Finite Group Databasebeta

← C3×#24379 #10642986

Subgroups — C3×#24379 #10642986

Order 768.

1924 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×#465C212yesmaximal, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C22×C3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#2848C211yesmaximal, characteristic, complemented
6C3×#2034C212yesmaximal, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1893C212yesmaximal, complemented
9C3×#1872C211yesmaximal, characteristic, complemented
10C3×#1853C211yesmaximal, characteristic, complemented
11C3×#1786C211yesmaximal, characteristic, complemented
12#24379C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4—21no—
14C23×C3×D4C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×C3×SD16C2212yescomplemented
17C23×C3×C8C2212yescomplemented
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×#465—28no—
29C3×#450—24no—
30C2×C3×#106C2212yescomplemented
31C2×C3×#103C2212yescomplemented
32C2×C3×#102C2212yescomplemented
33C2×C3×#102C2212yescomplemented
34C2×C3×#102C2212yescomplemented
35C2×C3×C22⋊C8—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×#465C2×C312yescomplemented
50C2×#450C2×C311yescharacteristic, complemented
51C22×C22⋊C8C2×C311yescharacteristic, complemented
52#2848C2×C311yescharacteristic, complemented
53#2034C2×C312yescomplemented
54#2000C2×C312yescomplemented
55#1893C2×C312yescomplemented
56#1872C2×C311yescharacteristic, complemented
57#1853C2×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—
87C22×C3×C8—24no—
88C22×C3×C8—24no—
89C22×C3×C8—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×#106—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
135C23×C8C22×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#465—28no—
147#450—24no—
148C2×#106C22×C312yescomplemented
149C2×#103C22×C312yescomplemented
150C2×#102C22×C312yescomplemented
151C2×#102C22×C312yescomplemented
152C2×#102C22×C312yescomplemented
153C2×C22⋊C8—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—22no—
170C24×C3—24no—
171C24×C3—22no—
172C24×C3—41no—
173C24×C3—41no—
174C24×C3—42no—
175C24×C3—42no—
176C24×C3—42no—
177C24×C3—42no—
178C24×C3—42no—
179C24×C3—42no—
180C24×C3SD1614yescomplemented
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—
242C2×C3×C8—22no—
243C2×C3×C8—22no—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—48no—
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—
295C22×C8—24no—
296C22×C8—24no—
297C22×C8—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#106—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—21no—
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—28no—
354C23×C3—28no—
355C23×C3—24no—
356C23×C3—44no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—44no—
361C23×C3—48no—
362C23×C3—48no—
363C23×C3—48no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—84no—
371C23×C3—84no—
372C23×C3—84no—
373C23×C3—84no—
374C23×C3#12012yes—
375C23×C3#12112yes—
376C23×C3C2×SD1612yes—
377C23×C3C2×SD1612yes—
378C23×C3C2×SD1612yes—
379C23×C3#13512yes—
380C23×C3AGL(1,ℤ/8)12yes—
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—22no—
435C24—24no—
436C24—22no—
437C24—41no—
438C24—41no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24C3×SD1614yescomplemented
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—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—48no—
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—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—416no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—816no—
556C22×C3—82no—
557C22×C3—82no—
558C22×C3—82no—
559C22×C3—82no—
560C22×C3#45014yescomplemented
561C22×C3#46514yescomplemented
562C22×C3C2×#12011yescharacteristic
563C22×C3C2×#12111yescharacteristic
564C22×C3#53411yescharacteristic
565C22×C3C22×SD1611yescharacteristic
566C22×C3C2×#13511yescharacteristic
567C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
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—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—28no—
591C23—28no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—24no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23—44no—
600C23—44no—
601C23—48no—
602C23—48no—
603C23—48no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—84no—
611C23—84no—
612C23—84no—
613C23—84no—
614C23C3×#12012yes—
615C23C3×#12112yes—
616C23C2×C3×SD1612yes—
617C23C2×C3×SD1612yes—
618C23C2×C3×SD1612yes—
619C23C3×#13512yes—
620C23C3×AGL(1,ℤ/8)12yes—
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—24no—
673C2×C3—42no—
674C2×C3—84no—
675C2×C3#241011yescharacteristic
676C2×C3C2×#45011yescharacteristic
677C2×C3#300211yescharacteristic
678C2×C3C2×#46511yescharacteristic
679C2×C3#305511yescharacteristic
680C2×C3#318711yescharacteristic
681C2×C3#318811yescharacteristic
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—22no—
695C22—22no—
696C22—22no—
697C22—416no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—816no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22C3×#45014yescomplemented
711C22C3×#46514yescomplemented
712C22C2×C3×#12011yescharacteristic
713C22C2×C3×#12111yescharacteristic
714C22C3×#53411yescharacteristic
715C22C22×C3×SD1611yescharacteristic
716C22C2×C3×#13511yescharacteristic
717C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
718C22C3×#57511yescharacteristic
719C4—22no—
720C4—22no—
721C4—41no—
722C4—44no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4C3×D4212yes—
728C4C3×#54612yes—
729C3#2437911yescharacteristic, direct product factor, Sylow
730C2—24no—
731C2—24no—
732C2—42no—
733C2—84no—
734C2C3×#241011yescharacteristic
735C2C2×C3×#45011yescharacteristic
736C2C3×#300211yescharacteristic
737C2C2×C3×#46511yescharacteristic
738C2C3×#305511yescharacteristic
739C2C3×#318711yescharacteristic
740C2C3×#318811yescharacteristic
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×#465C2semidirect
3. C2×C3×#450C2semidirect
4. C22×C3×C22⋊C8C2semidirect
5. C3×#2848C2semidirect
6. C3×#2034C2semidirect
7. C3×#2000C2semidirect
8. C3×#1893C2semidirect
9. C3×#1872C2semidirect
10. C3×#1853C2semidirect
11. C3×#1786C2semidirect
12. #24379C3direct (N × H)
16. C22×C3×SD16C22semidirect
17. C23×C3×C8C22semidirect
19. C2×C3×C22⋊Q8C22semidirect
20. C2×C3×C22⋊Q8C22semidirect
30. C2×C3×#106C22semidirect
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×#465C2×C3semidirect
50. C2×#450C2×C3semidirect
51. C22×C22⋊C8C2×C3semidirect
52. #2848C2×C3semidirect
53. #2034C2×C3semidirect
54. #2000C2×C3semidirect
55. #1893C2×C3semidirect
56. #1872C2×C3semidirect
57. #1853C2×C3semidirect
58. #1786C2×C3semidirect
127. C3×C22⋊C8D4semidirect
134. C22×SD16C22×C3semidirect
135. C23×C8C22×C3semidirect
137. C2×C22⋊Q8C22×C3semidirect
138. C2×C22⋊Q8C22×C3semidirect
148. C2×#106C22×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
180. C24×C3SD16semidirect
248. C2×C3×C8C2×D4semidirect
335. C22⋊C8C3×D4semidirect
445. C24C3×SD16semidirect
513. C2×C8C2×C3×D4semidirect
560. C22×C3#450semidirect
561. C22×C3#465semidirect
710. C22C3×#450semidirect
711. C22C3×#465semidirect
729. C3#24379direct (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×#4652
C2×C3×#4502
C22×C3×C22⋊C82
C3×#28482
C3×#20342
C3×#20002
C3×#18932
C3×#18722
C3×#18532
C3×#17862
#243793