Finite Group Databasebeta

← C3×#23391 #10641998

Subgroups — C3×#23391 #10641998

Order 768.

2514 conjugacy classes of subgroups.

The subgroup lattice has 718 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×#525C211yesmaximal, characteristic, complemented
3C22×C3×#121C211yesmaximal, characteristic, complemented
4C2×C3×#417C211yesmaximal, characteristic, complemented
5C2×C3×#418C211yesmaximal, characteristic, complemented
6C2×C3×#407C211yesmaximal, characteristic, complemented
7C3×#2000C214yesmaximal, complemented
8C3×#1999C214yesmaximal, complemented
9C3×#1736C211yesmaximal, characteristic, complemented
10#23391C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×#41C2211yescharacteristic
12C23×C3×D4—21no—
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C2×C3×AGL(1,ℤ/8)—24no—
16C2×C3×AGL(1,ℤ/8)—24no—
17C2×C3×AGL(1,ℤ/8)—24no—
18C22×C3×SD16C2212yescomplemented
19C22×C3×D8C2212yescomplemented
20C22×C3×M16C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic
22C3×#525—24no—
23C3×#525—24no—
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8C2212yescomplemented
26C2×C3×#121—24no—
27C2×C3×#121—22no—
28C2×C3×#121—24no—
29C2×C3×#121C2214yes—
30C2×C3×#121C2212yescomplemented
31C2×C3×#120—21no—
32C2×C3×C4×D4—22no—
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4—21no—
36C3×#418—24no—
37C3×#417—24no—
38C2×C3×#103C2212yescomplemented
39C2×C3×#102C2212yescomplemented
40C2×C3×#102C2214yescomplemented
41C3×#407—24no—
42C2×C3×C22⋊C8C2214yescomplemented
43C3×#340C2214yescomplemented
44C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
45C2×#525C2×C311yescharacteristic, complemented
46C22×#121C2×C311yescharacteristic, complemented
47C2×#417C2×C311yescharacteristic, complemented
48C2×#418C2×C311yescharacteristic, complemented
49C2×#407C2×C311yescharacteristic, complemented
50#2000C2×C314yescomplemented
51#1999C2×C314yescomplemented
52#1736C2×C311yescharacteristic, complemented
53C25×C3—21no—
54C25×C3D411yescharacteristic
55C2×C3×#41—22no—
56C2×C3×#41—22no—
57C2×C3×#41—22no—
58C2×C3×#41—22no—
59C2×C3×#41—22no—
60C2×C3×#41D414yescomplemented
61C22×C3×Q8C2311yescharacteristic
62C22×C3×D4—28no—
63C22×C3×D4—24no—
64C22×C3×D4—21no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—21no—
70C22×C3×D4—22no—
71C22×C3×D4—22no—
72C22×C3×D4—48no—
73C22×C3×D4D414yescomplemented
74C22×C3×D4C2312yes—
75C22×C3×D4C2311yescharacteristic
76C23×C3×C4—21no—
77C23×C3×C4—22no—
78C23×C3×C4—22no—
79C23×C3×C4—22no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—21no—
83C23×C3×C4—22no—
84C23×C3×C4D411yescharacteristic
85C23×C3×C4D412yes—
86C23×C3×C4C2312yes—
87C23×C3×C4C2311yescharacteristic
88C3×AGL(1,ℤ/8)—232no—
89C2×C3×SD16—24no—
90C2×C3×SD16—24no—
91C2×C3×SD16—24no—
92C2×C3×D8—24no—
93C2×C3×D8—24no—
94C2×C3×D8—24no—
95C2×C3×M16—22no—
96C2×C3×M16—22no—
97C2×C3×M16—22no—
98C2×C3×M16—22no—
99C2×C3×M16—22no—
100C2×C3×M16D414yescomplemented
101C22×C3×C8C2312yes—
102C22×C3×C8C2312yes—
103C3×#123—28no—
104C3×C22⋊Q8—24no—
105C3×C22⋊Q8—24no—
106C3×#121—216no—
107C3×#121—28no—
108C3×#121—24no—
109C3×#121—28no—
110C3×#121—24no—
111C3×#120—28no—
112C3×C4×D4—216no—
113C3×#117—22no—
114C3×#117D414yescomplemented
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—22no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4D414yescomplemented
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C22⋊C4—28no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—24no—
125C2×C3×C22⋊C4—22no—
126C2×C3×C42—21no—
127C3×#103—24no—
128C3×#102—24no—
129C3×#102—28no—
130C3×C22⋊C8—28no—
131C22×#41C22×C311yescharacteristic
132C23×D4—21no—
133C23×D4C22×C311yescharacteristic
134C24×C4C22×C311yescharacteristic
135C2×AGL(1,ℤ/8)—24no—
136C2×AGL(1,ℤ/8)—24no—
137C2×AGL(1,ℤ/8)—24no—
138C22×SD16C22×C312yescomplemented
139C22×D8C22×C312yescomplemented
140C22×M16C22×C311yescharacteristic
141C22×M16C22×C311yescharacteristic
142#525—24no—
143#525—24no—
144C2×#123—21no—
145C2×C22⋊Q8C22×C312yescomplemented
146C2×#121—24no—
147C2×#121—22no—
148C2×#121—24no—
149C2×#121C22×C314yes—
150C2×#121C22×C312yescomplemented
151C2×#120—21no—
152C2×C4×D4—22no—
153C2×#117C22×C311yescharacteristic
154C22×C4⋊C4C22×C311yescharacteristic
155C22×C22⋊C4—21no—
156#418—24no—
157#417—24no—
158C2×#103C22×C312yescomplemented
159C2×#102C22×C314yescomplemented
160C2×#102C22×C312yescomplemented
161#407—24no—
162C2×C22⋊C8C22×C314yescomplemented
163#340C22×C314yescomplemented
164C24×C3—22no—
165C24×C3—24no—
166C24×C3—24no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—42no—
172C24×C3—44no—
173C24×C3—44no—
174C24×C3—42no—
175C24×C3—42no—
176C24×C3C2×D412yes—
177C24×C3C2×D411yescharacteristic
178C3×#41—28no—
179C3×#41—28no—
180C3×#41—44no—
181C3×#41—44no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8C2×D412yescomplemented
188C2×C3×D4—28no—
189C2×C3×D4—216no—
190C2×C3×D4—24no—
191C2×C3×D4—28no—
192C2×C3×D4—24no—
193C2×C3×D4—28no—
194C2×C3×D4—22no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—21no—
202C2×C3×D4—22no—
203C2×C3×D4—21no—
204C2×C3×D4—44no—
205C2×C3×D4—432no—
206C2×C3×D4—48no—
207C2×C3×D4—42no—
208C2×C3×D4—42no—
209C2×C3×D4—44no—
210C2×C3×D4—48no—
211C2×C3×D4—42no—
212C2×C3×D4—44no—
213C2×C3×D4—42no—
214C2×C3×D4—44no—
215C2×C3×D4C2×D414yes—
216C2×C3×D4C2×D412yescomplemented
217C22×C3×C4—22no—
218C22×C3×C4—24no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—24no—
225C22×C3×C4—24no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—44no—
235C22×C3×C4—44no—
236C22×C3×C4—42no—
237C22×C3×C4—44no—
238C22×C3×C4—44no—
239C22×C3×C4—42no—
240C22×C3×C4—44no—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2×D412yes—
245C22×C3×C4C2×D412yes—
246C22×C3×C4C2×D412yes—
247C22×C3×C4C2×D412yes—
248C22×C3×C4#4112yes—
249C22×C3×C4C2411yescharacteristic
250C3×SD16—216no—
251C3×D8—216no—
252C3×M16—28no—
253C3×M16—44no—
254C2×C3×C8—22no—
255C2×C3×C8—22no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8C2×D414yescomplemented
260C3×C4⋊C4—28no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4C2×D414yes—
265C3×C4⋊C4C2×D414yescomplemented
266C3×C22⋊C4—216no—
267C3×C22⋊C4—28no—
268C3×C22⋊C4—28no—
269C3×C22⋊C4—24no—
270C3×C42—24no—
271C25—21no—
272C25C3×D411yescharacteristic
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41C3×D414yescomplemented
279C22×Q8C23×C311yescharacteristic
280C22×D4—28no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—24no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—48no—
291C22×D4C3×D414yescomplemented
292C22×D4C23×C312yes—
293C22×D4C23×C311yescharacteristic
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4C3×D411yescharacteristic
303C23×C4C3×D412yes—
304C23×C4C23×C312yes—
305C23×C4C23×C311yescharacteristic
306AGL(1,ℤ/8)—232no—
307C2×SD16—24no—
308C2×SD16—24no—
309C2×SD16—24no—
310C2×D8—24no—
311C2×D8—24no—
312C2×D8—24no—
313C2×M16—22no—
314C2×M16—22no—
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—22no—
318C2×M16C3×D414yescomplemented
319C22×C8C23×C312yes—
320C22×C8C23×C312yes—
321#123—28no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324#121—216no—
325#121—28no—
326#121—24no—
327#121—28no—
328#121—24no—
329#120—28no—
330C4×D4—216no—
331#117—22no—
332#117C3×D414yescomplemented
333C2×C4⋊C4—21no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4C3×D414yescomplemented
337C2×C4⋊C4C23×C312yes—
338C2×C4⋊C4C23×C312yes—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C42—21no—
345#103—24no—
346#102—24no—
347#102—28no—
348C22⋊C8—28no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—28no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—24no—
360C23×C3—48no—
361C23×C3—48no—
362C23×C3—44no—
363C23×C3—48no—
364C23×C3—48no—
365C23×C3—44no—
366C23×C3—41no—
367C23×C3—42no—
368C23×C3—41no—
369C23×C3—42no—
370C23×C3—44no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—44no—
374C23×C3—48no—
375C23×C3—88no—
376C23×C3—88no—
377C23×C3#12012yes—
378C23×C3#12012yes—
379C23×C3#12112yes—
380C23×C3AGL(1,ℤ/8)14yescomplemented
381C23×C3C22×D411yescharacteristic
382C3×Q8—22no—
383C3×Q8—22no—
384C3×Q8—41no—
385C3×Q8—41no—
386C3×D4—22no—
387C3×D4—24no—
388C3×D4—24no—
389C3×D4—22no—
390C3×D4—416no—
391C3×D4—432no—
392C3×D4—48no—
393C3×D4—42no—
394C3×D4—41no—
395C3×D4—42no—
396C3×D4—41no—
397C3×D4—48no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—24no—
403C2×C3×C4—22no—
404C2×C3×C4—48no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—44no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—44no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—48no—
416C2×C3×C4—48no—
417C2×C3×C4#12014yes—
418C2×C3×C4#12012yes—
419C2×C3×C4#12012yes—
420C2×C3×C4#12114yes—
421C2×C3×C4#12114yes—
422C2×C3×C4#12112yes—
423C2×C3×C4#12714yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C22×D411yescharacteristic
428C2×C3×C4C22×D411yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C3×C8—24no—
431C3×C8—42no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—42no—
440C24—44no—
441C24—44no—
442C24—42no—
443C24—42no—
444C24C2×C3×D412yes—
445C24C2×C3×D411yescharacteristic
446#41—28no—
447#41—28no—
448#41—44no—
449#41—44no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8C2×C3×D412yescomplemented
456C2×D4—28no—
457C2×D4—216no—
458C2×D4—24no—
459C2×D4—28no—
460C2×D4—24no—
461C2×D4—28no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—432no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—48no—
478C2×D4—44no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4C2×C3×D414yes—
484C2×D4C2×C3×D412yescomplemented
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—42no—
508C22×C4—44no—
509C22×C4C2×C3×D412yes—
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D412yes—
512C22×C4C2×C3×D412yes—
513C22×C4C2×C3×D412yes—
514C22×C4C2×C3×D412yes—
515C22×C4C2×C3×D412yes—
516C22×C4C3×#4112yes—
517C22×C4C24×C311yescharacteristic
518SD16—216no—
519D8—216no—
520M16—28no—
521M16—44no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8C2×C3×D414yescomplemented
528C4⋊C4—28no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4C2×C3×D414yes—
533C4⋊C4C2×C3×D414yescomplemented
534C22⋊C4—216no—
535C22⋊C4—28no—
536C22⋊C4—28no—
537C22⋊C4—24no—
538C42—24no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—24no—
546C22×C3—416no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3—44no—
556C22×C3—816no—
557C22×C3—81no—
558C22×C3—81no—
559C22×C3—84no—
560C22×C3—82no—
561C22×C3—84no—
562C22×C3#39214yes—
563C22×C3C2×#12011yescharacteristic
564C22×C3C2×#12011yescharacteristic
565C22×C3C2×#12111yescharacteristic
566C22×C3C2×AGL(1,ℤ/8)12yes—
567C22×C3#57512yes—
568C3×C4—42no—
569C3×C4—42no—
570C3×C4—44no—
571C3×C4—44no—
572C3×C4#39214yes—
573C3×C4C2×#12011yescharacteristic
574C3×C4C2×#12111yescharacteristic
575C3×C4C2×#12111yescharacteristic
576C3×C4C2×#12711yescharacteristic
577C23—22no—
578C23—22no—
579C23—28no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—48no—
589C23—48no—
590C23—44no—
591C23—48no—
592C23—48no—
593C23—44no—
594C23—44no—
595C23—42no—
596C23—42no—
597C23—44no—
598C23—48no—
599C23—41no—
600C23—42no—
601C23—41no—
602C23—42no—
603C23—88no—
604C23—88no—
605C23C3×#12012yes—
606C23C3×#12012yes—
607C23C3×#12112yes—
608C23C3×AGL(1,ℤ/8)14yescomplemented
609C23C22×C3×D411yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614D4—22no—
615D4—24no—
616D4—24no—
617D4—22no—
618D4—432no—
619D4—416no—
620D4—48no—
621D4—48no—
622D4—42no—
623D4—41no—
624D4—42no—
625D4—41no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—48no—
633C2×C4—44no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—44no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—48no—
640C2×C4—48no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4C3×#12012yes—
646C2×C4C3×#12012yes—
647C2×C4C3×#12014yes—
648C2×C4C3×#12112yes—
649C2×C4C3×#12114yes—
650C2×C4C3×#12114yes—
651C2×C4C3×#12714yes—
652C2×C4C22×C3×D411yescharacteristic
653C2×C4C22×C3×D411yescharacteristic
654C2×C4C22×C3×D411yescharacteristic
655C2×C4C22×C3×D411yescharacteristic
656C2×C4C22×C3×D411yescharacteristic
657C2×C4C2×C3×#4111yescharacteristic
658C8—24no—
659C8—42no—
660C2×C3—24no—
661C2×C3—44no—
662C2×C3—82no—
663C2×C3—84no—
664C2×C3C2×#39211yescharacteristic
665C2×C3#300311yescharacteristic
666C2×C3#300511yescharacteristic
667C2×C3#300612yes—
668C2×C3#305512yes—
669C22—22no—
670C22—22no—
671C22—24no—
672C22—24no—
673C22—24no—
674C22—24no—
675C22—24no—
676C22—416no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—44no—
683C22—44no—
684C22—44no—
685C22—44no—
686C22—816no—
687C22—81no—
688C22—81no—
689C22—84no—
690C22—84no—
691C22—82no—
692C22C3×#39214yes—
693C22C2×C3×#12011yescharacteristic
694C22C2×C3×#12011yescharacteristic
695C22C2×C3×#12111yescharacteristic
696C22C2×C3×AGL(1,ℤ/8)12yes—
697C22C3×#57512yes—
698C4—42no—
699C4—42no—
700C4—44no—
701C4—44no—
702C4C3×#39214yes—
703C4C2×C3×#12011yescharacteristic
704C4C2×C3×#12111yescharacteristic
705C4C2×C3×#12111yescharacteristic
706C4C2×C3×#12711yescharacteristic
707C3#2339111yescharacteristic, direct product factor, Sylow
708C2—24no—
709C2—44no—
710C2—84no—
711C2—82no—
712C2C2×C3×#39211yescharacteristic
713C2C3×#300311yescharacteristic
714C2C3×#300511yescharacteristic
715C2C3×#300612yes—
716C2C3×#305512yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C2×C3×#525C2semidirect
3. C22×C3×#121C2semidirect
4. C2×C3×#417C2semidirect
5. C2×C3×#418C2semidirect
6. C2×C3×#407C2semidirect
7. C3×#2000C2semidirect
8. C3×#1999C2semidirect
9. C3×#1736C2semidirect
10. #23391C3direct (N × H)
18. C22×C3×SD16C22semidirect
19. C22×C3×D8C22semidirect
25. C2×C3×C22⋊Q8C22semidirect
30. C2×C3×#121C22semidirect
38. C2×C3×#103C22semidirect
39. C2×C3×#102C22semidirect
40. C2×C3×#102C22semidirect
42. C2×C3×C22⋊C8C22semidirect
43. C3×#340C22semidirect
44. C22×AGL(1,ℤ/8)C2×C3semidirect
45. C2×#525C2×C3semidirect
46. C22×#121C2×C3semidirect
47. C2×#417C2×C3semidirect
48. C2×#418C2×C3semidirect
49. C2×#407C2×C3semidirect
50. #2000C2×C3semidirect
51. #1999C2×C3semidirect
52. #1736C2×C3semidirect
60. C2×C3×#41D4semidirect
73. C22×C3×D4D4semidirect
100. C2×C3×M16D4semidirect
114. C3×#117D4semidirect
118. C2×C3×C4⋊C4D4semidirect
138. C22×SD16C22×C3semidirect
139. C22×D8C22×C3semidirect
145. C2×C22⋊Q8C22×C3semidirect
150. C2×#121C22×C3semidirect
158. C2×#103C22×C3semidirect
159. C2×#102C22×C3semidirect
160. C2×#102C22×C3semidirect
162. C2×C22⋊C8C22×C3semidirect
163. #340C22×C3semidirect
187. C2×C3×Q8C2×D4semidirect
216. C2×C3×D4C2×D4semidirect
259. C2×C3×C8C2×D4semidirect
265. C3×C4⋊C4C2×D4semidirect
278. C2×#41C3×D4semidirect
291. C22×D4C3×D4semidirect
318. C2×M16C3×D4semidirect
332. #117C3×D4semidirect
336. C2×C4⋊C4C3×D4semidirect
380. C23×C3AGL(1,ℤ/8)semidirect
455. C2×Q8C2×C3×D4semidirect
484. C2×D4C2×C3×D4semidirect
527. C2×C8C2×C3×D4semidirect
533. C4⋊C4C2×C3×D4semidirect
608. C23C3×AGL(1,ℤ/8)semidirect
707. C3#23391direct (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×#5252
C22×C3×#1212
C2×C3×#4172
C2×C3×#4182
C2×C3×#4072
C3×#20002
C3×#19992
C3×#17362
#233913