Finite Group Databasebeta

← #6470516

Subgroups — #6470516

Order 512.

2400 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35000C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3#33094C212yesmaximal, complemented
4#32978C212yesmaximal, complemented
5#29906C212yesmaximal, complemented
6#29890C212yesmaximal, complemented
7#26198C214yesmaximal, complemented
8#26126C214yesmaximal, complemented
9#24933C214yesmaximal, complemented
10#24861C214yesmaximal, complemented
11#21940C211yesmaximal, characteristic, complemented
12#21758C211yesmaximal, characteristic, complemented
13#21738C211yesmaximal, characteristic, complemented
14C2×#1874C211yesmaximal, characteristic, complemented
15C2×#1852C211yesmaximal, characteristic, complemented
16C2×#534—21no—
17C22×#121C2211yescharacteristic
18C22×C4×D4—21no—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic, complemented
22C2×#480C2214yescomplemented
23C22×#107C2212yescomplemented
24C22×#102C2212yescomplemented
25C22×C22⋊C8C2211yescharacteristic
26C22×C22⋊C8C2211yescharacteristic
27#2854C2212yes—
28#2847C2212yes—
29#2618—21no—
30#2617—21no—
31#2543—22no—
32#2534—22no—
33#2486C2212yes—
34#2416C2212yes—
35#2416C2212yes—
36#2408C2212yes—
37D4×C4⋊C4—22no—
38D4×C4⋊C4—22no—
39D4×C4⋊C4C2214yes—
40D4×C4⋊C4C2214yescomplemented
41#2308—21no—
42C2×#389—21no—
43C2×#385—21no—
44C2×#385—21no—
45C2×#384C2211yescharacteristic, complemented
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic, complemented
49C2×C4×C4⋊C4C2211yescharacteristic, complemented
50#2099C2214yescomplemented
51#2093C2214yescomplemented
52#2083C2214yescomplemented
53#2075C2214yescomplemented
54#2075C2214yescomplemented
55#2071C2214yescomplemented
56#2033C2214yescomplemented
57#2033C2214yescomplemented
58#1925C2214yescomplemented
59#1925C2214yescomplemented
60#1918C2214yescomplemented
61#1918C2214yescomplemented
62#1893C2214yescomplemented
63#1874C2212yes—
64#1874C2212yes—
65#1874C2212yes—
66#1874C2212yes—
67#1874C2214yescomplemented
68#1874C2214yescomplemented
69#1869C2214yes—
70#1869C2214yescomplemented
71#1852C2212yescomplemented
72#1852C2214yescomplemented
73#1852C2214yescomplemented
74#1852C2212yescomplemented
75#1852C2212yescomplemented
76#1852C2212yescomplemented
77#1852C2212yescomplemented
78#1852C2212yescomplemented
79#1823C2214yescomplemented
80#1823C2212yescomplemented
81#1817C2212yescomplemented
82#1808C2214yescomplemented
83#1786C2212yescomplemented
84#1779C2212yescomplemented
85C2×#340C2212yescomplemented
86C2×#340C2212yescomplemented
87C23×D4—21no—
88C23×D4D411yescharacteristic
89C23×D4C2311yescharacteristic
90C24×C4—21no—
91C24×C4—21no—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C23×C8C2312yes—
95C23×C8C2312yes—
96#534—48no—
97C2×#123—22no—
98C2×#123—22no—
99C2×#121—22no—
100C2×#121—22no—
101C2×#121—21no—
102C2×#121—21no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121C2312yes—
106C2×#121C2312yes—
107C2×#121C2312yes—
108C2×#121C2312yes—
109C2×#120—22no—
110C2×#120—22no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—48no—
116C2×C4×D4D412yes—
117C2×C4×D4D412yes—
118C2×C4×D4C2312yes—
119C2×C4×D4C2312yes—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—22no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—44no—
128C22×C4⋊C4—44no—
129C22×C4⋊C4D411yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4D411yescharacteristic
145C22×C22⋊C4D411yescharacteristic
146C22×C42—21no—
147C22×C42C2311yescharacteristic
148#480—48no—
149C2×#107—44no—
150C2×#107C2314yes—
151C2×#107C2314yes—
152C2×#107C2314yes—
153C2×#107C2314yes—
154C2×#102—44no—
155C2×#102C2314yes—
156C2×#102C2314yes—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×C22⋊C8—24no—
160C2×C22⋊C8—24no—
161C2×C22⋊C8C2312yes—
162C2×C22⋊C8C2312yes—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2312yes—
165C2×C22⋊C8C2314yes—
166C2×C22⋊C8C2314yes—
167#398—22no—
168#397—22no—
169#396—22no—
170#396—22no—
171#394—22no—
172#394—22no—
173#394—22no—
174#392—22no—
175#390C2312yes—
176#390C2312yes—
177#389—24no—
178#389—24no—
179#389C2312yes—
180#389C2312yes—
181#388—22no—
182#388—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#386—22no—
187#386—22no—
188#386—22no—
189#385—24no—
190#385—24no—
191#385—24no—
192#385—24no—
193#384—22no—
194#384C2314yes—
195#381—22no—
196#380—21no—
197#380—21no—
198#380—22no—
199#380—21no—
200#380—21no—
201#380C2312yes—
202#380C2312yes—
203#380C2312yes—
204#380C2312yes—
205#380C2314yes—
206#380C2312yes—
207#380C2312yes—
208#379—22no—
209C4×C4⋊C4—22no—
210C4×C4⋊C4C2314yes—
211C2×#95—21no—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215#340C2314yes—
216#340C2314yes—
217#340C2314yes—
218#340C2314yes—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225C25—21no—
226C25C2×D411yescharacteristic
227C25C2×D411yescharacteristic
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—21no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4D818yes—
243C22×D4C2×D412yes—
244C22×D4C2×D412yes—
245C22×D4C2412yes—
246C23×C4—21no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4—21no—
252C23×C4—21no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—82no—
267C23×C4—82no—
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4#4114yes—
276C23×C4#4114yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C22×C8—24no—
282C22×C8—24no—
283C22×C8—42no—
284C22×C8—42no—
285C22×C8—42no—
286C22×C8—42no—
287C22×C8C2414yes—
288C22×C8C2414yes—
289#123—48no—
290#123—48no—
291#121—24no—
292#121—24no—
293#121—24no—
294#121—24no—
295#121—48no—
296#121—48no—
297#121—44no—
298#121—44no—
299#121—44no—
300#121—44no—
301#120—48no—
302#120—48no—
303C4×D4—28no—
304C4×D4—28no—
305C4×D4—24no—
306C4×D4—24no—
307C4×D4—24no—
308C4×D4—24no—
309C4×D4—416no—
310C4×D4—416no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—48no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—82no—
347C2×C4⋊C4C2×D412yes—
348C2×C4⋊C4C2×D412yes—
349C2×C4⋊C4C2412yes—
350C2×C4⋊C4C2412yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4C2×D412yes—
378C2×C22⋊C4C2×D412yes—
379C2×C22⋊C4C2×D412yes—
380C2×C22⋊C4C2×D412yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—44no—
385C2×C42C2×D412yes—
386C2×C42C2412yes—
387#107—28no—
388#107—44no—
389#107—44no—
390#107—44no—
391#102—28no—
392#102—44no—
393#102—44no—
394#102—44no—
395C22⋊C8—24no—
396C22⋊C8—24no—
397C22⋊C8—24no—
398C22⋊C8—24no—
399C22⋊C8—44no—
400C22⋊C8—44no—
401#95—24no—
402#95—24no—
403#95—22no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—22no—
409#95—22no—
410#95—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—41no—
415C24—41no—
416C24—41no—
417C24—41no—
418C24—41no—
419C24—41no—
420C24—41no—
421C24—41no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—81no—
426C24—81no—
427C24—81no—
428C24—81no—
429C24#12314yes—
430C24C2×D814yes—
431C24C2×D814yes—
432C24#13714yes—
433C24C22×D412yes—
434C24C22×D411yescharacteristic
435C24C22×D411yescharacteristic
436C24C22×D411yescharacteristic
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—232no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—48no—
447C2×D4—44no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—42no—
456C2×D4—84no—
457C2×D4—81no—
458C2×D4—81no—
459C2×D4—82no—
460C2×D4—82no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4—816no—
464C2×D4C2×D818yes—
465C2×D4C2×D818yes—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—48no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—84no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—816no—
535C22×C4—816no—
536C22×C4#12314yes—
537C22×C4#12314yes—
538C22×C4#12314yes—
539C22×C4C2×D814yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D412yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2511yescharacteristic
553C2×C8—24no—
554C2×C8—24no—
555C2×C8—24no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—48no—
560C2×C8—84no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—48no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—48no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—81no—
584C4⋊C4—81no—
585C4⋊C4—84no—
586C4⋊C4H(5,𝔽2)14yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—48no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C42—24no—
607C42—22no—
608C42—22no—
609C42—48no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—22no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—162no—
652C23—162no—
653C23—162no—
654C23—162no—
655C23#480116yescomplemented
656C23C2×#12312yes—
657C23C2×#12312yes—
658C23C2×#12312yes—
659C23C22×D814yes—
660C23C22×D812yes—
661C23C22×D812yes—
662C23C22×D812yes—
663C23C2×#13712yes—
664C23C2×#13712yes—
665C23C2×#13712yes—
666C23C23×D411yescharacteristic
667D4—216no—
668D4—216no—
669D4—44no—
670D4—44no—
671D4—84no—
672D4—88no—
673D4—88no—
674D4—164no—
675D4—164no—
676C2×C4—28no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—48no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—88no—
728C2×C4—88no—
729C2×C4—816no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—162no—
735C2×C4—162no—
736C2×C4C2×#12312yes—
737C2×C4C2×#12312yes—
738C2×C4C2×#12312yes—
739C2×C4C22×D814yes—
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×H(5,𝔽2)12yes—
743C2×C4#58512yes—
744C8—44no—
745C8—44no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—416no—
768C22—416no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—168no—
781C22C2×#48014yes—
782C22C2×#48014yes—
783C22C2×#48014yes—
784C22C22×#12311yescharacteristic
785C22#348411yescharacteristic
786C22#348511yescharacteristic
787C22C23×D811yescharacteristic
788C22C22×#13711yescharacteristic
789C22#358511yescharacteristic
790C22#358611yescharacteristic
791C4—24no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—44no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4#345912yes—
805C4#350512yes—
806C2—24no—
807C2—24no—
808C2—24no—
809C2—44no—
810C2—162no—
811C2#3498311yescharacteristic
812C2C22×#48011yescharacteristic
813C2#6051711yescharacteristic
814C2#6155911yescharacteristic
815C2#6157411yescharacteristic
816C2#6169411yescharacteristic
817C2#6170911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35000C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×D4×C4⋊C4C2semidirect
3. #33094C2semidirect
4. #32978C2semidirect
5. #29906C2semidirect
6. #29890C2semidirect
7. #26198C2semidirect
8. #26126C2semidirect
9. #24933C2semidirect
10. #24861C2semidirect
11. #21940C2semidirect
12. #21758C2semidirect
13. #21738C2semidirect
14. C2×#1874C2semidirect
15. C2×#1852C2semidirect
21. C23×C4⋊C4C22semidirect
22. C2×#480C22semidirect
23. C22×#107C22semidirect
24. C22×#102C22semidirect
40. D4×C4⋊C4C22semidirect
45. C2×#384C22semidirect
48. C2×#380C22semidirect
49. C2×C4×C4⋊C4C22semidirect
50. #2099C22semidirect
51. #2093C22semidirect
52. #2083C22semidirect
53. #2075C22semidirect
54. #2075C22semidirect
55. #2071C22semidirect
56. #2033C22semidirect
57. #2033C22semidirect
58. #1925C22semidirect
59. #1925C22semidirect
60. #1918C22semidirect
61. #1918C22semidirect
62. #1893C22semidirect
67. #1874C22semidirect
68. #1874C22semidirect
70. #1869C22semidirect
71. #1852C22semidirect
72. #1852C22semidirect
73. #1852C22semidirect
74. #1852C22semidirect
75. #1852C22semidirect
76. #1852C22semidirect
77. #1852C22semidirect
78. #1852C22semidirect
79. #1823C22semidirect
80. #1823C22semidirect
81. #1817C22semidirect
82. #1808C22semidirect
83. #1786C22semidirect
84. #1779C22semidirect
85. C2×#340C22semidirect
86. C2×#340C22semidirect
655. C23#480semidirect

Maximal subgroups

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

subgroupindex
#350002
C2×D4×C4⋊C42
#330942
#329782
#299062
#298902
#261982
#261262
#249332
#248612
#219402
#217582
#217382
C2×#18742
C2×#18522