Finite Group Databasebeta

← #6475298

Subgroups — #6475298

Order 512.

2388 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33149C212yesmaximal, complemented
4#32956C212yesmaximal, complemented
5#29967C212yesmaximal, complemented
6#29950C212yesmaximal, complemented
7#29238C214yesmaximal, complemented
8#29163C214yesmaximal, complemented
9#27677C212yesmaximal, complemented
10#24843C214yesmaximal, complemented
11#24299C212yesmaximal, complemented
12#21942C212yesmaximal, complemented
13#21764C212yesmaximal
14#20626C211yesmaximal, characteristic, complemented
15C22×C4⋊Q8C2211yescharacteristic, complemented
16C22×C22⋊Q8—21no—
17C22×#121C2211yescharacteristic
18C22×C4×D4—21no—
19C22×C4×D4C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#476C2214yescomplemented
22C2×#423C2212yescomplemented
23C2×#407C2212yes—
24#2857—21no—
25#2857—21no—
26#2857—21no—
27#2857—21no—
28#2857C2212yes—
29#2857C2212yes—
30#2857C2212yescomplemented
31#2857C2212yescomplemented
32C4×#121—21no—
33C4×#121—21no—
34C4×#121—21no—
35C4×#121—21no—
36C4×#121C2212yes—
37C4×#121C2212yes—
38C4×#121C2212yes—
39C4×#121C2212yes—
40C2×#391—21no—
41C2×#390C2211yescharacteristic
42C2×#389—21no—
43C2×#389C2211yescharacteristic
44C2×#389C2212yescomplemented
45C2×#388—21no—
46C2×#386—21no—
47C2×#384C2211yescharacteristic, complemented
48C2×#380—21no—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4—21no—
53#2099C2214yescomplemented
54#2093C2214yescomplemented
55#2088C2218yescomplemented
56#2067C2218yescomplemented
57#2058C2214yescomplemented
58#2023C2214yescomplemented
59#1987C2214yescomplemented
60#1947C2214yescomplemented
61#1921C2218yescomplemented
62#1895C2218yes—
63#1874C2214yes—
64#1874C2214yes—
65#1864C2218yescomplemented
66#1853C2214yes—
67#1853C2214yescomplemented
68#1852C2214yes—
69#1852C2214yescomplemented
70#1824C2214yes—
71#1809C2218yescomplemented
72#1802C2214yescomplemented
73#1797C2212yes—
74#1797C2212yes—
75#1797C2212yescomplemented
76#1797C2212yescomplemented
77#1786C2214yes—
78#1728C2212yescomplemented
79C23×Q8—21no—
80C23×D4—21no—
81C23×D4C2311yescharacteristic
82C24×C4—21no—
83C24×C4D411yescharacteristic
84C24×C4D411yescharacteristic
85C24×C4C2311yescharacteristic
86C22×M16C2314yes—
87C2×C4⋊Q8—21no—
88C2×C4⋊Q8—21no—
89C2×C4⋊Q8—44no—
90C2×C4⋊Q8C2312yes—
91C2×C4⋊Q8C2312yes—
92C2×C22⋊Q8—22no—
93C2×C22⋊Q8—22no—
94C2×C22⋊Q8—22no—
95C2×C22⋊Q8—22no—
96C2×C22⋊Q8—48no—
97C2×#121—21no—
98C2×#121—21no—
99C2×#121—24no—
100C2×#121Q818yescomplemented
101C2×#121C2312yes—
102C2×#121C2312yes—
103C2×C4×D4—22no—
104C2×C4×D4—22no—
105C2×C4×D4—22no—
106C2×C4×D4—22no—
107C2×C4×D4—21no—
108C2×C4×D4—21no—
109C2×C4×D4—44no—
110C2×C4×D4—48no—
111C2×C4×D4C2312yes—
112C2×C4×D4C2312yes—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—22no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—22no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C42—21no—
130C22×C42—44no—
131C22×C42D411yescharacteristic
132C22×C42D411yescharacteristic
133C22×C42D411yescharacteristic
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143#476—48no—
144C2×#107C2318yes—
145C2×#106C2318yes—
146#423—44no—
147C2×C4⋊C8C2314yes—
148C2×C4⋊C8C2314yes—
149C2×#102C2318yes—
150C2×#102C2318yes—
151#407—28no—
152C2×C22⋊C8C2314yes—
153C2×C22⋊C8C2314yes—
154#391—22no—
155#391—22no—
156#391—22no—
157#391—22no—
158#390—21no—
159#390—21no—
160#390C2312yes—
161#390C2312yes—
162#389—22no—
163#389—22no—
164#389—22no—
165#389—22no—
166#389—22no—
167#389—22no—
168#389—21no—
169#389—21no—
170#389C2312yes—
171#389C2314yes—
172#389C2312yes—
173#389C2314yes—
174#388—22no—
175#388—22no—
176#388—22no—
177#388—22no—
178#386—22no—
179#386—22no—
180#386—22no—
181#386—22no—
182#384—21no—
183#384—21no—
184#384C2312yes—
185#384C2312yes—
186#380—22no—
187#380—22no—
188#380—22no—
189#380—22no—
190#380—22no—
191#380—22no—
192#380—21no—
193#380—21no—
194#380C2312yes—
195#380C2314yes—
196#380C2314yes—
197#380C2312yes—
198C4×C4⋊C4—21no—
199C4×C4⋊C4—21no—
200C4×C4⋊C4C2312yes—
201C4×C4⋊C4C2312yes—
202C4×C22⋊C4—22no—
203C4×C22⋊C4—22no—
204C4×C22⋊C4—22no—
205C4×C22⋊C4—22no—
206C2×#95—21no—
207C2×#95—21no—
208C2×#95—21no—
209C2×#95—22no—
210C2×#95—22no—
211#340C2318yes—
212#340C2318yes—
213#340C2318yes—
214#340C2318yes—
215#336C2314yes—
216#336C2314yes—
217C25—21no—
218C25C2×D411yescharacteristic
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—44no—
222C22×Q8—44no—
223C22×Q8—44no—
224C22×D4—28no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—21no—
228C22×D4—22no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—44no—
232C22×D4—44no—
233C22×D4C2×Q814yescomplemented
234C22×D4C2412yes—
235C23×C4—21no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4C2×D411yescharacteristic
254C23×C4C2×D411yescharacteristic
255C23×C4C2×D411yescharacteristic
256C23×C4C2×D411yescharacteristic
257C23×C4C2×D411yescharacteristic
258C23×C4C2×D411yescharacteristic
259C23×C4C2×D411yescharacteristic
260C23×C4C2×D411yescharacteristic
261C23×C4C2×D411yescharacteristic
262C23×C4C2×D411yescharacteristic
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×Q814yes—
269C23×C4#4114yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C2×M16—28no—
274C2×M16—44no—
275C2×M16—44no—
276C22×C8C2418yes—
277C4⋊Q8—28no—
278C4⋊Q8—44no—
279C4⋊Q8—44no—
280C4⋊Q8—44no—
281C22⋊Q8—48no—
282C22⋊Q8—48no—
283C22⋊Q8—48no—
284C22⋊Q8—48no—
285#121—28no—
286#121—28no—
287#121—24no—
288#121—24no—
289#121C2×Q818yes—
290#121C2×Q818yescomplemented
291C4×D4—28no—
292C4×D4—44no—
293C4×D4—44no—
294C4×D4—44no—
295C4×D4—48no—
296C4×D4—48no—
297C4×D4—48no—
298C4×D4—48no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—48no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×Q814yescomplemented
325C2×C4⋊C4C2412yes—
326C2×C4⋊C4C2414yes—
327C2×C4⋊C4C2412yes—
328C2×C4⋊C4C2414yes—
329C2×C4⋊C4C2412yes—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—48no—
347C2×C22⋊C4—44no—
348C2×C42—24no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42—44no—
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42C2×D411yescharacteristic
369C2×C42C2×D411yescharacteristic
370C2×C42C2×D411yescharacteristic
371C2×C42C2×D411yescharacteristic
372C2×C42C2×D411yescharacteristic
373C2×C42C2×D411yescharacteristic
374C2×C42C2×D411yescharacteristic
375C2×C42C2411yescharacteristic
376C2×C42C2411yescharacteristic
377C2×C42C2411yescharacteristic
378C2×C42C2411yescharacteristic
379#107—48no—
380#106—48no—
381C4⋊C8—28no—
382C4⋊C8—44no—
383#102—48no—
384#102—48no—
385C22⋊C8—28no—
386C22⋊C8—28no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—24no—
402C24—22no—
403C24—41no—
404C24—41no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24C22⋊Q814yes—
412C24C22×D411yescharacteristic
413C24C22×D411yescharacteristic
414C24C22×D411yescharacteristic
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C2×Q8—44no—
420C2×Q8—44no—
421C2×Q8—816no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—24no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—48no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4—48no—
432C2×D4—44no—
433C2×D4—432no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4C22×Q814yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—48no—
474C22×C4—48no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—416no—
492C22×C4—416no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—44no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—44no—
507C22×C4—42no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—816no—
514C22×C4C22⋊Q814yes—
515C22×C4C22⋊Q814yes—
516C22×C4C22⋊Q814yes—
517C22×C4AGL(1,ℤ/8)14yes—
518C22×C4AGL(1,ℤ/8)14yes—
519C22×C4#13714yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×Q812yes—
532C22×C4C22×Q812yes—
533C22×C4C22×Q812yes—
534C22×C4C2×#4112yes—
535C22×C4C2×#4112yes—
536C22×C4C2×#4112yes—
537C22×C4C2511yescharacteristic
538M16—88no—
539C2×C8—28no—
540C2×C8—28no—
541C2×C8—28no—
542C4⋊C4—24no—
543C4⋊C4—22no—
544C4⋊C4—28no—
545C4⋊C4—24no—
546C4⋊C4—28no—
547C4⋊C4—24no—
548C4⋊C4—44no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4C22×Q814yes—
563C22⋊C4—28no—
564C22⋊C4—28no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—48no—
569C22⋊C4—44no—
570C22⋊C4—48no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—44no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—22no—
583C42—22no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—44no—
591C42—44no—
592C42H(5,𝔽2)14yes—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—28no—
602C23—28no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—24no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—48no—
616C23—48no—
617C23—48no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23C2×C22⋊Q812yes—
629C23C2×C22⋊Q812yes—
630C23C2×C22⋊Q812yes—
631C23C2×AGL(1,ℤ/8)12yes—
632C23C2×AGL(1,ℤ/8)12yes—
633C23C2×#13712yes—
634C23#57512yes—
635C23C23×D411yescharacteristic
636Q8—88no—
637Q8—88no—
638D4—28no—
639D4—48no—
640D4—416no—
641D4—416no—
642D4—44no—
643C2×C4—28no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—88no—
703C2×C4—88no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—88no—
707C2×C4—88no—
708C2×C4C2×C22⋊Q812yes—
709C2×C4C2×C22⋊Q812yes—
710C2×C4C2×C22⋊Q812yes—
711C2×C4#53412yes—
712C2×C4#53412yes—
713C2×C4C2×AGL(1,ℤ/8)12yes—
714C2×C4C2×AGL(1,ℤ/8)12yes—
715C2×C4C2×AGL(1,ℤ/8)12yes—
716C2×C4C2×AGL(1,ℤ/8)12yes—
717C2×C4C2×#13712yes—
718C2×C4C2×#13712yes—
719C2×C4C23×Q811yescharacteristic
720C2×C4C22×#4111yescharacteristic
721C2×C4C2×H(5,𝔽2)12yes—
722C2×C4#58512yes—
723C8—48no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—416no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—816no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22#307714yes—
753C22#307914yes—
754C22C22×C22⋊Q811yescharacteristic
755C22C2×#53411yescharacteristic
756C22#344911yescharacteristic
757C22C22×AGL(1,ℤ/8)11yescharacteristic
758C22C22×AGL(1,ℤ/8)11yescharacteristic
759C22C22×#13711yescharacteristic
760C22C2×#57511yescharacteristic
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—44no—
770C4—41no—
771C4—41no—
772C4—82no—
773C4—84no—
774C4—82no—
775C4—84no—
776C4#319314yes—
777C4#350112yes—
778C4#350512yes—
779C2—24no—
780C2—24no—
781C2—42no—
782C2—84no—
783C2#3501011yescharacteristic
784C2C2×#307711yescharacteristic
785C2C2×#307911yescharacteristic
786C2C2×#319311yescharacteristic
787C2#6075011yescharacteristic
788C2#6095011yescharacteristic
789C2#6096811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#2857C2semidirect
3. #33149C2semidirect
4. #32956C2semidirect
5. #29967C2semidirect
6. #29950C2semidirect
7. #29238C2semidirect
8. #29163C2semidirect
9. #27677C2semidirect
10. #24843C2semidirect
11. #24299C2semidirect
12. #21942C2semidirect
14. #20626C2semidirect
15. C22×C4⋊Q8C22semidirect
21. C2×#476C22semidirect
22. C2×#423C22semidirect
30. #2857C22semidirect
31. #2857C22semidirect
44. C2×#389C22semidirect
47. C2×#384C22semidirect
53. #2099C22semidirect
54. #2093C22semidirect
55. #2088C22semidirect
56. #2067C22semidirect
57. #2058C22semidirect
58. #2023C22semidirect
59. #1987C22semidirect
60. #1947C22semidirect
61. #1921C22semidirect
65. #1864C22semidirect
67. #1853C22semidirect
69. #1852C22semidirect
71. #1809C22semidirect
72. #1802C22semidirect
75. #1797C22semidirect
76. #1797C22semidirect
78. #1728C22semidirect
100. C2×#121Q8semidirect
233. C22×D4C2×Q8semidirect
290. #121C2×Q8semidirect
324. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×C4×#1212
#331492
#329562
#299672
#299502
#292382
#291632
#276772
#248432
#242992
#219422
#217642
#206262