Finite Group Databasebeta

← C3×#24385 #10642992

Subgroups — C3×#24385 #10642992

Order 768.

1892 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#121C211yesmaximal, characteristic
2C2×C3×#468C212yesmaximal, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×C3×#407C211yesmaximal, characteristic, complemented
5C3×#2848C211yesmaximal, characteristic, complemented
6C3×#2033C212yesmaximal, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1895C212yesmaximal, complemented
9C3×#1872C211yesmaximal, characteristic, complemented
10C3×#1852C211yesmaximal, characteristic, complemented
11C3×#1786C211yesmaximal, characteristic, complemented
12#24385C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4—21no—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×C3×SD16C2212yescomplemented
17C22×C3×M16C2212yescomplemented
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic, complemented
20C2×C3×C22⋊Q8C2211yescharacteristic, complemented
21C2×C3×#121—21no—
22C2×C3×#121—21no—
23C2×C3×#121—28no—
24C2×C3×#121C2212yes—
25C2×C3×#121C2212yes—
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4—21no—
28C3×#468—28no—
29C3×#450—24no—
30C2×C3×#107C2212yescomplemented
31C2×C3×#103C2212yescomplemented
32C2×C3×#102C2212yescomplemented
33C2×C3×#102C2212yescomplemented
34C2×C3×#102C2212yescomplemented
35C3×#407—24no—
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2212yescomplemented
39C3×#385—21no—
40C3×#385—21no—
41C3×#385—21no—
42C3×#380C2211yescharacteristic
43C3×#380C2211yescharacteristic, complemented
44C3×#380C2211yescharacteristic, complemented
45C3×#379—21no—
46C3×#340C2212yescomplemented
47C3×#340C2212yescomplemented
48C22×#121C2×C311yescharacteristic
49C2×#468C2×C312yescomplemented
50C2×#450C2×C311yescharacteristic, complemented
51C2×#407C2×C311yescharacteristic, complemented
52#2848C2×C311yescharacteristic, complemented
53#2033C2×C312yescomplemented
54#2000C2×C312yescomplemented
55#1895C2×C312yescomplemented
56#1872C2×C311yescharacteristic, complemented
57#1852C2×C311yescharacteristic, complemented
58#1786C2×C311yescharacteristic, complemented
59C25×C3—21no—
60C25×C3D411yescharacteristic
61C22×C3×Q8C2311yescharacteristic
62C22×C3×D4—28no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—24no—
66C22×C3×D4—21no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4—44no—
71C22×C3×D4—44no—
72C22×C3×D4C2312yes—
73C23×C3×C4—21no—
74C23×C3×C4—22no—
75C23×C3×C4—24no—
76C23×C3×C4—22no—
77C23×C3×C4—42no—
78C23×C3×C4D411yescharacteristic
79C23×C3×C4D411yescharacteristic
80C23×C3×C4D411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C2×C3×SD16—24no—
85C2×C3×SD16—24no—
86C2×C3×SD16—42no—
87C2×C3×M16—24no—
88C2×C3×M16—24no—
89C2×C3×M16—42no—
90C22×C3×C8C2312yes—
91C22×C3×C8C2312yes—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—24no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—42no—
96C3×#121—28no—
97C3×#121—28no—
98C3×#121—24no—
99C3×#121—24no—
100C3×#121—24no—
101C3×#121D418yes—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2312yes—
111C2×C3×C22⋊C4—28no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—21no—
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—
120C3×#107—24no—
121C3×#103—24no—
122C3×#102—24no—
123C3×#102—24no—
124C3×#102—42no—
125C3×C22⋊C8—22no—
126C3×C22⋊C8—24no—
127C3×C22⋊C8D414yescomplemented
128C3×#95—21no—
129C3×#95—21no—
130C3×#95—21no—
131C23×D4—21no—
132C23×D4C22×C311yescharacteristic
133C24×C4C22×C311yescharacteristic
134C22×SD16C22×C312yescomplemented
135C22×M16C22×C312yescomplemented
136C2×C22⋊Q8C22×C311yescharacteristic
137C2×C22⋊Q8C22×C311yescharacteristic, complemented
138C2×C22⋊Q8C22×C311yescharacteristic, complemented
139C2×#121—21no—
140C2×#121—21no—
141C2×#121—28no—
142C2×#121C22×C312yes—
143C2×#121C22×C312yes—
144C22×C4⋊C4C22×C311yescharacteristic
145C22×C22⋊C4—21no—
146#468—28no—
147#450—24no—
148C2×#107C22×C312yescomplemented
149C2×#103C22×C312yescomplemented
150C2×#102C22×C312yescomplemented
151C2×#102C22×C312yescomplemented
152C2×#102C22×C312yescomplemented
153#407—24no—
154C2×C22⋊C8C22×C311yescharacteristic
155C2×C22⋊C8C22×C311yescharacteristic
156C2×C22⋊C8C22×C312yescomplemented
157#385—21no—
158#385—21no—
159#385—21no—
160#380C22×C311yescharacteristic
161#380C22×C311yescharacteristic, complemented
162#380C22×C311yescharacteristic, complemented
163#379—21no—
164#340C22×C312yescomplemented
165#340C22×C312yescomplemented
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—24no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—41no—
174C24×C3—41no—
175C24×C3—42no—
176C24×C3—42no—
177C24×C3—42no—
178C24×C3—42no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3C2×D411yescharacteristic
182C24×C3C2×D411yescharacteristic
183C24×C3C2×D411yescharacteristic
184C2×C3×Q8—22no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—22no—
188C2×C3×D4—24no—
189C2×C3×D4—28no—
190C2×C3×D4—28no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—48no—
197C2×C3×D4—48no—
198C2×C3×D4—42no—
199C2×C3×D4—432no—
200C2×C3×D4—44no—
201C2×C3×D4—44no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4—42no—
205C2×C3×D4C2×D414yes—
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—24no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—41no—
228C22×C3×C4—41no—
229C22×C3×C4—41no—
230C22×C3×C4—48no—
231C22×C3×C4—48no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D414yes—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D412yes—
239C22×C3×C4#4112yes—
240C22×C3×C4C2411yescharacteristic
241C3×SD16—48no—
242C3×M16—48no—
243C2×C3×C8—22no—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—22no—
248C2×C3×C8C2×D414yescomplemented
249C3×C4⋊C4—24no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—42no—
256C3×C4⋊C4—42no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4C2×D414yes—
259C3×C22⋊C4—28no—
260C3×C22⋊C4—28no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—42no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C25—21no—
268C25C3×D411yescharacteristic
269C22×Q8C23×C311yescharacteristic
270C22×D4—28no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—21no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—42no—
278C22×D4—44no—
279C22×D4—44no—
280C22×D4C23×C312yes—
281C23×C4—21no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—42no—
286C23×C4C3×D411yescharacteristic
287C23×C4C3×D411yescharacteristic
288C23×C4C3×D411yescharacteristic
289C23×C4C23×C311yescharacteristic
290C23×C4C23×C311yescharacteristic
291C23×C4C23×C311yescharacteristic
292C2×SD16—24no—
293C2×SD16—24no—
294C2×SD16—42no—
295C2×M16—24no—
296C2×M16—24no—
297C2×M16—42no—
298C22×C8C23×C312yes—
299C22×C8C23×C312yes—
300C22⋊Q8—22no—
301C22⋊Q8—24no—
302C22⋊Q8—22no—
303C22⋊Q8—42no—
304#121—28no—
305#121—28no—
306#121—24no—
307#121—24no—
308#121—24no—
309#121C3×D418yes—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C4⋊C4C23×C311yescharacteristic
318C2×C4⋊C4C23×C312yes—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328#107—24no—
329#103—24no—
330#102—24no—
331#102—24no—
332#102—42no—
333C22⋊C8—22no—
334C22⋊C8—24no—
335C22⋊C8C3×D414yescomplemented
336#95—21no—
337#95—21no—
338#95—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—28no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—24no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—44no—
361C23×C3—44no—
362C23×C3—48no—
363C23×C3—48no—
364C23×C3—48no—
365C23×C3—44no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—42no—
371C23×C3—42no—
372C23×C3—84no—
373C23×C3—84no—
374C23×C3—84no—
375C23×C3—84no—
376C23×C3#12012yes—
377C23×C3#12112yes—
378C23×C3AGL(1,ℤ/8)12yes—
379C23×C3AGL(1,ℤ/8)12yes—
380C23×C3#13712yes—
381C23×C3C22×D411yescharacteristic
382C3×Q8—42no—
383C3×Q8—42no—
384C3×D4—24no—
385C3×D4—24no—
386C3×D4—48no—
387C3×D4—416no—
388C3×D4—416no—
389C3×D4—42no—
390C3×D4—42no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—21no—
400C2×C3×C4—24no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—44no—
404C2×C3×C4—44no—
405C2×C3×C4—44no—
406C2×C3×C4—48no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4#12012yes—
424C2×C3×C4#12112yes—
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D412yes—
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4H(5,𝔽2)12yes—
429C3×C8—24no—
430C3×C8—42no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—41no—
439C24—41no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24C2×C3×D411yescharacteristic
447C24C2×C3×D411yescharacteristic
448C24C2×C3×D411yescharacteristic
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×D4—24no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—42no—
464C2×D4—432no—
465C2×D4—44no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4C2×C3×D414yes—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4C2×C3×D411yescharacteristic
500C22×C4C2×C3×D411yescharacteristic
501C22×C4C2×C3×D414yes—
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C2×C3×D412yes—
504C22×C4C3×#4112yes—
505C22×C4C24×C311yescharacteristic
506SD16—48no—
507M16—48no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8C2×C3×D414yescomplemented
514C4⋊C4—24no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4C2×C3×D414yes—
524C22⋊C4—28no—
525C22⋊C4—28no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—416no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—816no—
557C22×C3—82no—
558C22×C3—82no—
559C22×C3—82no—
560C22×C3—82no—
561C22×C3#46814yescomplemented
562C22×C3C2×#12011yescharacteristic
563C22×C3C2×#12111yescharacteristic
564C22×C3#53411yescharacteristic
565C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
566C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
567C22×C3C2×#13711yescharacteristic
568C22×C3#57511yescharacteristic
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—41no—
572C3×C4—44no—
573C3×C4—81no—
574C3×C4—81no—
575C3×C4—81no—
576C3×C4—81no—
577C3×C4D4212yes—
578C3×C4#54612yes—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—28no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—24no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—48no—
603C23—48no—
604C23—48no—
605C23—44no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—84no—
613C23—84no—
614C23—84no—
615C23—84no—
616C23C3×#12012yes—
617C23C3×#12112yes—
618C23C3×AGL(1,ℤ/8)12yes—
619C23C3×AGL(1,ℤ/8)12yes—
620C23C3×#13712yes—
621C23C22×C3×D411yescharacteristic
622Q8—42no—
623Q8—42no—
624D4—24no—
625D4—24no—
626D4—48no—
627D4—416no—
628D4—416no—
629D4—42no—
630D4—42no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—21no—
640C2×C4—24no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—48no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4C3×#12012yes—
664C2×C4C3×#12112yes—
665C2×C4C22×C3×D411yescharacteristic
666C2×C4C22×C3×D412yes—
667C2×C4C2×C3×#4111yescharacteristic
668C2×C4C3×H(5,𝔽2)12yes—
669C8—24no—
670C8—42no—
671C2×C3—24no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—84no—
675C2×C3#241011yescharacteristic
676C2×C3#300311yescharacteristic
677C2×C3#300711yescharacteristic
678C2×C3C2×#46811yescharacteristic
679C2×C3#305511yescharacteristic
680C2×C3#319311yescharacteristic
681C2×C3#319411yescharacteristic
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—416no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—44no—
704C22—44no—
705C22—44no—
706C22—816no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22C3×#46814yescomplemented
712C22C2×C3×#12011yescharacteristic
713C22C2×C3×#12111yescharacteristic
714C22C3×#53411yescharacteristic
715C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
716C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
717C22C2×C3×#13711yescharacteristic
718C22C3×#57511yescharacteristic
719C4—22no—
720C4—22no—
721C4—41no—
722C4—44no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4C3×D4212yes—
728C4C3×#54612yes—
729C3#2438511yescharacteristic, direct product factor, Sylow
730C2—24no—
731C2—42no—
732C2—42no—
733C2—84no—
734C2C3×#241011yescharacteristic
735C2C3×#300311yescharacteristic
736C2C3×#300711yescharacteristic
737C2C2×C3×#46811yescharacteristic
738C2C3×#305511yescharacteristic
739C2C3×#319311yescharacteristic
740C2C3×#319411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#121C2
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
2. C2×C3×#468C2semidirect
3. C2×C3×#450C2semidirect
4. C2×C3×#407C2semidirect
5. C3×#2848C2semidirect
6. C3×#2033C2semidirect
7. C3×#2000C2semidirect
8. C3×#1895C2semidirect
9. C3×#1872C2semidirect
10. C3×#1852C2semidirect
11. C3×#1786C2semidirect
12. #24385C3direct (N × H)
16. C22×C3×SD16C22semidirect
17. C22×C3×M16C22semidirect
19. C2×C3×C22⋊Q8C22semidirect
20. C2×C3×C22⋊Q8C22semidirect
30. C2×C3×#107C22semidirect
31. C2×C3×#103C22semidirect
32. C2×C3×#102C22semidirect
33. C2×C3×#102C22semidirect
34. C2×C3×#102C22semidirect
38. C2×C3×C22⋊C8C22semidirect
43. C3×#380C22semidirect
44. C3×#380C22semidirect
46. C3×#340C22semidirect
47. C3×#340C22semidirect
49. C2×#468C2×C3semidirect
50. C2×#450C2×C3semidirect
51. C2×#407C2×C3semidirect
52. #2848C2×C3semidirect
53. #2033C2×C3semidirect
54. #2000C2×C3semidirect
55. #1895C2×C3semidirect
56. #1872C2×C3semidirect
57. #1852C2×C3semidirect
58. #1786C2×C3semidirect
127. C3×C22⋊C8D4semidirect
134. C22×SD16C22×C3semidirect
135. C22×M16C22×C3semidirect
137. C2×C22⋊Q8C22×C3semidirect
138. C2×C22⋊Q8C22×C3semidirect
148. C2×#107C22×C3semidirect
149. C2×#103C22×C3semidirect
150. C2×#102C22×C3semidirect
151. C2×#102C22×C3semidirect
152. C2×#102C22×C3semidirect
156. C2×C22⋊C8C22×C3semidirect
161. #380C22×C3semidirect
162. #380C22×C3semidirect
164. #340C22×C3semidirect
165. #340C22×C3semidirect
248. C2×C3×C8C2×D4semidirect
335. C22⋊C8C3×D4semidirect
513. C2×C8C2×C3×D4semidirect
561. C22×C3#468semidirect
711. C22C3×#468semidirect
729. C3#24385direct (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×#4682
C2×C3×#4502
C2×C3×#4072
C3×#28482
C3×#20332
C3×#20002
C3×#18952
C3×#18722
C3×#18522
C3×#17862
#243853