Finite Group Databasebeta

← C3×#10595506 #13175097

Subgroups — C3×#10595506 #13175097

Order 1728.

1986 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
1C22×C32×#67C211yesmaximal, characteristic
2C2×C3×#3757C211yesmaximal, characteristic, complemented
3C2×C32×#217C211yesmaximal, characteristic, complemented
4C3×#67⋊Dic3C214yesmaximal, complemented
5C3×Dic3×#67C214yesmaximal, complemented
6C3×D3×#217C212yesmaximal, complemented
7C3×#63955C212yesmaximal, complemented
8C3×#5798—31nomaximal
9C3×#5486—31nomaximal
10#10595506C311yesmaximal, characteristic, direct product factor
11C24×C33C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2212yescomplemented
14C2×C32×#67C418yescomplemented
15C2×C32×#67C2212yes—
16C2×C32×#67C2212yes—
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2212yescomplemented
19C2×C3×D3×Dic3C2214yescomplemented
20C3×#3757C2212yes—
21C3×#3757C2212yescomplemented
22C32×#217C2212yes—
23C32×#217C2212yescomplemented
24C3×Dic3⋊Dic3C2214yescomplemented
25C3×(C2×D3)⋊Dic3C2214yescomplemented
26C3×Dic32C2214yescomplemented
27C22×C32×D4—31no—
28C22×C3×#67—21no—
29C22×C3×#67D311yescharacteristic
30C22×C3×#67C2×C311yescharacteristic
31C2×C32×C22⋊C4—31no—
32C2×#3757C2×C311yescharacteristic, complemented
33C2×C3×#217—21no—
34C2×C3×#217—32no—
35C2×C3×#217—31no—
36C2×C3×#217—31no—
37C2×C3×#217—61no—
38C2×C3×#217D311yescharacteristic, complemented
39C2×C3×#217C2×C311yescharacteristic, complemented
40C3×D4×Dic3—34no—
41C3×D4×Dic3—34no—
42C3×C4×#67—34no—
43C3×#926—32no—
44C3×#67⋊C4—34no—
45C3×D3×C22⋊C4—32no—
46C3×#877—32no—
47#67⋊Dic3C2×C314yescomplemented
48Dic3×#67C2×C314yescomplemented
49D3×#217C2×C312yescomplemented
50#63955C2×C312yescomplemented
51C23×C33—42no—
52C23×C33C2×C414yescomplemented
53C23×C33C2311yescharacteristic
54C23×C33C2311yescharacteristic
55C23×C33C2311yescharacteristic
56C22×C32×D3—42no—
57C22×C32×D3C2×C414yescomplemented
58C22×C32×D3C2312yes—
59C2×C3×C3⋊Dic3—42no—
60C2×C3×C3⋊Dic3C2314yes—
61C32×#67C2×C418yescomplemented
62C32×#67C2×C418yescomplemented
63C2×C32×Dic3—42no—
64C2×C32×Dic3C2×C414yescomplemented
65C2×C32×Dic3C2314yes—
66C2×C32×Dic3C2312yes—
67C3×D3×Dic3—44no—
68C3×#518—91no—
69#5798—31no—
70#5486—31no—
71C24×C32—21no—
72C24×C32—21no—
73C24×C32—21no—
74C24×C32—31no—
75C24×C32—41no—
76C24×C32C2×D311yescharacteristic
77C24×C32C2×D311yescharacteristic
78C24×C32C22×C311yescharacteristic
79C23×C3×D3—21no—
80C23×C3×D3C2×D311yescharacteristic
81C23×C3×D3C22×C311yescharacteristic
82C2×C32×D4—38no—
83C2×C32×D4—32no—
84C2×C32×D4—32no—
85C22×C32×C4—31no—
86C22×C32×C4—32no—
87C22×C3⋊Dic3C22×C312yescomplemented
88C2×C3×#67—28no—
89C2×C3×#67—22no—
90C2×C3×#67—22no—
91C2×C3×#67Dic318yescomplemented
92C2×C3×#67C3×C418yescomplemented
93C2×C3×#67C2×D312yes—
94C2×C3×#67C2×D312yes—
95C2×C3×#67C22×C312yes—
96C2×C3×#67C22×C312yes—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—32no—
100C22×C3×Dic3—32no—
101C22×C3×Dic3—34no—
102C22×C3×Dic3—62no—
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D312yescomplemented
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C312yescomplemented
107C2×C3×C4×D3—34no—
108C2×D3×Dic3C22×C314yescomplemented
109C32×C22⋊C4—32no—
110C32×C22⋊C4—32no—
111#3757C22×C312yes—
112#3757C22×C312yescomplemented
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—32no—
116C3×#217—32no—
117C3×#217—32no—
118C3×#217—32no—
119C3×#217—34no—
120C3×#217—62no—
121C3×#217—62no—
122C3×#217C2×D312yes—
123C3×#217C2×D312yescomplemented
124C3×#217C22×C312yes—
125C3×#217C22×C312yescomplemented
126C3×(C2×D3)⋊C4—34no—
127C3×C4⋊Dic3—34no—
128C3×Dic3⋊C4—34no—
129C3×C4×Dic3—34no—
130C3×C4×Dic3—34no—
131Dic3⋊Dic3C22×C314yescomplemented
132(C2×D3)⋊Dic3C22×C314yescomplemented
133Dic32C22×C314yescomplemented
134C22×C33—22no—
135C22×C33—22no—
136C22×C33—22no—
137C22×C33—44no—
138C22×C33C22×C412yes—
139C22×C33C22×C412yes—
140C22×C33C22×C412yes—
141C22×C33C2411yescharacteristic
142C2×C32×D3—24no—
143C2×C32×D3—44no—
144C2×C32×D3C22×C414yes—
145C3×C3⋊Dic3—24no—
146C32×Dic3—24no—
147C32×Dic3C22×C414yes—
148C22×C3×D4—31no—
149C22×C3×D4—31no—
150C22×C3×D4—61no—
151C22×#67C3×D311yescharacteristic
152C3×C4×D4—94no—
153C3×C4×D4—94no—
154C3×#117—92no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C22⋊C4—92no—
159C2×C3×C22⋊C4—91no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—32no—
163C2×#217—61no—
164C2×#217C3×D311yescharacteristic, complemented
165D4×Dic3—34no—
166D4×Dic3—34no—
167C4×#67—34no—
168#926—32no—
169#67⋊C4—34no—
170D3×C22⋊C4—32no—
171#877—32no—
172C23×C32—24no—
173C23×C32—24no—
174C23×C32—24no—
175C23×C32—21no—
176C23×C32—21no—
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32—32no—
185C23×C32—34no—
186C23×C32—44no—
187C23×C32—41no—
188C23×C32—41no—
189C23×C32—41no—
190C23×C32—42no—
191C23×C32—42no—
192C23×C32—42no—
193C23×C32—44no—
194C23×C32—44no—
195C23×C32—44no—
196C23×C32—48no—
197C23×C32—122no—
198C23×C32C4×D314yescomplemented
199C23×C32C2×Dic314yescomplemented
200C23×C32C2×C3×C414yescomplemented
201C23×C32C22×D311yescharacteristic
202C23×C32C22×D311yescharacteristic
203C23×C32C22×D311yescharacteristic
204C23×C32C22×D311yescharacteristic
205C23×C32C22×D311yescharacteristic
206C23×C32C22×D311yescharacteristic
207C23×C32C23×C311yescharacteristic
208C23×C32C23×C311yescharacteristic
209C23×C32C23×C311yescharacteristic
210C22×C3×D3—24no—
211C22×C3×D3—22no—
212C22×C3×D3—42no—
213C22×C3×D3—42no—
214C22×C3×D3—44no—
215C22×C3×D3C2×Dic314yescomplemented
216C22×C3×D3C2×C3×C414yescomplemented
217C22×C3×D3C22×D312yes—
218C22×C3×D3C23×C312yes—
219C32×D4—38no—
220C32×D4—38no—
221C2×C32×C4—34no—
222C2×C32×C4—32no—
223C2×C32×C4—34no—
224C2×C32×C4—122no—
225C2×C3⋊Dic3—42no—
226C2×C3⋊Dic3C23×C314yes—
227C3×#67—28no—
228C3×#67—28no—
229C3×#67C2×Dic318yescomplemented
230C3×#67C2×Dic318yescomplemented
231C3×#67C2×C3×C418yescomplemented
232C3×#67C2×C3×C418yescomplemented
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—24no—
236C2×C3×Dic3—34no—
237C2×C3×Dic3—34no—
238C2×C3×Dic3—42no—
239C2×C3×Dic3—42no—
240C2×C3×Dic3—44no—
241C2×C3×Dic3—64no—
242C2×C3×Dic3—124no—
243C2×C3×Dic3—122no—
244C2×C3×Dic3—122no—
245C2×C3×Dic3—124no—
246C2×C3×Dic3C2×Dic314yescomplemented
247C2×C3×Dic3C2×C3×C414yescomplemented
248C2×C3×Dic3C22×D314yes—
249C2×C3×Dic3C22×D312yes—
250C2×C3×Dic3C23×C314yes—
251C2×C3×Dic3C23×C312yes—
252C3×C4×D3—124no—
253D3×Dic3—44no—
254#518—91noSylow
255C2×C33—22no—
256C2×C33—22no—
257C2×C33—22no—
258C2×C33C23×C411yescharacteristic
259C2×C33H(5,𝔽2)12yes—
260C32×D3—24no—
261C24×C3—21no—
262C24×C3—21no—
263C24×C3—21no—
264C24×C3—31no—
265C24×C3—31no—
266C24×C3—41no—
267C24×C3—61no—
268C24×C3D3211yescharacteristic
269C24×C3C2×C3×D311yescharacteristic
270C24×C3C2×C3×D311yescharacteristic
271C23×D3C2×C3×D311yescharacteristic
272C2×C3×D4—38no—
273C2×C3×D4—38no—
274C2×C3×D4—32no—
275C2×C3×D4—32no—
276C2×C3×D4—32no—
277C2×C3×D4—32no—
278C2×C3×D4—68no—
279C2×C3×D4—62no—
280C2×C3×D4—62no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—32no—
284C22×C3×C4—32no—
285C22×C3×C4—61no—
286C22×C3×C4—62no—
287C22×C3×C4—94no—
288C22×C3×C4—92no—
289C2×#67C3×Dic318yescomplemented
290C2×#67C2×C3×D312yes—
291C2×#67C2×C3×D312yes—
292C22×Dic3—32no—
293C22×Dic3—32no—
294C22×Dic3—34no—
295C22×Dic3—62no—
296C22×Dic3C2×C3×D311yescharacteristic
297C22×Dic3C2×C3×D312yescomplemented
298C2×C4×D3—34no—
299C3×C4⋊C4—94no—
300C3×C22⋊C4—32no—
301C3×C22⋊C4—32no—
302C3×C22⋊C4—32no—
303C3×C22⋊C4—32no—
304C3×C22⋊C4—62no—
305C3×C22⋊C4—62no—
306C3×C22⋊C4—94no—
307C3×C22⋊C4—92no—
308C3×C22⋊C4—92no—
309C3×C42—94no—
310#217—32no—
311#217—32no—
312#217—32no—
313#217—32no—
314#217—34no—
315#217—62no—
316#217—62no—
317#217C2×C3×D312yes—
318#217C2×C3×D312yescomplemented
319(C2×D3)⋊C4—34no—
320C4⋊Dic3—34no—
321Dic3⋊C4—34no—
322C4×Dic3—34no—
323C4×Dic3—34no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—22no—
344C22×C32—22no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—34no—
349C22×C32—42no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—41no—
353C22×C32—42no—
354C22×C32—42no—
355C22×C32—42no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32—42no—
359C22×C32—44no—
360C22×C32—44no—
361C22×C32—44no—
362C22×C32—44no—
363C22×C32—44no—
364C22×C32—44no—
365C22×C32—48no—
366C22×C32—48no—
367C22×C32—48no—
368C22×C32—416no—
369C22×C32—64no—
370C22×C32—124no—
371C22×C32C2×C4×D312yes—
372C22×C32C2×C4×D312yes—
373C22×C32C2×C4×D312yes—
374C22×C32C22×Dic312yes—
375C22×C32C22×Dic312yes—
376C22×C32C22×Dic312yes—
377C22×C32C22×C3×C412yes—
378C22×C32C22×C3×C412yes—
379C22×C32C22×C3×C412yes—
380C22×C32C23×D311yescharacteristic
381C22×C32C23×D311yescharacteristic
382C22×C32C24×C311yescharacteristic
383C2×C3×D3—24no—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
386C2×C3×D3—44no—
387C2×C3×D3—44no—
388C2×C3×D3—44no—
389C2×C3×D3—48no—
390C2×C3×D3C22×Dic314yes—
391C2×C3×D3C22×C3×C414yes—
392C32×C4—34no—
393C32×C4—64no—
394C3⋊Dic3—24no—
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3—24no—
398C3×Dic3—44no—
399C3×Dic3—64no—
400C3×Dic3—64no—
401C3×Dic3—124no—
402C3×Dic3C22×Dic314yes—
403C3×Dic3C22×C3×C414yes—
404C22×D4—31no—
405C4×D4—94no—
406C4×D4—94no—
407#117—92no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—92no—
410C2×C22⋊C4—91no—
411C33#51811yescharacteristic, complemented, Sylow
412C23×C3—24no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—32no—
425C23×C3—32no—
426C23×C3—34no—
427C23×C3—34no—
428C23×C3—42no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—48no—
435C23×C3—44no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—62no—
440C23×C3—64no—
441C23×C3—122no—
442C23×C3—122no—
443C23×C3—124no—
444C23×C3D3×Dic314yescomplemented
445C23×C3C3×C4×D314yescomplemented
446C23×C3C2×C3×Dic314yescomplemented
447C23×C3C2×D3211yescharacteristic
448C23×C3C2×D3211yescharacteristic
449C23×C3C2×D3211yescharacteristic
450C23×C3C22×C3×D311yescharacteristic
451C23×C3C22×C3×D311yescharacteristic
452C23×C3C22×C3×D311yescharacteristic
453C23×C3C22×C3×D311yescharacteristic
454C23×C3C22×C3×D311yescharacteristic
455C23×C3C22×C3×D311yescharacteristic
456C22×D3—42no—
457C22×D3C2×C3×Dic314yescomplemented
458C22×D3C22×C3×D312yes—
459C3×D4—38no—
460C3×D4—38no—
461C3×D4—38no—
462C3×D4—38no—
463C3×D4—68no—
464C3×D4—68no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—62no—
472C2×C3×C4—64no—
473C2×C3×C4—64no—
474C2×C3×C4—94no—
475C2×C3×C4—122no—
476C2×C3×C4—122no—
477C2×C3×C4—124no—
478C2×C3×C4—364no—
479C2×C3×C4—362no—
480#67C2×C3×Dic318yescomplemented
481#67C2×C3×Dic318yescomplemented
482C2×Dic3—34no—
483C2×Dic3—34no—
484C2×Dic3—42no—
485C2×Dic3—64no—
486C2×Dic3—124no—
487C2×Dic3—122no—
488C2×Dic3—122no—
489C2×Dic3—124no—
490C2×Dic3C2×C3×Dic314yescomplemented
491C2×Dic3C22×C3×D314yes—
492C2×Dic3C22×C3×D312yes—
493C4×D3—124no—
494C2×C32—22no—
495C2×C32—22no—
496C2×C32—22no—
497C2×C32—24no—
498C2×C32—24no—
499C2×C32—24no—
500C2×C32—22no—
501C2×C32—22no—
502C2×C32—22no—
503C2×C32—22no—
504C2×C32—22no—
505C2×C32—22no—
506C2×C32—21no—
507C2×C32—22no—
508C2×C32—21no—
509C2×C32—22no—
510C2×C32—22no—
511C2×C32—21no—
512C2×C32—41no—
513C2×C32—42no—
514C2×C32—42no—
515C2×C32—42no—
516C2×C32—42no—
517C2×C32—42no—
518C2×C32—42no—
519C2×C32—42no—
520C2×C32—44no—
521C2×C32—44no—
522C2×C32—44no—
523C2×C32—64no—
524C2×C32C22×C4×D311yescharacteristic
525C2×C32#100412yes—
526C2×C32#100412yes—
527C2×C32C23×Dic311yescharacteristic
528C2×C32C23×C3×C411yescharacteristic
529C2×C32C3×H(5,𝔽2)12yes—
530C3×D3—24no—
531C3×D3—24no—
532C3×D3—44no—
533C24—31no—
534C24C3×D3211yescharacteristic
535C2×D4—38no—
536C2×D4—32no—
537C2×D4—32no—
538C22×C4—31no—
539C22×C4—32no—
540C22×C4—94no—
541C22×C4—92no—
542C4⋊C4—94no—
543C22⋊C4—32no—
544C22⋊C4—32no—
545C22⋊C4—94no—
546C22⋊C4—92no—
547C22⋊C4—92no—
548C42—94no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—22no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—34no—
574C22×C3—34no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—44no—
587C22×C3—48no—
588C22×C3—48no—
589C22×C3—48no—
590C22×C3—416no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—124no—
599C22×C3—124no—
600C22×C3—124no—
601C22×C3—128no—
602C22×C3C2×D3×Dic312yes—
603C22×C3C2×D3×Dic312yes—
604C22×C3C2×D3×Dic312yes—
605C22×C3C2×C3×C4×D312yes—
606C22×C3C2×C3×C4×D312yes—
607C22×C3C2×C3×C4×D312yes—
608C22×C3C22×C3×Dic312yes—
609C22×C3C22×C3×Dic312yes—
610C22×C3C22×C3×Dic312yes—
611C22×C3C22×D3211yescharacteristic
612C22×C3C23×C3×D311yescharacteristic
613C22×C3C23×C3×D311yescharacteristic
614C2×D3—24no—
615C2×D3—44no—
616C2×D3C22×C3×Dic314yes—
617C3×C4—34no—
618C3×C4—34no—
619C3×C4—64no—
620C3×C4—64no—
621C3×C4—64no—
622C3×C4—124no—
623C3×C4—184no—
624Dic3—24no—
625Dic3—64no—
626Dic3—64no—
627Dic3—124no—
628Dic3C22×C3×Dic314yes—
629C32—21no—
630C32—21no—
631C32—21no—
632C32—41no—
633C32#548611yescharacteristic, complemented
634C32#579811yescharacteristic, complemented
635C32C3×#51811yescharacteristic, complemented
636C23—32no—
637C23—34no—
638C23—42no—
639C23—122no—
640C23C3×D3×Dic314yescomplemented
641C23C2×C3×D3211yescharacteristic
642C23C2×C3×D3211yescharacteristic
643C23C2×C3×D3211yescharacteristic
644D4—38no—
645D4—38no—
646C2×C4—32no—
647C2×C4—34no—
648C2×C4—34no—
649C2×C4—94no—
650C2×C4—122no—
651C2×C4—364no—
652C2×C4—362no—
653C2×C3—24no—
654C2×C3—24no—
655C2×C3—24no—
656C2×C3—22no—
657C2×C3—22no—
658C2×C3—22no—
659C2×C3—22no—
660C2×C3—22no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—22no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—22no—
669C2×C3—22no—
670C2×C3—22no—
671C2×C3—42no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—42no—
675C2×C3—42no—
676C2×C3—42no—
677C2×C3—44no—
678C2×C3—44no—
679C2×C3—44no—
680C2×C3—41no—
681C2×C3—42no—
682C2×C3—64no—
683C2×C3—64no—
684C2×C3—124no—
685C2×C3C22×D3×Dic311yescharacteristic
686C2×C3#6433012yes—
687C2×C3C22×C3×C4×D311yescharacteristic
688C2×C3C3×#100412yes—
689C2×C3C3×#100412yes—
690C2×C3C23×C3×Dic311yescharacteristic
691D3—24no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—34no—
696C22—44no—
697C22—64no—
698C22—124no—
699C22C2×C3×D3×Dic312yes—
700C22C2×C3×D3×Dic312yes—
701C22C2×C3×D3×Dic312yes—
702C22C22×C3×D3211yescharacteristic
703C4—34no—
704C4—64no—
705C4—184no—
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3#1059550611yescharacteristic, direct product factor
711C3C3×#548611yescharacteristic, complemented
712C3C3×#579811yescharacteristic, complemented
713C2—22no—
714C2—22no—
715C2—22no—
716C2—64no—
717C2C22×C3×D3×Dic311yescharacteristic
718C2C3×#6433012yes—
subgroupG/H
centerC22×C3C22×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
prime radicalC22×C32×#67C2
cosocleC22×C32C24×C3
hypercenterC24×C3D32
hypocenterC32C3×#518
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3757C2semidirect
3. C2×C32×#217C2semidirect
4. C3×#67⋊Dic3C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×D3×#217C2semidirect
7. C3×#63955C2semidirect
10. #10595506C3direct (N × H)
13. C22×C3×C3⋊Dic3C22semidirect
14. C2×C32×#67C4semidirect
18. C22×C32×Dic3C22semidirect
19. C2×C3×D3×Dic3C22semidirect
21. C3×#3757C22semidirect
23. C32×#217C22semidirect
24. C3×Dic3⋊Dic3C22semidirect
25. C3×(C2×D3)⋊Dic3C22semidirect
26. C3×Dic32C22semidirect
32. C2×#3757C2×C3semidirect
38. C2×C3×#217D3semidirect
39. C2×C3×#217C2×C3semidirect
47. #67⋊Dic3C2×C3semidirect
48. Dic3×#67C2×C3semidirect
49. D3×#217C2×C3semidirect
50. #63955C2×C3semidirect
52. C23×C33C2×C4semidirect
57. C22×C32×D3C2×C4semidirect
61. C32×#67C2×C4semidirect
62. C32×#67C2×C4semidirect
64. C2×C32×Dic3C2×C4semidirect
87. C22×C3⋊Dic3C22×C3semidirect
91. C2×C3×#67Dic3semidirect
92. C2×C3×#67C3×C4semidirect
104. C22×C3×Dic3C2×D3semidirect
106. C22×C3×Dic3C22×C3semidirect
108. C2×D3×Dic3C22×C3semidirect
112. #3757C22×C3semidirect
123. C3×#217C2×D3semidirect
125. C3×#217C22×C3semidirect
131. Dic3⋊Dic3C22×C3semidirect
132. (C2×D3)⋊Dic3C22×C3semidirect
133. Dic32C22×C3semidirect
164. C2×#217C3×D3semidirect
198. C23×C32C4×D3semidirect
199. C23×C32C2×Dic3semidirect
200. C23×C32C2×C3×C4semidirect
215. C22×C3×D3C2×Dic3semidirect
216. C22×C3×D3C2×C3×C4semidirect
229. C3×#67C2×Dic3semidirect
230. C3×#67C2×Dic3semidirect
231. C3×#67C2×C3×C4semidirect
232. C3×#67C2×C3×C4semidirect
246. C2×C3×Dic3C2×Dic3semidirect
247. C2×C3×Dic3C2×C3×C4semidirect
289. C2×#67C3×Dic3semidirect
297. C22×Dic3C2×C3×D3semidirect
318. #217C2×C3×D3semidirect
411. C33#518semidirect
444. C23×C3D3×Dic3semidirect
445. C23×C3C3×C4×D3semidirect
446. C23×C3C2×C3×Dic3semidirect
457. C22×D3C2×C3×Dic3semidirect
480. #67C2×C3×Dic3semidirect
481. #67C2×C3×Dic3semidirect
490. C2×Dic3C2×C3×Dic3semidirect
633. C32#5486semidirect
634. C32#5798semidirect
635. C32C3×#518semidirect
640. C23C3×D3×Dic3semidirect
710. C3#10595506direct (N × H)
711. C3C3×#5486semidirect
712. C3C3×#5798semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#672
C2×C3×#37572
C2×C32×#2172
C3×#67⋊Dic32
C3×Dic3×#672
C3×D3×#2172
C3×#639552
C3×#57983
C3×#54863
#105955063