42no—
154C23×C32—61no—
155C22×C3×D3—22no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C32×D4—21no—
159C32×D4—21no—
160C32×D4—22no—
161C32×D4—22no—
162C32×D4—21no—
163C32×D4—21no—
164C32×D4—21no—
165C32×D4—21no—
166C32×D4—41no—
167C32×D4—41no—
168C32×D4—41no—
169C32×D4—41no—
170C32×D4—42no—
171C32×D4—42no—
172C32×D4—61no—
173C32×D4—61no—
174C32×D4—122no—
175C32×D4—122no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—31no—
180C2×C32×C4—31no—
181C2×C32×C4—41no—
182C2×C32×C4—61no—
183C2×C32×C4C22×D311yescharacteristic
184C2×C32×C4C22×D311yescharacteristic
185C2×C32×C4C23×C311yescharacteristic
186C2×C3⋊Dic3—21no—
187C3×#67—44no—
188C3×#67—44no—
189C3×#67—42no—
190C3×#67—42no—
191C3×#67—42no—
192C3×#67—42no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3—61no—
199C2×C3×Dic3—61no—
200C2×C3×Dic3—121no—
201C2×C3×Dic3#6711yescharacteristic
202C2×C3×Dic3#6711yescharacteristic
203C2×C3×Dic3C3×D411yescharacteristic
204C2×C3×Dic3C3×D411yescharacteristic
205C3×D12—21no—
206C3×D12—21no—
207C3×D12—21no—
208C3×D12—21no—
209C3×D12—41no—
210C3×D12—41no—
211C3×Dic6—122no—
212C3×Dic6—122no—
213#627—42no—
214C32×C8—61no—
215C3⋊(C3⋊C8)—21no—
216C3×C3⋊C8—21no—
217C3×C3⋊C8—21no—
218C3×C3⋊C8—41no—
219C3×C3⋊C8—61no—
220C3×C3⋊C8—61no—
221C3×C3⋊C8—121no—
222#486—91noSylow
223C2×C33—81no—
224C2×C33#12411yescharacteristic
225C2×C33C2×D811yescharacteristic
226C2×C33C2×SD1611yescharacteristic
227C32×D3—81no—
228C2×C3×Q8—181no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—31no—
233C2×C3×D4—31no—
234C2×C3×D4—41no—
235C2×C3×D4—61no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—62no—
241C2×C3×D4—62no—
242C2×C3×D4D3211yescharacteristic
243C2×C3×D4C2×C3×D311yescharacteristic
244C2×C3×D4C2×C3×D311yescharacteristic
245C2×#67—21no—
246C2×#67—21no—
247C2×D12C2×C3×D311yescharacteristic
248C2×Dic6—61no—
249C2×Dic6—61no—
250C2×C3×C8—31no—
251C2×C3×C8—31no—
252C2×C3×C8—61no—
253C2×C3×C8—91no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—91no—
258C3×C4⋊C4—181no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—61no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3C2×C3×D311yescharacteristic
267Dic3⋊C4—61no—
268C4×Dic3C2×C3×D311yescharacteristic
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8C2×C3×D311yescharacteristic
273C22×C32—21no—
274C22×C32—21no—
275C22×C32—21no—
276C22×C32—41no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—44no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—42no—
287C22×C32—42no—
288C22×C32—41no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—81no—
293C22×C32—81no—
294C22×C32—81no—
295C22×C32—81no—
296C22×C32—82no—
297C22×C32—82no—
298C22×C32—121no—
299C22×C32—121no—
300C22×C32—121no—
301C22×C32D3×D411yescharacteristic
302C22×C32C2×#6711yescharacteristic
303C22×C32C2×C3×D411yescharacteristic
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C32×C4—21no—
314C32×C4—21no—
315C32×C4—21no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—21no—
319C32×C4—32no—
320C32×C4—32no—
321C32×C4—41no—
322C32×C4—41no—
323C32×C4—121no—
324C32×C4#23511yescharacteristic
325C32×C4#23711yescharacteristic
326C32×C4#23711yescharacteristic
327C32×C4#23711yescharacteristic
328C32×C4C3×#4111yescharacteristic
329C32×C4C3×#4111yescharacteristic
330C3⋊Dic3—41no—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—41no—
334C3×Dic3—41no—
335C3×Dic3—81no—
336C3×Dic3—121no—
337C3×Dic3—121no—
338C3×Dic3—241no—
339C3×Dic3#21312yes—
340C3×Dic3#21412yes—
341C3×Dic3C3×D812yes—
342C3×Dic3C3×SD1612yes—
343C4⋊Q8—91no—
344#127—31no—
345#102—31no—
346#102—91no—
347#102—91no—
348#102—91no—
349C4×C8—91no—
350C33#48611yescharacteristic, complemented, Sylow
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—42no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—61no—
361C22×D3—21no—
362C3×Q8—362no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—21no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—21no—
369C3×D4—21no—
370C3×D4—21no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—61no—
378C3×D4—61no—
379C3×D4—61no—
380C3×D4—61no—
381C3×D4—121no—
382C3×D4—121no—
383C3×D4—122no—
384C3×D4—122no—
385C3×D4—122no—
386C3×D4—122no—
387C3×D4—124no—
388C3×D4—124no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—41no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—121no—
402C2×C3×C4—181no—
403C2×C3×C4C2×D3211yescharacteristic
404C2×C3×C4C22×C3×D311yescharacteristic
405C2×C3×C4C22×C3×D311yescharacteristic
406#67—42no—
407#67—42no—
408C2×Dic3—21no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—121no—
412C2×Dic3C3×#6711yescharacteristic
413C2×Dic3C3×#6711yescharacteristic
414D12—21no—
415D12—21no—
416Dic6—122no—
417Dic6—122no—
418C3×C8—61no—
419C3×C8—61no—
420C3×C8—121no—
421C3×C8—181no—
422C3⋊C8—21no—
423C3⋊C8—61no—
424C3⋊C8—61no—
425C3⋊C8—121no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32—21no—
431C2×C32—21no—
432C2×C32—21no—
433C2×C32—21no—
434C2×C32—21no—
435C2×C32—41no—
436C2×C32—41no—
437C2×C32—41no—
438C2×C32—82no—
439C2×C32—82no—
440C2×C32—82no—
441C2×C32—84no—
442C2×C32—81no—
443C2×C32—81no—
444C2×C32—81no—
445C2×C32—241no—
446C2×C32#88511yescharacteristic
447C2×C32D3×D811yescharacteristic
448C2×C32D3×SD1611yescharacteristic
449C2×C32C2×#21311yescharacteristic
450C2×C32C2×#21411yescharacteristic
451C2×C32#93611yescharacteristic
452C2×C32C3×#12411yescharacteristic
453C2×C32C2×C3×D811yescharacteristic
454C2×C32C2×C3×SD1611yescharacteristic
455C3×D3—82no—
456C3×D3—81no—
457C3×D3—81no—
458C2×Q8—181no—
459C2×D4—31no—
460C2×D4—61no—
461C2×D4—61no—
462C2×D4C3×D3211yescharacteristic
463C2×C8—31no—
464C2×C8—91no—
465C4⋊C4—31no—
466C4⋊C4—91no—
467C4⋊C4—181no—
468C42—31no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—44no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—81no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—82no—
493C22×C3—82no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3—121no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3D3×#6711yescharacteristic
504C22×C3C3×D3×D411yescharacteristic
505C22×C3C2×C3×#6711yescharacteristic
506C2×D3—41no—
507C2×D3—41no—
508C2×D3—41no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—32no—
516C3×C4—32no—
517C3×C4—32no—
518C3×C4—32no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—121no—
524C3×C4—121no—
525C3×C4—241no—
526C3×C4—361no—
527C3×C4#380411yescharacteristic
528C3×C4#380511yescharacteristic
529C3×C4C3×#23511yescharacteristic
530C3×C4C3×#23711yescharacteristic
531C3×C4C3×#23711yescharacteristic
532C3×C4C3×#23711yescharacteristic
533Dic3—41no—
534Dic3—121no—
535Dic3—121no—
536Dic3—241no—
537Dic3C3×#21312yes—
538Dic3C3×#21412yes—
539C32—21no—
540C32—21no—
541C32—21no—
542C32—41no—
543C32#476011yescharacteristic, complemented
544C32#507011yescharacteristic, complemented
545C32C3×#48611yescharacteristic, complemented
546C23—21no—
547C23—61no—
548Q8—362no—
549D4—21no—
550D4—21no—
551D4—61no—
552D4—61no—
553D4—122no—
554D4—122no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—61no—
558C2×C4—181no—
559C2×C4C2×C3×D3211yescharacteristic
560C8—61no—
561C8—181no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—41no—
572C2×C3—41no—
573C2×C3—41no—
574C2×C3—82no—
575C2×C3—82no—
576C2×C3—82no—
577C2×C3—84no—
578C2×C3—81no—
579C2×C3—81no—
580C2×C3—81no—
581C2×C3—242no—
582C2×C3—241no—
583C2×C3—241no—
584C2×C3D3×#21311yescharacteristic
585C2×C3D3×#21411yescharacteristic
586C2×C3#6395911yescharacteristic
587C2×C3C3×#88511yescharacteristic
588C2×C3C3×D3×D811yescharacteristic
589C2×C3C3×D3×SD1611yescharacteristic
590C2×C3C2×C3×#21311yescharacteristic
591C2×C3C2×C3×#21411yescharacteristic
592C2×C3C3×#93611yescharacteristic
593D3—81no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—121no—
598C22—121no—
599C22—121no—
600C22C3×D3×#6711yescharacteristic
601C4—32no—
602C4—32no—
603C4—121no—
604C4—361no—
605C4C3×#380411yescharacteristic
606C4C3×#380511yescharacteristic
607C3—21no—
608C3—21no—
609C3—21no—
610C3—41no—
611C3#1059148711yescharacteristic, direct product factor
612C3C3×#476011yescharacteristic, complemented
613C3C3×#507011yescharacteristic, complemented
614C2—81no—
615C2—241no—
616C2C3×D3×#21311yescharacteristic
617C2C3×D3×#21411yescharacteristic
618C2C3×#6395911yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC32×#940C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#486
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×#63918C2semidirect
3. C3×#63659C2semidirect
4. C32×#832C2semidirect
5. C3×#63563C2semidirect
6. C3×#63562C2semidirect
7. C3×Dic3×C3⋊C8C2semidirect
10. #10591487C3direct (N × H)
28. #63918C2×C3semidirect
30. #63659C2×C3semidirect
37. C3×#832D3semidirect
38. C3×#832C2×C3semidirect
43. #63563C2×C3semidirect
44. #63562C2×C3semidirect
45. Dic3×C3⋊C8C2×C3semidirect
142. #832C3×D3semidirect
350. C33#486semidirect
543. C32#4760semidirect
544. C32#5070semidirect
545. C32C3×#486semidirect
611. C3#10591487direct (N × H)
612. C3C3×#4760semidirect
613. C3C3×#5070semidirect

Maximal subgroups

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

subgroupindex
C32×#9402
C3×#639182
C3×#636592
C32×#8322
C3×#635632
C3×#635622
C3×Dic3×C3⋊C82
C3×#50703
C3×#47603
#105914873