Finite Group Databasebeta

← C3×#24231 #10642838

Subgroups — C3×#24231 #10642838

Order 768.

1368 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3499C211yesmaximal, characteristic, complemented
2C3×#3036C211yesmaximal, characteristic, complemented
3C2×C3×#454C212yesmaximal, complemented
4C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
5C3×#2547C211yesmaximal, characteristic, complemented
6C3×#2038C212yesmaximal, complemented
7C3×#2003C212yesmaximal, complemented
8C3×#1980C211yesmaximal, characteristic, complemented
9C3×#1966C211yesmaximal, characteristic, complemented
10C3×#1806C211yesmaximal, characteristic, complemented
11C3×#1793C212yesmaximal, complemented
12#24231C311yesmaximal, characteristic, direct product factor, Sylow
13C2×C3×2−1+4C2212yes—
14C2×C3×AGL(1,ℤ/8)C2212yes—
15C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
16C3×D4×Q8—21no—
17C3×D4×Q8—21no—
18C3×#547—21no—
19C3×#547—21no—
20C3×#547—22no—
21C3×#547—22no—
22C3×#536—22no—
23C3×#536C2212yes—
24C3×#532—21no—
25C3×#532C2211yescharacteristic
26C2×C3×C4⋊Q8—21no—
27C2×C3×C4⋊Q8C2211yescharacteristic
28C2×C3×#124C2212yes—
29C3×C4×#41C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C3×#463—22no—
32C3×#461—21no—
33C3×#459—21no—
34C3×#454—28no—
35C3×#442—21no—
36C3×#440—21no—
37C3×C4×SD16—21no—
38C3×C4×D8—21no—
39C3×#428C2211yescharacteristic
40C3×#423C2211yescharacteristic
41C2×C3×#104C2212yes—
42C2×C3×#104C2212yes—
43C2×C3×#104C2212yes—
44C3×#418C2211yescharacteristic
45C3×#417C2212yes—
46C3×#417C2211yescharacteristic
47C2×C3×#101C2212yes—
48C2×C3×#101C2212yes—
49C3×C4×M16C2211yescharacteristic
50C3×#397—22no—
51C3×#391C2212yes—
52C3×#380—22no—
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×#339C2212yes—
55#3499C2×C311yescharacteristic, complemented
56#3036C2×C311yescharacteristic, complemented
57C2×#454C2×C312yescomplemented
58C4×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
59#2547C2×C311yescharacteristic, complemented
60#2038C2×C312yescomplemented
61#2003C2×C312yescomplemented
62#1980C2×C311yescharacteristic, complemented
63#1966C2×C311yescharacteristic, complemented
64#1806C2×C311yescharacteristic, complemented
65#1793C2×C312yescomplemented
66C3×2−1+4—24no—
67C3×2−1+4—24no—
68C3×2−1+4—42no—
69C3×2−1+4—42no—
70C2×C3×#41—22no—
71C2×C3×#41—22no—
72C2×C3×#41—24no—
73C2×C3×#41C2312yes—
74C2×C3×#41C2311yescharacteristic
75C22×C3×Q8—22no—
76C22×C3×Q8—22no—
77C22×C3×Q8C2312yes—
78C22×C3×D4C2311yescharacteristic
79C23×C3×C4—21no—
80C3×AGL(1,ℤ/8)—22no—
81C3×AGL(1,ℤ/8)—24no—
82C3×AGL(1,ℤ/8)—42no—
83C3×AGL(1,ℤ/8)D414yescomplemented
84C2×C3×SD16—21no—
85C2×C3×SD16—22no—
86C2×C3×D8—21no—
87C2×C3×D8—22no—
88C2×C3×M16C2312yes—
89C2×C3×M16C2311yescharacteristic
90C2×C3×M16C2311yescharacteristic
91C3×C4⋊Q8—22no—
92C3×C4⋊Q8—22no—
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—21no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—21no—
98C3×C4⋊Q8D411yescharacteristic
99C3×#127D411yescharacteristic
100C3×#124—22no—
101C3×#124—24no—
102C3×#124—42no—
103C3×#124D412yes—
104C3×#123—24no—
105C3×#123—24no—
106C3×#123—24no—
107C3×C22⋊Q8—24no—
108C3×C22⋊Q8—24no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—22no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—21no—
114C3×#121—21no—
115C3×C4×Q8D411yescharacteristic
116C3×C4×Q8D411yescharacteristic
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C3×C4×D4—21no—
120C3×C4×D4—21no—
121C3×C4×D4—21no—
122C3×C4×D4—21no—
123C3×C4×D4—21no—
124C3×C4×D4—21no—
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×C4×D4D411yescharacteristic
128C3×C4×D4D411yescharacteristic
129C3×#117—21no—
130C3×#117C2311yescharacteristic
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4D412yes—
135C2×C3×C4⋊C4D412yes—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—24no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C42—21no—
140C2×C3×C42C2312yes—
141C2×C3×C42C2311yescharacteristic
142C3×#107—21no—
143C3×#106—21no—
144C3×C4⋊C8—21no—
145C3×C4⋊C8—21no—
146C3×#104—24no—
147C3×#104—24no—
148C3×#104—42no—
149C3×#103—21no—
150C3×#103—22no—
151C3×#102—21no—
152C3×#102—22no—
153C3×#102—21no—
154C3×#102—21no—
155C3×#101—24no—
156C3×#101—42no—
157C3×#97—21no—
158C3×C4×C8—21no—
159C3×#95—21no—
160C3×#95—24no—
161C2×2−1+4C22×C312yes—
162C2×AGL(1,ℤ/8)C22×C312yes—
163C2×AGL(1,ℤ/8)C22×C311yescharacteristic
164D4×Q8—21no—
165D4×Q8—21no—
166#547—21no—
167#547—21no—
168#547—22no—
169#547—22no—
170#536—22no—
171#536C22×C312yes—
172#532—21no—
173#532C22×C311yescharacteristic
174C2×C4⋊Q8—21no—
175C2×C4⋊Q8C22×C311yescharacteristic
176C2×#124C22×C312yes—
177C4×#41C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179#463—22no—
180#461—21no—
181#459—21no—
182#454—28no—
183#442—21no—
184#440—21no—
185C4×SD16—21no—
186C4×D8—21no—
187#428C22×C311yescharacteristic
188#423C22×C311yescharacteristic
189C2×#104C22×C312yes—
190C2×#104C22×C312yes—
191C2×#104C22×C312yes—
192#418C22×C311yescharacteristic
193#417C22×C311yescharacteristic
194#417C22×C312yes—
195C2×#101C22×C312yes—
196C2×#101C22×C312yes—
197C4×M16C22×C311yescharacteristic
198#397—22no—
199#391C22×C312yes—
200#380—22no—
201C4×C4⋊C4C22×C311yescharacteristic
202#339C22×C312yes—
203C24×C3—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—22no—
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—44no—
211C3×#41—44no—
212C3×#41—48no—
213C3×#41—48no—
214C3×#41—44no—
215C3×#41—44no—
216C3×#41C2×D412yes—
217C3×#41#4112yes—
218C2×C3×Q8—24no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—22no—
222C2×C3×Q8—22no—
223C2×C3×Q8—22no—
224C2×C3×Q8—22no—
225C2×C3×Q8—44no—
226C2×C3×Q8—44no—
227C2×C3×Q8—44no—
228C2×C3×Q8—44no—
229C2×C3×Q8C2×D412yes—
230C2×C3×Q8C2×D411yescharacteristic
231C2×C3×D4—21no—
232C2×C3×D4—24no—
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4C2×D412yes—
242C2×C3×D4C2×D412yes—
243C2×C3×D4C2×D411yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—24no—
246C22×C3×C4—24no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—44no—
253C22×C3×C4—41no—
254C22×C3×C4—41no—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C3×SD16—24no—
260C3×SD16—44no—
261C3×D8—24no—
262C3×D8—44no—
263C3×M16—21no—
264C3×M16—22no—
265C3×M16—21no—
266C3×M16—22no—
267C3×M16—21no—
268C3×M16C2×D412yes—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—22no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4C2×D411yescharacteristic
286C3×C4⋊C4C2×D411yescharacteristic
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—21no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—48no—
295C3×C22⋊C4—41no—
296C3×C22⋊C4—41no—
297C3×C42—21no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—22no—
301C3×C42—22no—
302C3×C42C2×D411yescharacteristic
303C3×C42C2×D411yescharacteristic
304C3×C42C2×D411yescharacteristic
305C3×C42C2×D411yescharacteristic
3062−1+4—24no—
3072−1+4—24no—
3082−1+4—42no—
3092−1+4—42no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—24no—
313C2×#41C23×C312yes—
314C2×#41C23×C311yescharacteristic
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8C23×C312yes—
318C22×D4C23×C311yescharacteristic
319C23×C4—21no—
320AGL(1,ℤ/8)—22no—
321AGL(1,ℤ/8)—24no—
322AGL(1,ℤ/8)—42no—
323AGL(1,ℤ/8)C3×D414yescomplemented
324C2×SD16—21no—
325C2×SD16—22no—
326C2×D8—21no—
327C2×D8—22no—
328C2×M16C23×C312yes—
329C2×M16C23×C311yescharacteristic
330C2×M16C23×C311yescharacteristic
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8C3×D411yescharacteristic
339#127C3×D411yescharacteristic
340#124—22no—
341#124—24no—
342#124—42no—
343#124C3×D412yes—
344#123—24no—
345#123—24no—
346#123—24no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351#121—22no—
352#121—22no—
353#121—21no—
354#121—21no—
355C4×Q8C3×D411yescharacteristic
356C4×Q8C3×D411yescharacteristic
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4C3×D411yescharacteristic
368C4×D4C3×D411yescharacteristic
369#117—21no—
370#117C23×C311yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4C3×D412yes—
375C2×C4⋊C4C3×D412yes—
376C2×C4⋊C4C23×C311yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—24no—
379C2×C42—21no—
380C2×C42C23×C312yes—
381C2×C42C23×C311yescharacteristic
382#107—21no—
383#106—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386#104—24no—
387#104—24no—
388#104—42no—
389#103—21no—
390#103—22no—
391#102—21no—
392#102—22no—
393#102—21no—
394#102—21no—
395#101—24no—
396#101—42no—
397#97—21no—
398C4×C8—21no—
399#95—21no—
400#95—24no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3C22×D411yescharacteristic
409C3×Q8—21no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—48no—
413C3×Q8—42no—
414C3×Q8—42no—
415C3×Q8—42no—
416C3×Q8—42no—
417C3×Q8#12112yes—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—21no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—22no—
425C3×D4—42no—
426C3×D4—48no—
427C3×D4—42no—
428C3×D4—42no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—42no—
432C3×D4#12112yes—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—24no—
441C2×C3×C4—24no—
442C2×C3×C4—24no—
443C2×C3×C4—41no—
444C2×C3×C4—42no—
445C2×C3×C4—48no—
446C2×C3×C4—48no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—41no—
454C2×C3×C4—42no—
455C2×C3×C4—82no—
456C2×C3×C4—82no—
457C2×C3×C4#12011yescharacteristic
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12011yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4C22×D411yescharacteristic
463C2×C3×C4C22×D411yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465C2×C3×C4H(5,𝔽2)11yescharacteristic
466C2×C3×C4H(5,𝔽2)11yescharacteristic
467C3×C8—22no—
468C3×C8—41no—
469C3×C8—42no—
470C24—21no—
471#41—21no—
472#41—21no—
473#41—22no—
474#41—22no—
475#41—22no—
476#41—22no—
477#41—44no—
478#41—44no—
479#41—48no—
480#41—48no—
481#41—44no—
482#41—44no—
483#41C2×C3×D412yes—
484#41C3×#4112yes—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8C2×C3×D412yes—
497C2×Q8C2×C3×D411yescharacteristic
498C2×D4—21no—
499C2×D4—24no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C2×C3×D412yes—
509C2×D4C2×C3×D412yes—
510C2×D4C2×C3×D411yescharacteristic
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—44no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4C2×C3×D414yes—
523C22×C4C2×C3×D411yescharacteristic
524C22×C4C2×C3×D411yescharacteristic
525C22×C4C24×C311yescharacteristic
526SD16—24no—
527SD16—44no—
528D8—24no—
529D8—44no—
530M16—21no—
531M16—22no—
532M16—21no—
533M16—22no—
534M16—21no—
535M16C2×C3×D412yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—22no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4C2×C3×D411yescharacteristic
553C4⋊C4C2×C3×D411yescharacteristic
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—48no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—22no—
568C42—22no—
569C42C2×C3×D411yescharacteristic
570C42C2×C3×D411yescharacteristic
571C42C2×C3×D411yescharacteristic
572C42C2×C3×D411yescharacteristic
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—22no—
576C22×C3—44no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—82no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3C2×#12011yescharacteristic
587C22×C3D4211yescharacteristic
588C22×C3#54611yescharacteristic
589C3×C4—22no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—44no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—82no—
598C3×C4—81no—
599C3×C4#45412yescomplemented
600C3×C4C2×#12111yescharacteristic
601C3×C4#53511yescharacteristic
602C3×C4D4211yescharacteristic
603C3×C4#54611yescharacteristic
604C23—21no—
605C23—22no—
606C23—22no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23C22×C3×D411yescharacteristic
612Q8—21no—
613Q8—22no—
614Q8—22no—
615Q8—48no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8C3×#12112yes—
621D4—22no—
622D4—22no—
623D4—22no—
624D4—21no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—42no—
629D4—48no—
630D4—42no—
631D4—42no—
632D4—42no—
633D4—41no—
634D4—41no—
635D4C3×#12112yes—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—41no—
647C2×C4—48no—
648C2×C4—42no—
649C2×C4—48no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4C3×#12011yescharacteristic
661C2×C4C3×#12011yescharacteristic
662C2×C4C3×#12011yescharacteristic
663C2×C4C3×#12011yescharacteristic
664C2×C4C22×C3×D411yescharacteristic
665C2×C4C22×C3×D411yescharacteristic
666C2×C4C22×C3×D411yescharacteristic
667C2×C4C2×C3×#4111yescharacteristic
668C2×C4C3×H(5,𝔽2)11yescharacteristic
669C2×C4C3×H(5,𝔽2)11yescharacteristic
670C8—22no—
671C8—41no—
672C8—42no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—42no—
676C2×C3—82no—
677C2×C3—82no—
678C2×C3#240811yescharacteristic
679C2×C3C2×#45411yescharacteristic
680C2×C3#302011yescharacteristic
681C22—21no—
682C22—21no—
683C22—22no—
684C22—44no—
685C22—41no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—82no—
692C22—81no—
693C22—81no—
694C22C2×C3×#12011yescharacteristic
695C22C3×D4211yescharacteristic
696C22C3×#54611yescharacteristic
697C4—22no—
698C4—21no—
699C4—21no—
700C4—21no—
701C4—44no—
702C4—42no—
703C4—41no—
704C4—41no—
705C4—82no—
706C4—81no—
707C4C3×#45412yescomplemented
708C4C2×C3×#12111yescharacteristic
709C4C3×#53511yescharacteristic
710C4C3×D4211yescharacteristic
711C4C3×#54611yescharacteristic
712C3#2423111yescharacteristic, direct product factor, Sylow
713C2—21no—
714C2—21no—
715C2—42no—
716C2—82no—
717C2—82no—
718C2C3×#240811yescharacteristic
719C2C2×C3×#45411yescharacteristic
720C2C3×#302011yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3499C2semidirect
2. C3×#3036C2semidirect
3. C2×C3×#454C2semidirect
4. C3×C4×AGL(1,ℤ/8)C2semidirect
5. C3×#2547C2semidirect
6. C3×#2038C2semidirect
7. C3×#2003C2semidirect
8. C3×#1980C2semidirect
9. C3×#1966C2semidirect
10. C3×#1806C2semidirect
11. C3×#1793C2semidirect
12. #24231C3direct (N × H)
55. #3499C2×C3semidirect
56. #3036C2×C3semidirect
57. C2×#454C2×C3semidirect
58. C4×AGL(1,ℤ/8)C2×C3semidirect
59. #2547C2×C3semidirect
60. #2038C2×C3semidirect
61. #2003C2×C3semidirect
62. #1980C2×C3semidirect
63. #1966C2×C3semidirect
64. #1806C2×C3semidirect
65. #1793C2×C3semidirect
83. C3×AGL(1,ℤ/8)D4semidirect
323. AGL(1,ℤ/8)C3×D4semidirect
599. C3×C4#454semidirect
707. C4C3×#454semidirect
712. C3#24231direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34992
C3×#30362
C2×C3×#4542
C3×C4×AGL(1,ℤ/8)2
C3×#25472
C3×#20382
C3×#20032
C3×#19802
C3×#19662
C3×#18062
C3×#17932
#242313