Finite Group Databasebeta

← #6489125

Subgroups — #6489125

Order 512.

2116 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C2×C4×#124C211yesmaximal, characteristic, complemented
3#32909C212yesmaximal, complemented
4#32908C212yesmaximal, complemented
5#30044C214yesmaximal, complemented
6#29146C212yesmaximal, complemented
7#28446C212yesmaximal, complemented
8#28163C214yesmaximal, complemented
9#27983C211yesmaximal, characteristic, complemented
10#27982C211yesmaximal, characteristic, complemented
11#25731C211yesmaximal, characteristic
12#25730C211yesmaximal, characteristic, complemented
13#23937C212yesmaximal, complemented
14#23936C212yesmaximal, complemented
15#22273C212yesmaximal, complemented
16#22272C212yesmaximal, complemented
17#20778C211yesmaximal, characteristic, complemented
18C2×#529C2212yes—
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C2×#497C2212yes—
23C2×#496C2212yes—
24C2×#464C2214yescomplemented
25C2×#463C2214yes—
26C2×#451C2212yes—
27C2×#448C2212yes—
28C2×#450C2212yes—
29C2×#447C2212yes—
30#2861C2212yescomplemented
31#2860—21no—
32#2860—21no—
33#2859C2211yescharacteristic, complemented
34#2858C2211yescharacteristic, complemented
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2854—21no—
38#2854—21no—
39#2850C2212yes—
40C4×C4⋊Q8C2211yescharacteristic, complemented
41C4×#127C2211yescharacteristic, complemented
42C4×#124—21no—
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#124C2212yes—
47C4×#124C2212yes—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#124C2212yescomplemented
51C4×#121—21no—
52C4×#121—21no—
53C2×#391C2211yescharacteristic
54#2293—21no—
55#2293—21no—
56C2×#390C2211yescharacteristic
57C2×#388—21no—
58C2×#388—21no—
59C2×#382C2211yescharacteristic
60C2×C4×C22⋊C4—21no—
61C2×C4×C22⋊C4—21no—
62C2×C43C2211yescharacteristic
63#2074C2214yescomplemented
64#2073C2214yescomplemented
65#2026C2214yescomplemented
66#2025C2214yes—
67#2015C2214yes—
68#2015C2214yescomplemented
69#2012C2214yes—
70#2012C2214yes—
71#1961C2212yescomplemented
72#1960C2212yescomplemented
73#1959C2212yes—
74#1959C2212yes—
75#1880C2214yes—
76#1880C2214yescomplemented
77#1879C2214yes—
78#1879C2214yes—
79#1878C2214yescomplemented
80#1878C2214yescomplemented
81#1877C2214yes—
82#1877C2214yescomplemented
83#1874C2212yes—
84#1874C2212yes—
85#1872C2212yes—
86#1872C2212yes—
87#1839C2212yescomplemented
88#1836C2212yescomplemented
89#1836C2212yescomplemented
90#1831C2212yescomplemented
91#1817C2212yes—
92#1805C2214yescomplemented
93#1804C2214yes—
94#1797C2212yes—
95#1767C2212yescomplemented
96#1749C2211yescharacteristic
97#1749C2211yescharacteristic
98#1745C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×Q16C2314yes—
103C22×SD16C2314yes—
104C22×SD16C2314yes—
105C22×D8C2314yes—
106C2×C4⋊Q8C2311yescharacteristic
107C2×#127C2311yescharacteristic
108#529—44no—
109#529—44no—
110C2×#126—22no—
111C2×#125C2312yes—
112C2×#124—28no—
113C2×#124—21no—
114C2×#124—21no—
115C2×#124C2312yes—
116C2×#124C2312yes—
117C2×#124C2312yes—
118C2×#124C2312yes—
119C2×#123—22no—
120C2×C22⋊Q8C2312yes—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121C2312yes—
124C2×C4×Q8—21no—
125C2×C4×Q8—21no—
126C2×C4×Q8—44no—
127C2×C4×Q8C2312yes—
128C2×C4×Q8C2312yes—
129C2×C4×Q8C2312yes—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—44no—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×#117—22no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C42—21no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#497—28no—
157#496—28no—
158#464—48no—
159#463—48no—
160#451—44no—
161#450—44no—
162#448—44no—
163#447—44no—
164C2×C4⋊C8C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×#97C2312yes—
176C2×#97C2312yes—
177#391—21no—
178#391—21no—
179#391C2312yes—
180#391C2312yes—
181#391C2312yes—
182#391C2312yes—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#388—22no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#386—22no—
222#386—22no—
223#384C2311yescharacteristic
224#384C2311yescharacteristic
225#382—21no—
226#382—21no—
227#382C2312yes—
228#382C2312yes—
229#382C2312yes—
230#380—21no—
231#380—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C43D411yescharacteristic
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43C2311yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2314yes—
261#336C2314yes—
262#336C2314yes—
263#336C2312yes—
264#336C2312yes—
265C25—21no—
266C22×Q8—24no—
267C22×Q8—21no—
268C22×Q8—24no—
269C22×Q8—42no—
270C22×Q8C2412yes—
271C22×Q8C2412yes—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—24no—
278C22×D4—42no—
279C22×D4C2412yes—
280C22×D4C2412yes—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C2×Q16—28no—
298C2×Q16—44no—
299C2×Q16—44no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—44no—
303C2×SD16—44no—
304C2×SD16—44no—
305C2×SD16—44no—
306C2×D8—28no—
307C2×D8—44no—
308C2×D8—44no—
309C22×C8C2414yes—
310C22×C8C2414yes—
311C4⋊Q8—24no—
312#127—24no—
313#126—48no—
314#125—42no—
315#125—42no—
316#124—28no—
317#124—28no—
318#124—24no—
319#124—24no—
320#124—24no—
321#124—28no—
322#124—42no—
323#124—42no—
324#124#4118yes—
325#123—48no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328#121—24no—
329#121—24no—
330#121—44no—
331#121—44no—
332C4×Q8—28no—
333C4×Q8—44no—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8—44no—
337C4×Q8—44no—
338C4×D4—28no—
339C4×D4—44no—
340C4×D4—42no—
341C4×D4—42no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—44no—
345C4×D4—44no—
346C4×D4—48no—
347#117—48no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—44no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C4⋊C8—28no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445#97—24no—
446#97—24no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461C24—24no—
462C24—22no—
463C24—22no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24C22×D411yescharacteristic
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—416no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8C2×#4114yes—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—416no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4C2×#4114yes—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—816no—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4H(5,𝔽2)14yes—
563C22×C4C2511yescharacteristic
564Q16—88no—
565SD16—88no—
566SD16—88no—
567D8—88no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—28no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—44no—
642C42—44no—
643C42—44no—
644C42C2×#4114yes—
645C42H(5,𝔽2)14yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—48no—
652C23—48no—
653C23—48no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23#53512yes—
672C23#57512yes—
673C23#57512yes—
674C23C23×D411yescharacteristic
675Q8—28no—
676Q8—48no—
677Q8—44no—
678Q8—44no—
679Q8—44no—
680D4—28no—
681D4—48no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—84no—
686D4—84no—
687D4—88no—
688C2×C4—28no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—28no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—88no—
747C2×C4—88no—
748C2×C4—88no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4#52512yes—
752C2×C4#52512yes—
753C2×C4#53512yes—
754C2×C4#53512yes—
755C2×C4#53512yes—
756C2×C4#57512yes—
757C2×C4#57512yes—
758C2×C4C22×#4112yes—
759C2×C4C2×H(5,𝔽2)12yes—
760C2×C4C2×H(5,𝔽2)12yes—
761C8—44no—
762C8—44no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—816no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22#321914yes—
785C22C2×#52511yescharacteristic
786C22C2×#53511yescharacteristic
787C22C2×#53511yescharacteristic
788C22C2×#57511yescharacteristic
789C22C2×#57511yescharacteristic
790C22C2×#57511yescharacteristic
791C22C2×#57511yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—44no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4#351914yes—
812C2—24no—
813C2—84no—
814C2—162no—
815C2#3523711yescharacteristic
816C2#6056311yescharacteristic
817C2#6056311yescharacteristic
818C2C2×#321911yescharacteristic
819C2#6079011yescharacteristic
820C2#6079911yescharacteristic
821C2#6080511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25731C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36631C2semidirect
2. C2×C4×#124C2semidirect
3. #32909C2semidirect
4. #32908C2semidirect
5. #30044C2semidirect
6. #29146C2semidirect
7. #28446C2semidirect
8. #28163C2semidirect
9. #27983C2semidirect
10. #27982C2semidirect
12. #25730C2semidirect
13. #23937C2semidirect
14. #23936C2semidirect
15. #22273C2semidirect
16. #22272C2semidirect
17. #20778C2semidirect
24. C2×#464C22semidirect
30. #2861C22semidirect
33. #2859C22semidirect
34. #2858C22semidirect
40. C4×C4⋊Q8C22semidirect
41. C4×#127C22semidirect
50. C4×#124C22semidirect
63. #2074C22semidirect
64. #2073C22semidirect
65. #2026C22semidirect
68. #2015C22semidirect
71. #1961C22semidirect
72. #1960C22semidirect
76. #1880C22semidirect
79. #1878C22semidirect
80. #1878C22semidirect
82. #1877C22semidirect
87. #1839C22semidirect
88. #1836C22semidirect
89. #1836C22semidirect
90. #1831C22semidirect
92. #1805C22semidirect
95. #1767C22semidirect
98. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#366312
C2×C4×#1242
#329092
#329082
#300442
#291462
#284462
#281632
#279832
#279822
#257312
#257302
#239372
#239362
#222732
#222722
#207782