Finite Group Databasebeta

← #10822151

Subgroups — #10822151

Order 768.

2022 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic, complemented
2#87268C211yesmaximal, characteristic, complemented
3C2×#5822C211yesmaximal, characteristic, complemented
4#84086C211yesmaximal, characteristic, complemented
5C22×#837C211yesmaximal, characteristic, complemented
6C22×#825C211yesmaximal, characteristic, complemented
7#72110C214yesmaximal, complemented
8#72098C214yesmaximal, complemented
9#71987C211yesmaximal, characteristic, complemented
10#23406—31nomaximal, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C22×#235C2211yescharacteristic
14C3×#575—24no—
15C3×#575—24no—
16C2×C3×#137—21no—
17C2×C3×#137C2212yescomplemented
18C2×C3×AGL(1,ℤ/8)—21no—
19C2×C3×AGL(1,ℤ/8)C2212yescomplemented
20C2×C3×#135—22no—
21C22×C3×M16C2211yescharacteristic
22#5833C2214yes—
23#5832—22no—
24#5830—21no—
25#5828—22no—
26#5825—21no—
27C2×#951—21no—
28#5822—24no—
29#5822—24no—
30C2×#950—22no—
31C2×#949—21no—
32#5816—21no—
33C2×#942C2212yescomplemented
34#5805—21no—
35#5804—22no—
36C2×#932C2212yescomplemented
37#5791—22no—
38C2×#926C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×#208C2211yescharacteristic
41C2×#837—24no—
42C2×#837C2214yescomplemented
43#5229C2212yescomplemented
44#5221C2212yescomplemented
45#5220—22no—
46C4×#217—22no—
47C2×#825—24no—
48C2×#825C2214yescomplemented
49#4554C2214yescomplemented
50C2×#575—31no—
51C2×#575D311yescharacteristic, complemented
52#3449—31no—
53C22×#104—31no—
54C22×#104—31no—
55#2297—31no—
56#2007—34no—
57#2006—34no—
58#1742—31no—
59C2×C3×#41—21no—
60C2×C3×#41—21no—
61C2×C3×#41—22no—
62C2×C3×#41—21no—
63C2×C3×#41—21no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—22no—
68C2×C3×#41—21no—
69C2×C3×#41—21no—
70C2×C3×#41—22no—
71C2×C3×#41—22no—
72C2×C3×#41D412yes—
73C2×C3×#41D414yescomplemented
74C2×C3×#41C2312yes—
75C22×C3×Q8D411yescharacteristic
76C22×C3×Q8C2311yescharacteristic
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4D411yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C23×Dic3—21no—
86C2×#235—21no—
87C2×#235—21no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235D412yes—
93C2×#235C2312yes—
94C22×D12D411yescharacteristic
95C22×C4×D3—21no—
96C22×Dic6D411yescharacteristic
97C3×#137—28no—
98C3×#137—24no—
99C3×#137—24no—
100C3×AGL(1,ℤ/8)—28no—
101C3×AGL(1,ℤ/8)—24no—
102C3×AGL(1,ℤ/8)—24no—
103C3×#135—216no—
104C2×C3×Q16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×D8—22no—
108C2×C3×M16—21no—
109C2×C3×M16—22no—
110C2×C3×M16D414yescomplemented
111C2×C3×M16C2312yes—
112C22×C3×C8—21no—
113#953—24no—
114C2×#217—24no—
115C2×#217D412yes—
116#951—28no—
117#950—216no—
118#949—28no—
119#947—22no—
120#946—24no—
121#944—22no—
122C2×#216—22no—
123#942—24no—
124#942—24no—
125C2×#215—22no—
126#940—22no—
127#939—28no—
128#938—24no—
129#937—24no—
130#936—22no—
131#935—24no—
132C2×#214—22no—
133#932—24no—
134#932—24no—
135C2×#213—22no—
136#930—24no—
137#929—24no—
138C4×#67—28no—
139#926—21no—
140#926—21no—
141#926—21no—
142#926—21no—
143C2×C4⋊Dic3C2312yes—
144#924—24no—
145C2×C4×Dic3—22no—
146C2×C4×Dic3—22no—
147C2×C4×Dic3—21no—
148C2×C4×Dic3D412yes—
149C2×C4×Dic3C2312yes—
150C2×#208—21no—
151C2×#208—22no—
152C2×#208D414yescomplemented
153C2×#208C2312yes—
154C22×C3⋊C8—21no—
155#837—28no—
156C3⋊#95—24no—
157#825—28no—
158C22×#41—31no—
159C22×#41C2×D311yescharacteristic
160C22×#41C2×D311yescharacteristic
161#575—24no—
162#575—24no—
163#575—64no—
164#575—64no—
165C2×#137—21no—
166C2×#137—32no—
167C2×#137—61no—
168C2×#137C2×D312yescomplemented
169C2×AGL(1,ℤ/8)—21no—
170C2×AGL(1,ℤ/8)—32no—
171C2×AGL(1,ℤ/8)—61no—
172C2×AGL(1,ℤ/8)C2×D312yescomplemented
173C2×#135—22no—
174C2×#135—62no—
175C22×M16—31no—
176C22×M16C2×D311yescharacteristic
177#537—34no—
178#536—61no—
179#536—61no—
180#535—61no—
181#535—61no—
182#534—62no—
183#532—62no—
184#525—62no—
185#525—62no—
186C2×#117—31no—
187C22×C42—31no—
188C2×#104—34no—
189C2×#104—34no—
190C2×#104—64no—
191C2×#104—64no—
192#391—32no—
193#390—32no—
194#386—62no—
195C4×C22⋊C4—62no—
196#343—34no—
197C24×C3—21no—
198C24×C3—21no—
199C24×C3C2×D411yescharacteristic
200C23×D3—21no—
201C3×#41—24no—
202C3×#41—24no—
203C3×#41—24no—
204C3×#41—24no—
205C3×#41—24no—
206C3×#41—24no—
207C3×#41—22no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—22no—
211C3×#41—42no—
212C3×#41—42no—
213C3×#41—42no—
214C3×#41—42no—
215C3×#41—42no—
216C3×#41—42no—
217C3×#41—42no—
218C3×#41—42no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—22no—
222C2×C3×Q8—22no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×D4—22no—
230C2×C3×D4—24no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—21no—
234C2×C3×D4—22no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—41no—
241C2×C3×D4—41no—
242C2×C3×D4—42no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4C2×D412yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—22no—
250C22×C3×C4—24no—
251C22×C3×C4—22no—
252C22×C3×C4—41no—
253C22×C3×C4—42no—
254C22×C3×C4—41no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D412yes—
265C22×C3×C4#4112yes—
266C22×C3×C4C2411yescharacteristic
267C2×#67—22no—
268C2×#67—22no—
269C2×#67—28no—
270C2×#67—42no—
271C2×#67—42no—
272C22×Dic3—21no—
273C22×Dic3—22no—
274C22×Dic3—44no—
275C22×Dic3—42no—
276C22×Dic3C2×D414yes—
277#235—24no—
278#235—24no—
279#235—22no—
280#235—22no—
281#235—22no—
282#235—22no—
283#235—42no—
284#235—42no—
285#235—42no—
286#235—42no—
287C2×D12—22no—
288C2×D12—22no—
289C2×D12—21no—
290C2×D12C2×D412yes—
291C2×C4×D3—22no—
292C2×C4×D3—22no—
293C2×C4×D3—42no—
294C2×C4×D3—42no—
295C2×Dic6—22no—
296C2×Dic6—22no—
297C2×Dic6—21no—
298C2×Dic6C2×D412yes—
299C3×Q16—28no—
300C3×SD16—28no—
301C3×SD16—28no—
302C3×D8—28no—
303C3×M16—24no—
304C3×M16—22no—
305C3×M16C2×D414yes—
306C2×C3×C8—24no—
307C2×C3×C8—22no—
308#217—28no—
309#217—22no—
310#217—22no—
311#217—48no—
312#216—28no—
313#215—28no—
314#214—28no—
315#213—28no—
316(C2×D3)⋊C4—28no—
317C4⋊Dic3—22no—
318C4⋊Dic3—22no—
319Dic3⋊C4—28no—
320C4×Dic3—22no—
321C4×Dic3—22no—
322C4×Dic3—22no—
323C4×Dic3—22no—
324C4×Dic3—42no—
325#208—24no—
326#208—22no—
327#208C2×D414yes—
328C2×C3⋊C8—24no—
329C2×C3⋊C8—22no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—22no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—32no—
344C2×#41—32no—
345C2×#41—61no—
346C2×#41—61no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41—62no—
350C2×#41—62no—
351C2×#41#6712yes—
352C2×#41#6714yescomplemented
353C2×#41C22×D312yes—
354C22×Q8—31no—
355C22×Q8#6711yescharacteristic
356C22×Q8C22×D311yescharacteristic
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—31no—
360C22×D4—61no—
361C22×D4#6711yescharacteristic
362C22×D4C22×D311yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4—61no—
366C23×C4—61no—
367C23×C4C22×D311yescharacteristic
368#137—28no—
369#137—24no—
370#137—24no—
371#137—64no—
372#137—68no—
373#137—64no—
374AGL(1,ℤ/8)—28no—
375AGL(1,ℤ/8)—24no—
376AGL(1,ℤ/8)—24no—
377AGL(1,ℤ/8)—64no—
378AGL(1,ℤ/8)—68no—
379AGL(1,ℤ/8)—64no—
380#135—216no—
381#135—616no—
382C2×Q16—22no—
383C2×Q16—62no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×D8—22no—
389C2×D8—62no—
390C2×M16—21no—
391C2×M16—22no—
392C2×M16—34no—
393C2×M16—32no—
394C2×M16—61no—
395C2×M16—62no—
396C2×M16#6714yescomplemented
397C2×M16C22×D312yes—
398C22×C8—21no—
399C22×C8—61no—
400C4⋊Q8—62no—
401#127—62no—
402#124—62no—
403#124—62no—
404#123—64no—
405#123—64no—
406C22⋊Q8—64no—
407C22⋊Q8—64no—
408#121—64no—
409#121—68no—
410#121—64no—
411#120—64no—
412#120—64no—
413C4×D4—68no—
414#117—61no—
415#117—61no—
416#117—61no—
417#117—61no—
418C2×C4⋊C4—32no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—64no—
421C2×C42—32no—
422C2×C42—32no—
423C2×C42—62no—
424C2×C42—62no—
425C2×C42—61no—
426#104—68no—
427#104—68no—
428#95—64no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—42no—
432C23×C3—44no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—42no—
436C23×C3—82no—
437C23×C3#12011yescharacteristic
438C23×C3#12011yescharacteristic
439C23×C3#12112yes—
440C23×C3#12712yes—
441C23×C3C22×D411yescharacteristic
442C22×D3—22no—
443C22×D3—42no—
444C22×D3—82no—
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—22no—
448C3×Q8—22no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—42no—
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—42no—
457C3×D4—42no—
458C3×D4—44no—
459C3×D4—44no—
460C3×D4—44no—
461C3×D4—41no—
462C3×D4—41no—
463C3×D4—42no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—44no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4#12012yes—
475C2×C3×C4#12012yes—
476C2×C3×C4#12011yescharacteristic
477C2×C3×C4#12011yescharacteristic
478C2×C3×C4#12012yes—
479C2×C3×C4#12012yes—
480C2×C3×C4#12112yes—
481C2×C3×C4#12112yes—
482C2×C3×C4#12112yes—
483C2×C3×C4#12112yes—
484C2×C3×C4#12112yes—
485C2×C3×C4#12712yes—
486C2×C3×C4C22×D411yescharacteristic
487C2×C3×C4C22×D411yescharacteristic
488C2×C3×C4C22×D411yescharacteristic
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C22×D411yescharacteristic
491C2×C3×C4C2×#4111yescharacteristic
492#67—42no—
493#67—42no—
494#67—44no—
495#67—88no—
496C2×Dic3—24no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—42no—
500C2×Dic3—48no—
501C2×Dic3—42no—
502C2×Dic3—42no—
503C2×Dic3—44no—
504D12—22no—
505D12—22no—
506D12—42no—
507C4×D3—42no—
508C4×D3—42no—
509C4×D3—44no—
510Dic6—22no—
511Dic6—22no—
512Dic6—42no—
513C3×C8—24no—
514C3⋊C8—24no—
515C24—21no—
516C24—21no—
517C24—61no—
518C24D3×D411yescharacteristic
519#41—24no—
520#41—24no—
521#41—24no—
522#41—24no—
523#41—24no—
524#41—24no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—42no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—42no—
535#41—42no—
536#41—42no—
537#41—64no—
538#41—64no—
539#41—62no—
540#41—62no—
541#41—62no—
542#41—62no—
543#41—122no—
544#41—122no—
545#41—122no—
546#41—122no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—32no—
556C2×Q8—61no—
557C2×Q8—62no—
558C2×Q8—62no—
559C2×Q8C2×#6712yes—
560C2×Q8C2×#6712yes—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—32no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—68no—
581C2×D4—62no—
582C2×D4—61no—
583C2×D4—62no—
584C2×D4—122no—
585C2×D4—122no—
586C2×D4C2×#6712yes—
587C2×D4C2×#6712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—34no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—61no—
600C22×C4—62no—
601C22×C4—62no—
602C22×C4—62no—
603C22×C4—124no—
604C22×C4—122no—
605C22×C4—122no—
606C22×C4—122no—
607C22×C4D3×D411yescharacteristic
608C22×C4D3×D411yescharacteristic
609C22×C4D3×D412yes—
610C22×C4D3×D411yescharacteristic
611C22×C4#23712yes—
612C22×C4C2×#6712yes—
613C22×C4C2×#6711yescharacteristic
614C22×C4C2×#6711yescharacteristic
615C22×C4C2×#6712yes—
616C22×C4C23×D311yescharacteristic
617Q16—28no—
618Q16—68no—
619SD16—28no—
620SD16—28no—
621SD16—68no—
622SD16—68no—
623D8—28no—
624D8—68no—
625M16—24no—
626M16—22no—
627M16—34no—
628M16—64no—
629M16—62no—
630M16C2×#6714yes—
631C2×C8—24no—
632C2×C8—22no—
633C2×C8—64no—
634C2×C8—62no—
635C4⋊C4—68no—
636C4⋊C4—62no—
637C4⋊C4—62no—
638C22⋊C4—68no—
639C22⋊C4—68no—
640C22⋊C4—62no—
641C22⋊C4—62no—
642C22⋊C4—128no—
643C42—62no—
644C42—62no—
645C42—62no—
646C42—62no—
647C42—122no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—44no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—44no—
657C22×C3—82no—
658C22×C3—84no—
659C22×C3—82no—
660C22×C3#39212yes—
661C22×C3#39212yes—
662C22×C3C2×#12011yescharacteristic
663C22×C3C2×#12111yescharacteristic
664C22×C3C2×#12711yescharacteristic
665C2×D3—42no—
666C2×D3—44no—
667C2×D3—84no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4#39212yes—
671C3×C4#39212yes—
672C3×C4C2×#12011yescharacteristic
673C3×C4C2×#12011yescharacteristic
674C3×C4C2×#12111yescharacteristic
675C3×C4C2×#12111yescharacteristic
676Dic3—44no—
677Dic3—42no—
678Dic3—44no—
679C23—22no—
680C23—22no—
681C23—42no—
682C23—44no—
683C23—42no—
684C23—41no—
685C23—41no—
686C23—62no—
687C23—82no—
688C23—122no—
689C23—242no—
690C23#93711yescharacteristic
691C23#93711yescharacteristic
692C23#93912yes—
693C23#94012yes—
694C23C2×D3×D411yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—41no—
701Q8—41no—
702Q8—62no—
703Q8—62no—
704Q8—122no—
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—44no—
710D4—44no—
711D4—44no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—41no—
716D4—41no—
717D4—62no—
718D4—62no—
719D4—124no—
720D4—122no—
721D4—122no—
722D4—122no—
723D4—248no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—62no—
737C2×C4—122no—
738C2×C4—128no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—124no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—124no—
745C2×C4#93711yescharacteristic
746C2×C4#93712yes—
747C2×C4#93712yes—
748C2×C4#93711yescharacteristic
749C2×C4#93812yes—
750C2×C4#93812yes—
751C2×C4#93912yes—
752C2×C4#93912yes—
753C2×C4#93912yes—
754C2×C4#94012yes—
755C2×C4#95312yes—
756C2×C4#95312yes—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×#23711yescharacteristic
760C2×C4C22×#6711yescharacteristic
761C2×C4C22×#6711yescharacteristic
762C2×C4C22×#6711yescharacteristic
763C8—24no—
764C8—64no—
765C2×C3—21no—
766C2×C3—22no—
767C2×C3—21no—
768C2×C3—22no—
769C2×C3—82no—
770C2×C3—82no—
771C2×C3C2×#39211yescharacteristic
772C2×C3#301812yes—
773D3—82no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—82no—
784C22—84no—
785C22—82no—
786C22—124no—
787C22—122no—
788C22—244no—
789C22#522312yes—
790C22#522312yes—
791C22C2×#93711yescharacteristic
792C22C2×#93911yescharacteristic
793C22C2×#94011yescharacteristic
794C4—42no—
795C4—42no—
796C4—124no—
797C4—124no—
798C4—122no—
799C4#522312yes—
800C4#522312yes—
801C4C2×#93711yescharacteristic
802C4C2×#93811yescharacteristic
803C4C2×#93911yescharacteristic
804C4C2×#95311yescharacteristic
805C3#2340611yescharacteristic, complemented, Sylow
806C2—21no—
807C2—21no—
808C2—22no—
809C2—22no—
810C2—82no—
811C2—82no—
812C2—242no—
813C2#8400412yes—
814C2C2×#522311yescharacteristic
subgroupG/H
centerC2×C4#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#575C2
socleC22×C3C2×#120
hypercenterC2×#575D3
hypocenterC3#23406
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. #87268C2semidirect
3. C2×#5822C2semidirect
4. #84086C2semidirect
5. C22×#837C2semidirect
6. C22×#825C2semidirect
7. #72110C2semidirect
8. #72098C2semidirect
9. #71987C2semidirect
17. C2×C3×#137C22semidirect
19. C2×C3×AGL(1,ℤ/8)C22semidirect
33. C2×#942C22semidirect
36. C2×#932C22semidirect
42. C2×#837C22semidirect
43. #5229C22semidirect
44. #5221C22semidirect
48. C2×#825C22semidirect
49. #4554C22semidirect
51. C2×#575D3semidirect
73. C2×C3×#41D4semidirect
110. C2×C3×M16D4semidirect
152. C2×#208D4semidirect
168. C2×#137C2×D3semidirect
172. C2×AGL(1,ℤ/8)C2×D3semidirect
352. C2×#41#67semidirect
396. C2×M16#67semidirect
805. C3#23406semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5752
#872682
C2×#58222
#840862
C22×#8372
C22×#8252
#721102
#720982
#719872
#234063