Finite Group Databasebeta

← #10796705

Subgroups — #10796705

Order 768.

1778 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic
2C2×#5827C211yesmaximal, characteristic, complemented
3#84087C211yesmaximal, characteristic, complemented
4C2×#5236C211yesmaximal, characteristic, complemented
5#84072C211yesmaximal, characteristic, complemented
6#72100C214yesmaximal, complemented
7#72088C214yesmaximal, complemented
8C2×#4554C211yesmaximal, characteristic, complemented
9#71982C211yesmaximal, characteristic, complemented
10#20943—31nomaximal, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C3×#575—24no—
14C3×#575C418yescomplemented
15C2×C3×#137—21no—
16C2×C3×#137C2212yes—
17C2×C3×AGL(1,ℤ/8)—21no—
18C2×C3×AGL(1,ℤ/8)C2212yes—
19C2×C3×#135—22no—
20C22×C3×M16C2211yescharacteristic
21#5827—22no—
22#5827—22no—
23#5827—22no—
24#5827C2214yes—
25C2×Q8×Dic3—21no—
26C2×D4×Dic3—21no—
27C2×D4×Dic3—22no—
28C2×#926—21no—
29C2×#926C2211yescharacteristic
30C2×#926C2211yescharacteristic
31C22×C4⋊Dic3—21no—
32C22×C4⋊Dic3C2211yescharacteristic
33C22×#208C2211yescharacteristic
34#5236—24no—
35C2×#837C2214yes—
36#5233—22no—
37#5232—21no—
38#5232—21no—
39#5229C2212yescomplemented
40#5225C2212yescomplemented
41#5221C2212yescomplemented
42#5220—22no—
43#5215C2212yescomplemented
44#5212—22no—
45#4555C2214yescomplemented
46#4554C2214yescomplemented
47C2×#575D311yescharacteristic
48C2×#520—31no—
49C2×#421—31no—
50#2896—31no—
51#2311—31no—
52#1883—34no—
53#1882—34no—
54C2×#343—31no—
55#1733—31no—
56C2×C3×#41—21no—
57C2×C3×#41—21no—
58C2×C3×#41—22no—
59C2×C3×#41—22no—
60C2×C3×#41—22no—
61C2×C3×#41—21no—
62C2×C3×#41—21no—
63C2×C3×#41—22no—
64C2×C3×#41—21no—
65C2×C3×#41—21no—
66C2×C3×#41—22no—
67C2×C3×#41C2×C414yes—
68C2×C3×#41C2×C414yescomplemented
69C2×C3×#41D414yes—
70C2×C3×#41D412yes—
71C2×C3×#41C2312yes—
72C22×C3×Q8D411yescharacteristic
73C22×C3×Q8C2311yescharacteristic
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4D411yescharacteristic
77C22×C3×D4C2311yescharacteristic
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C23×Dic3—22no—
82C23×Dic3D412yes—
83C3×#137—24no—
84C3×#137—28no—
85C3×#137C2×C418yescomplemented
86C3×AGL(1,ℤ/8)—24no—
87C3×AGL(1,ℤ/8)—28no—
88C3×AGL(1,ℤ/8)C2×C418yescomplemented
89C3×#135—216no—
90C2×C3×Q16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C2×C3×D8—22no—
94C2×C3×M16—21no—
95C2×C3×M16—22no—
96C2×C3×M16C2×C414yescomplemented
97C2×C3×M16C2312yes—
98C22×C3×C8—21no—
99C2×#217—22no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—24no—
103Q8×Dic3—24no—
104Q8×Dic3—24no—
105D4×Dic3—28no—
106D4×Dic3—24no—
107D4×Dic3—24no—
108D4×Dic3—28no—
109#926—24no—
110#926—21no—
111#926—21no—
112#926—24no—
113#926—22no—
114#926—22no—
115#926D412yes—
116#926C2312yes—
117C2×C4⋊Dic3—22no—
118C2×C4⋊Dic3—24no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—24no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3D412yes—
126C2×C4⋊Dic3D411yescharacteristic
127C2×C4⋊Dic3D411yescharacteristic
128C2×C4⋊Dic3C2312yes—
129C2×C4×Dic3—22no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3C2312yes—
132C2×#208—21no—
133C2×#208—22no—
134C2×#208—22no—
135C2×#208C2312yes—
136C22×C3⋊C8—21no—
137#837—28no—
138#835—22no—
139#835—22no—
140#832—22no—
141#832—22no—
142C3⋊#95—24no—
143C22×#41C2×D311yescharacteristic
144C22×#41C2×D311yescharacteristic
145#575—24no—
146#575Dic318yescomplemented
147C2×#137—21no—
148C2×#137C2×D312yes—
149C2×AGL(1,ℤ/8)—21no—
150C2×AGL(1,ℤ/8)C2×D312yes—
151C2×#135—22no—
152C22×M16—31no—
153C22×M16C2×D311yescharacteristic
154#520—34no—
155#520—62no—
156#520—62no—
157#520—62no—
158C2×C4×Q8—61no—
159C2×C4×D4—62no—
160C2×C4×D4—61no—
161C2×#117—31no—
162C2×#117—31no—
163C2×#117—61no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—61no—
166#421—64no—
167C2×#104—34no—
168#419—32no—
169#418—32no—
170#417—61no—
171#417—61no—
172#416—62no—
173#391—32no—
174#390—32no—
175#386—62no—
176#380—62no—
177#343—34no—
178#339—34no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3C2×D411yescharacteristic
182C3×#41—24no—
183C3×#41—24no—
184C3×#41—24no—
185C3×#41—24no—
186C3×#41—24no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—24no—
190C3×#41—24no—
191C3×#41—24no—
192C3×#41—24no—
193C3×#41—42no—
194C3×#41—42no—
195C3×#41—42no—
196C3×#41—42no—
197C3×#41C22⋊C418yescomplemented
198C3×#41C22×C414yes—
199C3×#41C2×D414yes—
200C2×C3×Q8—21no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8C22⋊C414yescomplemented
208C2×C3×Q8C22×C412yescomplemented
209C2×C3×Q8C2×D412yes—
210C2×C3×D4—24no—
211C2×C3×D4—22no—
212C2×C3×D4—24no—
213C2×C3×D4—22no—
214C2×C3×D4—24no—
215C2×C3×D4—21no—
216C2×C3×D4—22no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—41no—
223C2×C3×D4—41no—
224C2×C3×D4—42no—
225C2×C3×D4C22⋊C414yescomplemented
226C2×C3×D4C22×C412yescomplemented
227C2×C3×D4C2×D412yes—
228C22×C3×C4—21no—
229C22×C3×C4—24no—
230C22×C3×C4—22no—
231C22×C3×C4—24no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
235C22×C3×C4—41no—
236C22×C3×C4—41no—
237C22×C3×C4—42no—
238C22×C3×C4C22×C412yes—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D412yes—
245C22×C3×C4#4112yes—
246C22×C3×C4#4112yes—
247C22×C3×C4C2411yescharacteristic
248C22×Dic3—21no—
249C22×Dic3—22no—
250C22×Dic3—21no—
251C22×Dic3—28no—
252C22×Dic3—22no—
253C22×Dic3—22no—
254C22×Dic3—82no—
255C22×Dic3—84no—
256C22×Dic3C2×D414yes—
257C3×Q16—28no—
258C3×SD16—28no—
259C3×SD16—28no—
260C3×D8—28no—
261C3×M16—24no—
262C3×M16—22no—
263C3×M16C22×C414yescomplemented
264C2×C3×C8—24no—
265C2×C3×C8—22no—
266#217—28no—
267#217—22no—
268#217—22no—
269#217—42no—
270#217—84no—
271C4⋊Dic3—28no—
272C4⋊Dic3—22no—
273C4⋊Dic3—21no—
274C4⋊Dic3—22no—
275C4⋊Dic3—21no—
276C4⋊Dic3—22no—
277C4⋊Dic3—22no—
278C4⋊Dic3—42no—
279C4⋊Dic3C2×D412yes—
280C4⋊Dic3C2×D412yes—
281C4×Dic3—28no—
282C4×Dic3—22no—
283C4×Dic3—22no—
284C4×Dic3—22no—
285C4×Dic3—22no—
286#208—22no—
287#208—22no—
288#208—42no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—42no—
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41—22no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—22no—
302C2×#41C2×Dic314yes—
303C2×#41C2×Dic314yescomplemented
304C2×#41#6714yes—
305C2×#41#6712yes—
306C2×#41C22×D312yes—
307C22×Q8#6711yescharacteristic
308C22×Q8C22×D311yescharacteristic
309C22×D4—21no—
310C22×D4—21no—
311C22×D4#6711yescharacteristic
312C22×D4C22×D311yescharacteristic
313C23×C4—21no—
314C23×C4—21no—
315C23×C4—32no—
316C23×C4—62no—
317C23×C4C22×D311yescharacteristic
318#137—24no—
319#137—28no—
320#137C2×Dic318yescomplemented
321AGL(1,ℤ/8)—24no—
322AGL(1,ℤ/8)—28no—
323AGL(1,ℤ/8)C2×Dic318yescomplemented
324#135—216no—
325C2×Q16—22no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×D8—22no—
329C2×M16—21no—
330C2×M16—22no—
331C2×M16—32no—
332C2×M16—61no—
333C2×M16—62no—
334C2×M16—62no—
335C2×M16C2×Dic314yescomplemented
336C2×M16C22×D312yes—
337C22×C8—21no—
338C22×C8—61no—
339C4×Q8—64no—
340C4×Q8—64no—
341C4×D4—68no—
342C4×D4—68no—
343C4×D4—64no—
344C4×D4—64no—
345#117—32no—
346#117—32no—
347#117—64no—
348#117—64no—
349#117—61no—
350#117—61no—
351#117—62no—
352#117—62no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—32no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—64no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—64no—
369C2×C42—32no—
370C2×C42—62no—
371C2×C42—61no—
372#104—68no—
373#103—62no—
374#103—62no—
375#102—62no—
376#102—62no—
377#95—64no—
378C23×C3—22no—
379C23×C3—24no—
380C23×C3—22no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3C4×D412yes—
390C23×C3#12011yescharacteristic
391C23×C3#12011yescharacteristic
392C23×C3#12112yes—
393C23×C3C22×D411yescharacteristic
394C3×Q8—22no—
395C3×Q8—24no—
396C3×Q8—22no—
397C3×Q8—22no—
398C3×Q8—41no—
399C3×Q8—41no—
400C3×Q8C2×C22⋊C414yes—
401C3×D4—24no—
402C3×D4—24no—
403C3×D4—28no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—22no—
407C3×D4—24no—
408C3×D4—44no—
409C3×D4—44no—
410C3×D4—41no—
411C3×D4—41no—
412C3×D4C2×C22⋊C414yes—
413C2×C3×C4—22no—
414C2×C3×C4—24no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—44no—
422C2×C3×C4—44no—
423C2×C3×C4C2×C22⋊C412yes—
424C2×C3×C4C2×C22⋊C412yes—
425C2×C3×C4C4×D412yes—
426C2×C3×C4C4×D412yes—
427C2×C3×C4C4×D412yes—
428C2×C3×C4#12011yescharacteristic
429C2×C3×C4#12011yescharacteristic
430C2×C3×C4#12112yes—
431C2×C3×C4#12112yes—
432C2×C3×C4#12112yes—
433C2×C3×C4#12312yes—
434C2×C3×C4#12312yes—
435C2×C3×C4C23×C411yescharacteristic
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×Dic3—22no—
442C2×Dic3—24no—
443C2×Dic3—22no—
444C2×Dic3—42no—
445C2×Dic3—44no—
446C2×Dic3—42no—
447C2×Dic3—44no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—82no—
452C2×Dic3—88no—
453C3×C8—24no—
454C3⋊C8—42no—
455C24—21no—
456C24—21no—
457C24D3×D411yescharacteristic
458#41—24no—
459#41—24no—
460#41—24no—
461#41—24no—
462#41—24no—
463#41—22no—
464#41—22no—
465#41—24no—
466#41—24no—
467#41—24no—
468#41—24no—
469#41—42no—
470#41—42no—
471#41—42no—
472#41—42no—
473#41#21718yescomplemented
474#41C22×Dic314yes—
475#41C2×#6714yes—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8#21714yescomplemented
484C2×Q8C22×Dic312yescomplemented
485C2×Q8C2×#6712yes—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—41no—
499C2×D4—41no—
500C2×D4—42no—
501C2×D4#21714yescomplemented
502C2×D4C22×Dic312yescomplemented
503C2×D4C2×#6712yes—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—34no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—62no—
518C22×C4—68no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—242no—
522C22×C4—244no—
523C22×C4D3×D411yescharacteristic
524C22×C4D3×D411yescharacteristic
525C22×C4D3×D411yescharacteristic
526C22×C4#23712yes—
527C22×C4#23712yes—
528C22×C4C22×Dic312yes—
529C22×C4C2×#6711yescharacteristic
530C22×C4C2×#6711yescharacteristic
531C22×C4C2×#6712yes—
532C22×C4C23×D311yescharacteristic
533Q16—28no—
534SD16—28no—
535SD16—28no—
536D8—28no—
537M16—24no—
538M16—22no—
539M16—62no—
540M16—62no—
541M16—122no—
542M16C22×Dic314yescomplemented
543C2×C8—24no—
544C2×C8—22no—
545C2×C8—62no—
546C2×C8—122no—
547C4⋊C4—32no—
548C4⋊C4—32no—
549C4⋊C4—68no—
550C4⋊C4—61no—
551C4⋊C4—62no—
552C4⋊C4—62no—
553C4⋊C4—61no—
554C4⋊C4—62no—
555C4⋊C4—62no—
556C4⋊C4—122no—
557C22⋊C4—68no—
558C22⋊C4—62no—
559C22⋊C4—62no—
560C22⋊C4—122no—
561C22⋊C4—244no—
562C42—68no—
563C42—62no—
564C42—62no—
565C42—62no—
566C42—62no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—24no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—48no—
577C22×C3—44no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—82no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3#38612yes—
585C22×C3#38612yes—
586C22×C3C2×C4×D411yescharacteristic
587C22×C3C2×#12011yescharacteristic
588C22×C3C2×#12111yescharacteristic
589C3×C4—24no—
590C3×C4—42no—
591C3×C4#38612yes—
592C3×C4#38612yes—
593C3×C4C22×C22⋊C411yescharacteristic
594C3×C4C2×C4×D411yescharacteristic
595C3×C4C2×#12111yescharacteristic
596C3×C4C2×#12311yescharacteristic
597Dic3—44no—
598Dic3—42no—
599Dic3—42no—
600Dic3—82no—
601C23—24no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23D4×Dic312yes—
613C23#93711yescharacteristic
614C23#93711yescharacteristic
615C23#93912yes—
616C23C2×D3×D411yescharacteristic
617Q8—24no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8C2×#21714yes—
624D4—28no—
625D4—24no—
626D4—24no—
627D4—24no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—44no—
632D4—44no—
633D4—41no—
634D4—41no—
635D4C2×#21714yes—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—28no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—64no—
649C2×C4—124no—
650C2×C4—122no—
651C2×C4—122no—
652C2×C4—124no—
653C2×C4—122no—
654C2×C4—122no—
655C2×C4—122no—
656C2×C4—242no—
657C2×C4—248no—
658C2×C4D4×Dic312yes—
659C2×C4D4×Dic312yes—
660C2×C4D4×Dic312yes—
661C2×C4#93512yes—
662C2×C4#93512yes—
663C2×C4#93711yescharacteristic
664C2×C4#93711yescharacteristic
665C2×C4#93912yes—
666C2×C4#93912yes—
667C2×C4#93912yes—
668C2×C4C2×#21712yes—
669C2×C4C2×#21712yes—
670C2×C4C2×D3×D411yescharacteristic
671C2×C4C2×#23711yescharacteristic
672C2×C4C2×#23711yescharacteristic
673C2×C4C23×Dic311yescharacteristic
674C2×C4C22×#6711yescharacteristic
675C2×C4C22×#6711yescharacteristic
676C8—24no—
677C8—122no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—22no—
681C2×C3—22no—
682C2×C3—44no—
683C2×C3—82no—
684C2×C3C2×#38611yescharacteristic
685C2×C3#301911yescharacteristic
686C2×C3#302011yescharacteristic
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—24no—
694C22—42no—
695C22—42no—
696C22—48no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—82no—
702C22—81no—
703C22—81no—
704C22#522012yes—
705C22#522012yes—
706C22C2×D4×Dic311yescharacteristic
707C22C2×#93711yescharacteristic
708C22C2×#93911yescharacteristic
709C4—24no—
710C4—42no—
711C4—124no—
712C4—122no—
713C4—122no—
714C4—242no—
715C4#522012yes—
716C4#522012yes—
717C4C2×D4×Dic311yescharacteristic
718C4C2×#93511yescharacteristic
719C4C2×#93911yescharacteristic
720C4C22×#21711yescharacteristic
721C3#2094311yescharacteristic, complemented, Sylow
722C2—21no—
723C2—22no—
724C2—21no—
725C2—22no—
726C2—44no—
727C2—82no—
728C2#8400511yescharacteristic
729C2#8400611yescharacteristic
730C2C2×#522011yescharacteristic
subgroupG/H
centerC22C2×#937
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
Fitting, prime radicalC2×C3×#575C2
socleC22×C3C2×#120
cosocleC22×C3×C4C24
hypercenterC2×#575D3
hypocenterC3#20943
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
2. C2×#5827C2semidirect
3. #84087C2semidirect
4. C2×#5236C2semidirect
5. #84072C2semidirect
6. #72100C2semidirect
7. #72088C2semidirect
8. C2×#4554C2semidirect
9. #71982C2semidirect
14. C3×#575C4semidirect
39. #5229C22semidirect
40. #5225C22semidirect
41. #5221C22semidirect
43. #5215C22semidirect
45. #4555C22semidirect
46. #4554C22semidirect
68. C2×C3×#41C2×C4semidirect
85. C3×#137C2×C4semidirect
88. C3×AGL(1,ℤ/8)C2×C4semidirect
96. C2×C3×M16C2×C4semidirect
146. #575Dic3semidirect
197. C3×#41C22⋊C4semidirect
207. C2×C3×Q8C22⋊C4semidirect
208. C2×C3×Q8C22×C4semidirect
225. C2×C3×D4C22⋊C4semidirect
226. C2×C3×D4C22×C4semidirect
263. C3×M16C22×C4semidirect
303. C2×#41C2×Dic3semidirect
320. #137C2×Dic3semidirect
323. AGL(1,ℤ/8)C2×Dic3semidirect
335. C2×M16C2×Dic3semidirect
473. #41#217semidirect
483. C2×Q8#217semidirect
484. C2×Q8C22×Dic3semidirect
501. C2×D4#217semidirect
502. C2×D4C22×Dic3semidirect
542. M16C22×Dic3semidirect
721. C3#20943semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×#58272
#840872
C2×#52362
#840722
#721002
#720882
C2×#45542
#719822
#209433