Finite Group Databasebeta

← C3×#25770 #10644377

Subgroups — C3×#25770 #10644377

Order 768.

1810 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#546C211yesmaximal, characteristic, complemented
2C2×C3×#496C211yesmaximal, characteristic, complemented
3C2×C3×#459C211yesmaximal, characteristic, complemented
4C2×C3×#449C212yesmaximal, complemented
5C2×C3×#447C212yesmaximal, complemented
6C3×#2541C211yesmaximal, characteristic, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1999C212yesmaximal, complemented
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1955C211yesmaximal, characteristic, complemented
11C3×#1762C211yesmaximal, characteristic, complemented
12#25770C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×D4C2211yescharacteristic
15C22×C3×SD16C2212yescomplemented
16C22×C3×D8C2212yes—
17C22×C3×D8C2212yes—
18C3×#546—24no—
19C3×#546—24no—
20C2×C3×#127—21no—
21C2×C3×#127C2211yescharacteristic, complemented
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121—21no—
26C2×C3×#121C2211yescharacteristic
27C2×C3×#121C2212yes—
28C2×C3×#121C2212yescomplemented
29C2×C3×#120—21no—
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C22⋊C4—21no—
33C3×#496—24no—
34C3×#459—24no—
35C3×#449—28no—
36C3×#447—28no—
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#103C2212yescomplemented
39C2×C3×#102C2212yes—
40C2×C3×#102C2212yes—
41C2×C3×#102C2212yescomplemented
42C2×C3×C22⋊C8C2212yes—
43C2×C3×C22⋊C8C2212yescomplemented
44C2×C3×#97C2211yescharacteristic, complemented
45C3×#392—21no—
46C3×#392—21no—
47C3×#390—21no—
48C3×C4×C4⋊C4C2211yescharacteristic, complemented
49C3×#340C2212yescomplemented
50C2×#546C2×C311yescharacteristic, complemented
51C2×#496C2×C311yescharacteristic, complemented
52C2×#459C2×C311yescharacteristic, complemented
53C2×#449C2×C312yescomplemented
54C2×#447C2×C312yescomplemented
55#2541C2×C311yescharacteristic, complemented
56#2000C2×C312yescomplemented
57#1999C2×C312yescomplemented
58#1983C2×C311yescharacteristic, complemented
59#1955C2×C311yescharacteristic, complemented
60#1762C2×C311yescharacteristic, complemented
61C25×C3—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—24no—
65C2×C3×#41—42no—
66C22×C3×Q8C2311yescharacteristic
67C22×C3×D4—21no—
68C22×C3×D4—21no—
69C22×C3×D4—22no—
70C22×C3×D4—22no—
71C22×C3×D4—24no—
72C22×C3×D4—22no—
73C22×C3×D4—22no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4—21no—
77C22×C3×D4—42no—
78C22×C3×D4D411yescharacteristic
79C22×C3×D4C2312yes—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C2×C3×SD16—24no—
87C2×C3×SD16—24no—
88C2×C3×SD16—42no—
89C2×C3×D8—24no—
90C2×C3×D8—24no—
91C2×C3×D8—24no—
92C2×C3×D8—24no—
93C2×C3×D8—24no—
94C2×C3×D8—42no—
95C22×C3×C8C2312yes—
96C22×C3×C8C2312yes—
97C3×#127—22no—
98C3×#127—22no—
99C3×#127—44no—
100C3×#124—22no—
101C3×#124D414yescomplemented
102C3×#123—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×#121—28no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—24no—
109C3×#121—24no—
110C3×#121—42no—
111C3×#121—42no—
112C3×#120—28no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4D414yescomplemented
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C22⋊C4—28no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C22⋊C4D411yescharacteristic
131C2×C3×C42—21no—
132C2×C3×C42C2311yescharacteristic
133C3×C4⋊C8—22no—
134C3×#103—24no—
135C3×#102—24no—
136C3×#102—24no—
137C3×#102D418yescomplemented
138C3×C22⋊C8—24no—
139C3×C22⋊C8—24no—
140C3×#97—22no—
141C3×#95—21no—
142C22×#41C22×C311yescharacteristic
143C23×D4C22×C311yescharacteristic
144C22×SD16C22×C312yescomplemented
145C22×D8C22×C312yes—
146C22×D8C22×C312yes—
147#546—24no—
148#546—24no—
149C2×#127—21no—
150C2×#127C22×C311yescharacteristic, complemented
151C2×#124C22×C311yescharacteristic
152C2×#123—21no—
153C2×C22⋊Q8C22×C311yescharacteristic
154C2×#121—21no—
155C2×#121C22×C311yescharacteristic
156C2×#121C22×C312yes—
157C2×#121C22×C312yescomplemented
158C2×#120—21no—
159C2×C4×D4C22×C311yescharacteristic
160C2×C4×D4C22×C311yescharacteristic
161C22×C22⋊C4—21no—
162#496—24no—
163#459—24no—
164#449—28no—
165#447—28no—
166C2×C4⋊C8C22×C311yescharacteristic, complemented
167C2×#103C22×C312yescomplemented
168C2×#102C22×C312yes—
169C2×#102C22×C312yes—
170C2×#102C22×C312yescomplemented
171C2×C22⋊C8C22×C312yes—
172C2×C22⋊C8C22×C312yescomplemented
173C2×#97C22×C311yescharacteristic, complemented
174#392—21no—
175#392—21no—
176#390—21no—
177C4×C4⋊C4C22×C311yescharacteristic, complemented
178#340C22×C312yescomplemented
179C24×C3—21no—
180C24×C3—24no—
181C24×C3—21no—
182C24×C3—22no—
183C24×C3—44no—
184C24×C3—42no—
185C24×C3—42no—
186C24×C3—82no—
187C24×C3C2×D411yescharacteristic
188C24×C3C2×D411yescharacteristic
189C3×#41—48no—
190C3×#41—44no—
191C3×#41—44no—
192C2×C3×Q8—21no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8C2×D412yes—
196C2×C3×D4—24no—
197C2×C3×D4—24no—
198C2×C3×D4—22no—
199C2×C3×D4—24no—
200C2×C3×D4—22no—
201C2×C3×D4—21no—
202C2×C3×D4—22no—
203C2×C3×D4—21no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—41no—
213C2×C3×D4—44no—
214C2×C3×D4—44no—
215C2×C3×D4—44no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—48no—
219C2×C3×D4—44no—
220C2×C3×D4—44no—
221C2×C3×D4—44no—
222C2×C3×D4—44no—
223C2×C3×D4—44no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4—82no—
227C2×C3×D4—82no—
228C2×C3×D4—82no—
229C2×C3×D4—82no—
230C2×C3×D4C2×D412yes—
231C2×C3×D4C2×D414yes—
232C2×C3×D4C2×D412yes—
233C22×C3×C4—24no—
234C22×C3×C4—22no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—24no—
246C22×C3×C4—44no—
247C22×C3×C4—82no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2411yescharacteristic
253C3×SD16—48no—
254C3×D8—48no—
255C3×D8—48no—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8C2×D414yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4C2×D412yes—
267C3×C4⋊C4C2×D414yes—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—24no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—44no—
276C3×C22⋊C4—44no—
277C3×C42—42no—
278C3×C42C2×D412yes—
279C3×C42C2×D412yes—
280C25—21no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—24no—
284C2×#41—42no—
285C22×Q8C23×C311yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—24no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—42no—
297C22×D4C3×D411yescharacteristic
298C22×D4C23×C312yes—
299C22×D4C23×C311yescharacteristic
300C22×D4C23×C311yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4C23×C311yescharacteristic
304C23×C4C23×C311yescharacteristic
305C2×SD16—24no—
306C2×SD16—24no—
307C2×SD16—42no—
308C2×D8—24no—
309C2×D8—24no—
310C2×D8—24no—
311C2×D8—24no—
312C2×D8—24no—
313C2×D8—42no—
314C22×C8C23×C312yes—
315C22×C8C23×C312yes—
316#127—22no—
317#127—22no—
318#127—44no—
319#124—22no—
320#124C3×D414yescomplemented
321#123—28no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324#121—28no—
325#121—22no—
326#121—22no—
327#121—24no—
328#121—24no—
329#121—42no—
330#121—42no—
331#120—28no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4C3×D414yescomplemented
336C2×C4⋊C4—21no—
337C2×C4⋊C4C3×D411yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C4⋊C4C23×C312yes—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4C3×D411yescharacteristic
349C2×C22⋊C4C3×D411yescharacteristic
350C2×C42—21no—
351C2×C42C23×C311yescharacteristic
352C4⋊C8—22no—
353#103—24no—
354#102—24no—
355#102—24no—
356#102C3×D418yescomplemented
357C22⋊C8—24no—
358C22⋊C8—24no—
359#97—22no—
360#95—21no—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—21no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—21no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—48no—
374C23×C3—48no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—42no—
389C23×C3—88no—
390C23×C3—84no—
391C23×C3—88no—
392C23×C3AGL(1,ℤ/8)12yes—
393C23×C3C22×D411yescharacteristic
394C3×Q8—24no—
395C3×Q8—41no—
396C3×Q8—41no—
397C3×D4—22no—
398C3×D4—24no—
399C3×D4—24no—
400C3×D4—44no—
401C3×D4—48no—
402C3×D4—48no—
403C3×D4—41no—
404C3×D4—42no—
405C3×D4—41no—
406C3×D4—42no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—84no—
410C3×D4—84no—
411C3×D4—88no—
412C3×D4—84no—
413C3×D4—88no—
414C3×D4#12714yescomplemented
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—24no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—48no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—84no—
437C2×C3×C4#12012yes—
438C2×C3×C4#12012yes—
439C2×C3×C4C22×D411yescharacteristic
440C2×C3×C4C22×D412yes—
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4H(5,𝔽2)12yes—
443C3×C8—24no—
444C3×C8—42no—
445C24—21no—
446C24—24no—
447C24—21no—
448C24—22no—
449C24—44no—
450C24—42no—
451C24—42no—
452C24—82no—
453C24C2×C3×D411yescharacteristic
454C24C2×C3×D411yescharacteristic
455#41—48no—
456#41—44no—
457#41—44no—
458C2×Q8—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8C2×C3×D412yes—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—22no—
465C2×D4—24no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—41no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—82no—
493C2×D4—82no—
494C2×D4—82no—
495C2×D4—82no—
496C2×D4C2×C3×D412yes—
497C2×D4C2×C3×D414yes—
498C2×D4C2×C3×D412yes—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—44no—
513C22×C4—82no—
514C22×C4C2×C3×D411yescharacteristic
515C22×C4C2×C3×D411yescharacteristic
516C22×C4C2×C3×D411yescharacteristic
517C22×C4C2×C3×D411yescharacteristic
518C22×C4C24×C311yescharacteristic
519SD16—48no—
520D8—48no—
521D8—48no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8C2×C3×D414yes—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4C2×C3×D412yes—
533C4⋊C4C2×C3×D414yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—22no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—22no—
541C22⋊C4—44no—
542C22⋊C4—44no—
543C42—42no—
544C42C2×C3×D412yes—
545C42C2×C3×D412yes—
546C22×C3—24no—
547C22×C3—22no—
548C22×C3—24no—
549C22×C3—41no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—41no—
553C22×C3—44no—
554C22×C3—42no—
555C22×C3—44no—
556C22×C3—41no—
557C22×C3—42no—
558C22×C3—41no—
559C22×C3—42no—
560C22×C3—41no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—816no—
565C22×C3—82no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—82no—
571C22×C3—82no—
572C22×C3—82no—
573C22×C3—82no—
574C22×C3C2×#12011yescharacteristic
575C22×C3D4212yes—
576C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
577C22×C3#57511yescharacteristic
578C22×C3#57612yes—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—42no—
584C3×C4—42no—
585C3×C4—44no—
586C3×C4C2×#12711yescharacteristic
587C3×C4#53511yescharacteristic
588C3×C4D4212yes—
589C23—21no—
590C23—22no—
591C23—21no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—21no—
596C23—21no—
597C23—22no—
598C23—22no—
599C23—21no—
600C23—22no—
601C23—48no—
602C23—48no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—88no—
618C23—84no—
619C23—88no—
620C23C3×AGL(1,ℤ/8)12yes—
621C23C22×C3×D411yescharacteristic
622Q8—24no—
623Q8—41no—
624Q8—41no—
625D4—22no—
626D4—24no—
627D4—24no—
628D4—44no—
629D4—48no—
630D4—48no—
631D4—41no—
632D4—42no—
633D4—41no—
634D4—42no—
635D4—42no—
636D4—42no—
637D4—84no—
638D4—84no—
639D4—88no—
640D4—84no—
641D4—88no—
642D4C3×#12714yescomplemented
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4C3×#12012yes—
666C2×C4C3×#12012yes—
667C2×C4C22×C3×D411yescharacteristic
668C2×C4C22×C3×D412yes—
669C2×C4C22×C3×D411yescharacteristic
670C2×C4C3×H(5,𝔽2)12yes—
671C8—24no—
672C8—42no—
673C2×C3—42no—
674C2×C3—44no—
675C2×C3—81no—
676C2×C3—82no—
677C2×C3—162no—
678C2×C3#243311yescharacteristic
679C2×C3#300611yescharacteristic
680C2×C3#300811yescharacteristic
681C2×C3#326412yes—
682C2×C3#326812yes—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—41no—
690C22—44no—
691C22—42no—
692C22—44no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—816no—
702C22—82no—
703C22—82no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22C2×C3×#12011yescharacteristic
712C22C3×D4212yes—
713C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
714C22C3×#57511yescharacteristic
715C22C3×#57612yes—
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—42no—
721C4—42no—
722C4—44no—
723C4C2×C3×#12711yescharacteristic
724C4C3×#53511yescharacteristic
725C4C3×D4212yes—
726C3#2577011yescharacteristic, direct product factor, Sylow
727C2—42no—
728C2—44no—
729C2—81no—
730C2—82no—
731C2—162no—
732C2C3×#243311yescharacteristic
733C2C3×#300611yescharacteristic
734C2C3×#300811yescharacteristic
735C2C3×#326412yes—
736C2C3×#326812yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#546C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#459C2semidirect
4. C2×C3×#449C2semidirect
5. C2×C3×#447C2semidirect
6. C3×#2541C2semidirect
7. C3×#2000C2semidirect
8. C3×#1999C2semidirect
9. C3×#1983C2semidirect
10. C3×#1955C2semidirect
11. C3×#1762C2semidirect
12. #25770C3direct (N × H)
15. C22×C3×SD16C22semidirect
21. C2×C3×#127C22semidirect
28. C2×C3×#121C22semidirect
37. C2×C3×C4⋊C8C22semidirect
38. C2×C3×#103C22semidirect
41. C2×C3×#102C22semidirect
43. C2×C3×C22⋊C8C22semidirect
44. C2×C3×#97C22semidirect
48. C3×C4×C4⋊C4C22semidirect
49. C3×#340C22semidirect
50. C2×#546C2×C3semidirect
51. C2×#496C2×C3semidirect
52. C2×#459C2×C3semidirect
53. C2×#449C2×C3semidirect
54. C2×#447C2×C3semidirect
55. #2541C2×C3semidirect
56. #2000C2×C3semidirect
57. #1999C2×C3semidirect
58. #1983C2×C3semidirect
59. #1955C2×C3semidirect
60. #1762C2×C3semidirect
101. C3×#124D4semidirect
116. C3×C4×D4D4semidirect
137. C3×#102D4semidirect
144. C22×SD16C22×C3semidirect
150. C2×#127C22×C3semidirect
157. C2×#121C22×C3semidirect
166. C2×C4⋊C8C22×C3semidirect
167. C2×#103C22×C3semidirect
170. C2×#102C22×C3semidirect
172. C2×C22⋊C8C22×C3semidirect
173. C2×#97C22×C3semidirect
177. C4×C4⋊C4C22×C3semidirect
178. #340C22×C3semidirect
320. #124C3×D4semidirect
335. C4×D4C3×D4semidirect
356. #102C3×D4semidirect
414. C3×D4#127semidirect
642. D4C3×#127semidirect
726. C3#25770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5462
C2×C3×#4962
C2×C3×#4592
C2×C3×#4492
C2×C3×#4472
C3×#25412
C3×#20002
C3×#19992
C3×#19832
C3×#19552
C3×#17622
#257703