Finite Group Databasebeta

← C3×#23393 #10642000

Subgroups — C3×#23393 #10642000

Order 768.

2206 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
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C3×#537C211yesmaximal, characteristic, complemented
3C2×C3×#535C211yesmaximal, characteristic, complemented
4C2×C3×#416C211yesmaximal, characteristic, complemented
5C22×C3×#102C211yesmaximal, characteristic, complemented
6C2×C3×#408C211yesmaximal, characteristic, complemented
7C3×#2000C214yesmaximal, complemented
8C3×#1999C214yesmaximal, complemented
9C3×#1736C211yesmaximal, characteristic, complemented
10#23393C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C23×C3×D4C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)—24no—
15C2×C3×AGL(1,ℤ/8)—24no—
16C2×C3×AGL(1,ℤ/8)—24no—
17C22×C3×SD16C2212yes—
18C22×C3×D8C2212yes—
19C22×C3×M16C2211yescharacteristic
20C23×C3×C8C2211yescharacteristic
21C3×#537—24no—
22C3×#537—24no—
23C3×#535—24no—
24C3×#535—24no—
25C2×C3×#127—21no—
26C2×C3×#124—21no—
27C2×C3×C22⋊Q8—21no—
28C2×C3×C22⋊Q8C2212yescomplemented
29C2×C3×#121—21no—
30C2×C3×#121—22no—
31C2×C3×#121C2214yes—
32C2×C3×#121C2212yescomplemented
33C2×C3×#120—22no—
34C2×C3×#117C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C3×#416—24no—
37C2×C3×#103C2212yescomplemented
38C2×C3×#102—24no—
39C2×C3×#102C2214yes—
40C2×C3×#102C2212yescomplemented
41C3×#408—24no—
42C2×C3×C22⋊C8C2214yescomplemented
43C3×#340C2214yescomplemented
44C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
45C2×#537C2×C311yescharacteristic, complemented
46C2×#535C2×C311yescharacteristic, complemented
47C2×#416C2×C311yescharacteristic, complemented
48C22×#102C2×C311yescharacteristic, complemented
49C2×#408C2×C311yescharacteristic, complemented
50#2000C2×C314yescomplemented
51#1999C2×C314yescomplemented
52#1736C2×C311yescharacteristic, complemented
53C25×C3—21no—
54C2×C3×#41—22no—
55C2×C3×#41—22no—
56C2×C3×#41—22no—
57C2×C3×#41—22no—
58C2×C3×#41—22no—
59C2×C3×#41—22no—
60C2×C3×#41—22no—
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41D414yescomplemented
66C22×C3×Q8D411yescharacteristic
67C22×C3×Q8C2311yescharacteristic
68C22×C3×D4—21no—
69C22×C3×D4—24no—
70C22×C3×D4—22no—
71C22×C3×D4—22no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—21no—
75C22×C3×D4—22no—
76C22×C3×D4—22no—
77C22×C3×D4D412yes—
78C22×C3×D4D411yescharacteristic
79C22×C3×D4D414yescomplemented
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2312yes—
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2312yes—
85C23×C3×C4C2311yescharacteristic
86C3×AGL(1,ℤ/8)—232no—
87C2×C3×SD16—24no—
88C2×C3×SD16—24no—
89C2×C3×SD16—24no—
90C2×C3×D8—24no—
91C2×C3×D8—24no—
92C2×C3×D8—24no—
93C2×C3×M16—22no—
94C2×C3×M16—22no—
95C2×C3×M16D414yescomplemented
96C22×C3×C8—22no—
97C22×C3×C8—22no—
98C22×C3×C8—22no—
99C22×C3×C8C2312yes—
100C22×C3×C8C2312yes—
101C3×#127—28no—
102C3×#124—28no—
103C3×C22⋊Q8—28no—
104C3×C22⋊Q8—24no—
105C3×C22⋊Q8—24no—
106C3×#121—216no—
107C3×#121—28no—
108C3×#121—28no—
109C3×#121—24no—
110C3×#121—28no—
111C3×#121—24no—
112C3×#120—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—21no—
122C2×C3×C22⋊C4—22no—
123C2×C3×C22⋊C4—24no—
124C2×C3×C22⋊C4—22no—
125C2×C3×C42—21no—
126C3×#103—24no—
127C3×#102—28no—
128C3×#102—24no—
129C3×C22⋊C8—28no—
130C22×#41C22×C311yescharacteristic
131C22×#41C22×C311yescharacteristic
132C23×D4C22×C311yescharacteristic
133C2×AGL(1,ℤ/8)—24no—
134C2×AGL(1,ℤ/8)—24no—
135C2×AGL(1,ℤ/8)—24no—
136C22×SD16C22×C312yes—
137C22×D8C22×C312yes—
138C22×M16C22×C311yescharacteristic
139C23×C8C22×C311yescharacteristic
140#537—24no—
141#537—24no—
142#535—24no—
143#535—24no—
144C2×#127—21no—
145C2×#124—21no—
146C2×C22⋊Q8—21no—
147C2×C22⋊Q8C22×C312yescomplemented
148C2×#121—21no—
149C2×#121—22no—
150C2×#121C22×C314yes—
151C2×#121C22×C312yescomplemented
152C2×#120—22no—
153C2×#117C22×C311yescharacteristic
154C22×C4⋊C4C22×C311yescharacteristic
155#416—24no—
156C2×#103C22×C312yescomplemented
157C2×#102—24no—
158C2×#102C22×C314yes—
159C2×#102C22×C312yescomplemented
160#408—24no—
161C2×C22⋊C8C22×C314yescomplemented
162#340C22×C314yescomplemented
163C24×C3—22no—
164C24×C3—21no—
165C24×C3—24no—
166C24×C3—42no—
167C24×C3—42no—
168C24×C3—82no—
169C24×C3—82no—
170C24×C3C2×D412yes—
171C24×C3C2×D411yescharacteristic
172C3×#41—28no—
173C3×#41—28no—
174C3×#41—44no—
175C3×#41—44no—
176C3×#41—44no—
177C3×#41—44no—
178C3×#41—44no—
179C3×#41—44no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—21no—
188C2×C3×Q8C2×D412yes—
189C2×C3×D4—24no—
190C2×C3×D4—24no—
191C2×C3×D4—24no—
192C2×C3×D4—24no—
193C2×C3×D4—216no—
194C2×C3×D4—28no—
195C2×C3×D4—28no—
196C2×C3×D4—22no—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—28no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—42no—
212C2×C3×D4—42no—
213C2×C3×D4—42no—
214C2×C3×D4—44no—
215C2×C3×D4—42no—
216C2×C3×D4—44no—
217C2×C3×D4—84no—
218C2×C3×D4—84no—
219C2×C3×D4—84no—
220C2×C3×D4C2×D412yes—
221C2×C3×D4C2×D414yes—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—24no—
226C22×C3×C4—24no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—82no—
236C22×C3×C4C2×D412yes—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D412yes—
239C22×C3×C4C2×D412yes—
240C22×C3×C4C2×D412yes—
241C22×C3×C4C2×D412yes—
242C22×C3×C4C2×D412yes—
243C22×C3×C4#4112yes—
244C22×C3×C4C2411yescharacteristic
245C3×SD16—216no—
246C3×D8—216no—
247C3×M16—28no—
248C2×C3×C8—22no—
249C2×C3×C8—22no—
250C2×C3×C8—22no—
251C2×C3×C8—22no—
252C2×C3×C8—22no—
253C2×C3×C8—44no—
254C2×C3×C8C2×D414yes—
255C3×C4⋊C4—28no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4C2×D414yes—
260C3×C4⋊C4C2×D414yes—
261C3×C22⋊C4—216no—
262C3×C22⋊C4—28no—
263C3×C22⋊C4—28no—
264C3×C22⋊C4—24no—
265C3×C42—24no—
266C25—21no—
267C2×#41—22no—
268C2×#41—22no—
269C2×#41—22no—
270C2×#41—22no—
271C2×#41—22no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41C3×D414yescomplemented
279C22×Q8C3×D411yescharacteristic
280C22×Q8C23×C311yescharacteristic
281C22×D4—21no—
282C22×D4—24no—
283C22×D4—22no—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4C3×D412yes—
291C22×D4C3×D411yescharacteristic
292C22×D4C3×D414yescomplemented
293C22×D4C23×C312yes—
294C22×D4C23×C311yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4C23×C312yes—
298C23×C4C23×C311yescharacteristic
299AGL(1,ℤ/8)—232no—
300C2×SD16—24no—
301C2×SD16—24no—
302C2×SD16—24no—
303C2×D8—24no—
304C2×D8—24no—
305C2×D8—24no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16C3×D414yescomplemented
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8C23×C312yes—
313C22×C8C23×C312yes—
314#127—28no—
315#124—28no—
316C22⋊Q8—28no—
317C22⋊Q8—24no—
318C22⋊Q8—24no—
319#121—216no—
320#121—28no—
321#121—28no—
322#121—24no—
323#121—28no—
324#121—24no—
325#120—216no—
326#117—22no—
327#117C3×D414yescomplemented
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4C3×D414yescomplemented
332C2×C4⋊C4C23×C312yes—
333C2×C4⋊C4C23×C312yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C42—21no—
339#103—24no—
340#102—28no—
341#102—24no—
342C22⋊C8—28no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—24no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—41no—
353C23×C3—42no—
354C23×C3—41no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—42no—
360C23×C3—48no—
361C23×C3—88no—
362C23×C3—84no—
363C23×C3—84no—
364C23×C3—88no—
365C23×C3#12012yes—
366C23×C3#12012yes—
367C23×C3#12112yes—
368C23×C3C22×D411yescharacteristic
369C3×Q8—22no—
370C3×Q8—22no—
371C3×Q8—41no—
372C3×Q8—41no—
373C3×Q8—44no—
374C3×D4—22no—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—48no—
379C3×D4—48no—
380C3×D4—42no—
381C3×D4—41no—
382C3×D4—42no—
383C3×D4—41no—
384C3×D4—48no—
385C3×D4—44no—
386C3×D4—88no—
387C3×D4—816no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—44no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—48no—
404C2×C3×C4—84no—
405C2×C3×C4#12014yes—
406C2×C3×C4#12012yes—
407C2×C3×C4#12012yes—
408C2×C3×C4#12114yes—
409C2×C3×C4#12114yes—
410C2×C3×C4#12112yes—
411C2×C3×C4#12714yes—
412C2×C3×C4C22×D411yescharacteristic
413C2×C3×C4C22×D411yescharacteristic
414C2×C3×C4C22×D411yescharacteristic
415C2×C3×C4C22×D411yescharacteristic
416C2×C3×C4C22×D411yescharacteristic
417C2×C3×C4C2×#4111yescharacteristic
418C3×C8—24no—
419C3×C8—42no—
420C24—21no—
421C24—22no—
422C24—24no—
423C24—42no—
424C24—42no—
425C24—82no—
426C24—82no—
427C24C2×C3×D412yes—
428C24C2×C3×D411yescharacteristic
429#41—28no—
430#41—28no—
431#41—44no—
432#41—44no—
433#41—44no—
434#41—44no—
435#41—44no—
436#41—44no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×C3×D412yes—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—216no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—28no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—84no—
475C2×D4—84no—
476C2×D4—84no—
477C2×D4C2×C3×D412yes—
478C2×D4C2×C3×D414yes—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—82no—
493C22×C4C2×C3×D412yes—
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D412yes—
496C22×C4C2×C3×D412yes—
497C22×C4C2×C3×D412yes—
498C22×C4C2×C3×D412yes—
499C22×C4C2×C3×D412yes—
500C22×C4C3×#4112yes—
501C22×C4C24×C311yescharacteristic
502SD16—216no—
503D8—216no—
504M16—28no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—44no—
511C2×C8C2×C3×D414yes—
512C4⋊C4—28no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4C2×C3×D414yes—
517C4⋊C4C2×C3×D414yes—
518C22⋊C4—216no—
519C22⋊C4—28no—
520C22⋊C4—28no—
521C22⋊C4—24no—
522C42—24no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—44no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—44no—
535C22×C3—48no—
536C22×C3—44no—
537C22×C3—816no—
538C22×C3—82no—
539C22×C3—82no—
540C22×C3—82no—
541C22×C3—82no—
542C22×C3—84no—
543C22×C3#39214yes—
544C22×C3C2×#12011yescharacteristic
545C22×C3C2×#12011yescharacteristic
546C22×C3C2×#12111yescharacteristic
547C22×C3#57612yes—
548C22×C3#57712yes—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—44no—
552C3×C4—44no—
553C3×C4#39214yes—
554C3×C4C2×#12011yescharacteristic
555C3×C4C2×#12111yescharacteristic
556C3×C4C2×#12111yescharacteristic
557C3×C4C2×#12711yescharacteristic
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—22no—
563C23—22no—
564C23—24no—
565C23—22no—
566C23—22no—
567C23—42no—
568C23—44no—
569C23—44no—
570C23—42no—
571C23—48no—
572C23—41no—
573C23—42no—
574C23—41no—
575C23—42no—
576C23—88no—
577C23—84no—
578C23—84no—
579C23—88no—
580C23C3×#12012yes—
581C23C3×#12012yes—
582C23C3×#12112yes—
583C23C22×C3×D411yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—44no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—24no—
591D4—24no—
592D4—22no—
593D4—48no—
594D4—48no—
595D4—48no—
596D4—44no—
597D4—42no—
598D4—41no—
599D4—42no—
600D4—41no—
601D4—88no—
602D4—816no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—48no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—84no—
620C2×C4C3×#12012yes—
621C2×C4C3×#12012yes—
622C2×C4C3×#12014yes—
623C2×C4C3×#12112yes—
624C2×C4C3×#12114yes—
625C2×C4C3×#12114yes—
626C2×C4C3×#12714yes—
627C2×C4C22×C3×D411yescharacteristic
628C2×C4C22×C3×D411yescharacteristic
629C2×C4C22×C3×D411yescharacteristic
630C2×C4C22×C3×D411yescharacteristic
631C2×C4C22×C3×D411yescharacteristic
632C2×C4C2×C3×#4111yescharacteristic
633C8—24no—
634C8—42no—
635C2×C3—24no—
636C2×C3—82no—
637C2×C3—82no—
638C2×C3—84no—
639C2×C3C2×#39211yescharacteristic
640C2×C3#300811yescharacteristic
641C2×C3#301011yescharacteristic
642C2×C3#301212yes—
643C2×C3#306212yes—
644C22—22no—
645C22—22no—
646C22—24no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—44no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—44no—
656C22—48no—
657C22—44no—
658C22—816no—
659C22—82no—
660C22—82no—
661C22—82no—
662C22—84no—
663C22—82no—
664C22C3×#39214yes—
665C22C2×C3×#12011yescharacteristic
666C22C2×C3×#12011yescharacteristic
667C22C2×C3×#12111yescharacteristic
668C22C3×#57612yes—
669C22C3×#57712yes—
670C4—42no—
671C4—42no—
672C4—44no—
673C4—44no—
674C4C3×#39214yes—
675C4C2×C3×#12011yescharacteristic
676C4C2×C3×#12111yescharacteristic
677C4C2×C3×#12111yescharacteristic
678C4C2×C3×#12711yescharacteristic
679C3#2339311yescharacteristic, direct product factor, Sylow
680C2—24no—
681C2—82no—
682C2—84no—
683C2—82no—
684C2C2×C3×#39211yescharacteristic
685C2C3×#300811yescharacteristic
686C2C3×#301011yescharacteristic
687C2C3×#301212yes—
688C2C3×#306212yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ 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×#537C2semidirect
3. C2×C3×#535C2semidirect
4. C2×C3×#416C2semidirect
5. C22×C3×#102C2semidirect
6. C2×C3×#408C2semidirect
7. C3×#2000C2semidirect
8. C3×#1999C2semidirect
9. C3×#1736C2semidirect
10. #23393C3direct (N × H)
28. C2×C3×C22⋊Q8C22semidirect
32. C2×C3×#121C22semidirect
37. C2×C3×#103C22semidirect
40. C2×C3×#102C22semidirect
42. C2×C3×C22⋊C8C22semidirect
43. C3×#340C22semidirect
44. C22×AGL(1,ℤ/8)C2×C3semidirect
45. C2×#537C2×C3semidirect
46. C2×#535C2×C3semidirect
47. C2×#416C2×C3semidirect
48. C22×#102C2×C3semidirect
49. C2×#408C2×C3semidirect
50. #2000C2×C3semidirect
51. #1999C2×C3semidirect
52. #1736C2×C3semidirect
65. C2×C3×#41D4semidirect
79. C22×C3×D4D4semidirect
95. C2×C3×M16D4semidirect
114. C3×#117D4semidirect
118. C2×C3×C4⋊C4D4semidirect
147. C2×C22⋊Q8C22×C3semidirect
151. C2×#121C22×C3semidirect
156. C2×#103C22×C3semidirect
159. C2×#102C22×C3semidirect
161. C2×C22⋊C8C22×C3semidirect
162. #340C22×C3semidirect
278. C2×#41C3×D4semidirect
292. C22×D4C3×D4semidirect
308. C2×M16C3×D4semidirect
327. #117C3×D4semidirect
331. C2×C4⋊C4C3×D4semidirect
679. C3#23393direct (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×#5372
C2×C3×#5352
C2×C3×#4162
C22×C3×#1022
C2×C3×#4082
C3×#20002
C3×#19992
C3×#17362
#233933