Finite Group Databasebeta

← #10826962

Subgroups — #10826962

Order 768.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic, complemented
2C2×#5627C211yesmaximal, characteristic
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5187C212yesmaximal, complemented
6#72071C212yesmaximal, complemented
7#71692C211yesmaximal, characteristic, complemented
8#70272C212yesmaximal, complemented
9#70269C212yesmaximal, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69932C211yesmaximal, characteristic, complemented
12#23922—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C22×#239C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×Q16C2212yescomplemented
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#946—21no—
19C2×#946—21no—
20C2×#946—28no—
21C2×#946C2212yes—
22C2×#946C2211yescharacteristic
23C2×#946C2212yes—
24C22×#215C2212yescomplemented
25C2×#930C2211yescharacteristic
26C22×(C2×D3)⋊C4—21no—
27C22×C4⋊Dic3C2211yescharacteristic
28C22×Dic3⋊C4—21no—
29#5627—24no—
30#5627—24no—
31C2×#895C2211yescharacteristic
32C2×#894—21no—
33C2×#893—21no—
34C2×#892C2211yescharacteristic
35C2×#882—21no—
36C2×#67⋊C4—21no—
37C3×#451—24no—
38C2×C3×#103C2212yescomplemented
39C2×C3×C22⋊C8C2211yescharacteristic
40#5227—24no—
41C2×#835C2212yescomplemented
42C2×#835C2212yescomplemented
43C2×#830C2211yescharacteristic
44#5187—28no—
45C2×#821C2212yescomplemented
46C2×(C2×D3)⋊C8C2212yes—
47C2×(C2×D3)⋊C8C2212yes—
48#4551C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C22×C22⋊Q8—31no—
52C2×#452—32no—
53C2×#451D311yescharacteristic, complemented
54C2×#448—31no—
55#2001—32no—
56#2000—32no—
57#1874—31no—
58#1873—32no—
59#1872—31no—
60#1779—31no—
61C24×D3D411yescharacteristic
62C22×C3×Q8—24no—
63C22×C3×Q8—21no—
64C22×C3×Q8—22no—
65C22×C3×Q8—22no—
66C22×C3×Q8—42no—
67C22×C3×Q8C2311yescharacteristic
68C22×C3×Q8C2312yes—
69C23×C3×C4—21no—
70C23×C3×C4C2311yescharacteristic
71C22×#67—21no—
72C23×Dic3—21no—
73C23×Dic3D411yescharacteristic
74C2×#239—22no—
75C2×#239—22no—
76C2×#239—24no—
77C2×#239—42no—
78C22×D12—21no—
79C22×D12—21no—
80C22×D12C2311yescharacteristic
81C22×C4×D3—22no—
82C22×C4×D3—22no—
83C22×C4×D3—21no—
84C22×C4×D3—24no—
85C22×C4×D3—42no—
86C22×C4×D3D411yescharacteristic
87C22×C4×D3D411yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C2×C3×Q16—24no—
91C2×C3×Q16—24no—
92C2×C3×Q16—42no—
93C22×C3×C8C2312yes—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8D414yes—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99#946—28no—
100#946—28no—
101#946—24no—
102#946—22no—
103#946—24no—
104#946—24no—
105#946—22no—
106#946D418yescomplemented
107C2×#215—24no—
108C2×#215—24no—
109C2×#215—42no—
110#930—22no—
111#930D414yes—
112C2×(C2×D3)⋊C4—28no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—24no—
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2312yes—
123C2×Dic3⋊C4—28no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—22no—
126C2×Dic3⋊C4—22no—
127C2×C4×Dic3—21no—
128C22×C3⋊C8C2312yes—
129#895—22no—
130#895—22no—
131#894—28no—
132#893—28no—
133#892—22no—
134#892—22no—
135#882—28no—
136#67⋊C4—28no—
137C3×#103—24no—
138C3×C22⋊C8—22no—
139#835—24no—
140#835—24no—
141#830—22no—
142#821—24no—
143(C2×D3)⋊C8—24no—
144(C2×D3)⋊C8—42no—
145C22×#41—31no—
146C23×Q8C2×D311yescharacteristic
147C24×C4—31no—
148C22×Q16C2×D312yescomplemented
149C22×SD16—32no—
150#525—64no—
151#525—64no—
152C2×#123—61no—
153C2×C22⋊Q8—32no—
154C2×C22⋊Q8—32no—
155C2×C22⋊Q8—31no—
156C2×C22⋊Q8—68no—
157C2×C22⋊Q8—61no—
158C2×C22⋊Q8—61no—
159C2×C22⋊Q8C2×D311yescharacteristic
160C2×#121—31no—
161C2×#121—31no—
162C2×#120—61no—
163C2×C4×D4—61no—
164C2×C4×D4—61no—
165C2×#117—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—61no—
168C22×C22⋊C4—61no—
169#452—68no—
170#451—24no—
171#448—64no—
172C2×#103—32no—
173C2×#103—32no—
174C2×#103C2×D312yescomplemented
175C2×#102—32no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—32no—
178C2×C22⋊C8—32no—
179C2×C22⋊C8C2×D311yescharacteristic
180#340—32no—
181#340—32no—
182C24×C3C2×D411yescharacteristic
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—22no—
188C23×D3—21no—
189C23×D3—41no—
190C23×D3—41no—
191C23×D3C2×D411yescharacteristic
192C23×D3C2×D411yescharacteristic
193C2×C3×Q8—24no—
194C2×C3×Q8—22no—
195C2×C3×Q8—21no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—22no—
202C2×C3×Q8—48no—
203C2×C3×Q8—48no—
204C2×C3×Q8—42no—
205C2×C3×Q8—42no—
206C2×C3×Q8C2×D414yes—
207C2×C3×Q8C2×D412yes—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D412yes—
219C22×C3×C4C2411yescharacteristic
220C2×#67—24no—
221C2×#67—42no—
222C2×#67—42no—
223C22×Dic3—24no—
224C22×Dic3—22no—
225C22×Dic3—21no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—41no—
229C22×Dic3—42no—
230C22×Dic3—42no—
231C22×Dic3C2×D411yescharacteristic
232C22×Dic3C2×D411yescharacteristic
233#239—48no—
234#239—48no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—24no—
238C2×D12—24no—
239C2×D12—21no—
240C2×D12—42no—
241C2×D12—42no—
242C2×D12—42no—
243C2×D12—42no—
244C2×D12C2×D412yes—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—22no—
248C2×C4×D3—24no—
249C2×C4×D3—22no—
250C2×C4×D3—22no—
251C2×C4×D3—22no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—22no—
255C2×C4×D3—22no—
256C2×C4×D3—22no—
257C2×C4×D3—48no—
258C2×C4×D3—48no—
259C2×C4×D3—41no—
260C2×C4×D3—41no—
261C2×C4×D3—42no—
262C2×C4×D3—42no—
263C2×C4×D3C2×D414yes—
264C3×Q16—48no—
265C2×C3×C8—22no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4C2×D412yes—
271C3×C22⋊C4—24no—
272#215—48no—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—24no—
275(C2×D3)⋊C4—24no—
276(C2×D3)⋊C4—28no—
277(C2×D3)⋊C4—28no—
278(C2×D3)⋊C4—24no—
279C4⋊Dic3—24no—
280C4⋊Dic3—21no—
281C4⋊Dic3—22no—
282C4⋊Dic3C2×D414yes—
283C4⋊Dic3C2×D412yes—
284Dic3⋊C4—24no—
285Dic3⋊C4—28no—
286Dic3⋊C4—28no—
287C4×Dic3—24no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C25—31no—
292C2×#41—64no—
293C2×#41—62no—
294C2×#41—62no—
295C2×#41—122no—
296C22×Q8—24no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—42no—
301C22×Q8C22×D312yes—
302C22×Q8C22×D311yescharacteristic
303C22×D4—31no—
304C22×D4—61no—
305C22×D4—61no—
306C22×D4—61no—
307C23×C4—21no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—61no—
314C23×C4—64no—
315C23×C4—61no—
316C23×C4—62no—
317C23×C4—62no—
318C23×C4—122no—
319C23×C4C22×D311yescharacteristic
320C2×Q16—24no—
321C2×Q16—24no—
322C2×Q16—42no—
323C2×SD16—64no—
324C2×SD16—64no—
325C2×SD16—122no—
326C22×C8—32no—
327C22×C8C22×D312yes—
328#123—68no—
329C22⋊Q8—22no—
330C22⋊Q8—38no—
331C22⋊Q8—64no—
332C22⋊Q8—62no—
333C22⋊Q8—64no—
334C22⋊Q8—68no—
335C22⋊Q8—68no—
336C22⋊Q8—64no—
337C22⋊Q8—62no—
338C22⋊Q8#6714yes—
339#121—34no—
340#121—62no—
341#121—62no—
342#121—62no—
343#120—68no—
344C4×D4—68no—
345C4×D4—68no—
346#117—62no—
347#117—62no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—32no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—64no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—68no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—62no—
361C2×C22⋊C4—62no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—68no—
365C2×C22⋊C4—61no—
366C2×C42—61no—
367#103—24no—
368#103—64no—
369#103—64no—
370#102—64no—
371C22⋊C8—22no—
372C22⋊C8—64no—
373C22⋊C8—62no—
374C22⋊C8—122no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3#12012yes—
380C23×C3#13512yes—
381C23×C3#13712yes—
382C23×C3C22×D411yescharacteristic
383C22×D3—28no—
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—22no—
397C22×D3—44no—
398C22×D3—44no—
399C22×D3—44no—
400C22×D3—44no—
401C22×D3—44no—
402C22×D3—44no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3#12012yes—
410C22×D3#13712yes—
411C3×Q8—24no—
412C3×Q8—24no—
413C3×Q8—24no—
414C3×Q8—48no—
415C3×Q8—42no—
416C3×Q8—42no—
417C3×Q8—42no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—48no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4#12012yes—
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C22×D412yes—
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4H(5,𝔽2)12yes—
437#67—48no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—24no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—44no—
446C2×Dic3—48no—
447C2×Dic3—42no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—42no—
451C2×Dic3#12012yes—
452D12—24no—
453D12—48no—
454D12—48no—
455D12—42no—
456C4×D3—24no—
457C4×D3—24no—
458C4×D3—44no—
459C4×D3—48no—
460C4×D3—44no—
461C4×D3—42no—
462C4×D3—42no—
463C3×C8—42no—
464C3⋊C8—42no—
465C24—31no—
466C24—31no—
467C24—62no—
468C24—62no—
469C24—62no—
470C24—62no—
471C24—62no—
472C24—61no—
473C24—121no—
474C24—121no—
475C24D3×D411yescharacteristic
476#41—128no—
477#41—128no—
478C2×Q8—24no—
479C2×Q8—21no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8D3×D414yes—
492C2×Q8C2×#6712yes—
493C2×D4—32no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—62no—
498C2×D4—62no—
499C2×D4—61no—
500C2×D4—122no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4—122no—
504C2×D4—122no—
505C2×D4—122no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—31no—
513C22×C4—34no—
514C22×C4—31no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—64no—
520C22×C4—62no—
521C22×C4—61no—
522C22×C4—62no—
523C22×C4—61no—
524C22×C4—64no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—61no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—121no—
535C22×C4—121no—
536C22×C4—128no—
537C22×C4—128no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4—121no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D412yes—
545C22×C4C2×#6712yes—
546C22×C4C23×D311yescharacteristic
547Q16—48no—
548SD16—128no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—62no—
553C2×C8—62no—
554C2×C8—62no—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—34no—
558C4⋊C4—32no—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—62no—
564C4⋊C4—61no—
565C4⋊C4C2×#6712yes—
566C22⋊C4—24no—
567C22⋊C4—68no—
568C22⋊C4—68no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C42—64no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3#45214yescomplemented
581C22×C3C2×#12011yescharacteristic
582C22×C3C2×#12011yescharacteristic
583C22×C3#53411yescharacteristic
584C22×C3C2×#13511yescharacteristic
585C22×C3C2×#13711yescharacteristic
586C22×C3C2×#13711yescharacteristic
587C22×C3#57511yescharacteristic
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—22no—
594C2×D3—416no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C3×C4—22no—
611C3×C4—42no—
612C3×C4—44no—
613C3×C4—42no—
614C3×C4D4212yes—
615C3×C4D4212yes—
616Dic3—22no—
617Dic3—41no—
618Dic3—42no—
619Dic3—44no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—32no—
625C23—32no—
626C23—68no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—62no—
640C23—124no—
641C23—124no—
642C23—124no—
643C23—124no—
644C23—124no—
645C23—124no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23#91812yes—
653C23#91912yes—
654C23#93712yes—
655C23C2×D3×D411yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—24no—
659Q8—48no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663D4—64no—
664D4—128no—
665D4—128no—
666D4—128no—
667D4—122no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—32no—
676C2×C4—48no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—64no—
686C2×C4—64no—
687C2×C4—62no—
688C2×C4—61no—
689C2×C4—64no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—124no—
693C2×C4—124no—
694C2×C4—128no—
695C2×C4—124no—
696C2×C4—128no—
697C2×C4—121no—
698C2×C4—122no—
699C2×C4—121no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4#93712yes—
704C2×C4C2×D3×D412yes—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4#100412yes—
707C2×C4C22×#6711yescharacteristic
708C8—42no—
709C8—122no—
710C2×C3—24no—
711C2×C3#240311yescharacteristic
712C2×C3C2×#45211yescharacteristic
713C2×C3#300211yescharacteristic
714C2×C3#300411yescharacteristic
715C2×C3#300711yescharacteristic
716C2×C3#319011yescharacteristic
717C2×C3#319611yescharacteristic
718D3—42no—
719D3—42no—
720D3—82no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—62no—
728C22—62no—
729C22—62no—
730C22—62no—
731C22—62no—
732C22—62no—
733C22—1216no—
734C22—121no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—122no—
743C22—122no—
744C22—122no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22#518714yescomplemented
750C22D3×#12011yescharacteristic
751C22#558911yescharacteristic
752C22C2×#91811yescharacteristic
753C22C2×#91911yescharacteristic
754C22D3×#13711yescharacteristic
755C22#577711yescharacteristic
756C22C2×#93711yescharacteristic
757C4—22no—
758C4—42no—
759C4—44no—
760C4—42no—
761C4—62no—
762C4—124no—
763C4—122no—
764C4—121no—
765C4#559012yes—
766C4D4×#6712yes—
767C3#2392211yescharacteristic, complemented, Sylow
768C2—24no—
769C2—122no—
770C2—122no—
771C2—242no—
772C2#8018211yescharacteristic
773C2#8018311yescharacteristic
774C2#8018811yescharacteristic
775C2#8019011yescharacteristic
776C2#8260411yescharacteristic
777C2C2×#518711yescharacteristic
778C2#8398111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
prime radicalC2×#5627C2
hypercenterC2×#451D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#946C2semidirect
3. C2×C3×#451C2semidirect
4. C2×#5227C2semidirect
5. C2×#5187C2semidirect
6. #72071C2semidirect
7. #71692C2semidirect
8. #70272C2semidirect
9. #70269C2semidirect
10. #69955C2semidirect
11. #69932C2semidirect
16. C22×C3×Q16C22semidirect
24. C22×#215C22semidirect
38. C2×C3×#103C22semidirect
41. C2×#835C22semidirect
42. C2×#835C22semidirect
45. C2×#821C22semidirect
48. #4551C22semidirect
49. #4529C22semidirect
53. C2×#451D3semidirect
106. #946D4semidirect
148. C22×Q16C2×D3semidirect
174. C2×#103C2×D3semidirect
580. C22×C3#452semidirect
749. C22#5187semidirect
767. C3#23922semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×#56272
C2×C3×#4512
C2×#52272
C2×#51872
#720712
#716922
#702722
#702692
#699552
#699322
#239223