Finite Group Databasebeta

← C2×C3×#63976 #13175104

Subgroups — C2×C3×#63976 #13175104

Order 1728.

3898 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
1C24×C32×D3C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C22×C3×#625C212yesmaximal, complemented
4C2×C3×#3757C211yesmaximal, characteristic, complemented
5C3×#63976C218yesmaximal, direct product factor
6C2×C3×(C2×D3)⋊Dic3C212yesmaximal, complemented
7C2×C3×#953—31nomaximal
8C2×C3×#937—31nomaximal
9C2×#63976C311yesmaximal, characteristic, direct product factor
10C24×C33C2211yescharacteristic
11C23×C32×D3—24no—
12C23×C32×D3—28no—
13C23×C32×D3C2212yes—
14C23×C32×D3C2214yescomplemented
15C23×C32×D3C2211yescharacteristic, complemented
16C22×C3×C3⋊Dic3C2212yescomplemented
17C2×C32×#67—24no—
18C2×C32×#67C2214yescomplemented
19C22×C32×Dic3C2211yescharacteristic, complemented
20C2×C3×#625—28no—
21C2×C3×#625C2218yescomplemented
22C3×#3757C2214yescomplemented
23C3×(C2×D3)⋊Dic3C2218yescomplemented
24C25×C32—31no—
25C24×C3×D3—21no—
26C24×C3×D3D311yescharacteristic, complemented
27C24×C3×D3C2×C311yescharacteristic, complemented
28C22×C32×D4—31no—
29C22×C3×#67—21no—
30C22×C3×#67—32no—
31C22×C3×#67—32no—
32C22×C3×#67D311yescharacteristic, complemented
33C22×C3×#67C2×C311yescharacteristic, complemented
34C22×#625C2×C312yescomplemented
35C2×#3757C2×C311yescharacteristic, complemented
36C3×#953—38no—
37C2×C3×#217—32no—
38C2×C3×#217—31no—
39C2×C3×#217—31no—
40C2×C3×#217—61no—
41C3×#937—38no—
42C2×C3×(C2×D3)⋊C4—32no—
43#63976C2×C318yesdirect product factor
44C2×(C2×D3)⋊Dic3C2×C312yescomplemented
45C23×C33—24no—
46C23×C33D414yescomplemented
47C23×C33C2312yes—
48C23×C33C2311yescharacteristic
49C22×C32×D3—232no—
50C22×C32×D3—24no—
51C22×C32×D3—24no—
52C22×C32×D3—28no—
53C22×C32×D3—216no—
54C22×C32×D3—22no—
55C22×C32×D3—24no—
56C22×C32×D3D418yescomplemented
57C22×C32×D3C2314yes—
58C22×C32×D3C2312yescomplemented
59C2×C3×C3⋊Dic3—24no—
60C2×C3×C3⋊Dic3C2314yescomplemented
61C32×#67—28no—
62C2×C32×Dic3—22no—
63C2×C32×Dic3C2312yescomplemented
64C3×#625—216no—
65C2×C3×#120—91no—
66C2×#953—31no—
67C2×#937—31no—
68C24×C32—21no—
69C24×C32—21no—
70C24×C32—21no—
71C24×C32—32no—
72C24×C32—34no—
73C24×C32—31no—
74C24×C32—41no—
75C24×C32—68no—
76C24×C32—64no—
77C24×C32C2×D311yescharacteristic
78C24×C32C2×D311yescharacteristic
79C24×C32C22×C311yescharacteristic
80C23×C3×D3—28no—
81C23×C3×D3—216no—
82C23×C3×D3—22no—
83C23×C3×D3—24no—
84C23×C3×D3—24no—
85C23×C3×D3—24no—
86C23×C3×D3—28no—
87C23×C3×D3—28no—
88C23×C3×D3—21no—
89C23×C3×D3C2×D312yes—
90C23×C3×D3C2×D314yescomplemented
91C23×C3×D3C2×D311yescharacteristic, complemented
92C23×C3×D3C22×C312yes—
93C23×C3×D3C22×C314yescomplemented
94C23×C3×D3C22×C311yescharacteristic, complemented
95C2×C32×D4—34no—
96C2×C32×D4—64no—
97C22×C32×C4—31no—
98C22×C3⋊Dic3C22×C312yescomplemented
99C2×C3×#67—28no—
100C2×C3×#67—24no—
101C2×C3×#67—24no—
102C2×C3×#67—24no—
103C2×C3×#67—38no—
104C2×C3×#67—38no—
105C2×C3×#67—68no—
106C2×C3×#67—68no—
107C2×C3×#67C2×D314yescomplemented
108C2×C3×#67C22×C314yescomplemented
109C22×C3×Dic3—21no—
110C22×C3×Dic3—32no—
111C22×C3×Dic3—32no—
112C22×C3×Dic3—62no—
113C22×C3×Dic3C2×D311yescharacteristic, complemented
114C22×C3×Dic3C22×C311yescharacteristic, complemented
115C2×#625—28no—
116C2×#625C22×C318yescomplemented
117#3757C22×C314yescomplemented
118C3×#217—34no—
119C3×#217—34no—
120C3×#217—38no—
121C3×#217—64no—
122C3×(C2×D3)⋊C4—38no—
123(C2×D3)⋊Dic3C22×C318yescomplemented
124C22×C33—28no—
125C22×C33—24no—
126C22×C33C2×D414yes—
127C22×C33C2×D412yes—
128C22×C33C2×D414yescomplemented
129C22×C33C2411yescharacteristic
130C2×C32×D3—232no—
131C2×C32×D3—216no—
132C2×C32×D3—24no—
133C2×C32×D3—24no—
134C2×C32×D3—22no—
135C2×C32×D3—24no—
136C2×C32×D3—44no—
137C2×C32×D3C2×D418yescomplemented
138C3×C3⋊Dic3—24no—
139C32×Dic3—22no—
140C25×C3—31no—
141C25×C3—31no—
142C25×C3—61no—
143C24×D3C3×D311yescharacteristic, complemented
144C22×C3×D4—31no—
145C22×C3×D4—31no—
146C22×C3×D4—61no—
147C22×C3×D4—92no—
148C22×#67—32no—
149C22×#67—32no—
150C22×#67C3×D311yescharacteristic, complemented
151C3×#120—98no—
152C2×C3×C22⋊C4—92no—
153C2×C3×C22⋊C4—91no—
154#953—38no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—32no—
158C2×#217—61no—
159#937—38no—
160C2×(C2×D3)⋊C4—32no—
161C23×C32—24no—
162C23×C32—28no—
163C23×C32—24no—
164C23×C32—24no—
165C23×C32—24no—
166C23×C32—24no—
167C23×C32—24no—
168C23×C32—22no—
169C23×C32—21no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—22no—
174C23×C32—38no—
175C23×C32—34no—
176C23×C32—32no—
177C23×C32—44no—
178C23×C32—41no—
179C23×C32—42no—
180C23×C32—44no—
181C23×C32—44no—
182C23×C32—48no—
183C23×C32—616no—
184C23×C32—632no—
185C23×C32—64no—
186C23×C32—64no—
187C23×C32—68no—
188C23×C32—62no—
189C23×C32—64no—
190C23×C32#6714yescomplemented
191C23×C32#6714yescomplemented
192C23×C32C3×D414yescomplemented
193C23×C32C22×D312yes—
194C23×C32C22×D312yes—
195C23×C32C22×D311yescharacteristic
196C23×C32C22×D311yescharacteristic
197C23×C32C23×C312yes—
198C23×C32C23×C311yescharacteristic
199C22×C3×D3—264no—
200C22×C3×D3—232no—
201C22×C3×D3—232no—
202C22×C3×D3—28no—
203C22×C3×D3—28no—
204C22×C3×D3—216no—
205C22×C3×D3—232no—
206C22×C3×D3—24no—
207C22×C3×D3—24no—
208C22×C3×D3—28no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3—28no—
212C22×C3×D3—216no—
213C22×C3×D3—216no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3—22no—
217C22×C3×D3—24no—
218C22×C3×D3—22no—
219C22×C3×D3—28no—
220C22×C3×D3—24no—
221C22×C3×D3—22no—
222C22×C3×D3—44no—
223C22×C3×D3#6718yescomplemented
224C22×C3×D3C3×D418yescomplemented
225C22×C3×D3C22×D314yes—
226C22×C3×D3C22×D312yescomplemented
227C22×C3×D3C23×C314yes—
228C22×C3×D3C23×C312yescomplemented
229C32×D4—68no—
230C2×C32×C4—32no—
231C2×C32×C4—62no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C23×C314yescomplemented
234C3×#67—216no—
235C3×#67—28no—
236C3×#67—28no—
237C3×#67—616no—
238C3×#67—616no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—34no—
244C2×C3×Dic3—34no—
245C2×C3×Dic3—64no—
246C2×C3×Dic3—64no—
247C2×C3×Dic3—64no—
248C2×C3×Dic3—124no—
249C2×C3×Dic3C22×D312yescomplemented
250C2×C3×Dic3C23×C312yescomplemented
251#625—216no—
252C2×#120—91noSylow
253C2×C33—24no—
254C2×C33#12014yescomplemented
255C2×C33C22×D412yes—
256C2×C33C22×D411yescharacteristic
257C32×D3—28no—
258C32×D3—42no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—32no—
263C24×C3—32no—
264C24×C3—34no—
265C24×C3—31no—
266C24×C3—34no—
267C24×C3—31no—
268C24×C3—41no—
269C24×C3—62no—
270C24×C3—64no—
271C24×C3—61no—
272C24×C3—68no—
273C24×C3—68no—
274C24×C3—616no—
275C24×C3—68no—
276C24×C3—64no—
277C24×C3—64no—
278C24×C3D3211yescharacteristic
279C24×C3C2×C3×D311yescharacteristic
280C24×C3C2×C3×D311yescharacteristic
281C23×D3—24no—
282C23×D3—28no—
283C23×D3C2×C3×D312yes—
284C23×D3C2×C3×D314yescomplemented
285C23×D3C2×C3×D311yescharacteristic, complemented
286C2×C3×D4—34no—
287C2×C3×D4—34no—
288C2×C3×D4—64no—
289C2×C3×D4—68no—
290C2×C3×D4—64no—
291C2×C3×D4—64no—
292C2×C3×D4—98no—
293C2×C3×D4—188no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C22×C3×C4—92no—
298C2×#67—24no—
299C2×#67—38no—
300C2×#67—38no—
301C2×#67—68no—
302C2×#67—68no—
303C2×#67C2×C3×D314yescomplemented
304C22×Dic3—32no—
305C22×Dic3—32no—
306C22×Dic3—62no—
307C22×Dic3C2×C3×D311yescharacteristic, complemented
308C3×C22⋊C4—98no—
309C3×C22⋊C4—94no—
310#217—34no—
311#217—34no—
312#217—38no—
313#217—64no—
314(C2×D3)⋊C4—38no—
315C22×C32—28no—
316C22×C32—24no—
317C22×C32—216no—
318C22×C32—28no—
319C22×C32—28no—
320C22×C32—28no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—24no—
333C22×C32—24no—
334C22×C32—24no—
335C22×C32—38no—
336C22×C32—42no—
337C22×C32—44no—
338C22×C32—44no—
339C22×C32—41no—
340C22×C32—48no—
341C22×C32—44no—
342C22×C32—44no—
343C22×C32—48no—
344C22×C32—416no—
345C22×C32—48no—
346C22×C32—632no—
347C22×C32—616no—
348C22×C32—64no—
349C22×C32—64no—
350C22×C32—62no—
351C22×C32—64no—
352C22×C32—124no—
353C22×C32D3×D414yes—
354C22×C32C2×#6712yes—
355C22×C32C2×#6712yes—
356C22×C32C2×#6714yes—
357C22×C32C2×#6714yescomplemented
358C22×C32C2×#6714yescomplemented
359C22×C32C2×C3×D414yes—
360C22×C32C2×C3×D412yes—
361C22×C32C2×C3×D414yescomplemented
362C22×C32C23×D311yescharacteristic
363C22×C32C23×D311yescharacteristic
364C22×C32C24×C311yescharacteristic
365C2×C3×D3—264no—
366C2×C3×D3—232no—
367C2×C3×D3—232no—
368C2×C3×D3—232no—
369C2×C3×D3—28no—
370C2×C3×D3—28no—
371C2×C3×D3—216no—
372C2×C3×D3—216no—
373C2×C3×D3—24no—
374C2×C3×D3—24no—
375C2×C3×D3—24no—
376C2×C3×D3—24no—
377C2×C3×D3—24no—
378C2×C3×D3—24no—
379C2×C3×D3—22no—
380C2×C3×D3—24no—
381C2×C3×D3—22no—
382C2×C3×D3—28no—
383C2×C3×D3—44no—
384C2×C3×D3—48no—
385C2×C3×D3—44no—
386C2×C3×D3—44no—
387C2×C3×D3C2×#6718yescomplemented
388C2×C3×D3C2×C3×D418yescomplemented
389C32×C4—62no—
390C3⋊Dic3—24no—
391C3×Dic3—24no—
392C3×Dic3—22no—
393C3×Dic3—22no—
394C3×Dic3—64no—
395C3×Dic3—64no—
396C3×Dic3—124no—
397C25—31no—
398C22×D4—31no—
399C22×D4—92no—
400#120—98no—
401C2×C22⋊C4—92no—
402C2×C22⋊C4—91no—
403C33C2×#12011yescharacteristic, complemented, Sylow
404C23×C3—28no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—34no—
418C23×C3—34no—
419C23×C3—38no—
420C23×C3—38no—
421C23×C3—32no—
422C23×C3—32no—
423C23×C3—44no—
424C23×C3—44no—
425C23×C3—48no—
426C23×C3—44no—
427C23×C3—42no—
428C23×C3—41no—
429C23×C3—64no—
430C23×C3—68no—
431C23×C3—62no—
432C23×C3—616no—
433C23×C3—616no—
434C23×C3—632no—
435C23×C3—664no—
436C23×C3—632no—
437C23×C3—632no—
438C23×C3—68no—
439C23×C3—616no—
440C23×C3—68no—
441C23×C3—64no—
442C23×C3—64no—
443C23×C3—68no—
444C23×C3—64no—
445C23×C3—64no—
446C23×C3—64no—
447C23×C3—68no—
448C23×C3—62no—
449C23×C3—64no—
450C23×C3—64no—
451C23×C3—62no—
452C23×C3—124no—
453C23×C3#62514yescomplemented
454C23×C3C3×#6714yescomplemented
455C23×C3C3×#6714yescomplemented
456C23×C3C2×D3212yes—
457C23×C3C2×D3211yescharacteristic
458C23×C3C22×C3×D312yes—
459C23×C3C22×C3×D312yes—
460C23×C3C22×C3×D311yescharacteristic
461C23×C3C22×C3×D311yescharacteristic
462C22×D3—232no—
463C22×D3—24no—
464C22×D3—24no—
465C22×D3—28no—
466C22×D3—216no—
467C22×D3—24no—
468C22×D3—22no—
469C22×D3C3×#6718yescomplemented
470C22×D3C22×C3×D314yes—
471C22×D3C22×C3×D312yescomplemented
472C3×D4—616no—
473C3×D4—68no—
474C3×D4—68no—
475C3×D4—1816no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—62no—
479C2×C3×C4—64no—
480C2×C3×C4—62no—
481C2×C3×C4—62no—
482C2×C3×C4—94no—
483C2×C3×C4—184no—
484#67—28no—
485#67—616no—
486#67—616no—
487C2×Dic3—22no—
488C2×Dic3—34no—
489C2×Dic3—34no—
490C2×Dic3—64no—
491C2×Dic3—64no—
492C2×Dic3—64no—
493C2×Dic3—124no—
494C2×Dic3C22×C3×D312yescomplemented
495C2×C32—24no—
496C2×C32—28no—
497C2×C32—24no—
498C2×C32—24no—
499C2×C32—24no—
500C2×C32—21no—
501C2×C32—22no—
502C2×C32—24no—
503C2×C32—22no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—22no—
507C2×C32—24no—
508C2×C32—44no—
509C2×C32—41no—
510C2×C32—42no—
511C2×C32—44no—
512C2×C32—44no—
513C2×C32—48no—
514C2×C32—68no—
515C2×C32—122no—
516C2×C32#93714yescomplemented
517C2×C32#95314yescomplemented
518C2×C32C3×#12014yescomplemented
519C2×C32C2×D3×D412yes—
520C2×C32C22×#6711yescharacteristic
521C2×C32C22×#6711yescharacteristic
522C2×C32C22×#6712yes—
523C2×C32C22×C3×D412yes—
524C2×C32C22×C3×D411yescharacteristic
525C3×D3—216no—
526C3×D3—28no—
527C3×D3—28no—
528C3×D3—44no—
529C3×D3—42no—
530C3×D3—42no—
531C24—32no—
532C24—34no—
533C24—31no—
534C24—68no—
535C24—64no—
536C24C3×D3211yescharacteristic
537C2×D4—34no—
538C2×D4—64no—
539C2×D4—98no—
540C2×D4—188no—
541C22×C4—31no—
542C22×C4—92no—
543C22⋊C4—98no—
544C22⋊C4—94no—
545C22×C3—28no—
546C22×C3—216no—
547C22×C3—28no—
548C22×C3—24no—
549C22×C3—28no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—28no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—38no—
566C22×C3—38no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—48no—
570C22×C3—48no—
571C22×C3—48no—
572C22×C3—416no—
573C22×C3—41no—
574C22×C3—42no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—68no—
578C22×C3—664no—
579C22×C3—632no—
580C22×C3—632no—
581C22×C3—68no—
582C22×C3—68no—
583C22×C3—632no—
584C22×C3—64no—
585C22×C3—616no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—64no—
589C22×C3—64no—
590C22×C3—616no—
591C22×C3—62no—
592C22×C3—64no—
593C22×C3—64no—
594C22×C3—62no—
595C22×C3—124no—
596C22×C3—128no—
597C22×C3—124no—
598C22×C3—124no—
599C22×C3C2×#62512yes—
600C22×C3C2×#62514yescomplemented
601C22×C3D3×#6714yes—
602C22×C3C3×D3×D414yes—
603C22×C3C2×C3×#6712yes—
604C22×C3C2×C3×#6712yes—
605C22×C3C2×C3×#6714yes—
606C22×C3C2×C3×#6714yescomplemented
607C22×C3C2×C3×#6714yescomplemented
608C22×C3C22×D3211yescharacteristic
609C22×C3C23×C3×D311yescharacteristic
610C22×C3C23×C3×D311yescharacteristic
611C2×D3—232no—
612C2×D3—216no—
613C2×D3—24no—
614C2×D3—24no—
615C2×D3—24no—
616C2×D3—22no—
617C2×D3—44no—
618C2×D3C2×C3×#6718yescomplemented
619C3×C4—64no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—184no—
623Dic3—22no—
624Dic3—64no—
625Dic3—64no—
626Dic3—124no—
627C32—21no—
628C32—21no—
629C32—21no—
630C32—41no—
631C32C2×#93711yescharacteristic, complemented
632C32C2×#95311yescharacteristic, complemented
633C32C2×C3×#12011yescharacteristic, complemented
634C23—24no—
635C23—34no—
636C23—38no—
637C23—32no—
638C23—616no—
639C23—632no—
640C23—64no—
641C23—68no—
642C23—64no—
643C23—62no—
644C23—64no—
645C23C3×#62514yescomplemented
646C23C2×C3×D3212yes—
647C23C2×C3×D3211yescharacteristic
648D4—68no—
649D4—1816no—
650C2×C4—32no—
651C2×C4—62no—
652C2×C4—94no—
653C2×C4—184no—
654C2×C3—28no—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—24no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—24no—
667C2×C3—44no—
668C2×C3—44no—
669C2×C3—48no—
670C2×C3—41no—
671C2×C3—42no—
672C2×C3—44no—
673C2×C3—616no—
674C2×C3—68no—
675C2×C3—68no—
676C2×C3—124no—
677C2×C3—122no—
678C2×C3—122no—
679C2×C3#6397614yesdirect product factor
680C2×C3C3×#93714yescomplemented
681C2×C3C3×#95314yescomplemented
682C2×C3C22×#62511yescharacteristic
683C2×C3C2×D3×#6712yes—
684C2×C3C2×C3×D3×D412yes—
685C2×C3C22×C3×#6711yescharacteristic
686C2×C3C22×C3×#6711yescharacteristic
687C2×C3C22×C3×#6712yes—
688D3—28no—
689D3—42no—
690C22—24no—
691C22—28no—
692C22—38no—
693C22—632no—
694C22—64no—
695C22—64no—
696C22—616no—
697C22—62no—
698C22—64no—
699C22—124no—
700C22C2×C3×#62512yes—
701C22C2×C3×#62514yescomplemented
702C22C3×D3×#6714yes—
703C22C22×C3×D3211yescharacteristic
704C4—62no—
705C4—184no—
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3C2×#6397611yescharacteristic, direct product factor
711C3C2×C3×#93711yescharacteristic, complemented
712C3C2×C3×#95311yescharacteristic, complemented
713C2—24no—
714C2—68no—
715C2—122no—
716C2C3×#6397614yesdirect product factor
717C2C22×C3×#62511yescharacteristic
718C2C2×C3×D3×#6712yes—
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C24×C32×D3C2semidirect
2. C22×C32×#67C2semidirect
3. C22×C3×#625C2semidirect
4. C2×C3×#3757C2semidirect
5. C3×#63976C2direct (N × H)
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
9. C2×#63976C3direct (N × H)
14. C23×C32×D3C22semidirect
15. C23×C32×D3C22semidirect
16. C22×C3×C3⋊Dic3C22semidirect
18. C2×C32×#67C22semidirect
19. C22×C32×Dic3C22semidirect
21. C2×C3×#625C22semidirect
22. C3×#3757C22semidirect
23. C3×(C2×D3)⋊Dic3C22semidirect
26. C24×C3×D3D3semidirect
27. C24×C3×D3C2×C3semidirect
32. C22×C3×#67D3semidirect
33. C22×C3×#67C2×C3semidirect
34. C22×#625C2×C3semidirect
35. C2×#3757C2×C3semidirect
43. #63976C2×C3direct (N × H)
44. C2×(C2×D3)⋊Dic3C2×C3semidirect
46. C23×C33D4semidirect
56. C22×C32×D3D4semidirect
58. C22×C32×D3C23semidirect
60. C2×C3×C3⋊Dic3C23semidirect
63. C2×C32×Dic3C23semidirect
90. C23×C3×D3C2×D3semidirect
91. C23×C3×D3C2×D3semidirect
93. C23×C3×D3C22×C3semidirect
94. C23×C3×D3C22×C3semidirect
98. C22×C3⋊Dic3C22×C3semidirect
107. C2×C3×#67C2×D3semidirect
108. C2×C3×#67C22×C3semidirect
113. C22×C3×Dic3C2×D3semidirect
114. C22×C3×Dic3C22×C3semidirect
116. C2×#625C22×C3semidirect
117. #3757C22×C3semidirect
123. (C2×D3)⋊Dic3C22×C3semidirect
128. C22×C33C2×D4semidirect
137. C2×C32×D3C2×D4semidirect
143. C24×D3C3×D3semidirect
150. C22×#67C3×D3semidirect
190. C23×C32#67semidirect
191. C23×C32#67semidirect
192. C23×C32C3×D4semidirect
223. C22×C3×D3#67semidirect
224. C22×C3×D3C3×D4semidirect
226. C22×C3×D3C22×D3semidirect
228. C22×C3×D3C23×C3semidirect
233. C2×C3⋊Dic3C23×C3semidirect
249. C2×C3×Dic3C22×D3semidirect
250. C2×C3×Dic3C23×C3semidirect
254. C2×C33#120semidirect
284. C23×D3C2×C3×D3semidirect
285. C23×D3C2×C3×D3semidirect
303. C2×#67C2×C3×D3semidirect
307. C22×Dic3C2×C3×D3semidirect
357. C22×C32C2×#67semidirect
358. C22×C32C2×#67semidirect
361. C22×C32C2×C3×D4semidirect
387. C2×C3×D3C2×#67semidirect
388. C2×C3×D3C2×C3×D4semidirect
403. C33C2×#120semidirect
453. C23×C3#625semidirect
454. C23×C3C3×#67semidirect
455. C23×C3C3×#67semidirect
469. C22×D3C3×#67semidirect
471. C22×D3C22×C3×D3semidirect
494. C2×Dic3C22×C3×D3semidirect
516. C2×C32#937semidirect
517. C2×C32#953semidirect
518. C2×C32C3×#120semidirect
600. C22×C3C2×#625semidirect
606. C22×C3C2×C3×#67semidirect
607. C22×C3C2×C3×#67semidirect
618. C2×D3C2×C3×#67semidirect
631. C32C2×#937semidirect
632. C32C2×#953semidirect
633. C32C2×C3×#120semidirect
645. C23C3×#625semidirect
679. C2×C3#63976direct (N × H)
680. C2×C3C3×#937semidirect
681. C2×C3C3×#953semidirect
701. C22C2×C3×#625semidirect
710. C3C2×#63976direct (N × H)
711. C3C2×C3×#937semidirect
712. C3C2×C3×#953semidirect
716. C2C3×#63976direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C32×D32
C22×C32×#672
C22×C3×#6252
C2×C3×#37572
C3×#639762
C2×C3×(C2×D3)⋊Dic32
C2×C3×#9533
C2×C3×#9373
C2×#639763