Finite Group Databasebeta

← C3×#10591421 #13158515

Subgroups — C3×#10591421 #13158515

Order 1728.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C3×#63841C211yesmaximal, characteristic, complemented
3C2×C3×#3711C211yesmaximal, characteristic, complemented
4C3×#63659C211yesmaximal, characteristic, complemented
5C32×#832C211yesmaximal, characteristic, complemented
6C3×#63563C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8C3×#5215—31nomaximal
9C3×#4770—31nomaximal
10#10591421C311yesmaximal, characteristic, direct product factor
11C23×C32×D3—21no—
12C2×C33×D4C2211yescharacteristic
13C2×C32×#67—21no—
14C32×D3×D4—22no—
15C32×D3×D4C414yescomplemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
20C32×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C32×C3⋊C8C2211yescharacteristic, complemented
22C3×(C2×D3)⋊Dic3—21no—
23C3×Dic32—21no—
24C3×#3711—22no—
25C22×C32×D4—31no—
26C2×C3×D3×D4—21no—
27C2×C3×D3×D4D311yescharacteristic
28C2×C3×D3×D4C2×C311yescharacteristic
29C3×#926—31no—
30C2×C3×#208—31no—
31C2×C3×ΓL(1,𝔽25)—31no—
32C3×#892—31no—
33#63841C2×C311yescharacteristic, complemented
34C2×#3711C2×C311yescharacteristic, complemented
35C32×#102—31no—
36#63659C2×C311yescharacteristic, complemented
37C3×#832—21no—
38C3×#832—31no—
39C3×#832—31no—
40C3×#832—31no—
41C3×#832—31no—
42C3×#832—61no—
43C3×#832D311yescharacteristic, complemented
44C3×#832C2×C311yescharacteristic, complemented
45C3×#821—31no—
46C3×#809—31no—
47#63563C2×C311yescharacteristic, complemented
48#63562C2×C311yescharacteristic, complemented
49C23×C33—21no—
50C22×C32×D3—21no—
51C22×C32×D3—24no—
52C22×C32×D3—42no—
53C22×C32×D3—42no—
54C22×C32×D3D411yescharacteristic
55C33×D4—21no—
56C33×D4C2×C412yes—
57C2×C33×C4C2311yescharacteristic
58C2×C3×C3⋊Dic3—21no—
59C32×#67—24no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3D411yescharacteristic
62C32×D12—21no—
63C32×D12C2×C412yes—
64C32×C4×D3C2×C412yes—
65C32×C4×D3D412yes—
66C3×C3⋊(C3⋊C8)—21no—
67C32×C3⋊C8—21no—
68C3×#418—91no—
69#5215—31no—
70#4770—31no—
71C24×C32—61no—
72C23×C3×D3—22no—
73C23×C3×D3—21no—
74C23×C3×D3—21no—
75C2×C32×D4—21no—
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4—34no—
79C2×C32×D4—31no—
80C2×C32×D4—41no—
81C2×C32×D4—62no—
82C2×C32×D4—61no—
83C2×C32×D4C2×D311yescharacteristic
84C2×C32×D4C2×D311yescharacteristic
85C2×C32×D4C22×C311yescharacteristic
86C22×C32×C4—31no—
87C2×C3×#67—22no—
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C3×D3×D4—24no—
91C3×D3×D4—24no—
92C3×D3×D4—22no—
93C3×D3×D4—22no—
94C3×D3×D4Dic314yescomplemented
95C3×D3×D4C3×C414yescomplemented
96C2×C3×D12—21no—
97C2×C3×D12C2×D311yescharacteristic
98C2×C3×D12C22×C311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2×D311yescharacteristic
101C2×C3×C4×D3C22×C311yescharacteristic
102C2×C32×C8—31no—
103C32×C4⋊C4—31no—
104C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
105C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
106C3×#217—61no—
107C3×(C2×D3)⋊C4—61no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3—31no—
110C3×C4⋊Dic3—31no—
111C3×C4⋊Dic3—61no—
112C3×C4⋊Dic3C2×D311yescharacteristic, complemented
113C3×C4⋊Dic3C22×C311yescharacteristic, complemented
114C3×C4×Dic3—61no—
115C3×C4×Dic3—61no—
116C3×#208—62no—
117C2×C3×C3⋊C8—21no—
118C2×C3×C3⋊C8—31no—
119C2×C3×C3⋊C8—31no—
120C2×C3×C3⋊C8—61no—
121C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
122C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
123C3×ΓL(1,𝔽25)—62no—
124(C2×D3)⋊Dic3—21no—
125Dic32—21no—
126#3711—22no—
127C22×C33—22no—
128C22×C33—41no—
129C22×C33—41no—
130C22×C33C2×D411yescharacteristic
131C2×C32×D3—21no—
132C2×C32×D3—21no—
133C2×C32×D3—22no—
134C2×C32×D3—48no—
135C2×C32×D3—41no—
136C2×C32×D3—41no—
137C2×C32×D3C22⋊C412yes—
138C33×C4C22×C411yescharacteristic
139C33×C4C2×D411yescharacteristic
140C3×C3⋊Dic3—41no—
141C32×Dic3—41no—
142C32×Dic3C22⋊C412yes—
143C22×C3×D4—31no—
144C22×C3×D4—31no—
145C22×C3×D4—61no—
146C2×D3×D4C3×D311yescharacteristic
147C2×C3×M16—91no—
148C3×#117—91no—
149#926—31no—
150C2×#208—31no—
151C2×ΓL(1,𝔽25)—31no—
152#892—31no—
153C3×#102—31no—
154C3×#102—31no—
155C3×#102—61no—
156C3×#102—91no—
157C3×#102—91no—
158C3×#102—91no—
159#832—31no—
160#832—31no—
161#832—31no—
162#832—31no—
163#832—61no—
164#832C3×D311yescharacteristic, complemented
165#821—31no—
166#809—31no—
167C23×C32—21no—
168C23×C32—22no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—31no—
172C23×C32—41no—
173C23×C32—41no—
174C23×C32—42no—
175C23×C32—64no—
176C23×C32—61no—
177C23×C32—122no—
178C23×C32—122no—
179C22×C3×D3—22no—
180C22×C3×D3—28no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—24no—
184C22×C3×D3—24no—
185C22×C3×D3—21no—
186C22×C3×D3—44no—
187C22×C3×D3—44no—
188C22×C3×D3—42no—
189C22×C3×D3—42no—
190C22×C3×D3—42no—
191C22×C3×D3—42no—
192C22×C3×D3#6711yescharacteristic
193C22×C3×D3C3×D411yescharacteristic
194C32×D4—21no—
195C32×D4—22no—
196C32×D4—21no—
197C32×D4—21no—
198C32×D4—22no—
199C32×D4—22no—
200C32×D4—22no—
201C32×D4—32no—
202C32×D4—42no—
203C32×D4—41no—
204C32×D4—41no—
205C32×D4—42no—
206C32×D4—64no—
207C32×D4—61no—
208C32×D4C4×D312yes—
209C32×D4C2×Dic312yes—
210C32×D4C2×C3×C412yes—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—31no—
215C2×C32×C4—32no—
216C2×C32×C4—32no—
217C2×C32×C4—41no—
218C2×C32×C4—61no—
219C2×C32×C4C22×D311yescharacteristic
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C23×C311yescharacteristic
222C2×C3⋊Dic3—21no—
223C3×#67—28no—
224C3×#67—24no—
225C3×#67—24no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—41no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3#6711yescharacteristic
234C2×C3×Dic3C3×D411yescharacteristic
235C3×D12—22no—
236C3×D12—21no—
237C3×D12—21no—
238C3×D12—22no—
239C3×D12C2×Dic312yes—
240C3×D12C2×C3×C412yes—
241C3×C4×D3—22no—
242C3×C4×D3—22no—
243C3×C4×D3C2×Dic312yes—
244C3×C4×D3#6712yes—
245C3×C4×D3C2×C3×C412yes—
246C3×C4×D3C3×D412yes—
247C32×C8—61no—
248C3⋊(C3⋊C8)—21no—
249C3×C3⋊C8—21no—
250C3×C3⋊C8—21no—
251C3×C3⋊C8—41no—
252C3×C3⋊C8—61no—
253C3×C3⋊C8—61no—
254C3×C3⋊C8—121no—
255#418—91noSylow
256C2×C33—42no—
257C2×C33C2×C22⋊C411yescharacteristic
258C2×C33AGL(1,ℤ/8)11yescharacteristic
259C2×C33AGL(1,ℤ/8)11yescharacteristic
260C32×D3—22no—
261C32×D3—42no—
262C24×C3—61no—
263C24×C3—61no—
264C24×C3—62no—
265C23×D3—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—34no—
270C2×C3×D4—34no—
271C2×C3×D4—31no—
272C2×C3×D4—31no—
273C2×C3×D4—41no—
274C2×C3×D4—61no—
275C2×C3×D4—64no—
276C2×C3×D4—62no—
277C2×C3×D4—62no—
278C2×C3×D4—61no—
279C2×C3×D4—61no—
280C2×C3×D4—64no—
281C2×C3×D4—62no—
282C2×C3×D4D3211yescharacteristic
283C2×C3×D4C2×C3×D311yescharacteristic
284C2×C3×D4C2×C3×D311yescharacteristic
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—61no—
288C2×#67—21no—
289D3×D4—22no—
290D3×D4C3×Dic314yescomplemented
291C2×D12C2×C3×D311yescharacteristic
292C2×C4×D3C2×C3×D311yescharacteristic
293C3×M16—182no—
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8—61no—
297C2×C3×C8—91no—
298C3×C4⋊C4—31no—
299C3×C4⋊C4—31no—
300C3×C4⋊C4—61no—
301C3×C4⋊C4—91no—
302C3×C22⋊C4—181no—
303C3×C42—181no—
304#217—61no—
305(C2×D3)⋊C4—61no—
306C4⋊Dic3—31no—
307C4⋊Dic3—31no—
308C4⋊Dic3—61no—
309C4⋊Dic3C2×C3×D311yescharacteristic, complemented
310C4×Dic3—61no—
311C4×Dic3—61no—
312#208—62no—
313C2×C3⋊C8—31no—
314C2×C3⋊C8—31no—
315C2×C3⋊C8—61no—
316C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
317ΓL(1,𝔽25)—62no—
318C22×C32—22no—
319C22×C32—24no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—32no—
326C22×C32—41no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32—44no—
330C22×C32—41no—
331C22×C32—41no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—61no—
339C22×C32—61no—
340C22×C32—62no—
341C22×C32—81no—
342C22×C32—81no—
343C22×C32—81no—
344C22×C32—81no—
345C22×C32—82no—
346C22×C32—82no—
347C22×C32—128no—
348C22×C32—121no—
349C22×C32—121no—
350C22×C32D3×D411yescharacteristic
351C22×C32C2×#6711yescharacteristic
352C22×C32C2×C3×D411yescharacteristic
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—21no—
356C2×C3×D3—21no—
357C2×C3×D3—21no—
358C2×C3×D3—21no—
359C2×C3×D3—24no—
360C2×C3×D3—22no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—416no—
364C2×C3×D3—48no—
365C2×C3×D3—48no—
366C2×C3×D3—42no—
367C2×C3×D3—42no—
368C2×C3×D3—41no—
369C2×C3×D3—41no—
370C2×C3×D3—41no—
371C2×C3×D3—41no—
372C2×C3×D3#21712yes—
373C2×C3×D3C3×C22⋊C412yes—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—21no—
380C32×C4—32no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—121no—
384C32×C4C2×C4×D311yescharacteristic
385C32×C4D3×D411yescharacteristic
386C32×C4C22×Dic311yescharacteristic
387C32×C4C2×#6711yescharacteristic
388C32×C4C22×C3×C411yescharacteristic
389C32×C4C2×C3×D411yescharacteristic
390C3⋊Dic3—41no—
391C3×Dic3—22no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3—81no—
395C3×Dic3—121no—
396C3×Dic3—121no—
397C3×Dic3—241no—
398C3×Dic3#21712yes—
399C3×Dic3C3×C22⋊C412yes—
400C22×D4—31no—
401C2×M16—91no—
402#117—91no—
403#102—31no—
404#102—91no—
405#102—91no—
406#102—91no—
407C33#41811yescharacteristic, complemented, Sylow
408C23×C3—22no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—31no—
413C23×C3—31no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—42no—
417C23×C3—61no—
418C23×C3—64no—
419C23×C3—64no—
420C23×C3—68no—
421C23×C3—62no—
422C23×C3—61no—
423C23×C3—61no—
424C23×C3—124no—
425C23×C3—124no—
426C23×C3—122no—
427C23×C3—122no—
428C23×C3—122no—
429C23×C3—122no—
430C22×D3—21no—
431C22×D3—24no—
432C22×D3—42no—
433C22×D3—42no—
434C22×D3C3×#6711yescharacteristic
435C3×D4—22no—
436C3×D4—21no—
437C3×D4—21no—
438C3×D4—21no—
439C3×D4—22no—
440C3×D4—22no—
441C3×D4—22no—
442C3×D4—32no—
443C3×D4—32no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—42no—
447C3×D4—42no—
448C3×D4—62no—
449C3×D4—62no—
450C3×D4—64no—
451C3×D4—64no—
452C3×D4—68no—
453C3×D4—61no—
454C3×D4—61no—
455C3×D4D3×Dic312yes—
456C3×D4C3×C4×D312yes—
457C3×D4C2×C3×Dic312yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—41no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—121no—
474C2×C3×C4—181no—
475C2×C3×C4C2×D3211yescharacteristic
476C2×C3×C4C22×C3×D311yescharacteristic
477C2×C3×C4C22×C3×D311yescharacteristic
478#67—24no—
479C2×Dic3—21no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—121no—
483C2×Dic3C3×#6711yescharacteristic
484D12—21no—
485D12C2×C3×Dic312yes—
486C4×D3C2×C3×Dic312yes—
487C4×D3C3×#6712yes—
488C3×C8—61no—
489C3×C8—61no—
490C3×C8—121no—
491C3×C8—181no—
492C3⋊C8—21no—
493C3⋊C8—61no—
494C3⋊C8—61no—
495C3⋊C8—121no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—42no—
509C2×C32—44no—
510C2×C32—42no—
511C2×C32—42no—
512C2×C32—62no—
513C2×C32—82no—
514C2×C32—82no—
515C2×C32—84no—
516C2×C32—122no—
517C2×C32D3×C22⋊C411yescharacteristic
518C2×C32#91111yescharacteristic
519C2×C32#91411yescharacteristic
520C2×C32#93211yescharacteristic
521C2×C32#93211yescharacteristic
522C2×C32C2×#21711yescharacteristic
523C2×C32C2×C3×C22⋊C411yescharacteristic
524C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
525C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
526C3×D3—24no—
527C3×D3—22no—
528C3×D3—22no—
529C3×D3—44no—
530C3×D3—42no—
531C3×D3—42no—
532C24—61no—
533C2×D4—34no—
534C2×D4—31no—
535C2×D4—62no—
536C2×D4—61no—
537C2×D4C3×D3211yescharacteristic
538C22×C4—31no—
539M16—182no—
540C2×C8—31no—
541C2×C8—91no—
542C4⋊C4—31no—
543C4⋊C4—91no—
544C22⋊C4—181no—
545C42—181no—
546C22×C3—24no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—32no—
554C22×C3—32no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—44no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3—64no—
571C22×C3—61no—
572C22×C3—61no—
573C22×C3—61no—
574C22×C3—61no—
575C22×C3—62no—
576C22×C3—62no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—122no—
584C22×C3—122no—
585C22×C3—1216no—
586C22×C3—128no—
587C22×C3—128no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3D3×#6711yescharacteristic
593C22×C3C3×D3×D411yescharacteristic
594C22×C3C2×C3×#6711yescharacteristic
595C2×D3—21no—
596C2×D3—21no—
597C2×D3—22no—
598C2×D3—48no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3C3×#21712yes—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—32no—
609C3×C4—32no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—62no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4—241no—
616C3×C4—361no—
617C3×C4C2×D3×Dic311yescharacteristic
618C3×C4D3×#6711yescharacteristic
619C3×C4C2×C3×C4×D311yescharacteristic
620C3×C4C3×D3×D411yescharacteristic
621C3×C4C22×C3×Dic311yescharacteristic
622C3×C4C2×C3×#6711yescharacteristic
623Dic3—41no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3C3×#21712yes—
628C32—21no—
629C32—21no—
630C32—21no—
631C32—41no—
632C32#477011yescharacteristic, complemented
633C32#521511yescharacteristic, complemented
634C32C3×#41811yescharacteristic, complemented
635C23—21no—
636C23—31no—
637C23—64no—
638C23—61no—
639C23—122no—
640C23—122no—
641D4—21no—
642D4—32no—
643D4—64no—
644D4—61no—
645D4C3×D3×Dic312yes—
646C2×C4—31no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—61no—
650C2×C4—181no—
651C2×C4C2×C3×D3211yescharacteristic
652C8—61no—
653C8—181no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—44no—
664C2×C3—42no—
665C2×C3—42no—
666C2×C3—42no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—41no—
670C2×C3—64no—
671C2×C3—62no—
672C2×C3—62no—
673C2×C3—82no—
674C2×C3—82no—
675C2×C3—84no—
676C2×C3—124no—
677C2×C3—122no—
678C2×C3—122no—
679C2×C3#6393211yescharacteristic
680C2×C3#6393411yescharacteristic
681C2×C3D3×#21711yescharacteristic
682C2×C3C3×D3×C22⋊C411yescharacteristic
683C2×C3C3×#91111yescharacteristic
684C2×C3C3×#91411yescharacteristic
685C2×C3C3×#93211yescharacteristic
686C2×C3C3×#93211yescharacteristic
687C2×C3C2×C3×#21711yescharacteristic
688D3—22no—
689D3—42no—
690C22—22no—
691C22—32no—
692C22—41no—
693C22—41no—
694C22—61no—
695C22—61no—
696C22—62no—
697C22—128no—
698C22—121no—
699C22—121no—
700C22C3×D3×#6711yescharacteristic
701C4—32no—
702C4—121no—
703C4—361no—
704C4C2×C3×D3×Dic311yescharacteristic
705C4C3×D3×#6711yescharacteristic
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3#1059142111yescharacteristic, direct product factor
711C3C3×#477011yescharacteristic, complemented
712C3C3×#521511yescharacteristic, complemented
713C2—42no—
714C2—62no—
715C2—122no—
716C2C3×#6393211yescharacteristic
717C2C3×#6393411yescharacteristic
718C2C3×D3×#21711yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutatorC32×C4C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC2×C32×D3×D4C2
cosocleC2×C32×C4C23×C3
hypercenterC2×C3×D4D32
hypocenterC32C3×#418
LCSG ▷ 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. C2×C3×#3711C2semidirect
4. C3×#63659C2semidirect
5. C32×#832C2semidirect
6. C3×#63563C2semidirect
7. C3×#63562C2semidirect
10. #10591421C3direct (N × H)
15. C32×D3×D4C4semidirect
18. C3×C4⋊(C3⋊Dic3)C22semidirect
19. C2×C3×C3⋊(C3⋊C8)C22semidirect
20. C32×C4⋊Dic3C22semidirect
21. C2×C32×C3⋊C8C22semidirect
33. #63841C2×C3semidirect
34. C2×#3711C2×C3semidirect
36. #63659C2×C3semidirect
43. C3×#832D3semidirect
44. C3×#832C2×C3semidirect
47. #63563C2×C3semidirect
48. #63562C2×C3semidirect
94. C3×D3×D4Dic3semidirect
95. C3×D3×D4C3×C4semidirect
104. C4⋊(C3⋊Dic3)C22×C3semidirect
105. C2×C3⋊(C3⋊C8)C22×C3semidirect
112. C3×C4⋊Dic3C2×D3semidirect
113. C3×C4⋊Dic3C22×C3semidirect
121. C2×C3×C3⋊C8C2×D3semidirect
122. C2×C3×C3⋊C8C22×C3semidirect
164. #832C3×D3semidirect
290. D3×D4C3×Dic3semidirect
309. C4⋊Dic3C2×C3×D3semidirect
316. C2×C3⋊C8C2×C3×D3semidirect
407. C33#418semidirect
632. C32#4770semidirect
633. C32#5215semidirect
634. C32C3×#418semidirect
710. C3#10591421direct (N × H)
711. C3C3×#4770semidirect
712. C3C3×#5215semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C3×#638412
C2×C3×#37112
C3×#636592
C32×#8322
C3×#635632
C3×#635622
C3×#52153
C3×#47703
#105914213