Finite Group Databasebeta

← #6491691

Subgroups — #6491691

Order 512.

2444 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3206C211yesmaximal, characteristic, complemented
2C2×#2920C211yesmaximal, characteristic, complemented
3#36624C211yesmaximal, characteristic
4C2×#2857C211yesmaximal, characteristic, complemented
5#33174C212yesmaximal, complemented
6#33049C212yesmaximal, complemented
7#29844C212yesmaximal, complemented
8#29807C212yesmaximal, complemented
9#24759C214yesmaximal, complemented
10#24659C214yesmaximal, complemented
11#24509C214yesmaximal, complemented
12#24387C214yesmaximal, complemented
13#21982C211yesmaximal, characteristic, complemented
14#21859C211yesmaximal, characteristic, complemented
15#21804C211yesmaximal, characteristic, complemented
16C2×#532C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C2×#525—21no—
19C22×C22⋊Q8C2212yes—
20C23×C42C2211yescharacteristic
21#3206—28no—
22C2×#492C2212yescomplemented
23C2×#487C2212yescomplemented
24C2×#468C2218yes—
25C2×#461C2214yescomplemented
26C2×#448C2214yes—
27#2920—28no—
28C2×#432C2212yes—
29C2×#432C2212yes—
30C2×#431C2211yescharacteristic
31C2×#431C2212yes—
32C2×#431C2211yescharacteristic
33C2×#423C2212yes—
34C2×#407C2212yes—
35C2×C4×M16C2212yes—
36#2857—21no—
37#2857—21no—
38#2857—21no—
39#2857—21no—
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2857C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2857C2212yes—
46#2856C2211yescharacteristic
47#2856C2211yescharacteristic
48#2854—21no—
49#2854C2212yes—
50#2850—21no—
51#2850—21no—
52#2847—21no—
53#2847C2212yes—
54C4×#121—21no—
55C4×#121—21no—
56C4×#121C2212yes—
57C4×#121C2212yes—
58#2297—21no—
59C2×#391C2212yes—
60C2×#389—21no—
61C2×#389—21no—
62#2285C2211yescharacteristic
63C2×#384C2211yescharacteristic
64C2×#380—21no—
65C2×#380—21no—
66#2068C2218yescomplemented
67#2055C2218yescomplemented
68#2036C2218yes—
69#2000C2218yes—
70#1990C2212yescomplemented
71#1981C2214yescomplemented
72#1973C2218yescomplemented
73#1957C2212yescomplemented
74#1956C2212yescomplemented
75#1956C2212yescomplemented
76#1947C2214yescomplemented
77#1935C2218yescomplemented
78#1894C2218yes—
79#1874C2214yes—
80#1852C2214yes—
81#1845C2212yescomplemented
82#1834C2212yescomplemented
83#1802C2214yescomplemented
84#1787C2214yes—
85C22×#41—21no—
86C23×Q8C2312yes—
87C24×C4D411yescharacteristic
88C24×C4D411yescharacteristic
89C24×C4C2311yescharacteristic
90C22×SD16C2318yes—
91C22×M16C2314yes—
92#532—24no—
93#532—24no—
94C2×C4⋊Q8—21no—
95C2×C4⋊Q8—21no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8C2312yes—
99C2×C4⋊Q8C2312yes—
100C2×C4⋊Q8C2311yescharacteristic
101C2×#127C2311yescharacteristic
102C2×#124—21no—
103#525—48no—
104C2×#123—22no—
105C2×C22⋊Q8—21no—
106C2×C22⋊Q8—21no—
107C2×C22⋊Q8—22no—
108C2×C22⋊Q8—22no—
109C2×C22⋊Q8—48no—
110C2×C22⋊Q8C2314yes—
111C2×C22⋊Q8C2314yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121C2312yes—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×#120—22no—
121C2×C4×D4—22no—
122C2×C4×D4—22no—
123C2×C4×D4—21no—
124C2×C4×D4C2312yes—
125C2×#117—21no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4—22no—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#492—28no—
148#487—28no—
149#468—416no—
150#461—216no—
151#448—216no—
152#432—28no—
153#432—28no—
154#431—24no—
155#431—28no—
156#431D418yescomplemented
157C2×#107C2318yes—
158#423—28no—
159C2×C4⋊C8C2314yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#103C2318yes—
163C2×#103C2318yes—
164C2×#103C2318yes—
165C2×#102C2318yes—
166#407—28no—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2312yes—
170C4×M16—28no—
171C2×#97C2314yes—
172C2×C4×C8C2312yes—
173C2×C4×C8C2312yes—
174#391—21no—
175#391—21no—
176#391—22no—
177#391—22no—
178#391C2314yes—
179#391C2314yes—
180#390—21no—
181#390—21no—
182#390—21no—
183#390—21no—
184#390C2312yes—
185#390C2312yes—
186#389—21no—
187#389—21no—
188#389—22no—
189#389—22no—
190#389—22no—
191#389—22no—
192#389—22no—
193#389—22no—
194#389—22no—
195#389—22no—
196#389C2312yes—
197#389C2312yes—
198#388—22no—
199#388—22no—
200#388—22no—
201#388—22no—
202#386—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#384—21no—
209#384—21no—
210#384C2312yes—
211#384C2311yescharacteristic
212#384C2311yescharacteristic
213#384C2312yes—
214#382—21no—
215#380—21no—
216#380—21no—
217#380—21no—
218#380—22no—
219#380—22no—
220#380—22no—
221#380—22no—
222#380—22no—
223#380—22no—
224#380—22no—
225#380—22no—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229C4×C4⋊C4—21no—
230C4×C4⋊C4C2312yes—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C2×#95—22no—
234C2×#95—22no—
235#340C2318yes—
236#340C2318yes—
237C25C2×D411yescharacteristic
238C2×#41—44no—
239C2×#41—44no—
240C2×#41—44no—
241C22×Q8—21no—
242C22×Q8—22no—
243C22×Q8—24no—
244C22×Q8—24no—
245C22×Q8—44no—
246C22×Q8—44no—
247C22×Q8C2414yes—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4C2412yes—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C2×SD16—216no—
286C2×SD16—48no—
287C2×SD16—48no—
288C2×M16—28no—
289C2×M16—28no—
290C2×M16—44no—
291C22×C8C2414yes—
292C22×C8C2414yes—
293C4⋊Q8—22no—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8—22no—
297C4⋊Q8—24no—
298C4⋊Q8—24no—
299C4⋊Q8—44no—
300C4⋊Q8—44no—
301#127—22no—
302#127—22no—
303#124—44no—
304#123—48no—
305C22⋊Q8—216no—
306C22⋊Q8—48no—
307C22⋊Q8—48no—
308C22⋊Q8—48no—
309C22⋊Q8—44no—
310C22⋊Q8—44no—
311#121—24no—
312#121—24no—
313#121—28no—
314#121—44no—
315#121—44no—
316#121—44no—
317#121—44no—
318#121—44no—
319#121—44no—
320#120—48no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—48no—
324C4×D4—48no—
325C4×D4—44no—
326#117—44no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—48no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4C2414yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
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—48no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42C2×D411yescharacteristic
387C2×C42C2×D411yescharacteristic
388C2×C42C2×D411yescharacteristic
389C2×C42C2×D411yescharacteristic
390C2×C42C2×D411yescharacteristic
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D414yes—
399C2×C42#4114yes—
400C2×C42C2411yescharacteristic
401C2×C42C2411yescharacteristic
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404#107—48no—
405C4⋊C8—28no—
406C4⋊C8—24no—
407C4⋊C8C2×D418yes—
408#103—216no—
409#103—48no—
410#103—48no—
411#102—48no—
412C22⋊C8—24no—
413C22⋊C8—28no—
414C22⋊C8C2×D418yes—
415#97—28no—
416C4×C8—24no—
417C4×C8C2×D418yes—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—41no—
435C24—41no—
436C24C22×D411yescharacteristic
437C24C22×D411yescharacteristic
438C24C22×D411yescharacteristic
439#41—816no—
440C2×Q8—24no—
441C2×Q8—24no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—42no—
447C2×Q8—44no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8—88no—
451C2×Q8—88no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—416no—
528C22×C4—416no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4#12114yes—
539C22×C4#12114yes—
540C22×C4AGL(1,ℤ/8)14yes—
541C22×C4#13714yes—
542C22×C4#13714yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C2×#4112yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C4C2511yescharacteristic
558SD16—816no—
559M16—416no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8—24no—
564C2×C8—24no—
565C2×C8C22×D418yes—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—28no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—48no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—44no—
617C42#12114yes—
618C42#12114yes—
619C42C22×D412yes—
620C42C22×D412yes—
621C42C2×#4112yes—
622C42C2×#4112yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—28no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23C2×#12112yes—
654C23#53512yes—
655C23C2×AGL(1,ℤ/8)12yes—
656C23C2×#13712yes—
657C23C2×#13712yes—
658C23C23×D411yescharacteristic
659Q8—48no—
660Q8—48no—
661Q8—88no—
662Q8—84no—
663D4—44no—
664D4—44no—
665D4—88no—
666D4—88no—
667D4—88no—
668D4—84no—
669D4—84no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—88no—
726C2×C4—88no—
727C2×C4—88no—
728C2×C4#468116yescomplemented
729C2×C4C2×#12112yes—
730C2×C4C2×#12112yes—
731C2×C4C2×#12112yes—
732C2×C4C2×#12112yes—
733C2×C4C2×#12112yes—
734C2×C4#53512yes—
735C2×C4C2×AGL(1,ℤ/8)12yes—
736C2×C4C2×AGL(1,ℤ/8)12yes—
737C2×C4C2×#13712yes—
738C2×C4C2×#13712yes—
739C2×C4C2×#13712yes—
740C2×C4C2×#13712yes—
741C2×C4#57512yes—
742C2×C4C23×D411yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C2×H(5,𝔽2)12yes—
745C2×C4#58512yes—
746C8—28no—
747C8—44no—
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—416no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#46814yes—
777C22C22×#12111yescharacteristic
778C22C2×#53511yescharacteristic
779C22#344911yescharacteristic
780C22C22×AGL(1,ℤ/8)11yescharacteristic
781C22C22×#13711yescharacteristic
782C22C22×#13711yescharacteristic
783C22C2×#57511yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—82no—
793C4—82no—
794C4—84no—
795C4—82no—
796C4—84no—
797C4C2×#46814yes—
798C4C2×#46814yes—
799C4#305614yes—
800C4#348812yes—
801C4#349412yes—
802C2—24no—
803C2—42no—
804C2—42no—
805C2—162no—
806C2#3525211yescharacteristic
807C2C22×#46811yescharacteristic
808C2C2×#305611yescharacteristic
809C2#6080011yescharacteristic
810C2#6080311yescharacteristic
811C2#6096611yescharacteristic
812C2#6096911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3206C2semidirect
2. C2×#2920C2semidirect
4. C2×#2857C2semidirect
5. #33174C2semidirect
6. #33049C2semidirect
7. #29844C2semidirect
8. #29807C2semidirect
9. #24759C2semidirect
10. #24659C2semidirect
11. #24509C2semidirect
12. #24387C2semidirect
13. #21982C2semidirect
14. #21859C2semidirect
15. #21804C2semidirect
22. C2×#492C22semidirect
23. C2×#487C22semidirect
25. C2×#461C22semidirect
66. #2068C22semidirect
67. #2055C22semidirect
70. #1990C22semidirect
71. #1981C22semidirect
72. #1973C22semidirect
73. #1957C22semidirect
74. #1956C22semidirect
75. #1956C22semidirect
76. #1947C22semidirect
77. #1935C22semidirect
81. #1845C22semidirect
82. #1834C22semidirect
83. #1802C22semidirect
156. #431D4semidirect
728. C2×C4#468semidirect

Maximal subgroups

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

subgroupindex
C2×#32062
C2×#29202
#366242
C2×#28572
#331742
#330492
#298442
#298072
#247592
#246592
#245092
#243872
#219822
#218592
#218042