Finite Group Databasebeta

← C3×#24354 #10642961

Subgroups — C3×#24354 #10642961

Order 768.

1872 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D8C211yesmaximal, characteristic, complemented
2C2×C3×#459C212yesmaximal, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C3×#2433C211yesmaximal, characteristic, complemented
5C3×D4×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#2054C212yesmaximal, complemented
7C3×#2011C212yesmaximal, complemented
8C3×#1893C211yesmaximal, characteristic, complemented
9C3×#1879C212yesmaximal, complemented
10C3×#1850C211yesmaximal, characteristic, complemented
11C3×#1786C211yesmaximal, characteristic, complemented
12#24354C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×C3×D8—24no—
16C22×C3×D8—28no—
17C22×C3×D8C2212yes—
18C22×C3×D8C2212yes—
19C22×C3×D8C2211yescharacteristic, complemented
20C22×C3×D8C2211yescharacteristic, complemented
21C23×C3×C8C2211yescharacteristic
22C2×C3×#127C2212yescomplemented
23C2×C3×#121C2211yescharacteristic
24C2×C3×#120—21no—
25C2×C3×#120—21no—
26C2×C3×C4×D4C2212yescomplemented
27C22×C3×C22⋊C4—21no—
28C3×#459—28no—
29C3×#447—24no—
30C2×C3×C4⋊C8C2212yescomplemented
31C2×C3×#102C2212yescomplemented
32C2×C3×#102C2212yescomplemented
33C2×C3×#102C2211yescharacteristic, complemented
34C2×C3×#102C2211yescharacteristic, complemented
35C2×C3×#102C2212yescomplemented
36C2×C3×C22⋊C8C2211yescharacteristic
37C3×#392—22no—
38C3×#390C2212yescomplemented
39C3×#390C2212yescomplemented
40C3×#386—22no—
41C3×#380C2211yescharacteristic
42C3×#379—21no—
43C3×C4×C22⋊C4C2211yescharacteristic
44C3×#340C2212yescomplemented
45C3×#336C2212yescomplemented
46C23×D8C2×C311yescharacteristic, complemented
47C2×#459C2×C312yescomplemented
48C2×#447C2×C311yescharacteristic, complemented
49#2433C2×C311yescharacteristic, complemented
50D4×C22⋊C4C2×C311yescharacteristic, complemented
51#2054C2×C312yescomplemented
52#2011C2×C312yescomplemented
53#1893C2×C311yescharacteristic, complemented
54#1879C2×C312yescomplemented
55#1850C2×C311yescharacteristic, complemented
56#1786C2×C311yescharacteristic, complemented
57C25×C3—21no—
58C25×C3—21no—
59C22×C3×D4—24no—
60C22×C3×D4—24no—
61C22×C3×D4—21no—
62C22×C3×D4—22no—
63C22×C3×D4—21no—
64C22×C3×D4—21no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4—22no—
68C22×C3×D4—22no—
69C22×C3×D4—42no—
70C22×C3×D4—42no—
71C22×C3×D4D414yescomplemented
72C22×C3×D4C2311yescharacteristic
73C22×C3×D4C2311yescharacteristic
74C22×C3×D4C2312yes—
75C22×C3×D4C2311yescharacteristic
76C23×C3×C4—22no—
77C23×C3×C4C2311yescharacteristic
78C2×C3×D8—232no—
79C2×C3×D8—24no—
80C2×C3×D8—24no—
81C2×C3×D8—24no—
82C2×C3×D8—24no—
83C2×C3×D8—22no—
84C2×C3×D8—22no—
85C2×C3×D8—24no—
86C2×C3×D8—24no—
87C2×C3×D8—42no—
88C2×C3×D8D418yescomplemented
89C22×C3×C8—22no—
90C22×C3×C8—24no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2312yes—
94C3×#127—24no—
95C3×#127—42no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#120—44no—
99C3×#120—44no—
100C3×C4×D4—24no—
101C3×C4×D4—42no—
102C2×C3×C4⋊C4C2312yes—
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—22no—
107C2×C3×C22⋊C4—22no—
108C2×C3×C22⋊C4—22no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—44no—
112C2×C3×C22⋊C4D411yescharacteristic
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C42C2312yes—
115C3×C4⋊C8—24no—
116C3×#102—22no—
117C3×#102—22no—
118C3×#102—24no—
119C3×#102—24no—
120C3×#102—42no—
121C3×C22⋊C8—22no—
122C3×#95—21no—
123C3×#95D412yes—
124C23×D4C22×C311yescharacteristic
125C23×D4C22×C311yescharacteristic
126C22×D8—24no—
127C22×D8—28no—
128C22×D8C22×C312yes—
129C22×D8C22×C312yes—
130C22×D8C22×C311yescharacteristic, complemented
131C22×D8C22×C311yescharacteristic, complemented
132C23×C8C22×C311yescharacteristic
133C2×#127C22×C312yescomplemented
134C2×#121C22×C311yescharacteristic
135C2×#120—21no—
136C2×#120—21no—
137C2×C4×D4C22×C312yescomplemented
138C22×C22⋊C4—21no—
139#459—28no—
140#447—24no—
141C2×C4⋊C8C22×C312yescomplemented
142C2×#102C22×C311yescharacteristic, complemented
143C2×#102C22×C312yescomplemented
144C2×#102C22×C311yescharacteristic, complemented
145C2×#102C22×C312yescomplemented
146C2×#102C22×C312yescomplemented
147C2×C22⋊C8C22×C311yescharacteristic
148#392—22no—
149#390C22×C312yescomplemented
150#390C22×C312yescomplemented
151#386—22no—
152#380C22×C311yescharacteristic
153#379—21no—
154C4×C22⋊C4C22×C311yescharacteristic
155#340C22×C312yescomplemented
156#336C22×C312yescomplemented
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—22no—
160C24×C3—24no—
161C24×C3—21no—
162C24×C3—44no—
163C24×C3—44no—
164C24×C3—42no—
165C24×C3—42no—
166C24×C3—42no—
167C24×C3—42no—
168C24×C3—42no—
169C24×C3—82no—
170C24×C3—82no—
171C24×C3C2×D411yescharacteristic
172C2×C3×D4—28no—
173C2×C3×D4—28no—
174C2×C3×D4—24no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—22no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—22no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—44no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—44no—
193C2×C3×D4—44no—
194C2×C3×D4—44no—
195C2×C3×D4—44no—
196C2×C3×D4—44no—
197C2×C3×D4—44no—
198C2×C3×D4—42no—
199C2×C3×D4—42no—
200C2×C3×D4—42no—
201C2×C3×D4—42no—
202C2×C3×D4—44no—
203C2×C3×D4—82no—
204C2×C3×D4—82no—
205C2×C3×D4C2×D414yes—
206C2×C3×D4C2×D412yes—
207C2×C3×D4C2×D412yes—
208C2×C3×D4C2×D414yes—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—44no—
214C22×C3×C4—44no—
215C22×C3×C4—82no—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4#4112yes—
221C22×C3×C4C2411yescharacteristic
222C3×D8—216no—
223C3×D8—216no—
224C3×D8—44no—
225C3×D8—44no—
226C2×C3×C8—28no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8C2×D414yes—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C22⋊C4—22no—
239C3×C22⋊C4—44no—
240C3×C22⋊C4—44no—
241C3×C22⋊C4—42no—
242C3×C22⋊C4—42no—
243C3×C22⋊C4—44no—
244C3×C22⋊C4—44no—
245C3×C22⋊C4—82no—
246C3×C22⋊C4D814yescomplemented
247C3×C42—22no—
248C3×C42—22no—
249C25—21no—
250C25—21no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—21no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4C3×D414yescomplemented
264C22×D4C23×C311yescharacteristic
265C22×D4C23×C312yes—
266C22×D4C23×C311yescharacteristic
267C22×D4C23×C311yescharacteristic
268C23×C4—22no—
269C23×C4C23×C311yescharacteristic
270C2×D8—232no—
271C2×D8—24no—
272C2×D8—24no—
273C2×D8—24no—
274C2×D8—24no—
275C2×D8—22no—
276C2×D8—22no—
277C2×D8—24no—
278C2×D8—24no—
279C2×D8—42no—
280C2×D8C3×D418yescomplemented
281C22×C8—22no—
282C22×C8—24no—
283C22×C8C23×C311yescharacteristic
284C22×C8C23×C311yescharacteristic
285C22×C8C23×C312yes—
286#127—24no—
287#127—42no—
288#121—22no—
289#121—22no—
290#120—44no—
291#120—44no—
292C4×D4—24no—
293C4×D4—42no—
294C2×C4⋊C4C23×C312yes—
295C2×C4⋊C4C23×C311yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—44no—
304C2×C22⋊C4C3×D411yescharacteristic
305C2×C22⋊C4C3×D411yescharacteristic
306C2×C42C23×C312yes—
307C4⋊C8—24no—
308#102—22no—
309#102—22no—
310#102—24no—
311#102—24no—
312#102—42no—
313C22⋊C8—22no—
314#95—21no—
315#95C3×D412yes—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—24no—
320C23×C3—22no—
321C23×C3—24no—
322C23×C3—48no—
323C23×C3—48no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—41no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—41no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—48no—
338C23×C3—41no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—42no—
343C23×C3—84no—
344C23×C3—88no—
345C23×C3—88no—
346C23×C3—88no—
347C23×C3—88no—
348C23×C3—84no—
349C23×C3—84no—
350C23×C3#12112yes—
351C23×C3C2×D812yes—
352C23×C3AGL(1,ℤ/8)12yes—
353C23×C3C22×D411yescharacteristic
354C3×D4—22no—
355C3×D4—24no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—24no—
359C3×D4—24no—
360C3×D4—48no—
361C3×D4—48no—
362C3×D4—41no—
363C3×D4—42no—
364C3×D4—41no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—42no—
368C3×D4—88no—
369C3×D4—88no—
370C3×D4—84no—
371C3×D4#12014yescomplemented
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—41no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—88no—
388C2×C3×C4#12112yes—
389C2×C3×C4C2×D814yescomplemented
390C2×C3×C4C22×D411yescharacteristic
391C2×C3×C4C22×D412yes—
392C2×C3×C4C2×#4111yescharacteristic
393C2×C3×C4H(5,𝔽2)12yes—
394C3×C8—24no—
395C3×C8—41no—
396C3×C8—41no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—24no—
401C24—21no—
402C24—44no—
403C24—44no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—82no—
410C24—82no—
411C24C2×C3×D411yescharacteristic
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—82no—
444C2×D4—82no—
445C2×D4C2×C3×D414yes—
446C2×D4C2×C3×D412yes—
447C2×D4C2×C3×D412yes—
448C2×D4C2×C3×D414yes—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—82no—
456C22×C4C2×C3×D412yes—
457C22×C4C2×C3×D411yescharacteristic
458C22×C4C2×C3×D412yes—
459C22×C4C2×C3×D412yes—
460C22×C4C3×#4112yes—
461C22×C4C24×C311yescharacteristic
462D8—216no—
463D8—216no—
464D8—44no—
465D8—44no—
466C2×C8—28no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8C2×C3×D414yes—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—44no—
480C22⋊C4—44no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—44no—
484C22⋊C4—44no—
485C22⋊C4—82no—
486C22⋊C4C3×D814yescomplemented
487C42—22no—
488C42—22no—
489C22×C3—22no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—22no—
493C22×C3—24no—
494C22×C3—44no—
495C22×C3—44no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—816no—
505C22×C3—816no—
506C22×C3—82no—
507C22×C3—82no—
508C22×C3—82no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3—82no—
512C22×C3—81no—
513C22×C3—82no—
514C22×C3—82no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3#45914yescomplemented
518C22×C3C2×#12111yescharacteristic
519C22×C3D4212yes—
520C22×C3C22×D811yescharacteristic
521C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
522C22×C3#57612yes—
523C3×C4—22no—
524C3×C4—24no—
525C3×C4—42no—
526C3×C4—82no—
527C3×C4—81no—
528C3×C4C2×#12011yescharacteristic
529C3×C4#53411yescharacteristic
530C3×C4#54612yes—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23—48no—
538C23—48no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—48no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—41no—
554C23—41no—
555C23—42no—
556C23—41no—
557C23—42no—
558C23—84no—
559C23—88no—
560C23—88no—
561C23—88no—
562C23—88no—
563C23—84no—
564C23—84no—
565C23C3×#12112yes—
566C23C2×C3×D812yes—
567C23C3×AGL(1,ℤ/8)12yes—
568C23C22×C3×D411yescharacteristic
569D4—22no—
570D4—24no—
571D4—22no—
572D4—22no—
573D4—24no—
574D4—24no—
575D4—48no—
576D4—48no—
577D4—41no—
578D4—42no—
579D4—41no—
580D4—42no—
581D4—42no—
582D4—42no—
583D4—88no—
584D4—88no—
585D4—84no—
586D4C3×#12014yescomplemented
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—88no—
603C2×C4C3×#12112yes—
604C2×C4C2×C3×D814yescomplemented
605C2×C4C22×C3×D411yescharacteristic
606C2×C4C22×C3×D412yes—
607C2×C4C2×C3×#4111yescharacteristic
608C2×C4C3×H(5,𝔽2)12yes—
609C8—24no—
610C8—41no—
611C8—41no—
612C2×C3—24no—
613C2×C3—44no—
614C2×C3—84no—
615C2×C3—82no—
616C2×C3—161no—
617C2×C3#241011yescharacteristic
618C2×C3C2×#45911yescharacteristic
619C2×C3#304111yescharacteristic
620C2×C3#326412yes—
621C2×C3D4×D812yes—
622C22—22no—
623C22—24no—
624C22—24no—
625C22—22no—
626C22—24no—
627C22—44no—
628C22—44no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—44no—
634C22—44no—
635C22—42no—
636C22—42no—
637C22—816no—
638C22—816no—
639C22—82no—
640C22—82no—
641C22—82no—
642C22—82no—
643C22—82no—
644C22—82no—
645C22—81no—
646C22—82no—
647C22—82no—
648C22—81no—
649C22—81no—
650C22C3×#45914yescomplemented
651C22C2×C3×#12111yescharacteristic
652C22C3×D4212yes—
653C22C22×C3×D811yescharacteristic
654C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
655C22C3×#57612yes—
656C4—22no—
657C4—24no—
658C4—42no—
659C4—82no—
660C4—81no—
661C4C2×C3×#12011yescharacteristic
662C4C3×#53411yescharacteristic
663C4C3×#54612yes—
664C3#2435411yescharacteristic, direct product factor, Sylow
665C2—24no—
666C2—44no—
667C2—84no—
668C2—82no—
669C2—161no—
670C2C3×#241011yescharacteristic
671C2C2×C3×#45911yescharacteristic
672C2C3×#304111yescharacteristic
673C2C3×#326412yes—
674C2C3×D4×D812yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×D8C2semidirect
2. C2×C3×#459C2semidirect
3. C2×C3×#447C2semidirect
4. C3×#2433C2semidirect
5. C3×D4×C22⋊C4C2semidirect
6. C3×#2054C2semidirect
7. C3×#2011C2semidirect
8. C3×#1893C2semidirect
9. C3×#1879C2semidirect
10. C3×#1850C2semidirect
11. C3×#1786C2semidirect
12. #24354C3direct (N × H)
19. C22×C3×D8C22semidirect
20. C22×C3×D8C22semidirect
22. C2×C3×#127C22semidirect
26. C2×C3×C4×D4C22semidirect
30. C2×C3×C4⋊C8C22semidirect
31. C2×C3×#102C22semidirect
32. C2×C3×#102C22semidirect
33. C2×C3×#102C22semidirect
34. C2×C3×#102C22semidirect
35. C2×C3×#102C22semidirect
38. C3×#390C22semidirect
39. C3×#390C22semidirect
44. C3×#340C22semidirect
45. C3×#336C22semidirect
46. C23×D8C2×C3semidirect
47. C2×#459C2×C3semidirect
48. C2×#447C2×C3semidirect
49. #2433C2×C3semidirect
50. D4×C22⋊C4C2×C3semidirect
51. #2054C2×C3semidirect
52. #2011C2×C3semidirect
53. #1893C2×C3semidirect
54. #1879C2×C3semidirect
55. #1850C2×C3semidirect
56. #1786C2×C3semidirect
71. C22×C3×D4D4semidirect
88. C2×C3×D8D4semidirect
130. C22×D8C22×C3semidirect
131. C22×D8C22×C3semidirect
133. C2×#127C22×C3semidirect
137. C2×C4×D4C22×C3semidirect
141. C2×C4⋊C8C22×C3semidirect
142. C2×#102C22×C3semidirect
143. C2×#102C22×C3semidirect
144. C2×#102C22×C3semidirect
145. C2×#102C22×C3semidirect
146. C2×#102C22×C3semidirect
149. #390C22×C3semidirect
150. #390C22×C3semidirect
155. #340C22×C3semidirect
156. #336C22×C3semidirect
246. C3×C22⋊C4D8semidirect
263. C22×D4C3×D4semidirect
280. C2×D8C3×D4semidirect
371. C3×D4#120semidirect
389. C2×C3×C4C2×D8semidirect
486. C22⋊C4C3×D8semidirect
517. C22×C3#459semidirect
586. D4C3×#120semidirect
604. C2×C4C2×C3×D8semidirect
650. C22C3×#459semidirect
664. C3#24354direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D82
C2×C3×#4592
C2×C3×#4472
C3×#24332
C3×D4×C22⋊C42
C3×#20542
C3×#20112
C3×#18932
C3×#18792
C3×#18502
C3×#17862
#243543