Finite Group Databasebeta

← C3×#25665 #10644272

Subgroups — C3×#25665 #10644272

Order 768.

1136 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3505C211yesmaximal, characteristic
2C3×#2591C211yesmaximal, characteristic, complemented
3C3×#2583C211yesmaximal, characteristic, complemented
4C3×#2579C211yesmaximal, characteristic, complemented
5C3×#2044C212yesmaximal, complemented
6C3×#2044C212yesmaximal, complemented
7C3×#1996C211yesmaximal, characteristic, complemented
8C3×#1964C211yesmaximal, characteristic, complemented
9C3×#1867C212yesmaximal, complemented
10C3×#1867C212yesmaximal, complemented
11C3×C4×#99C211yesmaximal, characteristic, complemented
12#25665C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#553—22no—
14C3×#553—21no—
15C3×#552—21no—
16C3×#551—22no—
17C3×#548—21no—
18C3×#546—21no—
19C3×#539—21no—
20C3×#538—21no—
21C3×#534C2212yes—
22C3×#529—21no—
23C3×#525—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C3×#518C2212yes—
27C2×C3×C4×D4C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C2×C3×#99C2212yes—
30C2×C3×#99C2212yes—
31C2×C3×#99C2212yes—
32C3×#400—21no—
33C3×#398—21no—
34C3×#398—21no—
35C3×#396—21no—
36C3×#395—21no—
37C3×#394—21no—
38C3×#389—22no—
39C3×#388—22no—
40C3×#387—21no—
41C3×#386C2211yescharacteristic
42C3×#386C2211yescharacteristic
43C3×#386C2212yes—
44C3×#386C2212yes—
45C3×#385—21no—
46C3×#385C2212yes—
47C3×#385C2212yes—
48C3×#385C2211yescharacteristic
49C3×#385C2211yescharacteristic
50C3×#380C2211yescharacteristic
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×C4×C22⋊C4C2211yescharacteristic
53C3×#342C2212yes—
54C3×#342C2212yes—
55C3×#342C2212yes—
56#3505C2×C311yescharacteristic
57#2591C2×C311yescharacteristic, complemented
58#2583C2×C311yescharacteristic, complemented
59#2579C2×C311yescharacteristic, complemented
60#2044C2×C312yescomplemented
61#2044C2×C312yescomplemented
62#1996C2×C311yescharacteristic, complemented
63#1964C2×C311yescharacteristic, complemented
64#1867C2×C312yescomplemented
65#1867C2×C312yescomplemented
66C4×#99C2×C311yescharacteristic, complemented
67C2×C3×#41—21no—
68C22×C3×Q8D411yescharacteristic
69C22×C3×D4D411yescharacteristic
70C22×C3×D4C2311yescharacteristic
71C22×C3×D4C2312yes—
72C23×C3×C4D411yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C3×#126—22no—
77C3×#126—22no—
78C3×#126—22no—
79C3×#125—21no—
80C3×#125—22no—
81C3×#124—21no—
82C3×#124—22no—
83C3×#123—22no—
84C3×#123—22no—
85C3×#123—22no—
86C3×#123—22no—
87C3×#123—22no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—21no—
91C3×C22⋊Q8—21no—
92C3×C22⋊Q8—21no—
93C3×C22⋊Q8—21no—
94C3×#121—21no—
95C3×#121—22no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121—21no—
99C3×#121—21no—
100C3×#121—22no—
101C3×#121—22no—
102C3×#120—22no—
103C3×#120—22no—
104C3×C4×Q8—21no—
105C3×C4×D4—22no—
106C3×C4×D4—21no—
107C3×C4×D4—21no—
108C3×C4×D4—21no—
109C3×C4×D4—21no—
110C3×C4×D4—21no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×#117—21no—
116C3×#117—22no—
117C3×#117—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4D412yes—
130C2×C3×C4⋊C4D411yescharacteristic
131C2×C3×C4⋊C4D411yescharacteristic
132C2×C3×C4⋊C4D411yescharacteristic
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—22no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4D412yes—
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C22⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4C2311yescharacteristic
143C2×C3×C22⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4C2312yes—
145C2×C3×C22⋊C4C2312yes—
146C2×C3×C42—21no—
147C2×C3×C42—21no—
148C2×C3×C42D411yescharacteristic
149C3×#99—24no—
150C3×#99—24no—
151C3×#99—24no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—21no—
160C3×#95—21no—
161C3×#95—22no—
162C3×#95—22no—
163#553—22no—
164#553—21no—
165#552—21no—
166#551—22no—
167#548—21no—
168#546—21no—
169#539—21no—
170#538—21no—
171#534C22×C312yes—
172#529—21no—
173#525—21no—
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176#518C22×C312yes—
177C2×C4×D4C22×C311yescharacteristic
178C22×C4⋊C4C22×C311yescharacteristic
179C2×#99C22×C312yes—
180C2×#99C22×C312yes—
181C2×#99C22×C312yes—
182#400—21no—
183#398—21no—
184#398—21no—
185#396—21no—
186#395—21no—
187#394—21no—
188#389—22no—
189#388—22no—
190#387—21no—
191#386C22×C311yescharacteristic
192#386C22×C311yescharacteristic
193#386C22×C312yes—
194#386C22×C312yes—
195#385—21no—
196#385C22×C311yescharacteristic
197#385C22×C311yescharacteristic
198#385C22×C312yes—
199#385C22×C312yes—
200#380C22×C311yescharacteristic
201C4×C22⋊C4C22×C311yescharacteristic
202C4×C22⋊C4C22×C311yescharacteristic
203#342C22×C312yes—
204#342C22×C312yes—
205#342C22×C312yes—
206C24×C3C2×D412yes—
207C24×C3C2×D411yescharacteristic
208C24×C3C2411yescharacteristic
209C3×#41—82no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—81no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—81no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—42no—
243C22×C3×C4—81no—
244C22×C3×C4—81no—
245C22×C3×C4—81no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D412yes—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D412yes—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—42no—
271C3×C4⋊C4—44no—
272C3×C4⋊C4—41no—
273C3×C4⋊C4—41no—
274C3×C4⋊C4—41no—
275C3×C4⋊C4—41no—
276C3×C4⋊C4—81no—
277C3×C4⋊C4—82no—
278C3×C4⋊C4—81no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—22no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—21no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—21no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—44no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—82no—
301C3×C22⋊C4—81no—
302C3×C22⋊C4#4114yescomplemented
303C3×C42—22no—
304C3×C42—22no—
305C3×C42—21no—
306C3×C42—21no—
307C3×C42—81no—
308C3×C42—81no—
309C2×#41—21no—
310C22×Q8C3×D411yescharacteristic
311C22×D4C3×D411yescharacteristic
312C22×D4C23×C311yescharacteristic
313C22×D4C23×C312yes—
314C23×C4C3×D411yescharacteristic
315C23×C4C23×C311yescharacteristic
316C23×C4C23×C311yescharacteristic
317C23×C4C23×C311yescharacteristic
318#126—22no—
319#126—22no—
320#126—22no—
321#125—21no—
322#125—22no—
323#124—21no—
324#124—22no—
325#123—22no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336#121—21no—
337#121—22no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—22no—
343#121—22no—
344#120—22no—
345#120—22no—
346C4×Q8—21no—
347C4×D4—22no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357#117—21no—
358#117—22no—
359#117—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4C3×D411yescharacteristic
372C2×C4⋊C4C3×D411yescharacteristic
373C2×C4⋊C4C3×D412yes—
374C2×C4⋊C4C3×D411yescharacteristic
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4C3×D411yescharacteristic
381C2×C22⋊C4C3×D412yes—
382C2×C22⋊C4C23×C312yes—
383C2×C22⋊C4C23×C311yescharacteristic
384C2×C22⋊C4C23×C311yescharacteristic
385C2×C22⋊C4C23×C311yescharacteristic
386C2×C22⋊C4C23×C312yes—
387C2×C22⋊C4C23×C312yes—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C3×D411yescharacteristic
391#99—24no—
392#99—24no—
393#99—24no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—22no—
400#95—22no—
401#95—21no—
402#95—21no—
403#95—22no—
404#95—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—42no—
416C23×C3—42no—
417C23×C3C22×D411yescharacteristic
418C23×C3C22×D411yescharacteristic
419C23×C3C22×D411yescharacteristic
420C23×C3C2×#4112yes—
421C23×C32−1+412yes—
422C3×Q8—42no—
423C3×Q8—81no—
424C3×D4—42no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—42no—
428C3×D4—42no—
429C3×D4—42no—
430C3×D4—42no—
431C3×D4—81no—
432C3×D4—82no—
433C3×D4—82no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—24no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—42no—
463C2×C3×C4—41no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—41no—
467C2×C3×C4—42no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—42no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—42no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—42no—
479C2×C3×C4—81no—
480C2×C3×C4—82no—
481C2×C3×C4—82no—
482C2×C3×C4#12011yescharacteristic
483C2×C3×C4#12011yescharacteristic
484C2×C3×C4#12011yescharacteristic
485C2×C3×C4#12011yescharacteristic
486C24C2×C3×D412yes—
487C24C2×C3×D411yescharacteristic
488C24C24×C311yescharacteristic
489#41—82no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—81no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—81no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D412yes—
528C22×C4C2×C3×D411yescharacteristic
529C22×C4C2×C3×D412yes—
530C22×C4C2×C3×D411yescharacteristic
531C22×C4C2×C3×D412yes—
532C22×C4C2×C3×D411yescharacteristic
533C22×C4C2×C3×D411yescharacteristic
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—44no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—41no—
555C4⋊C4—41no—
556C4⋊C4—81no—
557C4⋊C4—82no—
558C4⋊C4—81no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—22no—
567C22⋊C4—21no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—44no—
579C22⋊C4—42no—
580C22⋊C4—82no—
581C22⋊C4—81no—
582C22⋊C4C3×#4114yescomplemented
583C42—22no—
584C42—22no—
585C42—21no—
586C42—21no—
587C42—81no—
588C42—81no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—81no—
605C22×C3—82no—
606C22×C3—82no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#53211yescharacteristic
609C22×C3#53611yescharacteristic
610C22×C3#54712yes—
611C22×C3#54812yes—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—44no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4—82no—
627C3×C4—81no—
628C23—22no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23C22×C3×D411yescharacteristic
641C23C22×C3×D411yescharacteristic
642C23C22×C3×D411yescharacteristic
643C23C2×C3×#4112yes—
644C23C3×2−1+412yes—
645Q8—42no—
646Q8—81no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—81no—
655D4—82no—
656D4—82no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C3×#12011yescharacteristic
706C2×C4C3×#12011yescharacteristic
707C2×C4C3×#12011yescharacteristic
708C2×C4C3×#12011yescharacteristic
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—22no—
712C2×C3—21no—
713C2×C3—81no—
714C2×C3—82no—
715C2×C3#243211yescharacteristic
716C2×C3#302511yescharacteristic
717C2×C3#302611yescharacteristic
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—81no—
734C22—82no—
735C22—82no—
736C22C2×C3×#12011yescharacteristic
737C22C3×#53211yescharacteristic
738C22C3×#53611yescharacteristic
739C22C3×#54712yes—
740C22C3×#54812yes—
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—44no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—81no—
754C4—81no—
755C4—82no—
756C4—81no—
757C3#2566511yescharacteristic, direct product factor, Sylow
758C2—22no—
759C2—21no—
760C2—22no—
761C2—21no—
762C2—81no—
763C2—82no—
764C2C3×#243211yescharacteristic
765C2C3×#302511yescharacteristic
766C2C3×#302611yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC24C24×C3
prime radicalC3×#3505C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2591C2semidirect
3. C3×#2583C2semidirect
4. C3×#2579C2semidirect
5. C3×#2044C2semidirect
6. C3×#2044C2semidirect
7. C3×#1996C2semidirect
8. C3×#1964C2semidirect
9. C3×#1867C2semidirect
10. C3×#1867C2semidirect
11. C3×C4×#99C2semidirect
12. #25665C3direct (N × H)
57. #2591C2×C3semidirect
58. #2583C2×C3semidirect
59. #2579C2×C3semidirect
60. #2044C2×C3semidirect
61. #2044C2×C3semidirect
62. #1996C2×C3semidirect
63. #1964C2×C3semidirect
64. #1867C2×C3semidirect
65. #1867C2×C3semidirect
66. C4×#99C2×C3semidirect
302. C3×C22⋊C4#41semidirect
582. C22⋊C4C3×#41semidirect
757. C3#25665direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35052
C3×#25912
C3×#25832
C3×#25792
C3×#20442
C3×#19962
C3×#19642
C3×#18672
C3×C4×#992
#256653