Finite Group Databasebeta

← C2×C3×#2002 #10642002

Subgroups — C2×C3×#2002 #10642002

Order 768.

2750 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C3×#535C211yesmaximal, characteristic, complemented
3C22×C3×#127C211yesmaximal, characteristic, complemented
4C22×C3×#104C211yesmaximal, characteristic, complemented
5C2×C3×#418C211yesmaximal, characteristic, complemented
6C22×C3×#100C211yesmaximal, characteristic, complemented
7C3×#2002C218yesmaximal, direct product factor
8C2×C3×#339C211yesmaximal, characteristic, complemented
9C2×#2002C311yesmaximal, characteristic, direct product factor, Sylow
10C22×C3×#41C2211yescharacteristic
11C23×C3×D4—22no—
12C23×C3×D4C2211yescharacteristic
13C23×C3×D4C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)—22no—
15C2×C3×AGL(1,ℤ/8)—24no—
16C2×C3×AGL(1,ℤ/8)—24no—
17C2×C3×AGL(1,ℤ/8)C2214yescomplemented
18C22×C3×SD16—21no—
19C22×C3×D8—21no—
20C22×C3×M16C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic
22C3×#535—22no—
23C3×#535—22no—
24C3×#535—22no—
25C3×#535C2214yescomplemented
26C2×C3×#127—22no—
27C2×C3×#127—24no—
28C2×C3×#127—21no—
29C2×C3×#127—24no—
30C2×C3×#127C2214yescomplemented
31C2×C3×#124—21no—
32C2×C3×#121—22no—
33C2×C3×#120—22no—
34C2×C3×#117C2211yescharacteristic
35C22×C3×C42C2211yescharacteristic
36C2×C3×#104—24no—
37C2×C3×#104C2214yescomplemented
38C3×#418—22no—
39C3×#418C2214yescomplemented
40C2×C3×#102—22no—
41C2×C3×#100—24no—
42C2×C3×#100C2214yescomplemented
43C3×#339C2214yescomplemented
44C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
45C2×#535C2×C311yescharacteristic, complemented
46C22×#127C2×C311yescharacteristic, complemented
47C22×#104C2×C311yescharacteristic, complemented
48C2×#418C2×C311yescharacteristic, complemented
49C22×#100C2×C311yescharacteristic, complemented
50#2002C2×C318yesdirect product factor
51C2×#339C2×C311yescharacteristic, complemented
52C25×C3—21no—
53C25×C3D412yes—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—22no—
57C2×C3×#41—22no—
58C2×C3×#41—22no—
59C2×C3×#41—22no—
60C2×C3×#41D412yescomplemented
61C2×C3×#41C2312yes—
62C22×C3×Q8D411yescharacteristic, complemented
63C22×C3×D4—216no—
64C22×C3×D4—28no—
65C22×C3×D4—21no—
66C22×C3×D4—24no—
67C22×C3×D4—21no—
68C22×C3×D4—21no—
69C22×C3×D4—22no—
70C22×C3×D4—21no—
71C22×C3×D4—21no—
72C22×C3×D4—22no—
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4—22no—
77C22×C3×D4—22no—
78C22×C3×D4—22no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—416no—
84C22×C3×D4D412yes—
85C22×C3×D4D411yescharacteristic, complemented
86C22×C3×D4D414yescomplemented
87C22×C3×D4C2312yes—
88C22×C3×D4C2312yes—
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C3×AGL(1,ℤ/8)—216no—
93C3×AGL(1,ℤ/8)—28no—
94C3×AGL(1,ℤ/8)—28no—
95C2×C3×SD16—28no—
96C2×C3×SD16—24no—
97C2×C3×D8—28no—
98C2×C3×D8—24no—
99C2×C3×M16—22no—
100C2×C3×M16—21no—
101C2×C3×M16—21no—
102C2×C3×M16—22no—
103C2×C3×M16—22no—
104C2×C3×M16D414yescomplemented
105C2×C3×M16C2312yes—
106C2×C3×M16C2312yes—
107C22×C3×C8—21no—
108C22×C3×C8—21no—
109C3×#127—216no—
110C3×#127—24no—
111C3×#127—28no—
112C3×#127—24no—
113C3×#127—28no—
114C3×#124—24no—
115C3×#124—24no—
116C3×#121—28no—
117C3×#121—28no—
118C3×#120—28no—
119C3×#120—28no—
120C3×#117—21no—
121C3×#117—21no—
122C3×#117D412yescomplemented
123C3×#117C2312yes—
124C2×C3×C4⋊C4D412yescomplemented
125C2×C3×C22⋊C4—24no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C42—21no—
128C2×C3×C42—22no—
129C2×C3×C42—21no—
130C2×C3×C42D414yescomplemented
131C2×C3×C42C2312yes—
132C3×#104—28no—
133C3×#102—28no—
134C3×#100—28no—
135C22×#41C22×C311yescharacteristic
136C23×D4—22no—
137C23×D4C22×C311yescharacteristic
138C23×D4C22×C311yescharacteristic
139C2×AGL(1,ℤ/8)—22no—
140C2×AGL(1,ℤ/8)—24no—
141C2×AGL(1,ℤ/8)—24no—
142C2×AGL(1,ℤ/8)C22×C314yescomplemented
143C22×SD16—21no—
144C22×D8—21no—
145C22×M16C22×C311yescharacteristic
146C22×M16C22×C311yescharacteristic
147#535—22no—
148#535—22no—
149#535—22no—
150#535C22×C314yescomplemented
151C2×#127—22no—
152C2×#127—24no—
153C2×#127—21no—
154C2×#127—24no—
155C2×#127C22×C314yescomplemented
156C2×#124—21no—
157C2×#121—22no—
158C2×#120—22no—
159C2×#117C22×C311yescharacteristic
160C22×C42C22×C311yescharacteristic
161C2×#104—24no—
162C2×#104C22×C314yescomplemented
163#418—22no—
164#418C22×C314yescomplemented
165C2×#102—22no—
166C2×#100—24no—
167C2×#100C22×C314yescomplemented
168#339C22×C314yescomplemented
169C24×C3—24no—
170C24×C3—24no—
171C24×C3—22no—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3—24no—
176C24×C3—48no—
177C24×C3—48no—
178C24×C3—41no—
179C24×C3—41no—
180C24×C3—42no—
181C24×C3C2×D411yescharacteristic
182C24×C3C2×D414yes—
183C3×#41—24no—
184C3×#41—24no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—22no—
188C3×#41—22no—
189C3×#41—42no—
190C3×#41—42no—
191C3×#41—42no—
192C3×#41—42no—
193C2×C3×Q8—21no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8C2×D412yescomplemented
197C2×C3×D4—232no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—216no—
201C2×C3×D4—22no—
202C2×C3×D4—24no—
203C2×C3×D4—24no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—24no—
207C2×C3×D4—24no—
208C2×C3×D4—21no—
209C2×C3×D4—24no—
210C2×C3×D4—24no—
211C2×C3×D4—22no—
212C2×C3×D4—24no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—22no—
224C2×C3×D4—432no—
225C2×C3×D4—464no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—42no—
229C2×C3×D4—42no—
230C2×C3×D4—41no—
231C2×C3×D4—41no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—42no—
243C2×C3×D4—88no—
244C2×C3×D4C2×D412yescomplemented
245C2×C3×D4C2×D414yescomplemented
246C22×C3×C4—28no—
247C22×C3×C4—24no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—22no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D412yes—
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4#4112yes—
264C22×C3×C4C2411yescharacteristic
265C3×SD16—216no—
266C3×D8—216no—
267C3×M16—24no—
268C3×M16—22no—
269C3×M16—22no—
270C3×M16—22no—
271C3×M16—42no—
272C3×M16C2×D414yescomplemented
273C2×C3×C8—24no—
274C2×C3×C8—22no—
275C2×C3×C8—22no—
276C2×C3×C8—42no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4C2×D414yescomplemented
279C3×C22⋊C4—216no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C42—24no—
283C3×C42—22no—
284C3×C42—22no—
285C3×C42—22no—
286C3×C42C2×D414yescomplemented
287C25—21no—
288C25C3×D412yes—
289C2×#41—21no—
290C2×#41—21no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41C3×D412yescomplemented
296C2×#41C23×C312yes—
297C22×Q8C3×D411yescharacteristic, complemented
298C22×D4—216no—
299C22×D4—21no—
300C22×D4—28no—
301C22×D4—24no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—22no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—416no—
319C22×D4C3×D412yes—
320C22×D4C3×D411yescharacteristic, complemented
321C22×D4C3×D414yescomplemented
322C22×D4C23×C312yes—
323C22×D4C23×C312yes—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C311yescharacteristic
327AGL(1,ℤ/8)—216no—
328AGL(1,ℤ/8)—28no—
329AGL(1,ℤ/8)—28no—
330C2×SD16—28no—
331C2×SD16—24no—
332C2×D8—28no—
333C2×D8—24no—
334C2×M16—22no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—22no—
338C2×M16—22no—
339C2×M16C3×D414yescomplemented
340C2×M16C23×C312yes—
341C2×M16C23×C312yes—
342C22×C8—21no—
343C22×C8—21no—
344#127—216no—
345#127—24no—
346#127—28no—
347#127—24no—
348#127—28no—
349#124—24no—
350#124—24no—
351#121—28no—
352#121—28no—
353#120—28no—
354#120—28no—
355#117—21no—
356#117—21no—
357#117C3×D412yescomplemented
358#117C23×C312yes—
359C2×C4⋊C4C3×D412yescomplemented
360C2×C22⋊C4—24no—
361C2×C22⋊C4—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—22no—
365C2×C42C3×D414yescomplemented
366C2×C42C23×C312yes—
367#104—28no—
368#102—28no—
369#100—28no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—48no—
377C23×C3—48no—
378C23×C3—416no—
379C23×C3—416no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—44no—
384C23×C3—44no—
385C23×C3—44no—
386C23×C3—44no—
387C23×C3—44no—
388C23×C3—48no—
389C23×C3—84no—
390C23×C3—88no—
391C23×C3—84no—
392C23×C3—88no—
393C23×C3—84no—
394C23×C3#12011yescharacteristic
395C23×C3#12012yes—
396C23×C3#12011yescharacteristic
397C23×C3#12112yes—
398C23×C3C22×D411yescharacteristic
399C3×Q8—22no—
400C3×Q8—22no—
401C3×Q8—42no—
402C3×D4—22no—
403C3×D4—24no—
404C3×D4—24no—
405C3×D4—22no—
406C3×D4—464no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—44no—
410C3×D4—42no—
411C3×D4—42no—
412C3×D4—42no—
413C3×D4—42no—
414C3×D4—42no—
415C3×D4—42no—
416C3×D4—44no—
417C3×D4—44no—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—42no—
421C3×D4—816no—
422C2×C3×C4—28no—
423C2×C3×C4—216no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—42no—
428C2×C3×C4—44no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—44no—
432C2×C3×C4#12012yes—
433C2×C3×C4#12012yes—
434C2×C3×C4#12012yes—
435C2×C3×C4#12011yescharacteristic
436C2×C3×C4#12011yescharacteristic
437C2×C3×C4#12112yes—
438C2×C3×C4#12112yes—
439C2×C3×C4#12112yes—
440C2×C3×C4#12112yes—
441C2×C3×C4#12112yes—
442C2×C3×C4#12712yes—
443C2×C3×C4#12712yes—
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C3×C8—24no—
451C3×C8—42no—
452C24—22no—
453C24—21no—
454C24—24no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—48no—
460C24—48no—
461C24—41no—
462C24—41no—
463C24—42no—
464C24C2×C3×D411yescharacteristic
465C24C2×C3×D414yes—
466#41—24no—
467#41—24no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—22no—
472#41—42no—
473#41—42no—
474#41—42no—
475#41—42no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8C2×C3×D412yescomplemented
480C2×D4—232no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—216no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—22no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—432no—
508C2×D4—464no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—88no—
527C2×D4C2×C3×D412yescomplemented
528C2×D4C2×C3×D414yescomplemented
529C22×C4—28no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D411yescharacteristic
540C22×C4C2×C3×D412yes—
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D412yes—
543C22×C4C2×C3×D412yes—
544C22×C4C2×C3×D411yescharacteristic
545C22×C4C2×C3×D411yescharacteristic
546C22×C4C3×#4112yes—
547C22×C4C24×C311yescharacteristic
548SD16—216no—
549D8—216no—
550M16—24no—
551M16—22no—
552M16—22no—
553M16—22no—
554M16—42no—
555M16C2×C3×D414yescomplemented
556C2×C8—24no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—42no—
560C4⋊C4—22no—
561C4⋊C4C2×C3×D414yescomplemented
562C22⋊C4—216no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C42—24no—
566C42—22no—
567C42—22no—
568C42—22no—
569C42C2×C3×D414yescomplemented
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—48no—
575C22×C3—48no—
576C22×C3—42no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—48no—
581C22×C3—84no—
582C22×C3—84no—
583C22×C3—88no—
584C22×C3—88no—
585C22×C3—84no—
586C22×C3—84no—
587C22×C3—88no—
588C22×C3—88no—
589C22×C3#39212yes—
590C22×C3#39212yes—
591C22×C3#45314yes—
592C22×C3C2×#12011yescharacteristic
593C22×C3C2×#12011yescharacteristic
594C22×C3C2×#12111yescharacteristic
595C3×C4—28no—
596C3×C4—42no—
597C3×C4—44no—
598C3×C4#39212yes—
599C3×C4#39212yes—
600C3×C4C2×#12011yescharacteristic
601C3×C4C2×#12111yescharacteristic
602C3×C4C2×#12111yescharacteristic
603C3×C4C2×#12711yescharacteristic
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—48no—
611C23—416no—
612C23—416no—
613C23—48no—
614C23—42no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—48no—
621C23—42no—
622C23—42no—
623C23—84no—
624C23—88no—
625C23—88no—
626C23—84no—
627C23—84no—
628C23C3×#12011yescharacteristic
629C23C3×#12012yes—
630C23C3×#12011yescharacteristic
631C23C3×#12112yes—
632C23C22×C3×D411yescharacteristic
633Q8—22no—
634Q8—22no—
635Q8—42no—
636D4—22no—
637D4—24no—
638D4—24no—
639D4—22no—
640D4—464no—
641D4—44no—
642D4—42no—
643D4—42no—
644D4—44no—
645D4—44no—
646D4—44no—
647D4—44no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—42no—
654D4—42no—
655D4—816no—
656C2×C4—216no—
657C2×C4—28no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4C3×#12012yes—
667C2×C4C3×#12011yescharacteristic
668C2×C4C3×#12011yescharacteristic
669C2×C4C3×#12012yes—
670C2×C4C3×#12012yes—
671C2×C4C3×#12112yes—
672C2×C4C3×#12112yes—
673C2×C4C3×#12112yes—
674C2×C4C3×#12112yes—
675C2×C4C3×#12112yes—
676C2×C4C3×#12712yes—
677C2×C4C3×#12712yes—
678C2×C4C22×C3×D411yescharacteristic
679C2×C4C22×C3×D411yescharacteristic
680C2×C4C22×C3×D411yescharacteristic
681C2×C4C22×C3×D411yescharacteristic
682C2×C4C22×C3×D411yescharacteristic
683C2×C4C2×C3×#4111yescharacteristic
684C8—24no—
685C8—42no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—22no—
689C2×C3—84no—
690C2×C3—82no—
691C2×C3—84no—
692C2×C3#200214yesdirect product factor
693C2×C3C2×#39211yescharacteristic
694C2×C3C2×#45312yes—
695C22—24no—
696C22—24no—
697C22—22no—
698C22—22no—
699C22—48no—
700C22—48no—
701C22—42no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—48no—
706C22—84no—
707C22—88no—
708C22—88no—
709C22—84no—
710C22—88no—
711C22—88no—
712C22—84no—
713C22—84no—
714C22C3×#39212yes—
715C22C3×#39212yes—
716C22C3×#45314yes—
717C22C2×C3×#12011yescharacteristic
718C22C2×C3×#12011yescharacteristic
719C22C2×C3×#12111yescharacteristic
720C4—28no—
721C4—42no—
722C4—44no—
723C4C3×#39212yes—
724C4C3×#39212yes—
725C4C2×C3×#12011yescharacteristic
726C4C2×C3×#12111yescharacteristic
727C4C2×C3×#12111yescharacteristic
728C4C2×C3×#12711yescharacteristic
729C3C2×#200211yescharacteristic, direct product factor, Sylow
730C2—21no—
731C2—22no—
732C2—21no—
733C2—84no—
734C2—84no—
735C2—82no—
736C2C3×#200214yesdirect product factor
737C2C2×C3×#39211yescharacteristic
738C2C2×C3×#45312yes—
subgroupG/H
center, socleC23×C3#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C2×C3×#535C2semidirect
3. C22×C3×#127C2semidirect
4. C22×C3×#104C2semidirect
5. C2×C3×#418C2semidirect
6. C22×C3×#100C2semidirect
7. C3×#2002C2direct (N × H)
8. C2×C3×#339C2semidirect
9. C2×#2002C3direct (N × H)
17. C2×C3×AGL(1,ℤ/8)C22semidirect
25. C3×#535C22semidirect
30. C2×C3×#127C22semidirect
37. C2×C3×#104C22semidirect
39. C3×#418C22semidirect
42. C2×C3×#100C22semidirect
43. C3×#339C22semidirect
44. C22×AGL(1,ℤ/8)C2×C3semidirect
45. C2×#535C2×C3semidirect
46. C22×#127C2×C3semidirect
47. C22×#104C2×C3semidirect
48. C2×#418C2×C3semidirect
49. C22×#100C2×C3semidirect
50. #2002C2×C3direct (N × H)
51. C2×#339C2×C3semidirect
60. C2×C3×#41D4semidirect
62. C22×C3×Q8D4semidirect
85. C22×C3×D4D4semidirect
86. C22×C3×D4D4semidirect
104. C2×C3×M16D4semidirect
122. C3×#117D4semidirect
124. C2×C3×C4⋊C4D4semidirect
130. C2×C3×C42D4semidirect
142. C2×AGL(1,ℤ/8)C22×C3semidirect
150. #535C22×C3semidirect
155. C2×#127C22×C3semidirect
162. C2×#104C22×C3semidirect
164. #418C22×C3semidirect
167. C2×#100C22×C3semidirect
168. #339C22×C3semidirect
196. C2×C3×Q8C2×D4semidirect
244. C2×C3×D4C2×D4semidirect
245. C2×C3×D4C2×D4semidirect
272. C3×M16C2×D4semidirect
278. C3×C4⋊C4C2×D4semidirect
286. C3×C42C2×D4semidirect
295. C2×#41C3×D4semidirect
297. C22×Q8C3×D4semidirect
320. C22×D4C3×D4semidirect
321. C22×D4C3×D4semidirect
339. C2×M16C3×D4semidirect
357. #117C3×D4semidirect
359. C2×C4⋊C4C3×D4semidirect
365. C2×C42C3×D4semidirect
479. C2×Q8C2×C3×D4semidirect
527. C2×D4C2×C3×D4semidirect
528. C2×D4C2×C3×D4semidirect
555. M16C2×C3×D4semidirect
561. C4⋊C4C2×C3×D4semidirect
569. C42C2×C3×D4semidirect
692. C2×C3#2002direct (N × H)
729. C3C2×#2002direct (N × H)
736. C2C3×#2002direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
C2×C3×#5352
C22×C3×#1272
C22×C3×#1042
C2×C3×#4182
C22×C3×#1002
C3×#20022
C2×C3×#3392
C2×#20023