Finite Group Databasebeta

← C3×#83944 #11863918

Subgroups — C3×#83944 #11863918

Order 1152.

2137 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×D4C211yesmaximal, characteristic, complemented
2C2×C32×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6C3×#5169C214yesmaximal, complemented
7C3×#5156C214yesmaximal, complemented
8C3×#5131C211yesmaximal, characteristic, complemented
9C3×#5126C211yesmaximal, characteristic, complemented
10C3×#3003—31nomaximal
11#83944C311yesmaximal, characteristic, direct product factor
12C24×C3×D3—21no—
13C2×C32×#41C2211yescharacteristic, complemented
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—21no—
16C2×C3×D3×D4—24no—
17C2×C3×D3×D4—24no—
18C2×C3×D3×D4—22no—
19C2×C3×D3×D4C2214yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C32×AGL(1,ℤ/8)—24no—
23C2×C32×SD16C2212yescomplemented
24C2×C32×D8C2212yescomplemented
25C2×C32×M16C2211yescharacteristic, complemented
26C3×#949—24no—
27C3×#946C2212yescomplemented
28C2×C3×#215C2212yescomplemented
29C3×#938C2212yescomplemented
30C3×#937—21no—
31C3×#935—21no—
32C2×C3×#213C2212yescomplemented
33C3×C4×#67—22no—
34C3×#926C2211yescharacteristic, complemented
35C2×C3×#208C2211yescharacteristic, complemented
36C3×#832C2214yescomplemented
37C3×#821C2214yescomplemented
38C3×(C2×D3)⋊C8C2214yescomplemented
39C23×C3×D4—31no—
40C22×D3×D4C2×C311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—21no—
42C2×C3×AGL(1,ℤ/8)—31no—
43C2×C3×AGL(1,ℤ/8)D311yescharacteristic, complemented
44C2×C3×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
45C3×#525—31no—
46#5828C2×C311yescharacteristic, complemented
47C2×#949C2×C311yescharacteristic, complemented
48C3×#450—34no—
49C3×#447—34no—
50C3×#418—31no—
51C3×#418—31no—
52C3×#407—31no—
53#5215C2×C311yescharacteristic, complemented
54#5169C2×C314yescomplemented
55#5156C2×C314yescomplemented
56#5131C2×C311yescharacteristic, complemented
57#5126C2×C311yescharacteristic, complemented
58C24×C32—21no—
59C23×C3×D3—28no—
60C23×C3×D3—21no—
61C23×C3×D3—24no—
62C23×C3×D3—48no—
63C23×C3×D3D411yescharacteristic
64C32×#41—22no—
65C32×#41—22no—
66C2×C32×Q8C2311yescharacteristic, complemented
67C2×C32×D4—21no—
68C2×C32×D4—21no—
69C2×C32×D4—22no—
70C2×C32×D4D414yescomplemented
71C2×C32×D4C2312yes—
72C2×C32×D4C2311yescharacteristic, complemented
73C22×C32×C4—21no—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—28no—
76C2×C3×#67—22no—
77C2×C3×#67—24no—
78C22×C3×Dic3D411yescharacteristic
79C3×D3×D4—216no—
80C3×D3×D4—28no—
81C3×D3×D4—28no—
82C2×C3×D12—21no—
83C2×C3×D12—22no—
84C2×C3×D12D414yescomplemented
85C2×C3×D12C2312yes—
86C2×C3×C4×D3—22no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3D412yes—
89C2×C3×C4×D3C2312yes—
90C32×SD16—24no—
91C32×D8—24no—
92C32×M16—22no—
93C2×C32×C8C2312yescomplemented
94C3×#217—21no—
95C3×#217—22no—
96C3×#215—24no—
97C3×#213—24no—
98C3×(C2×D3)⋊C4—22no—
99C3×C4⋊Dic3C2312yescomplemented
100C3×Dic3⋊C4—22no—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yescomplemented
104#3003—31noSylow
105C25×C3—61no—
106C24×D3—21no—
107C2×C3×#41—21no—
108C2×C3×#41C2×D311yescharacteristic, complemented
109C2×C3×#41C22×C311yescharacteristic, complemented
110C22×C3×D4—21no—
111C22×C3×D4—34no—
112C22×C3×D4—31no—
113C22×C3×D4—62no—
114C22×C3×D4—61no—
115C22×C3×D4—64no—
116C22×C3×D4—64no—
117C22×C3×D4C2×D311yescharacteristic
118C22×C3×D4C22×C311yescharacteristic
119C23×C3×C4—31no—
120C22×#67—21no—
121C2×D3×D4—24no—
122C2×D3×D4—24no—
123C2×D3×D4—22no—
124C2×D3×D4C22×C314yes—
125C22×D12C22×C311yescharacteristic
126C22×C4×D3C22×C311yescharacteristic
127C3×AGL(1,ℤ/8)—28no—
128C3×AGL(1,ℤ/8)—24no—
129C3×AGL(1,ℤ/8)—24no—
130C3×AGL(1,ℤ/8)—64no—
131C2×C3×SD16—22no—
132C2×C3×SD16—32no—
133C2×C3×SD16C2×D312yescomplemented
134C2×C3×SD16C22×C312yescomplemented
135C2×C3×D8—22no—
136C2×C3×D8—32no—
137C2×C3×D8C2×D312yescomplemented
138C2×C3×D8C22×C312yescomplemented
139C2×C3×M16—21no—
140C2×C3×M16—31no—
141C2×C3×M16C2×D311yescharacteristic, complemented
142C2×C3×M16C22×C311yescharacteristic, complemented
143C3×#123—61no—
144C3×C22⋊Q8—32no—
145C3×#121—32no—
146C3×#120—61no—
147C3×C4×D4—62no—
148C3×#117—31no—
149#949—24no—
150#946C22×C312yescomplemented
151C2×#215C22×C312yescomplemented
152#938C22×C312yescomplemented
153#937—21no—
154#935—21no—
155C2×#213C22×C312yescomplemented
156C4×#67—22no—
157#926C22×C311yescharacteristic, complemented
158C2×#208C22×C311yescharacteristic, complemented
159C3×#102—34no—
160C3×#102—34no—
161C3×C22⋊C8—34no—
162#832C22×C314yescomplemented
163#821C22×C314yescomplemented
164(C2×D3)⋊C8C22×C314yescomplemented
165C23×C32—24no—
166C23×C32—22no—
167C23×C32—21no—
168C23×C32—44no—
169C23×C32C2×D411yescharacteristic
170C22×C3×D3—22no—
171C22×C3×D3—24no—
172C22×C3×D3—216no—
173C22×C3×D3—24no—
174C22×C3×D3—22no—
175C22×C3×D3—432no—
176C22×C3×D3—48no—
177C22×C3×D3—44no—
178C22×C3×D3—48no—
179C22×C3×D3C2×D412yes—
180C32×Q8—21no—
181C32×Q8—21no—
182C32×D4—21no—
183C32×D4—24no—
184C32×D4—22no—
185C32×D4—21no—
186C32×D4—42no—
187C32×D4C2×D414yes—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2411yescharacteristic
194C3×#67—216no—
195C3×#67—44no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C2×D412yes—
199C3×D12—24no—
200C3×D12—22no—
201C3×D12C2×D414yes—
202C3×C4×D3—24no—
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207C23×D4—31no—
208C2×AGL(1,ℤ/8)—31no—
209C2×AGL(1,ℤ/8)C3×D311yescharacteristic, complemented
210#525—31no—
211#450—34no—
212#447—34no—
213#418—31no—
214#418—31no—
215#407—31no—
216C24×C3—21no—
217C24×C3—21no—
218C24×C3—31no—
219C24×C3—41no—
220C24×C3—64no—
221C24×C3—68no—
222C24×C3—61no—
223C24×C3—128no—
224C23×D3—28no—
225C23×D3—21no—
226C23×D3—24no—
227C23×D3—48no—
228C23×D3C3×D411yescharacteristic
229C3×#41—24no—
230C3×#41—22no—
231C3×#41—22no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—42no—
235C2×C3×Q8—21no—
236C2×C3×Q8C22×D311yescharacteristic, complemented
237C2×C3×Q8C23×C311yescharacteristic, complemented
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—22no—
242C2×C3×D4—21no—
243C2×C3×D4—22no—
244C2×C3×D4—24no—
245C2×C3×D4—22no—
246C2×C3×D4—21no—
247C2×C3×D4—34no—
248C2×C3×D4—32no—
249C2×C3×D4—41no—
250C2×C3×D4—42no—
251C2×C3×D4—41no—
252C2×C3×D4—64no—
253C2×C3×D4—68no—
254C2×C3×D4—616no—
255C2×C3×D4—68no—
256C2×C3×D4—68no—
257C2×C3×D4—62no—
258C2×C3×D4—61no—
259C2×C3×D4—62no—
260C2×C3×D4#6714yescomplemented
261C2×C3×D4C3×D414yescomplemented
262C2×C3×D4C22×D312yes—
263C2×C3×D4C22×D311yescharacteristic, complemented
264C2×C3×D4C23×C312yes—
265C2×C3×D4C23×C311yescharacteristic, complemented
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—31no—
270C22×C3×C4—32no—
271C22×C3×C4—32no—
272C22×C3×C4—41no—
273C22×C3×C4—62no—
274C22×C3×C4—62no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C23×C311yescharacteristic
277C2×#67—28no—
278C2×#67—22no—
279C2×#67—24no—
280C22×Dic3C3×D411yescharacteristic
281D3×D4—216no—
282D3×D4—28no—
283D3×D4—28no—
284C2×D12—21no—
285C2×D12—22no—
286C2×D12C3×D414yescomplemented
287C2×D12C23×C312yes—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×C4×D3C3×D412yes—
291C2×C4×D3C23×C312yes—
292C3×SD16—28no—
293C3×SD16—24no—
294C3×SD16—24no—
295C3×SD16—64no—
296C3×D8—28no—
297C3×D8—24no—
298C3×D8—24no—
299C3×D8—64no—
300C3×M16—24no—
301C3×M16—22no—
302C3×M16—22no—
303C3×M16—62no—
304C2×C3×C8—22no—
305C2×C3×C8—32no—
306C2×C3×C8C22×D312yescomplemented
307C2×C3×C8C23×C312yescomplemented
308C3×C4⋊C4—32no—
309C3×C4⋊C4—62no—
310C3×C22⋊C4—62no—
311C3×C22⋊C4—62no—
312C3×C22⋊C4—61no—
313C3×C42—61no—
314#217—21no—
315#217—22no—
316#215—24no—
317#213—24no—
318(C2×D3)⋊C4—22no—
319C4⋊Dic3C23×C312yescomplemented
320Dic3⋊C4—22no—
321C4×Dic3—21no—
322#208—22no—
323C2×C3⋊C8C23×C312yescomplemented
324C22×C32—22no—
325C22×C32—24no—
326C22×C32—41no—
327C22×C32—48no—
328C22×C32—44no—
329C22×C32—42no—
330C22×C32#12012yes—
331C22×C32C22×D411yescharacteristic
332C2×C3×D3—28no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—24no—
336C2×C3×D3—432no—
337C2×C3×D3—48no—
338C2×C3×D3—44no—
339C2×C3×D3AGL(1,ℤ/8)14yescomplemented
340C32×C4—41no—
341C32×C4#12012yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—22no—
345C3×Dic3—42no—
346C25—61no—
347C2×#41C2×C3×D311yescharacteristic, complemented
348C22×D4—34no—
349C22×D4—31no—
350C22×D4—62no—
351C22×D4—61no—
352C22×D4—64no—
353C22×D4—64no—
354C22×D4C2×C3×D311yescharacteristic
355C23×C4—31no—
356AGL(1,ℤ/8)—24no—
357AGL(1,ℤ/8)—64no—
358C2×SD16—32no—
359C2×SD16C2×C3×D312yescomplemented
360C2×D8—32no—
361C2×D8C2×C3×D312yescomplemented
362C2×M16—31no—
363C2×M16C2×C3×D311yescharacteristic, complemented
364#123—61no—
365C22⋊Q8—32no—
366#121—32no—
367#120—61no—
368C4×D4—62no—
369#117—31no—
370#102—34no—
371#102—34no—
372C22⋊C8—34no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—32no—
381C23×C3—41no—
382C23×C3—44no—
383C23×C3—42no—
384C23×C3—44no—
385C23×C3—44no—
386C23×C3—64no—
387C23×C3—616no—
388C23×C3—62no—
389C23×C3—64no—
390C23×C3—62no—
391C23×C3—84no—
392C23×C3—124no—
393C23×C3—128no—
394C23×C3—1232no—
395C23×C3—128no—
396C23×C3D3×D411yescharacteristic
397C23×C3C2×C3×D411yescharacteristic
398C22×D3—22no—
399C22×D3—24no—
400C22×D3—216no—
401C22×D3—24no—
402C22×D3—22no—
403C22×D3—432no—
404C22×D3—48no—
405C22×D3—44no—
406C22×D3—48no—
407C22×D3C2×C3×D412yes—
408C3×Q8—22no—
409C3×Q8—21no—
410C3×Q8—21no—
411C3×Q8—21no—
412C3×Q8—21no—
413C3×Q8—41no—
414C3×D4—22no—
415C3×D4—24no—
416C3×D4—24no—
417C3×D4—22no—
418C3×D4—21no—
419C3×D4—21no—
420C3×D4—22no—
421C3×D4—21no—
422C3×D4—21no—
423C3×D4—24no—
424C3×D4—34no—
425C3×D4—44no—
426C3×D4—42no—
427C3×D4—41no—
428C3×D4—44no—
429C3×D4—42no—
430C3×D4—42no—
431C3×D4—616no—
432C3×D4—64no—
433C3×D4—62no—
434C3×D4—124no—
435C3×D4C2×#6714yes—
436C3×D4C2×C3×D414yes—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—32no—
444C2×C3×C4—41no—
445C2×C3×C4—44no—
446C2×C3×C4—42no—
447C2×C3×C4—42no—
448C2×C3×C4—62no—
449C2×C3×C4—64no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4D3×D411yescharacteristic
454C2×C3×C4D3×D412yes—
455C2×C3×C4C2×#6712yes—
456C2×C3×C4C2×C3×D411yescharacteristic
457C2×C3×C4C2×C3×D412yes—
458C2×C3×C4C2×C3×D412yes—
459C2×C3×C4C23×D311yescharacteristic
460C2×C3×C4C24×C311yescharacteristic
461#67—216no—
462#67—44no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3C2×C3×D412yes—
466D12—24no—
467D12—22no—
468D12C2×C3×D414yes—
469C4×D3—24no—
470C4×D3—22no—
471C4×D3—22no—
472C3×C8—24no—
473C3×C8—22no—
474C3×C8—22no—
475C3×C8—62no—
476C3⋊C8—22no—
477C2×C32—22no—
478C2×C32—44no—
479C2×C32—81no—
480C2×C32C2×#12011yescharacteristic
481C2×C32C2×AGL(1,ℤ/8)12yes—
482C3×D3—24no—
483C3×D3—44no—
484C24—21no—
485C24—31no—
486C24—64no—
487C24—68no—
488C24—61no—
489C24—128no—
490#41—22no—
491#41—22no—
492C2×Q8C22×C3×D311yescharacteristic, complemented
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—32no—
497C2×D4—34no—
498C2×D4—64no—
499C2×D4—68no—
500C2×D4—616no—
501C2×D4—68no—
502C2×D4—68no—
503C2×D4—62no—
504C2×D4—61no—
505C2×D4—62no—
506C2×D4C3×#6714yescomplemented
507C2×D4C22×C3×D312yes—
508C2×D4C22×C3×D311yescharacteristic, complemented
509C22×C4—21no—
510C22×C4—31no—
511C22×C4—32no—
512C22×C4—32no—
513C22×C4—62no—
514C22×C4—62no—
515C22×C4C22×C3×D311yescharacteristic
516SD16—24no—
517SD16—64no—
518D8—24no—
519D8—64no—
520M16—22no—
521M16—62no—
522C2×C8—32no—
523C2×C8C22×C3×D312yescomplemented
524C4⋊C4—32no—
525C4⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—62no—
528C22⋊C4—61no—
529C42—61no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—24no—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—21no—
536C22×C3—34no—
537C22×C3—42no—
538C22×C3—44no—
539C22×C3—48no—
540C22×C3—48no—
541C22×C3—42no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—68no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—64no—
552C22×C3—84no—
553C22×C3—82no—
554C22×C3—88no—
555C22×C3—128no—
556C22×C3—1232no—
557C22×C3—124no—
558C22×C3#93712yes—
559C22×C3C3×#12012yes—
560C22×C3C2×D3×D411yescharacteristic
561C22×C3C22×C3×D411yescharacteristic
562C2×D3—28no—
563C2×D3—22no—
564C2×D3—22no—
565C2×D3—24no—
566C2×D3—432no—
567C2×D3—48no—
568C2×D3—44no—
569C2×D3C3×AGL(1,ℤ/8)14yescomplemented
570C3×C4—22no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—42no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—62no—
577C3×C4—122no—
578C3×C4#93712yes—
579C3×C4C3×#12012yes—
580C3×C4C2×D3×D411yescharacteristic
581C3×C4C22×#6711yescharacteristic
582C3×C4C22×C3×D411yescharacteristic
583C3×C4C22×C3×D411yescharacteristic
584Dic3—22no—
585Dic3—42no—
586C32#300311yescharacteristic, complemented, Sylow
587C23—24no—
588C23—22no—
589C23—21no—
590C23—32no—
591C23—44no—
592C23—64no—
593C23—616no—
594C23—62no—
595C23—64no—
596C23—62no—
597C23—124no—
598C23—128no—
599C23—1232no—
600C23—128no—
601C23C3×D3×D411yescharacteristic
602Q8—21no—
603Q8—21no—
604D4—24no—
605D4—22no—
606D4—21no—
607D4—21no—
608D4—34no—
609D4—42no—
610D4—616no—
611D4—64no—
612D4—62no—
613D4—124no—
614D4C2×C3×#6714yes—
615C2×C4—21no—
616C2×C4—32no—
617C2×C4—42no—
618C2×C4—62no—
619C2×C4—64no—
620C2×C4—62no—
621C2×C4—62no—
622C2×C4—62no—
623C2×C4C3×D3×D411yescharacteristic
624C2×C4C3×D3×D412yes—
625C2×C4C2×C3×#6712yes—
626C2×C4C23×C3×D311yescharacteristic
627C8—22no—
628C8—62no—
629C2×C3—22no—
630C2×C3—22no—
631C2×C3—22no—
632C2×C3—21no—
633C2×C3—42no—
634C2×C3—44no—
635C2×C3—44no—
636C2×C3—64no—
637C2×C3—84no—
638C2×C3—82no—
639C2×C3—81no—
640C2×C3—81no—
641C2×C3—124no—
642C2×C3D3×AGL(1,ℤ/8)12yes—
643C2×C3C2×#93711yescharacteristic
644C2×C3C2×C3×#12011yescharacteristic
645C2×C3C2×C3×AGL(1,ℤ/8)12yes—
646D3—24no—
647D3—44no—
648C22—22no—
649C22—24no—
650C22—34no—
651C22—48no—
652C22—44no—
653C22—42no—
654C22—41no—
655C22—68no—
656C22—62no—
657C22—62no—
658C22—64no—
659C22—128no—
660C22—1232no—
661C22—124no—
662C22C3×#93712yes—
663C22C2×C3×D3×D411yescharacteristic
664C4—41no—
665C4—62no—
666C4—122no—
667C4C3×#93712yes—
668C4C2×C3×D3×D411yescharacteristic
669C4C22×C3×#6711yescharacteristic
670C3—21no—
671C3#8394411yescharacteristic, direct product factor
672C3C3×#300311yescharacteristic, complemented
673C2—22no—
674C2—44no—
675C2—64no—
676C2—81no—
677C2—124no—
678C2C3×D3×AGL(1,ℤ/8)12yes—
679C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×AGL(1,ℤ/8)C2
socleC22×C32C22×D4
hypercenterC2×C3×AGL(1,ℤ/8)D3
hypocenterC3C3×#3003
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×D4C2semidirect
2. C2×C32×AGL(1,ℤ/8)C2semidirect
3. C3×#5828C2semidirect
4. C2×C3×#949C2semidirect
5. C3×#5215C2semidirect
6. C3×#5169C2semidirect
7. C3×#5156C2semidirect
8. C3×#5131C2semidirect
9. C3×#5126C2semidirect
11. #83944C3direct (N × H)
13. C2×C32×#41C22semidirect
23. C2×C32×SD16C22semidirect
24. C2×C32×D8C22semidirect
25. C2×C32×M16C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#938C22semidirect
32. C2×C3×#213C22semidirect
34. C3×#926C22semidirect
35. C2×C3×#208C22semidirect
36. C3×#832C22semidirect
37. C3×#821C22semidirect
38. C3×(C2×D3)⋊C8C22semidirect
40. C22×D3×D4C2×C3semidirect
43. C2×C3×AGL(1,ℤ/8)D3semidirect
44. C2×C3×AGL(1,ℤ/8)C2×C3semidirect
46. #5828C2×C3semidirect
47. C2×#949C2×C3semidirect
53. #5215C2×C3semidirect
54. #5169C2×C3semidirect
55. #5156C2×C3semidirect
56. #5131C2×C3semidirect
57. #5126C2×C3semidirect
66. C2×C32×Q8C23semidirect
70. C2×C32×D4D4semidirect
72. C2×C32×D4C23semidirect
84. C2×C3×D12D4semidirect
93. C2×C32×C8C23semidirect
99. C3×C4⋊Dic3C23semidirect
103. C2×C3×C3⋊C8C23semidirect
108. C2×C3×#41C2×D3semidirect
109. C2×C3×#41C22×C3semidirect
133. C2×C3×SD16C2×D3semidirect
134. C2×C3×SD16C22×C3semidirect
137. C2×C3×D8C2×D3semidirect
138. C2×C3×D8C22×C3semidirect
141. C2×C3×M16C2×D3semidirect
142. C2×C3×M16C22×C3semidirect
150. #946C22×C3semidirect
151. C2×#215C22×C3semidirect
152. #938C22×C3semidirect
155. C2×#213C22×C3semidirect
157. #926C22×C3semidirect
158. C2×#208C22×C3semidirect
162. #832C22×C3semidirect
163. #821C22×C3semidirect
164. (C2×D3)⋊C8C22×C3semidirect
209. C2×AGL(1,ℤ/8)C3×D3semidirect
236. C2×C3×Q8C22×D3semidirect
237. C2×C3×Q8C23×C3semidirect
260. C2×C3×D4#67semidirect
261. C2×C3×D4C3×D4semidirect
263. C2×C3×D4C22×D3semidirect
265. C2×C3×D4C23×C3semidirect
286. C2×D12C3×D4semidirect
306. C2×C3×C8C22×D3semidirect
307. C2×C3×C8C23×C3semidirect
319. C4⋊Dic3C23×C3semidirect
323. C2×C3⋊C8C23×C3semidirect
339. C2×C3×D3AGL(1,ℤ/8)semidirect
347. C2×#41C2×C3×D3semidirect
359. C2×SD16C2×C3×D3semidirect
361. C2×D8C2×C3×D3semidirect
363. C2×M16C2×C3×D3semidirect
492. C2×Q8C22×C3×D3semidirect
506. C2×D4C3×#67semidirect
508. C2×D4C22×C3×D3semidirect
523. C2×C8C22×C3×D3semidirect
569. C2×D3C3×AGL(1,ℤ/8)semidirect
586. C32#3003semidirect
671. C3#83944direct (N × H)
672. C3C3×#3003semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×D42
C2×C32×AGL(1,ℤ/8)2
C3×#58282
C2×C3×#9492
C3×#52152
C3×#51692
C3×#51562
C3×#51312
C3×#51262
C3×#30033
#839443