Finite Group Databasebeta

← C3×#14765 #10633372

Subgroups — C3×#14765 #10633372

Order 768.

2154 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#393C211yesmaximal, characteristic, complemented
3C2×C3×#388C212yesmaximal, complemented
4C2×C3×#386C211yesmaximal, characteristic
5C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#1446C211yesmaximal, characteristic, complemented
7C3×#1442C211yesmaximal, characteristic, complemented
8C3×#1440C212yesmaximal, complemented
9C3×#1439C211yesmaximal, characteristic, complemented
10C3×#1438C212yesmaximal
11C3×#1436C212yesmaximal, complemented
12#14765C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—28no—
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2212yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2212yes—
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2212yes—
28C3×#393—24no—
29C3×#388—28no—
30C3×#386—24no—
31C3×C4×C22⋊C4—24no—
32C2×C3×#95C2212yes—
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2212yes—
40C2×C3×#95C2212yes—
41C2×C3×#95C2211yescharacteristic
42C22×C22⋊Q8C2×C311yescharacteristic, complemented
43C2×#393C2×C311yescharacteristic, complemented
44C2×#388C2×C312yescomplemented
45C2×#386C2×C311yescharacteristic
46C2×C4×C22⋊C4C2×C311yescharacteristic, complemented
47#1446C2×C311yescharacteristic, complemented
48#1442C2×C311yescharacteristic, complemented
49#1440C2×C312yescomplemented
50#1439C2×C311yescharacteristic, complemented
51#1438C2×C312yes—
52#1436C2×C312yescomplemented
53C25×C3C2311yescharacteristic
54C25×C3C2311yescharacteristic
55C22×C3×Q8—24no—
56C22×C3×Q8—22no—
57C22×C3×Q8—22no—
58C22×C3×Q8—22no—
59C22×C3×Q8—42no—
60C22×C3×D4—22no—
61C22×C3×D4—22no—
62C22×C3×D4—24no—
63C22×C3×D4—22no—
64C22×C3×D4—42no—
65C23×C3×C4—22no—
66C23×C3×C4—24no—
67C23×C3×C4—22no—
68C23×C3×C4—42no—
69C23×C3×C4D414yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2312yes—
73C23×C3×C4C2312yes—
74C23×C3×C4C2312yes—
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2312yes—
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C3×C22⋊Q8—232no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4D418yescomplemented
85C2×C3×C22⋊C4—24no—
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—24no—
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C22⋊C4—22no—
97C2×C3×C22⋊C4—22no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4—24no—
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—22no—
102C2×C3×C22⋊C4—22no—
103C2×C3×C22⋊C4—42no—
104C2×C3×C42—24no—
105C2×C3×C42—24no—
106C2×C3×C42—42no—
107C3×#95—22no—
108C3×#95—22no—
109C3×#95—22no—
110C3×#95—24no—
111C3×#95—24no—
112C3×#95—24no—
113C3×#95—24no—
114C3×#95—24no—
115C3×#95—42no—
116C3×#95D414yescomplemented
117C23×Q8C22×C311yescharacteristic
118C23×D4C22×C311yescharacteristic
119C24×C4C22×C311yescharacteristic
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—28no—
122C22×C4⋊C4C22×C311yescharacteristic
123C22×C4⋊C4C22×C312yes—
124C22×C22⋊C4C22×C311yescharacteristic
125C22×C22⋊C4C22×C312yes—
126C22×C22⋊C4C22×C312yes—
127C22×C22⋊C4C22×C312yes—
128C22×C22⋊C4C22×C311yescharacteristic
129C22×C22⋊C4C22×C311yescharacteristic
130C22×C22⋊C4C22×C312yes—
131C22×C42C22×C312yes—
132#393—24no—
133#388—28no—
134#386—24no—
135C4×C22⋊C4—24no—
136C2×#95C22×C312yes—
137C2×#95C22×C311yescharacteristic
138C2×#95C22×C312yes—
139C2×#95C22×C312yes—
140C2×#95C22×C311yescharacteristic
141C2×#95C22×C312yes—
142C2×#95C22×C312yes—
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C312yes—
145C2×#95C22×C311yescharacteristic
146C24×C3—22no—
147C24×C3—21no—
148C24×C3—22no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—22no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—22no—
159C24×C3—21no—
160C24×C3—21no—
161C24×C3—22no—
162C24×C3—22no—
163C24×C3—21no—
164C24×C3—21no—
165C24×C3C2×D412yes—
166C24×C3#4112yes—
167C24×C3#4114yes—
168C24×C3C2411yescharacteristic
169C2×C3×Q8—28no—
170C2×C3×Q8—48no—
171C2×C3×Q8—48no—
172C2×C3×Q8—44no—
173C2×C3×Q8—44no—
174C2×C3×D4—28no—
175C2×C3×D4—48no—
176C2×C3×D4—48no—
177C2×C3×D4—44no—
178C2×C3×D4—44no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—28no—
213C22×C3×C4—28no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—44no—
225C22×C3×C4—48no—
226C22×C3×C4—48no—
227C22×C3×C4C2×D414yes—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D412yes—
231C22×C3×C4C2×D414yes—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4#4112yes—
235C22×C3×C4#4114yes—
236C22×C3×C4#4112yes—
237C3×C4⋊C4—28no—
238C3×C4⋊C4—216no—
239C3×C22⋊C4—216no—
240C3×C22⋊C4—216no—
241C3×C22⋊C4—216no—
242C3×C22⋊C4—48no—
243C3×C22⋊C4—44no—
244C3×C22⋊C4—44no—
245C3×C22⋊C4—44no—
246C3×C42—48no—
247C25C23×C311yescharacteristic
248C25C23×C311yescharacteristic
249C22×Q8—24no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—42no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—42no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—42no—
263C23×C4C3×D414yes—
264C23×C4C23×C311yescharacteristic
265C23×C4C23×C311yescharacteristic
266C23×C4C23×C312yes—
267C23×C4C23×C312yes—
268C23×C4C23×C312yes—
269C23×C4C23×C312yes—
270C23×C4C23×C311yescharacteristic
271C23×C4C23×C311yescharacteristic
272C23×C4C23×C311yescharacteristic
273C22⋊Q8—232no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4C3×D418yescomplemented
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—24no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—42no—
298C2×C42—24no—
299C2×C42—24no—
300C2×C42—42no—
301#95—22no—
302#95—22no—
303#95—22no—
304#95—24no—
305#95—24no—
306#95—24no—
307#95—24no—
308#95—24no—
309#95—42no—
310#95C3×D414yescomplemented
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—24no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—24no—
327C23×C3—22no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—42no—
341C23×C3—41no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—41no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—41no—
356C23×C3#12414yes—
357C23×C3C22×D411yescharacteristic
358C23×C3C22×D412yes—
359C23×C3C22×D411yescharacteristic
360C23×C3C2×#4111yescharacteristic
361C23×C3C2×#4111yescharacteristic
362C23×C3C2×#4112yes—
363C23×C3C2×#4112yes—
364C23×C3C2×#4111yescharacteristic
365C23×C3H(5,𝔽2)12yes—
366C23×C32−1+411yescharacteristic
367C23×C32−1+411yescharacteristic
368C3×Q8—416no—
369C3×D4—416no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—416no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—42no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4#12014yes—
423C2×C3×C4#12114yes—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24C2×C3×D412yes—
444C24C3×#4112yes—
445C24C3×#4114yes—
446C24C24×C311yescharacteristic
447C2×Q8—28no—
448C2×Q8—48no—
449C2×Q8—48no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×D4—28no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—44no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—44no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4C2×C3×D414yes—
506C22×C4C2×C3×D414yes—
507C22×C4C2×C3×D414yes—
508C22×C4C2×C3×D412yes—
509C22×C4C2×C3×D414yes—
510C22×C4C2×C3×D412yes—
511C22×C4C2×C3×D412yes—
512C22×C4C3×#4112yes—
513C22×C4C3×#4114yes—
514C22×C4C3×#4112yes—
515C4⋊C4—28no—
516C4⋊C4—216no—
517C22⋊C4—216no—
518C22⋊C4—216no—
519C22⋊C4—216no—
520C22⋊C4—48no—
521C22⋊C4—44no—
522C22⋊C4—44no—
523C22⋊C4—44no—
524C42—48no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—44no—
529C22×C3—42no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—44no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—42no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—82no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—82no—
547C22×C3C2×#12011yescharacteristic
548C22×C3C2×#12111yescharacteristic
549C22×C3#52511yescharacteristic
550C22×C3#52512yes—
551C22×C3#52512yes—
552C22×C3C2×#12411yescharacteristic
553C22×C3#52912yes—
554C22×C3#53212yes—
555C22×C3#53211yescharacteristic
556C22×C3#53411yescharacteristic
557C22×C3#53611yescharacteristic
558C22×C3#53912yes—
559C22×C3#54212yes—
560C22×C3D4212yes—
561C22×C3#54612yes—
562C22×C3#54711yescharacteristic
563C22×C3#54812yes—
564C22×C3#54811yescharacteristic
565C22×C3#54812yes—
566C22×C3#55112yes—
567C22×C3#55112yes—
568C22×C3#55211yescharacteristic
569C22×C3#55611yescharacteristic
570C3×C4—24no—
571C3×C4—24no—
572C3×C4—42no—
573C3×C4—44no—
574C3×C4—44no—
575C3×C4—44no—
576C3×C4—44no—
577C3×C4—81no—
578C3×C4—81no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—22no—
583C23—24no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—41no—
610C23—42no—
611C23—41no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—41no—
624C23C3×#12414yes—
625C23C22×C3×D411yescharacteristic
626C23C22×C3×D412yes—
627C23C22×C3×D411yescharacteristic
628C23C2×C3×#4111yescharacteristic
629C23C2×C3×#4111yescharacteristic
630C23C2×C3×#4112yes—
631C23C2×C3×#4112yes—
632C23C2×C3×#4111yescharacteristic
633C23C3×H(5,𝔽2)12yes—
634C23C3×2−1+411yescharacteristic
635C23C3×2−1+411yescharacteristic
636Q8—416no—
637D4—416no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—416no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4C3×#12014yes—
691C2×C4C3×#12114yes—
692C2×C3—44no—
693C2×C3—82no—
694C2×C3#238811yescharacteristic
695C2×C3#241011yescharacteristic
696C2×C3#241511yescharacteristic
697C2×C3#243611yescharacteristic
698C2×C3#246112yes—
699C2×C3#246312yes—
700C2×C3#247712yes—
701C2×C3#256012yes—
702C2×C3#256111yescharacteristic
703C2×C3#266311yescharacteristic
704C2×C3#285011yescharacteristic
705C22—24no—
706C22—24no—
707C22—24no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—42no—
717C22—42no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—82no—
725C22—82no—
726C22—81no—
727C22C2×C3×#12011yescharacteristic
728C22C2×C3×#12111yescharacteristic
729C22C3×#52511yescharacteristic
730C22C3×#52512yes—
731C22C3×#52512yes—
732C22C2×C3×#12411yescharacteristic
733C22C3×#52912yes—
734C22C3×#53211yescharacteristic
735C22C3×#53212yes—
736C22C3×#53411yescharacteristic
737C22C3×#53611yescharacteristic
738C22C3×#53912yes—
739C22C3×#54212yes—
740C22C3×D4212yes—
741C22C3×#54612yes—
742C22C3×#54711yescharacteristic
743C22C3×#54811yescharacteristic
744C22C3×#54812yes—
745C22C3×#54812yes—
746C22C3×#55112yes—
747C22C3×#55112yes—
748C22C3×#55211yescharacteristic
749C22C3×#55611yescharacteristic
750C4—24no—
751C4—24no—
752C4—44no—
753C4—44no—
754C4—44no—
755C4—44no—
756C4—42no—
757C4—81no—
758C4—81no—
759C3#1476511yescharacteristic, direct product factor, Sylow
760C2—44no—
761C2—82no—
762C2C3×#238811yescharacteristic
763C2C3×#241011yescharacteristic
764C2C3×#241511yescharacteristic
765C2C3×#243611yescharacteristic
766C2C3×#246112yes—
767C2C3×#246312yes—
768C2C3×#247712yes—
769C2C3×#256012yes—
770C2C3×#256111yescharacteristic
771C2C3×#266311yescharacteristic
772C2C3×#285011yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C2×C3×#393C2semidirect
3. C2×C3×#388C2semidirect
5. C2×C3×C4×C22⋊C4C2semidirect
6. C3×#1446C2semidirect
7. C3×#1442C2semidirect
8. C3×#1440C2semidirect
9. C3×#1439C2semidirect
11. C3×#1436C2semidirect
12. #14765C3direct (N × H)
42. C22×C22⋊Q8C2×C3semidirect
43. C2×#393C2×C3semidirect
44. C2×#388C2×C3semidirect
46. C2×C4×C22⋊C4C2×C3semidirect
47. #1446C2×C3semidirect
48. #1442C2×C3semidirect
49. #1440C2×C3semidirect
50. #1439C2×C3semidirect
52. #1436C2×C3semidirect
84. C2×C3×C4⋊C4D4semidirect
116. C3×#95D4semidirect
278. C2×C4⋊C4C3×D4semidirect
310. #95C3×D4semidirect
759. C3#14765direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#3932
C2×C3×#3882
C2×C3×#3862
C2×C3×C4×C22⋊C42
C3×#14462
C3×#14422
C3×#14402
C3×#14392
C3×#14382
C3×#14362
#147653