Finite Group Databasebeta

← C3×#24384 #10642991

Subgroups — C3×#24384 #10642991

Order 768.

1970 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic, complemented
2C2×C3×#469C212yesmaximal, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C2×C3×#407C211yesmaximal, characteristic, complemented
5C3×#2847C211yesmaximal, characteristic, complemented
6C3×#2034C212yesmaximal, complemented
7C3×#1999C212yesmaximal, complemented
8C3×#1895C212yesmaximal, complemented
9C3×#1874C211yesmaximal, characteristic, complemented
10C3×#1853C211yesmaximal, characteristic, complemented
11C3×#1786C211yesmaximal, characteristic, complemented
12#24384C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4—21no—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×C3×D8C2212yescomplemented
17C22×C3×M16C2212yescomplemented
18C2×C3×#121—21no—
19C2×C3×#121—21no—
20C2×C3×#121—28no—
21C2×C3×#121C2212yes—
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2212yes—
24C2×C3×#121C2211yescharacteristic, complemented
25C2×C3×#121C2211yescharacteristic, complemented
26C2×C3×#120—21no—
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4—21no—
29C3×#469—28no—
30C3×#447—24no—
31C2×C3×#106C2212yescomplemented
32C2×C3×#102C2212yescomplemented
33C2×C3×#102C2212yescomplemented
34C2×C3×#102C2212yescomplemented
35C2×C3×#102C2212yescomplemented
36C3×#407—24no—
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2212yescomplemented
40C3×#386—21no—
41C3×#386—21no—
42C3×#386—21no—
43C3×#380C2211yescharacteristic
44C3×#380C2211yescharacteristic, complemented
45C3×#380C2211yescharacteristic, complemented
46C3×#340C2212yescomplemented
47C3×#340C2212yescomplemented
48C22×#121C2×C311yescharacteristic, complemented
49C2×#469C2×C312yescomplemented
50C2×#447C2×C311yescharacteristic, complemented
51C2×#407C2×C311yescharacteristic, complemented
52#2847C2×C311yescharacteristic, complemented
53#2034C2×C312yescomplemented
54#1999C2×C312yescomplemented
55#1895C2×C312yescomplemented
56#1874C2×C311yescharacteristic, complemented
57#1853C2×C311yescharacteristic, complemented
58#1786C2×C311yescharacteristic, complemented
59C25×C3—21no—
60C25×C3D411yescharacteristic
61C22×C3×D4—28no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—24no—
65C22×C3×D4—21no—
66C22×C3×D4—21no—
67C22×C3×D4—21no—
68C22×C3×D4—21no—
69C22×C3×D4—22no—
70C22×C3×D4—22no—
71C22×C3×D4—42no—
72C22×C3×D4—44no—
73C22×C3×D4—44no—
74C22×C3×D4C2311yescharacteristic
75C22×C3×D4C2312yes—
76C23×C3×C4—21no—
77C23×C3×C4—22no—
78C23×C3×C4—24no—
79C23×C3×C4—22no—
80C23×C3×C4—42no—
81C23×C3×C4D411yescharacteristic
82C23×C3×C4D411yescharacteristic
83C23×C3×C4D411yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C2×C3×D8—24no—
88C2×C3×D8—24no—
89C2×C3×D8—42no—
90C2×C3×M16—24no—
91C2×C3×M16—24no—
92C2×C3×M16—42no—
93C22×C3×C8C2312yes—
94C22×C3×C8C2312yes—
95C3×#121—28no—
96C3×#121—28no—
97C3×#121—24no—
98C3×#121—24no—
99C3×#121—24no—
100C3×#121—22no—
101C3×#121—24no—
102C3×#121—22no—
103C3×#121—42no—
104C3×#121D418yescomplemented
105C3×#120—44no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2312yes—
112C2×C3×C22⋊C4—28no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C3×#106—24no—
122C3×#102—24no—
123C3×#102—24no—
124C3×#102—24no—
125C3×#102—42no—
126C3×C22⋊C8—22no—
127C3×C22⋊C8—24no—
128C3×C22⋊C8D414yescomplemented
129C3×#95—21no—
130C3×#95—21no—
131C3×#95—21no—
132C23×D4—21no—
133C23×D4C22×C311yescharacteristic
134C24×C4C22×C311yescharacteristic
135C22×D8C22×C312yescomplemented
136C22×M16C22×C312yescomplemented
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—28no—
140C2×#121C22×C311yescharacteristic
141C2×#121C22×C312yes—
142C2×#121C22×C312yes—
143C2×#121C22×C311yescharacteristic, complemented
144C2×#121C22×C311yescharacteristic, complemented
145C2×#120—21no—
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C22⋊C4—21no—
148#469—28no—
149#447—24no—
150C2×#106C22×C312yescomplemented
151C2×#102C22×C312yescomplemented
152C2×#102C22×C312yescomplemented
153C2×#102C22×C312yescomplemented
154C2×#102C22×C312yescomplemented
155#407—24no—
156C2×C22⋊C8C22×C311yescharacteristic
157C2×C22⋊C8C22×C311yescharacteristic
158C2×C22⋊C8C22×C312yescomplemented
159#386—21no—
160#386—21no—
161#386—21no—
162#380C22×C311yescharacteristic
163#380C22×C311yescharacteristic, complemented
164#380C22×C311yescharacteristic, complemented
165#340C22×C312yescomplemented
166#340C22×C312yescomplemented
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—24no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—41no—
176C24×C3—41no—
177C24×C3—42no—
178C24×C3—42no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3—42no—
182C24×C3—42no—
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C2×C3×D4—24no—
187C2×C3×D4—28no—
188C2×C3×D4—28no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—22no—
194C2×C3×D4—21no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—48no—
199C2×C3×D4—48no—
200C2×C3×D4—42no—
201C2×C3×D4—432no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4—44no—
205C2×C3×D4—44no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—42no—
210C2×C3×D4—42no—
211C2×C3×D4—42no—
212C2×C3×D4—42no—
213C2×C3×D4—42no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4C2×D414yes—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—24no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—41no—
238C22×C3×C4—41no—
239C22×C3×C4—41no—
240C22×C3×C4—48no—
241C22×C3×C4—48no—
242C22×C3×C4—42no—
243C22×C3×C4—42no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D414yes—
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D412yes—
249C22×C3×C4#4112yes—
250C22×C3×C4C2411yescharacteristic
251C3×D8—48no—
252C3×M16—48no—
253C2×C3×C8—22no—
254C2×C3×C8—22no—
255C2×C3×C8—22no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8C2×D414yescomplemented
259C3×C4⋊C4—24no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4C2×D414yes—
266C3×C22⋊C4—28no—
267C3×C22⋊C4—28no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C25—21no—
275C25C3×D411yescharacteristic
276C22×D4—28no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—24no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—42no—
287C22×D4—44no—
288C22×D4—44no—
289C22×D4C23×C311yescharacteristic
290C22×D4C23×C312yes—
291C23×C4—21no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—42no—
296C23×C4C3×D411yescharacteristic
297C23×C4C3×D411yescharacteristic
298C23×C4C3×D411yescharacteristic
299C23×C4C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C23×C4C23×C311yescharacteristic
302C2×D8—24no—
303C2×D8—24no—
304C2×D8—42no—
305C2×M16—24no—
306C2×M16—24no—
307C2×M16—42no—
308C22×C8C23×C312yes—
309C22×C8C23×C312yes—
310#121—28no—
311#121—28no—
312#121—24no—
313#121—24no—
314#121—24no—
315#121—22no—
316#121—24no—
317#121—22no—
318#121—42no—
319#121C3×D418yescomplemented
320#120—44no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C4⋊C4C23×C312yes—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336#106—24no—
337#102—24no—
338#102—24no—
339#102—24no—
340#102—42no—
341C22⋊C8—22no—
342C22⋊C8—24no—
343C22⋊C8C3×D414yescomplemented
344#95—21no—
345#95—21no—
346#95—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—28no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—24no—
365C23×C3—44no—
366C23×C3—44no—
367C23×C3—44no—
368C23×C3—44no—
369C23×C3—44no—
370C23×C3—48no—
371C23×C3—48no—
372C23×C3—48no—
373C23×C3—44no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—84no—
388C23×C3—84no—
389C23×C3—84no—
390C23×C3—84no—
391C23×C3#12012yes—
392C23×C3#12112yes—
393C23×C3AGL(1,ℤ/8)12yes—
394C23×C3AGL(1,ℤ/8)12yes—
395C23×C3AGL(1,ℤ/8)12yes—
396C23×C3C22×D411yescharacteristic
397C3×D4—24no—
398C3×D4—24no—
399C3×D4—48no—
400C3×D4—416no—
401C3×D4—416no—
402C3×D4—42no—
403C3×D4—42no—
404C3×D4—42no—
405C3×D4—42no—
406C3×D4—84no—
407C3×D4—84no—
408C3×D4—84no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—21no—
418C2×C3×C4—24no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—44no—
422C2×C3×C4—44no—
423C2×C3×C4—44no—
424C2×C3×C4—48no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4#12012yes—
439C2×C3×C4#12112yes—
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D412yes—
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4H(5,𝔽2)12yes—
444C3×C8—24no—
445C3×C8—42no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—41no—
455C24—41no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24C2×C3×D411yescharacteristic
463C24C2×C3×D411yescharacteristic
464C24C2×C3×D411yescharacteristic
465C2×D4—24no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—42no—
480C2×D4—432no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4C2×C3×D414yes—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4C2×C3×D411yescharacteristic
524C22×C4C2×C3×D411yescharacteristic
525C22×C4C2×C3×D414yes—
526C22×C4C2×C3×D411yescharacteristic
527C22×C4C2×C3×D412yes—
528C22×C4C3×#4112yes—
529C22×C4C24×C311yescharacteristic
530D8—48no—
531M16—48no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8C2×C3×D414yescomplemented
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4C2×C3×D414yes—
545C22⋊C4—28no—
546C22⋊C4—28no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
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—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—416no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—44no—
575C22×C3—44no—
576C22×C3—44no—
577C22×C3—816no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3#46914yescomplemented
590C22×C3C2×#12011yescharacteristic
591C22×C3C2×#12111yescharacteristic
592C22×C3#53411yescharacteristic
593C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
594C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
595C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
596C22×C3#57511yescharacteristic
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—41no—
600C3×C4—44no—
601C3×C4—81no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4D4212yes—
605C3×C4#54612yes—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—28no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—24no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—48no—
630C23—48no—
631C23—48no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23C3×#12012yes—
651C23C3×#12112yes—
652C23C3×AGL(1,ℤ/8)12yes—
653C23C3×AGL(1,ℤ/8)12yes—
654C23C3×AGL(1,ℤ/8)12yes—
655C23C22×C3×D411yescharacteristic
656D4—24no—
657D4—24no—
658D4—48no—
659D4—416no—
660D4—416no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—84no—
666D4—84no—
667D4—84no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4C3×#12012yes—
698C2×C4C3×#12112yes—
699C2×C4C22×C3×D411yescharacteristic
700C2×C4C22×C3×D412yes—
701C2×C4C2×C3×#4111yescharacteristic
702C2×C4C3×H(5,𝔽2)12yes—
703C8—24no—
704C8—42no—
705C2×C3—24no—
706C2×C3—42no—
707C2×C3—42no—
708C2×C3—84no—
709C2×C3—161no—
710C2×C3#241011yescharacteristic
711C2×C3#300311yescharacteristic
712C2×C3#300611yescharacteristic
713C2×C3C2×#46911yescharacteristic
714C2×C3#305511yescharacteristic
715C2×C3#319211yescharacteristic
716C2×C3#319411yescharacteristic
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—416no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—816no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22C3×#46914yescomplemented
754C22C2×C3×#12011yescharacteristic
755C22C2×C3×#12111yescharacteristic
756C22C3×#53411yescharacteristic
757C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
758C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
759C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
760C22C3×#57511yescharacteristic
761C4—22no—
762C4—22no—
763C4—41no—
764C4—44no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C3×D4212yes—
769C4C3×#54612yes—
770C3#2438411yescharacteristic, direct product factor, Sylow
771C2—24no—
772C2—42no—
773C2—42no—
774C2—84no—
775C2—161no—
776C2C3×#241011yescharacteristic
777C2C3×#300311yescharacteristic
778C2C3×#300611yescharacteristic
779C2C2×C3×#46911yescharacteristic
780C2C3×#305511yescharacteristic
781C2C3×#319211yescharacteristic
782C2C3×#319411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×#121C2semidirect
2. C2×C3×#469C2semidirect
3. C2×C3×#447C2semidirect
4. C2×C3×#407C2semidirect
5. C3×#2847C2semidirect
6. C3×#2034C2semidirect
7. C3×#1999C2semidirect
8. C3×#1895C2semidirect
9. C3×#1874C2semidirect
10. C3×#1853C2semidirect
11. C3×#1786C2semidirect
12. #24384C3direct (N × H)
16. C22×C3×D8C22semidirect
17. C22×C3×M16C22semidirect
24. C2×C3×#121C22semidirect
25. C2×C3×#121C22semidirect
31. C2×C3×#106C22semidirect
32. C2×C3×#102C22semidirect
33. C2×C3×#102C22semidirect
34. C2×C3×#102C22semidirect
35. C2×C3×#102C22semidirect
39. C2×C3×C22⋊C8C22semidirect
44. C3×#380C22semidirect
45. C3×#380C22semidirect
46. C3×#340C22semidirect
47. C3×#340C22semidirect
48. C22×#121C2×C3semidirect
49. C2×#469C2×C3semidirect
50. C2×#447C2×C3semidirect
51. C2×#407C2×C3semidirect
52. #2847C2×C3semidirect
53. #2034C2×C3semidirect
54. #1999C2×C3semidirect
55. #1895C2×C3semidirect
56. #1874C2×C3semidirect
57. #1853C2×C3semidirect
58. #1786C2×C3semidirect
104. C3×#121D4semidirect
128. C3×C22⋊C8D4semidirect
135. C22×D8C22×C3semidirect
136. C22×M16C22×C3semidirect
143. C2×#121C22×C3semidirect
144. C2×#121C22×C3semidirect
150. C2×#106C22×C3semidirect
151. C2×#102C22×C3semidirect
152. C2×#102C22×C3semidirect
153. C2×#102C22×C3semidirect
154. C2×#102C22×C3semidirect
158. C2×C22⋊C8C22×C3semidirect
163. #380C22×C3semidirect
164. #380C22×C3semidirect
165. #340C22×C3semidirect
166. #340C22×C3semidirect
258. C2×C3×C8C2×D4semidirect
319. #121C3×D4semidirect
343. C22⋊C8C3×D4semidirect
537. C2×C8C2×C3×D4semidirect
589. C22×C3#469semidirect
753. C22C3×#469semidirect
770. C3#24384direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1212
C2×C3×#4692
C2×C3×#4472
C2×C3×#4072
C3×#28472
C3×#20342
C3×#19992
C3×#18952
C3×#18742
C3×#18532
C3×#17862
#243843