Finite Group Databasebeta

← C3×#23426 #10642033

Subgroups — C3×#23426 #10642033

Order 768.

2178 conjugacy classes of subgroups.

The subgroup lattice has 732 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
2C22×C3×#135C211yesmaximal, characteristic, complemented
3C2×C3×#535C211yesmaximal, characteristic, complemented
4C2×C3×#417C211yesmaximal, characteristic, complemented
5C22×C3×#102C211yesmaximal, characteristic, complemented
6C3×#2311C211yesmaximal, characteristic, complemented
7C3×#2015C212yesmaximal, complemented
8C3×#2014C212yesmaximal, complemented
9C3×#2012C212yesmaximal, complemented
10C3×#2011C212yesmaximal, complemented
11C3×#1729C211yesmaximal, characteristic, complemented
12#23426C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C22×C3×#41C2211yescharacteristic
15C23×C3×D4C2211yescharacteristic
16C2×C3×AGL(1,ℤ/8)—24no—
17C2×C3×AGL(1,ℤ/8)—24no—
18C2×C3×AGL(1,ℤ/8)—24no—
19C2×C3×#135—24no—
20C2×C3×#135—24no—
21C2×C3×#135—24no—
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2212yes—
24C22×C3×SD16C2211yescharacteristic, complemented
25C22×C3×SD16C2211yescharacteristic, complemented
26C22×C3×D8C2212yes—
27C22×C3×D8C2211yescharacteristic, complemented
28C22×C3×M16C2211yescharacteristic
29C23×C3×C8C2211yescharacteristic
30C3×#535—24no—
31C3×#535—24no—
32C2×C3×#127C2212yes—
33C2×C3×#124C2212yes—
34C2×C3×#121—22no—
35C2×C3×#120—22no—
36C2×C3×#117C2211yescharacteristic
37C22×C3×C4⋊C4C2211yescharacteristic
38C3×#417—24no—
39C2×C3×#103C2212yescomplemented
40C2×C3×#102—24no—
41C2×C3×#102C2212yes—
42C2×C3×#102C2212yes—
43C2×C3×#102C2212yescomplemented
44C3×#391C2212yescomplemented
45C3×#390C2212yescomplemented
46C3×#386—22no—
47C3×#380—22no—
48C3×#336C2212yescomplemented
49C3×#336C2212yescomplemented
50C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
51C22×#135C2×C311yescharacteristic, complemented
52C2×#535C2×C311yescharacteristic, complemented
53C2×#417C2×C311yescharacteristic, complemented
54C22×#102C2×C311yescharacteristic, complemented
55#2311C2×C311yescharacteristic, complemented
56#2015C2×C312yescomplemented
57#2014C2×C312yescomplemented
58#2012C2×C312yescomplemented
59#2011C2×C312yescomplemented
60#1729C2×C311yescharacteristic, complemented
61C25×C3—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—22no—
68C2×C3×#41—22no—
69C2×C3×#41—22no—
70C2×C3×#41—22no—
71C2×C3×#41—22no—
72C2×C3×#41D414yes—
73C2×C3×#41D414yescomplemented
74C22×C3×Q8C2311yescharacteristic
75C22×C3×Q8C2311yescharacteristic
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4—22no—
79C22×C3×D4—22no—
80C22×C3×D4—22no—
81C22×C3×D4—21no—
82C22×C3×D4—22no—
83C22×C3×D4—24no—
84C22×C3×D4—22no—
85C22×C3×D4D414yes—
86C22×C3×D4C2311yescharacteristic
87C22×C3×D4C2312yes—
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C3×AGL(1,ℤ/8)—232no—
94C3×#135—232no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×SD16—24no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—24no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—24no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×D8—24no—
108C2×C3×D8—24no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8—24no—
112C2×C3×D8—22no—
113C2×C3×M16—22no—
114C2×C3×M16—22no—
115C2×C3×M16D414yescomplemented
116C22×C3×C8—22no—
117C22×C3×C8—22no—
118C22×C3×C8D414yescomplemented
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2312yes—
122C3×#127—24no—
123C3×#127—24no—
124C3×#124—24no—
125C3×#124—24no—
126C3×#121—216no—
127C3×#120—216no—
128C3×#117—22no—
129C3×#117—22no—
130C2×C3×C4⋊C4—22no—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4D412yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C22⋊C4—24no—
136C2×C3×C22⋊C4—24no—
137C2×C3×C22⋊C4D412yes—
138C2×C3×C42C2312yes—
139C3×#103—24no—
140C3×#102—24no—
141C3×#102—24no—
142C3×#102—24no—
143C3×#95—24no—
144C22×#41C22×C311yescharacteristic
145C22×#41C22×C311yescharacteristic
146C23×D4C22×C311yescharacteristic
147C2×AGL(1,ℤ/8)—24no—
148C2×AGL(1,ℤ/8)—24no—
149C2×AGL(1,ℤ/8)—24no—
150C2×#135—24no—
151C2×#135—24no—
152C2×#135—24no—
153C22×Q16C22×C311yescharacteristic, complemented
154C22×SD16C22×C312yes—
155C22×SD16C22×C311yescharacteristic, complemented
156C22×SD16C22×C311yescharacteristic, complemented
157C22×D8C22×C312yes—
158C22×D8C22×C311yescharacteristic, complemented
159C22×M16C22×C311yescharacteristic
160C23×C8C22×C311yescharacteristic
161#535—24no—
162#535—24no—
163C2×#127C22×C312yes—
164C2×#124C22×C312yes—
165C2×#121—22no—
166C2×#120—22no—
167C2×#117C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
169#417—24no—
170C2×#103C22×C312yescomplemented
171C2×#102—24no—
172C2×#102C22×C312yes—
173C2×#102C22×C312yes—
174C2×#102C22×C312yescomplemented
175#391C22×C312yescomplemented
176#390C22×C312yescomplemented
177#386—22no—
178#380—22no—
179#336C22×C312yescomplemented
180#336C22×C312yescomplemented
181C24×C3—22no—
182C24×C3—21no—
183C24×C3—21no—
184C24×C3—24no—
185C24×C3—42no—
186C24×C3—42no—
187C24×C3—82no—
188C24×C3—82no—
189C24×C3C2×D411yescharacteristic
190C3×#41—28no—
191C3×#41—28no—
192C3×#41—28no—
193C3×#41—28no—
194C3×#41—44no—
195C3×#41—44no—
196C3×#41—44no—
197C3×#41—44no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8C2×D412yes—
209C2×C3×Q8C2×D412yes—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—216no—
213C2×C3×D4—28no—
214C2×C3×D4—24no—
215C2×C3×D4—28no—
216C2×C3×D4—22no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—22no—
221C2×C3×D4—22no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—44no—
236C2×C3×D4—44no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—84no—
240C2×C3×D4—84no—
241C2×C3×D4C2×D414yes—
242C2×C3×D4C2×D412yes—
243C2×C3×D4C2×D412yes—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—24no—
247C22×C3×C4—24no—
248C22×C3×C4—22no—
249C22×C3×C4—42no—
250C22×C3×C4—42no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4—82no—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2×D412yes—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4#4112yes—
263C22×C3×C4C2411yescharacteristic
264C3×Q16—28no—
265C3×SD16—28no—
266C3×SD16—28no—
267C3×SD16—216no—
268C3×D8—28no—
269C3×D8—216no—
270C3×M16—28no—
271C2×C3×C8—28no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—22no—
277C2×C3×C8—22no—
278C2×C3×C8C2×D412yes—
279C2×C3×C8C2×D412yes—
280C2×C3×C8C2×D414yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—42no—
285C3×C22⋊C4—216no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—84no—
288C3×C42—22no—
289C3×C42—22no—
290C25—21no—
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—22no—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—22no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41C3×D414yes—
302C2×#41C3×D414yescomplemented
303C22×Q8C23×C311yescharacteristic
304C22×Q8C23×C311yescharacteristic
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—21no—
311C22×D4—22no—
312C22×D4—24no—
313C22×D4—22no—
314C22×D4C3×D414yes—
315C22×D4C23×C312yes—
316C22×D4C23×C311yescharacteristic
317C22×D4C23×C311yescharacteristic
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C311yescharacteristic
322AGL(1,ℤ/8)—232no—
323#135—232no—
324C2×Q16—22no—
325C2×Q16—22no—
326C2×Q16—22no—
327C2×SD16—24no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—24no—
331C2×SD16—22no—
332C2×SD16—22no—
333C2×SD16—24no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×D8—24no—
337C2×D8—24no—
338C2×D8—22no—
339C2×D8—22no—
340C2×D8—24no—
341C2×D8—22no—
342C2×M16—22no—
343C2×M16—22no—
344C2×M16C3×D414yescomplemented
345C22×C8—22no—
346C22×C8—22no—
347C22×C8C3×D414yescomplemented
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350C22×C8C23×C312yes—
351#127—24no—
352#127—24no—
353#124—24no—
354#124—24no—
355#121—216no—
356#120—216no—
357#117—22no—
358#117—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C3×D412yes—
363C2×C4⋊C4C23×C312yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4C3×D412yes—
367C2×C42C23×C312yes—
368#103—24no—
369#102—24no—
370#102—24no—
371#102—24no—
372#95—24no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—44no—
387C23×C3—42no—
388C23×C3—44no—
389C23×C3—42no—
390C23×C3—48no—
391C23×C3—88no—
392C23×C3—84no—
393C23×C3—84no—
394C23×C3—88no—
395C23×C3#12012yes—
396C23×C3#12112yes—
397C23×C3#12712yes—
398C23×C3C22×D411yescharacteristic
399C3×Q8—22no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—22no—
403C3×Q8—41no—
404C3×Q8—41no—
405C3×Q8—41no—
406C3×Q8—41no—
407C3×D4—22no—
408C3×D4—24no—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—24no—
412C3×D4—22no—
413C3×D4—48no—
414C3×D4—48no—
415C3×D4—42no—
416C3×D4—41no—
417C3×D4—42no—
418C3×D4—41no—
419C3×D4—41no—
420C3×D4—41no—
421C3×D4—48no—
422C3×D4—816no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—48no—
433C2×C3×C4—48no—
434C2×C3×C4—42no—
435C2×C3×C4—44no—
436C2×C3×C4—84no—
437C2×C3×C4#12014yes—
438C2×C3×C4#12014yes—
439C2×C3×C4#12012yes—
440C2×C3×C4#12114yes—
441C2×C3×C4#12114yes—
442C2×C3×C4#12112yes—
443C2×C3×C4#12712yes—
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C3×C8—22no—
451C3×C8—22no—
452C3×C8—24no—
453C24—21no—
454C24—22no—
455C24—21no—
456C24—24no—
457C24—42no—
458C24—42no—
459C24—82no—
460C24—82no—
461C24C2×C3×D411yescharacteristic
462#41—28no—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—44no—
467#41—44no—
468#41—44no—
469#41—44no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8C2×C3×D412yes—
481C2×Q8C2×C3×D412yes—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—216no—
485C2×D4—28no—
486C2×D4—24no—
487C2×D4—28no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—42no—
511C2×D4—84no—
512C2×D4—84no—
513C2×D4C2×C3×D414yes—
514C2×D4C2×C3×D412yes—
515C2×D4C2×C3×D412yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—82no—
527C22×C4C2×C3×D414yes—
528C22×C4C2×C3×D412yes—
529C22×C4C2×C3×D412yes—
530C22×C4C2×C3×D412yes—
531C22×C4C2×C3×D411yescharacteristic
532C22×C4C2×C3×D412yes—
533C22×C4C2×C3×D412yes—
534C22×C4C3×#4112yes—
535C22×C4C24×C311yescharacteristic
536Q16—28no—
537SD16—28no—
538SD16—28no—
539SD16—216no—
540D8—28no—
541D8—216no—
542M16—28no—
543C2×C8—28no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8C2×C3×D412yes—
551C2×C8C2×C3×D412yes—
552C2×C8C2×C3×D414yes—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—42no—
557C22⋊C4—216no—
558C22⋊C4—24no—
559C22⋊C4—84no—
560C42—22no—
561C42—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—48no—
571C22×C3—44no—
572C22×C3—816no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3—82no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—84no—
582C22×C3#39214yes—
583C22×C3C2×#12011yescharacteristic
584C22×C3C2×#12111yescharacteristic
585C22×C3C2×#12711yescharacteristic
586C22×C3#57612yes—
587C22×C3#57712yes—
588C3×C4—42no—
589C3×C4—42no—
590C3×C4—44no—
591C3×C4—82no—
592C3×C4#39214yes—
593C3×C4C2×#12011yescharacteristic
594C3×C4C2×#12011yescharacteristic
595C3×C4C2×#12111yescharacteristic
596C3×C4C2×#12111yescharacteristic
597C23—22no—
598C23—22no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—42no—
603C23—42no—
604C23—44no—
605C23—42no—
606C23—44no—
607C23—42no—
608C23—48no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—88no—
616C23—84no—
617C23—84no—
618C23—88no—
619C23C3×#12012yes—
620C23C3×#12112yes—
621C23C3×#12712yes—
622C23C22×C3×D411yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—22no—
632D4—24no—
633D4—22no—
634D4—22no—
635D4—24no—
636D4—22no—
637D4—48no—
638D4—48no—
639D4—48no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—41no—
644D4—41no—
645D4—41no—
646D4—816no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—48no—
657C2×C4—48no—
658C2×C4—44no—
659C2×C4—42no—
660C2×C4—84no—
661C2×C4C3×#12012yes—
662C2×C4C3×#12014yes—
663C2×C4C3×#12014yes—
664C2×C4C3×#12112yes—
665C2×C4C3×#12114yes—
666C2×C4C3×#12114yes—
667C2×C4C3×#12712yes—
668C2×C4C22×C3×D411yescharacteristic
669C2×C4C22×C3×D411yescharacteristic
670C2×C4C22×C3×D411yescharacteristic
671C2×C4C22×C3×D411yescharacteristic
672C2×C4C22×C3×D411yescharacteristic
673C2×C4C2×C3×#4111yescharacteristic
674C8—22no—
675C8—22no—
676C8—24no—
677C2×C3—24no—
678C2×C3—82no—
679C2×C3—82no—
680C2×C3—84no—
681C2×C3C2×#39211yescharacteristic
682C2×C3#301212yes—
683C2×C3#304512yes—
684C2×C3#315411yescharacteristic
685C2×C3#315511yescharacteristic
686C22—22no—
687C22—22no—
688C22—24no—
689C22—24no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—44no—
694C22—48no—
695C22—44no—
696C22—816no—
697C22—82no—
698C22—81no—
699C22—81no—
700C22—82no—
701C22—81no—
702C22—81no—
703C22—82no—
704C22—84no—
705C22—82no—
706C22C3×#39214yes—
707C22C2×C3×#12011yescharacteristic
708C22C2×C3×#12111yescharacteristic
709C22C2×C3×#12711yescharacteristic
710C22C3×#57612yes—
711C22C3×#57712yes—
712C4—42no—
713C4—42no—
714C4—44no—
715C4—82no—
716C4C3×#39214yes—
717C4C2×C3×#12011yescharacteristic
718C4C2×C3×#12011yescharacteristic
719C4C2×C3×#12111yescharacteristic
720C4C2×C3×#12111yescharacteristic
721C3#2342611yescharacteristic, direct product factor, Sylow
722C2—24no—
723C2—84no—
724C2—82no—
725C2—82no—
726C2C2×C3×#39211yescharacteristic
727C2C3×#301212yes—
728C2C3×#304512yes—
729C2C3×#315411yescharacteristic
730C2C3×#315511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C22×C3×#135C2semidirect
3. C2×C3×#535C2semidirect
4. C2×C3×#417C2semidirect
5. C22×C3×#102C2semidirect
6. C3×#2311C2semidirect
7. C3×#2015C2semidirect
8. C3×#2014C2semidirect
9. C3×#2012C2semidirect
10. C3×#2011C2semidirect
11. C3×#1729C2semidirect
12. #23426C3direct (N × H)
22. C22×C3×Q16C22semidirect
24. C22×C3×SD16C22semidirect
25. C22×C3×SD16C22semidirect
27. C22×C3×D8C22semidirect
39. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C3×#391C22semidirect
45. C3×#390C22semidirect
48. C3×#336C22semidirect
49. C3×#336C22semidirect
50. C22×AGL(1,ℤ/8)C2×C3semidirect
51. C22×#135C2×C3semidirect
52. C2×#535C2×C3semidirect
53. C2×#417C2×C3semidirect
54. C22×#102C2×C3semidirect
55. #2311C2×C3semidirect
56. #2015C2×C3semidirect
57. #2014C2×C3semidirect
58. #2012C2×C3semidirect
59. #2011C2×C3semidirect
60. #1729C2×C3semidirect
73. C2×C3×#41D4semidirect
115. C2×C3×M16D4semidirect
118. C22×C3×C8D4semidirect
153. C22×Q16C22×C3semidirect
155. C22×SD16C22×C3semidirect
156. C22×SD16C22×C3semidirect
158. C22×D8C22×C3semidirect
170. C2×#103C22×C3semidirect
174. C2×#102C22×C3semidirect
175. #391C22×C3semidirect
176. #390C22×C3semidirect
179. #336C22×C3semidirect
180. #336C22×C3semidirect
302. C2×#41C3×D4semidirect
344. C2×M16C3×D4semidirect
347. C22×C8C3×D4semidirect
721. C3#23426direct (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
C22×C3×#1352
C2×C3×#5352
C2×C3×#4172
C22×C3×#1022
C3×#23112
C3×#20152
C3×#20142
C3×#20122
C3×#20112
C3×#17292
#234263