Finite Group Databasebeta

← C2×C3×#3006 #10678964

Subgroups — C2×C3×#3006 #10678964

Order 768.

5422 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#41C211yesmaximal, characteristic, complemented
2C22×C3×AGL(1,ℤ/8)C212yesmaximal, complemented
3C22×C3×#121C211yesmaximal, characteristic, complemented
4C3×#3006C2116yesmaximal, direct product factor
5C2×C3×#449C214yesmaximal, complemented
6C2×C3×#448C212yesmaximal, complemented
7C2×C3×#447C212yesmaximal, complemented
8C2×C3×#417C212yesmaximal, complemented
9C2×C3×#407C211yesmaximal, characteristic, complemented
10C2×#3006C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×#41—216no—
12C22×C3×#41—21no—
13C22×C3×#41—21no—
14C22×C3×#41—24no—
15C22×C3×#41C2212yes—
16C22×C3×#41C2212yescomplemented
17C22×C3×#41C2218yescomplemented
18C23×C3×Q8C2211yescharacteristic, complemented
19C23×C3×D4—21no—
20C23×C3×D4—21no—
21C23×C3×D4C2211yescharacteristic, complemented
22C23×C3×D4C2211yescharacteristic, complemented
23C24×C3×C4—21no—
24C24×C3×C4C2211yescharacteristic
25C2×C3×AGL(1,ℤ/8)—216no—
26C2×C3×AGL(1,ℤ/8)C22116yescomplemented
27C22×C3×SD16C2214yescomplemented
28C22×C3×D8C2214yescomplemented
29C22×C3×M16C2212yescomplemented
30C2×C3×#121—21no—
31C2×C3×#121—24no—
32C2×C3×#121—21no—
33C2×C3×#121C2212yes—
34C2×C3×#121C2212yescomplemented
35C2×C3×#121C2218yescomplemented
36C22×C3×C4⋊C4C2211yescharacteristic, complemented
37C22×C3×C22⋊C4—21no—
38C3×#449C22132yescomplemented
39C3×#448C22116yescomplemented
40C3×#447C22116yescomplemented
41C3×#417C22116yescomplemented
42C2×C3×#103C2214yescomplemented
43C2×C3×#102C2214yescomplemented
44C3×#407C2218yescomplemented
45C2×C3×C22⋊C8C2212yescomplemented
46C2×C3×C22⋊C8C2212yescomplemented
47C23×#41C2×C311yescharacteristic, complemented
48C22×AGL(1,ℤ/8)C2×C312yescomplemented
49C22×#121C2×C311yescharacteristic, complemented
50#3006C2×C3116yesdirect product factor
51C2×#449C2×C314yescomplemented
52C2×#448C2×C312yescomplemented
53C2×#447C2×C312yescomplemented
54C2×#417C2×C312yescomplemented
55C2×#407C2×C311yescharacteristic, complemented
56C25×C3—21no—
57C25×C3—21no—
58C25×C3D411yescharacteristic
59C2×C3×#41—216no—
60C2×C3×#41—264no—
61C2×C3×#41—216no—
62C2×C3×#41—264no—
63C2×C3×#41—28no—
64C2×C3×#41—28no—
65C2×C3×#41—28no—
66C2×C3×#41—24no—
67C2×C3×#41—28no—
68C2×C3×#41—28no—
69C2×C3×#41—24no—
70C2×C3×#41D4116yescomplemented
71C2×C3×#41C2318yes—
72C2×C3×#41C2318yescomplemented
73C22×C3×Q8—28no—
74C22×C3×Q8—22no—
75C22×C3×Q8—21no—
76C22×C3×Q8C2312yes—
77C22×C3×Q8C2314yescomplemented
78C22×C3×D4—216no—
79C22×C3×D4—22no—
80C22×C3×D4—28no—
81C22×C3×D4—22no—
82C22×C3×D4—28no—
83C22×C3×D4—22no—
84C22×C3×D4—28no—
85C22×C3×D4—22no—
86C22×C3×D4—22no—
87C22×C3×D4—21no—
88C22×C3×D4—28no—
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4—48no—
92C22×C3×D4C2312yes—
93C22×C3×D4C2312yes—
94C22×C3×D4C2314yescomplemented
95C22×C3×D4C2314yescomplemented
96C23×C3×C4—216no—
97C23×C3×C4—21no—
98C23×C3×C4—22no—
99C23×C3×C4—28no—
100C23×C3×C4—22no—
101C23×C3×C4—28no—
102C23×C3×C4—21no—
103C23×C3×C4D411yescharacteristic
104C23×C3×C4D411yescharacteristic
105C23×C3×C4D414yes—
106C23×C3×C4D411yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2314yes—
110C23×C3×C4C2311yescharacteristic
111C3×AGL(1,ℤ/8)—264no—
112C2×C3×SD16—216no—
113C2×C3×SD16C23116yescomplemented
114C2×C3×D8—216no—
115C2×C3×D8C23116yescomplemented
116C2×C3×M16—28no—
117C2×C3×M16C2318yescomplemented
118C22×C3×C8C2314yes—
119C3×#121—24no—
120C3×#121—28no—
121C3×#121—24no—
122C3×#121—28no—
123C3×#121C2318yes—
124C3×#121C2318yescomplemented
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2314yescomplemented
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—28no—
131C2×C3×C22⋊C4—22no—
132C3×#103C23116yescomplemented
133C3×#102C23116yescomplemented
134C3×C22⋊C8C2318yescomplemented
135C3×C22⋊C8C2318yescomplemented
136C22×#41—216no—
137C22×#41—21no—
138C22×#41—21no—
139C22×#41—24no—
140C22×#41C22×C312yes—
141C22×#41C22×C312yescomplemented
142C22×#41C22×C318yescomplemented
143C23×Q8C22×C311yescharacteristic, complemented
144C23×D4—21no—
145C23×D4—21no—
146C23×D4C22×C311yescharacteristic, complemented
147C23×D4C22×C311yescharacteristic, complemented
148C24×C4—21no—
149C24×C4C22×C311yescharacteristic
150C2×AGL(1,ℤ/8)—216no—
151C2×AGL(1,ℤ/8)C22×C3116yescomplemented
152C22×SD16C22×C314yescomplemented
153C22×D8C22×C314yescomplemented
154C22×M16C22×C312yescomplemented
155C2×#121—21no—
156C2×#121—24no—
157C2×#121—21no—
158C2×#121C22×C312yes—
159C2×#121C22×C312yescomplemented
160C2×#121C22×C318yescomplemented
161C22×C4⋊C4C22×C311yescharacteristic, complemented
162C22×C22⋊C4—21no—
163#449C22×C3132yescomplemented
164#448C22×C3116yescomplemented
165#447C22×C3116yescomplemented
166#417C22×C3116yescomplemented
167C2×#103C22×C314yescomplemented
168C2×#102C22×C314yescomplemented
169#407C22×C318yescomplemented
170C2×C22⋊C8C22×C312yescomplemented
171C2×C22⋊C8C22×C312yescomplemented
172C24×C3—28no—
173C24×C3—24no—
174C24×C3—24no—
175C24×C3—24no—
176C24×C3—22no—
177C24×C3—24no—
178C24×C3—22no—
179C24×C3—42no—
180C24×C3—44no—
181C24×C3—44no—
182C24×C3—44no—
183C24×C3—44no—
184C24×C3—44no—
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D414yes—
187C24×C3C2×D411yescharacteristic
188C24×C3C2×D411yescharacteristic
189C3×#41—264no—
190C3×#41—232no—
191C3×#41—264no—
192C3×#41—216no—
193C3×#41—216no—
194C3×#41—232no—
195C3×#41—216no—
196C3×#41C2×D4132yescomplemented
197C2×C3×Q8—216no—
198C2×C3×Q8—28no—
199C2×C3×Q8—216no—
200C2×C3×Q8—24no—
201C2×C3×Q8—22no—
202C2×C3×Q8—24no—
203C2×C3×Q8C2×D418yescomplemented
204C2×C3×Q8C2414yes—
205C2×C3×D4—264no—
206C2×C3×D4—216no—
207C2×C3×D4—28no—
208C2×C3×D4—216no—
209C2×C3×D4—216no—
210C2×C3×D4—28no—
211C2×C3×D4—28no—
212C2×C3×D4—216no—
213C2×C3×D4—28no—
214C2×C3×D4—28no—
215C2×C3×D4—22no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—28no—
219C2×C3×D4—216no—
220C2×C3×D4—22no—
221C2×C3×D4—24no—
222C2×C3×D4—432no—
223C2×C3×D4—48no—
224C2×C3×D4—48no—
225C2×C3×D4—44no—
226C2×C3×D4—48no—
227C2×C3×D4C2×D418yescomplemented
228C2×C3×D4C2414yes—
229C2×C3×D4C2414yes—
230C22×C3×C4—28no—
231C22×C3×C4—264no—
232C22×C3×C4—216no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—22no—
236C22×C3×C4—24no—
237C22×C3×C4—216no—
238C22×C3×C4—24no—
239C22×C3×C4—216no—
240C22×C3×C4—28no—
241C22×C3×C4—28no—
242C22×C3×C4—24no—
243C22×C3×C4—24no—
244C22×C3×C4—216no—
245C22×C3×C4—24no—
246C22×C3×C4—22no—
247C22×C3×C4—44no—
248C22×C3×C4C2×D414yes—
249C22×C3×C4C2×D414yes—
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2×D414yes—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D412yes—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D418yes—
258C22×C3×C4C2412yes—
259C22×C3×C4C2412yes—
260C22×C3×C4C2412yes—
261C22×C3×C4C2411yescharacteristic
262C3×SD16—232no—
263C3×D8—232no—
264C3×M16—216no—
265C2×C3×C8—28no—
266C2×C3×C8C2418yes—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4C2414yes—
270C3×C22⋊C4—28no—
271C3×C22⋊C4—28no—
272C25—21no—
273C25—21no—
274C25C3×D411yescharacteristic
275C2×#41—216no—
276C2×#41—264no—
277C2×#41—216no—
278C2×#41—264no—
279C2×#41—28no—
280C2×#41—28no—
281C2×#41—28no—
282C2×#41—24no—
283C2×#41—28no—
284C2×#41—28no—
285C2×#41—24no—
286C2×#41C3×D4116yescomplemented
287C2×#41C23×C318yes—
288C2×#41C23×C318yescomplemented
289C22×Q8—28no—
290C22×Q8—21no—
291C22×Q8—22no—
292C22×Q8C23×C312yes—
293C22×Q8C23×C314yescomplemented
294C22×D4—216no—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—28no—
298C22×D4—28no—
299C22×D4—22no—
300C22×D4—22no—
301C22×D4—28no—
302C22×D4—21no—
303C22×D4—22no—
304C22×D4—28no—
305C22×D4—21no—
306C22×D4—22no—
307C22×D4—48no—
308C22×D4C23×C312yes—
309C22×D4C23×C312yes—
310C22×D4C23×C314yescomplemented
311C22×D4C23×C314yescomplemented
312C23×C4—216no—
313C23×C4—21no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—28no—
317C23×C4—28no—
318C23×C4—21no—
319C23×C4C3×D411yescharacteristic
320C23×C4C3×D411yescharacteristic
321C23×C4C3×D411yescharacteristic
322C23×C4C3×D414yes—
323C23×C4C23×C311yescharacteristic
324C23×C4C23×C311yescharacteristic
325C23×C4C23×C314yes—
326C23×C4C23×C311yescharacteristic
327AGL(1,ℤ/8)—264no—
328C2×SD16—216no—
329C2×SD16C23×C3116yescomplemented
330C2×D8—216no—
331C2×D8C23×C3116yescomplemented
332C2×M16—28no—
333C2×M16C23×C318yescomplemented
334C22×C8C23×C314yes—
335#121—24no—
336#121—28no—
337#121—24no—
338#121—28no—
339#121C23×C318yes—
340#121C23×C318yescomplemented
341C2×C4⋊C4—22no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4C23×C312yes—
344C2×C4⋊C4C23×C314yescomplemented
345C2×C22⋊C4—22no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—22no—
348#103C23×C3116yescomplemented
349#102C23×C3116yescomplemented
350C22⋊C8C23×C318yescomplemented
351C22⋊C8C23×C318yescomplemented
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—216no—
357C23×C3—28no—
358C23×C3—22no—
359C23×C3—28no—
360C23×C3—22no—
361C23×C3—28no—
362C23×C3—22no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—44no—
366C23×C3—416no—
367C23×C3—432no—
368C23×C3—48no—
369C23×C3—48no—
370C23×C3—48no—
371C23×C3—44no—
372C23×C3—48no—
373C23×C3—44no—
374C23×C3—48no—
375C23×C3—44no—
376C23×C3—44no—
377C23×C3—44no—
378C23×C3—816no—
379C23×C3#12014yes—
380C23×C3AGL(1,ℤ/8)14yescomplemented
381C23×C3C22×D412yes—
382C23×C3C22×D412yes—
383C23×C3C22×D412yes—
384C23×C3C22×D411yescharacteristic
385C3×Q8—216no—
386C3×Q8—28no—
387C3×Q8—24no—
388C3×Q8C22×D418yescomplemented
389C3×D4—232no—
390C3×D4—216no—
391C3×D4—232no—
392C3×D4—28no—
393C3×D4—24no—
394C3×D4—28no—
395C3×D4—416no—
396C3×D4—416no—
397C3×D4—48no—
398C3×D4—44no—
399C3×D4C22×D418yescomplemented
400C2×C3×C4—216no—
401C2×C3×C4—232no—
402C2×C3×C4—22no—
403C2×C3×C4—28no—
404C2×C3×C4—22no—
405C2×C3×C4—28no—
406C2×C3×C4—24no—
407C2×C3×C4—28no—
408C2×C3×C4—232no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—28no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—24no—
415C2×C3×C4—48no—
416C2×C3×C4—44no—
417C2×C3×C4#12014yes—
418C2×C3×C4#12018yes—
419C2×C3×C4C22×D412yes—
420C2×C3×C4C22×D412yes—
421C2×C3×C4C22×D412yes—
422C2×C3×C4C22×D411yescharacteristic
423C2×C3×C4C22×D414yes—
424C2×C3×C4C22×D418yes—
425C2×C3×C4C2511yescharacteristic
426C3×C8—28no—
427C24—28no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—42no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—44no—
440C24C2×C3×D411yescharacteristic
441C24C2×C3×D414yes—
442C24C2×C3×D411yescharacteristic
443C24C2×C3×D411yescharacteristic
444#41—264no—
445#41—232no—
446#41—264no—
447#41—216no—
448#41—216no—
449#41—232no—
450#41—216no—
451#41C2×C3×D4132yescomplemented
452C2×Q8—216no—
453C2×Q8—28no—
454C2×Q8—216no—
455C2×Q8—22no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8C2×C3×D418yescomplemented
459C2×Q8C24×C314yes—
460C2×D4—264no—
461C2×D4—216no—
462C2×D4—28no—
463C2×D4—216no—
464C2×D4—216no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—216no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—28no—
474C2×D4—216no—
475C2×D4—22no—
476C2×D4—24no—
477C2×D4—432no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4C2×C3×D418yescomplemented
483C2×D4C24×C314yes—
484C2×D4C24×C314yes—
485C22×C4—28no—
486C22×C4—264no—
487C22×C4—216no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—216no—
493C22×C4—24no—
494C22×C4—216no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—216no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—44no—
503C22×C4C2×C3×D411yescharacteristic
504C22×C4C2×C3×D411yescharacteristic
505C22×C4C2×C3×D414yes—
506C22×C4C2×C3×D414yes—
507C22×C4C2×C3×D412yes—
508C22×C4C2×C3×D412yes—
509C22×C4C2×C3×D414yes—
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D412yes—
512C22×C4C2×C3×D418yes—
513C22×C4C24×C312yes—
514C22×C4C24×C312yes—
515C22×C4C24×C311yescharacteristic
516C22×C4C24×C312yes—
517SD16—232no—
518D8—232no—
519M16—216no—
520C2×C8—28no—
521C2×C8C24×C318yes—
522C4⋊C4—22no—
523C4⋊C4—24no—
524C4⋊C4C24×C314yes—
525C22⋊C4—28no—
526C22⋊C4—28no—
527C22×C3—22no—
528C22×C3—28no—
529C22×C3—28no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—28no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—416no—
538C22×C3—432no—
539C22×C3—44no—
540C22×C3—416no—
541C22×C3—44no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—44no—
546C22×C3—816no—
547C22×C3—88no—
548C22×C3C2×#12014yes—
549C22×C3C2×#12012yes—
550C22×C3C2×AGL(1,ℤ/8)12yes—
551C22×C3C2×AGL(1,ℤ/8)14yescomplemented
552C22×C3#57512yes—
553C22×C3C23×D411yescharacteristic
554C3×C4—22no—
555C3×C4—28no—
556C3×C4—22no—
557C3×C4—44no—
558C3×C4C2×#12014yes—
559C3×C4C2×#12012yes—
560C3×C4C23×D412yes—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—216no—
566C23—22no—
567C23—28no—
568C23—22no—
569C23—24no—
570C23—28no—
571C23—22no—
572C23—28no—
573C23—24no—
574C23—44no—
575C23—416no—
576C23—432no—
577C23—48no—
578C23—48no—
579C23—48no—
580C23—44no—
581C23—48no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—48no—
586C23—44no—
587C23—816no—
588C23C3×#12014yes—
589C23C3×AGL(1,ℤ/8)14yescomplemented
590C23C22×C3×D412yes—
591C23C22×C3×D412yes—
592C23C22×C3×D412yes—
593C23C22×C3×D411yescharacteristic
594Q8—216no—
595Q8—24no—
596Q8—28no—
597Q8C22×C3×D418yescomplemented
598D4—232no—
599D4—216no—
600D4—232no—
601D4—24no—
602D4—28no—
603D4—28no—
604D4—416no—
605D4—416no—
606D4—48no—
607D4—44no—
608D4C22×C3×D418yescomplemented
609C2×C4—216no—
610C2×C4—232no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—28no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—28no—
619C2×C4—232no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—28no—
623C2×C4—24no—
624C2×C4—48no—
625C2×C4—44no—
626C2×C4C3×#12014yes—
627C2×C4C3×#12018yes—
628C2×C4C22×C3×D412yes—
629C2×C4C22×C3×D412yes—
630C2×C4C22×C3×D414yes—
631C2×C4C22×C3×D418yes—
632C2×C4C22×C3×D412yes—
633C2×C4C22×C3×D411yescharacteristic
634C2×C4C25×C311yescharacteristic
635C8—28no—
636C2×C3—24no—
637C2×C3—24no—
638C2×C3—42no—
639C2×C3—48no—
640C2×C3—84no—
641C2×C3#300614yesdirect product factor
642C2×C3C22×#12011yescharacteristic
643C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C3C2×#57511yescharacteristic
645C22—22no—
646C22—28no—
647C22—28no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—28no—
653C22—22no—
654C22—22no—
655C22—416no—
656C22—432no—
657C22—44no—
658C22—416no—
659C22—44no—
660C22—44no—
661C22—44no—
662C22—44no—
663C22—44no—
664C22—816no—
665C22—88no—
666C22C2×C3×#12014yes—
667C22C2×C3×#12012yes—
668C22C2×C3×AGL(1,ℤ/8)12yes—
669C22C2×C3×AGL(1,ℤ/8)14yescomplemented
670C22C3×#57512yes—
671C22C23×C3×D411yescharacteristic
672C4—22no—
673C4—28no—
674C4—22no—
675C4—44no—
676C4C2×C3×#12014yes—
677C4C2×C3×#12012yes—
678C4C23×C3×D412yes—
679C3C2×#300611yescharacteristic, direct product factor, Sylow
680C2—24no—
681C2—24no—
682C2—42no—
683C2—48no—
684C2—84no—
685C2C3×#300614yesdirect product factor
686C2C22×C3×#12011yescharacteristic
687C2C22×C3×AGL(1,ℤ/8)11yescharacteristic
688C2C2×C3×#57511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC2×C4C25×C3
LCSG ▷ C2×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. C23×C3×#41C2semidirect
2. C22×C3×AGL(1,ℤ/8)C2semidirect
3. C22×C3×#121C2semidirect
4. C3×#3006C2direct (N × H)
5. C2×C3×#449C2semidirect
6. C2×C3×#448C2semidirect
7. C2×C3×#447C2semidirect
8. C2×C3×#417C2semidirect
9. C2×C3×#407C2semidirect
10. C2×#3006C3direct (N × H)
16. C22×C3×#41C22semidirect
17. C22×C3×#41C22semidirect
18. C23×C3×Q8C22semidirect
21. C23×C3×D4C22semidirect
22. C23×C3×D4C22semidirect
26. C2×C3×AGL(1,ℤ/8)C22semidirect
27. C22×C3×SD16C22semidirect
28. C22×C3×D8C22semidirect
29. C22×C3×M16C22semidirect
34. C2×C3×#121C22semidirect
35. C2×C3×#121C22semidirect
36. C22×C3×C4⋊C4C22semidirect
38. C3×#449C22semidirect
39. C3×#448C22semidirect
40. C3×#447C22semidirect
41. C3×#417C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C3×#407C22semidirect
45. C2×C3×C22⋊C8C22semidirect
46. C2×C3×C22⋊C8C22semidirect
47. C23×#41C2×C3semidirect
48. C22×AGL(1,ℤ/8)C2×C3semidirect
49. C22×#121C2×C3semidirect
50. #3006C2×C3direct (N × H)
51. C2×#449C2×C3semidirect
52. C2×#448C2×C3semidirect
53. C2×#447C2×C3semidirect
54. C2×#417C2×C3semidirect
55. C2×#407C2×C3semidirect
70. C2×C3×#41D4semidirect
72. C2×C3×#41C23semidirect
77. C22×C3×Q8C23semidirect
94. C22×C3×D4C23semidirect
95. C22×C3×D4C23semidirect
113. C2×C3×SD16C23semidirect
115. C2×C3×D8C23semidirect
117. C2×C3×M16C23semidirect
124. C3×#121C23semidirect
128. C2×C3×C4⋊C4C23semidirect
132. C3×#103C23semidirect
133. C3×#102C23semidirect
134. C3×C22⋊C8C23semidirect
135. C3×C22⋊C8C23semidirect
141. C22×#41C22×C3semidirect
142. C22×#41C22×C3semidirect
143. C23×Q8C22×C3semidirect
146. C23×D4C22×C3semidirect
147. C23×D4C22×C3semidirect
151. C2×AGL(1,ℤ/8)C22×C3semidirect
152. C22×SD16C22×C3semidirect
153. C22×D8C22×C3semidirect
154. C22×M16C22×C3semidirect
159. C2×#121C22×C3semidirect
160. C2×#121C22×C3semidirect
161. C22×C4⋊C4C22×C3semidirect
163. #449C22×C3semidirect
164. #448C22×C3semidirect
165. #447C22×C3semidirect
166. #417C22×C3semidirect
167. C2×#103C22×C3semidirect
168. C2×#102C22×C3semidirect
169. #407C22×C3semidirect
170. C2×C22⋊C8C22×C3semidirect
171. C2×C22⋊C8C22×C3semidirect
196. C3×#41C2×D4semidirect
203. C2×C3×Q8C2×D4semidirect
227. C2×C3×D4C2×D4semidirect
286. C2×#41C3×D4semidirect
288. C2×#41C23×C3semidirect
293. C22×Q8C23×C3semidirect
310. C22×D4C23×C3semidirect
311. C22×D4C23×C3semidirect
329. C2×SD16C23×C3semidirect
331. C2×D8C23×C3semidirect
333. C2×M16C23×C3semidirect
340. #121C23×C3semidirect
344. C2×C4⋊C4C23×C3semidirect
348. #103C23×C3semidirect
349. #102C23×C3semidirect
350. C22⋊C8C23×C3semidirect
351. C22⋊C8C23×C3semidirect
380. C23×C3AGL(1,ℤ/8)semidirect
388. C3×Q8C22×D4semidirect
399. C3×D4C22×D4semidirect
451. #41C2×C3×D4semidirect
458. C2×Q8C2×C3×D4semidirect
482. C2×D4C2×C3×D4semidirect
551. C22×C3C2×AGL(1,ℤ/8)semidirect
589. C23C3×AGL(1,ℤ/8)semidirect
597. Q8C22×C3×D4semidirect
608. D4C22×C3×D4semidirect
641. C2×C3#3006direct (N × H)
669. C22C2×C3×AGL(1,ℤ/8)semidirect
679. C3C2×#3006direct (N × H)
685. C2C3×#3006direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#412
C22×C3×AGL(1,ℤ/8)2
C22×C3×#1212
C3×#30062
C2×C3×#4492
C2×C3×#4482
C2×C3×#4472
C2×C3×#4172
C2×C3×#4072
C2×#30063