Finite Group Databasebeta

← #360139

Subgroups — #360139

Order 512.

2162 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×SD16C211yesmaximal, characteristic
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×#1877C212yesmaximal
4C2×#1803C211yesmaximal, characteristic, complemented
5C2×#1802C211yesmaximal, characteristic
6#13926C211yesmaximal, characteristic, complemented
7#11220C212yesmaximal, complemented
8#11067C212yesmaximal, complemented
9#10841C211yesmaximal, characteristic, complemented
10#10834C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal
12C23×SD16C2211yescharacteristic
13C22×C4×Q8C2211yescharacteristic
14C22×C4×D4C2212yes—
15C22×C4×D4C2211yescharacteristic
16C23×C4⋊C4—21no—
17C2×C4×SD16—24no—
18C2×C4×SD16—24no—
19C2×C4×SD16C418yescomplemented
20C22×#106C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2212yes—
23C22×#103C2211yescharacteristic
24C22×#102C2212yes—
25C22×#102C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27D4×C4⋊C4—24no—
28D4×C4⋊C4—24no—
29C2×#391C2212yes—
30C2×#389C2212yes—
31C2×#385—22no—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×C4×C4⋊C4C2211yescharacteristic
36#1877—28no—
37#1803—24no—
38#1802—24no—
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#336C2212yes—
44C2×#336C2212yes—
45#1441—22no—
46C4⋊#95—21no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C23×Q8C2311yescharacteristic
50C23×D4C2311yescharacteristic
51C24×C4—21no—
52C24×C4—22no—
53C22×SD16—22no—
54C22×SD16—22no—
55C22×SD16—22no—
56C22×SD16—22no—
57C22×SD16C2×C414yes—
58C22×SD16D414yes—
59C22×SD16Q814yes—
60C23×C8C2312yes—
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C2×C4×Q8—22no—
64C2×C4×Q8—22no—
65C2×C4×Q8—22no—
66C2×C4×Q8—22no—
67C2×C4×Q8—22no—
68C2×C4×Q8C2×C414yescomplemented
69C2×C4×D4—24no—
70C2×C4×D4—24no—
71C2×C4×D4—24no—
72C2×C4×D4—24no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—42no—
77C2×C4×D4—42no—
78C2×C4×D4C2×C414yes—
79C2×C4×D4D414yes—
80C2×C4×D4D414yes—
81C22×C4⋊C4—28no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—44no—
89C22×C4⋊C4—44no—
90C22×C4⋊C4D411yescharacteristic
91C22×C4⋊C4D411yescharacteristic
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—22no—
98C22×C42—21no—
99C22×C42C2312yes—
100C22×C42C2311yescharacteristic
101C4×SD16—232no—
102C2×#106—22no—
103C2×#106—22no—
104C2×#106C2×C414yescomplemented
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—24no—
111C2×#103—24no—
112C2×#103—42no—
113C2×#103C2×C414yescomplemented
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—24no—
117C2×#102—24no—
118C2×#102—24no—
119C2×#102C2×C414yes—
120C2×C4×C8—22no—
121C2×C4×C8—22no—
122C2×C4×C8C2×C414yescomplemented
123#391—24no—
124#391—42no—
125#389—24no—
126#389—24no—
127#385—216no—
128#384—22no—
129#384—22no—
130#384—22no—
131#384D414yes—
132#380—28no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—22no—
135C2×#95—22no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—22no—
139C2×#95—22no—
140C2×#95D412yes—
141#340—24no—
142#340—24no—
143#340—24no—
144#340—42no—
145#336—24no—
146#336—42no—
147C25—21no—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8C22×C412yes—
160C22×Q8C2×D412yes—
161C22×Q8C2×Q812yes—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4C22×C412yes—
170C22×D4C2×D412yes—
171C22×D4C2×D412yes—
172C22×D4C2×D412yes—
173C22×D4C2×Q812yes—
174C22×D4#4112yes—
175C22×D4#4112yes—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—24no—
179C23×C4—24no—
180C23×C4—24no—
181C23×C4—22no—
182C23×C4—21no—
183C23×C4—28no—
184C23×C4—22no—
185C23×C4—44no—
186C23×C4—44no—
187C23×C4—44no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—44no—
193C23×C4—82no—
194C23×C4—82no—
195C23×C4C2×D412yes—
196C23×C4C2×D412yes—
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2411yescharacteristic
200C2×SD16—28no—
201C2×SD16—28no—
202C2×SD16—28no—
203C2×SD16—28no—
204C2×SD16—28no—
205C2×SD16—28no—
206C2×SD16C4⋊C4116yescomplemented
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—22no—
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8C22×C412yes—
225C22×C8C22×C412yes—
226C22×C8C2×D412yes—
227C22×C8C2×Q812yes—
228C4×Q8—28no—
229C4×Q8—28no—
230C4×Q8—44no—
231C4×Q8—44no—
232C4×D4—28no—
233C4×D4—28no—
234C4×D4—28no—
235C4×D4—48no—
236C4×D4—48no—
237C4×D4—48no—
238C4×D4—48no—
239C4×D4C22⋊C4116yes—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—432no—
269C2×C4⋊C4—44no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—44no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—81no—
280C2×C4⋊C4—81no—
281C2×C4⋊C4—81no—
282C2×C4⋊C4—81no—
283C2×C4⋊C4SD1614yescomplemented
284C2×C4⋊C4C22×C412yes—
285C2×C4⋊C4C22×C412yes—
286C2×C4⋊C4C2×D414yes—
287C2×C4⋊C4C2×D412yes—
288C2×C4⋊C4C2×D412yes—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—28no—
293C2×C22⋊C4—44no—
294C2×C22⋊C4—44no—
295C2×C42—24no—
296C2×C42—22no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—42no—
303C2×C42—42no—
304C2×C42C22×C412yes—
305C2×C42C2×D412yes—
306C2×C42C2×D412yes—
307C2×C42C2×D412yes—
308C2×C42#4112yes—
309C2×C42#4112yes—
310#106—28no—
311C4⋊C8—44no—
312#103—28no—
313#103—48no—
314#102—28no—
315#102—48no—
316C4×C8—28no—
317#95—28no—
318#95—24no—
319#95—44no—
320#95—44no—
321#95—82no—
322#95—82no—
323C24—22no—
324C24—22no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—41no—
331C24—41no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24C22×D411yescharacteristic
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×Q8—41no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8C2×C4⋊C414yescomplemented
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4C2×C22⋊C414yes—
389C2×D4C2×C4⋊C414yes—
390C2×D4#11714yes—
391C2×D4#12114yes—
392C2×D4#12114yes—
393C2×D4C22⋊Q814yes—
394C2×D4C22⋊Q814yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—216no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—416no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—416no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—41no—
444C22×C4—42no—
445C22×C4—41no—
446C22×C4—42no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—88no—
457C22×C4—88no—
458C22×C4—88no—
459C22×C4—88no—
460C22×C4—88no—
461C22×C4C4×D412yes—
462C22×C4C4×D412yes—
463C22×C4#12012yes—
464C22×C4#12012yes—
465C22×C4#12112yes—
466C22×C4#12112yes—
467C22×C4C2×SD1614yes—
468C22×C4C2×SD1612yes—
469C22×C4#13512yes—
470C22×C4AGL(1,ℤ/8)12yes—
471C22×C4#13712yes—
472C22×C4C23×C411yescharacteristic
473C22×C4C22×D411yescharacteristic
474C22×C4C22×D411yescharacteristic
475C22×C4C22×D411yescharacteristic
476C22×C4C22×D411yescharacteristic
477C22×C4C22×Q811yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4H(5,𝔽2)11yescharacteristic
483C22×C4H(5,𝔽2)11yescharacteristic
484C22×C42−1+411yescharacteristic
485C22×C42−1+411yescharacteristic
486SD16—232no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—42no—
501C2×C8—42no—
502C2×C8—42no—
503C2×C8—42no—
504C2×C8—42no—
505C2×C8—42no—
506C2×C8—42no—
507C2×C8C2×C4⋊C414yescomplemented
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—28no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—416no—
517C4⋊C4—42no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—42no—
521C4⋊C4—48no—
522C4⋊C4—48no—
523C4⋊C4—44no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—84no—
529C4⋊C4—84no—
530C4⋊C4—84no—
531C4⋊C4C2×C22⋊C414yes—
532C22⋊C4—216no—
533C22⋊C4—416no—
534C42—42no—
535C42—42no—
536C42—42no—
537C42—42no—
538C42—48no—
539C42C2×C22⋊C414yes—
540C42C4×D414yes—
541C42#12114yes—
542C42#12314yes—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23C2×C4×D411yescharacteristic
579C23C2×#12011yescharacteristic
580C23C2×#12111yescharacteristic
581C23D4211yescharacteristic
582C23#54611yescharacteristic
583C23#54811yescharacteristic
584C23D4×Q811yescharacteristic
585C23C22×SD1611yescharacteristic
586C23C2×#13511yescharacteristic
587C23C2×AGL(1,ℤ/8)11yescharacteristic
588C23C2×#13711yescharacteristic
589C23#57611yescharacteristic
590C23#57711yescharacteristic
591C23#57711yescharacteristic
592C23#57811yescharacteristic
593Q8—24no—
594Q8—24no—
595Q8—42no—
596Q8—42no—
597Q8—42no—
598Q8—42no—
599Q8—42no—
600Q8—42no—
601D4—24no—
602D4—24no—
603D4—24no—
604D4—24no—
605D4—24no—
606D4—24no—
607D4—24no—
608D4#38018yes—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—432no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—44no—
643C2×C4—42no—
644C2×C4—44no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—832no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—82no—
654C2×C4—82no—
655C2×C4—82no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4#38614yes—
667C2×C4#38614yes—
668C2×C4C4×SD1614yes—
669C2×C4#44014yes—
670C2×C4#45014yes—
671C2×C4#45214yes—
672C2×C4#46114yes—
673C2×C4#46314yes—
674C2×C4C22×C22⋊C411yescharacteristic
675C2×C4C22×C4⋊C411yescharacteristic
676C2×C4C2×#11711yescharacteristic
677C2×C4C2×C4×D411yescharacteristic
678C2×C4#52011yescharacteristic
679C2×C4#52011yescharacteristic
680C2×C4C2×#12111yescharacteristic
681C2×C4C2×#12111yescharacteristic
682C2×C4C2×#12111yescharacteristic
683C2×C4C2×C22⋊Q811yescharacteristic
684C2×C4C2×C22⋊Q811yescharacteristic
685C2×C4C2×#12311yescharacteristic
686C2×C4#53511yescharacteristic
687C2×C4#53611yescharacteristic
688C2×C4#53711yescharacteristic
689C2×C4#53711yescharacteristic
690C2×C4D4211yescharacteristic
691C2×C4#54611yescharacteristic
692C2×C4#54711yescharacteristic
693C2×C4#54711yescharacteristic
694C2×C4#54811yescharacteristic
695C2×C4D4×Q811yescharacteristic
696C2×C4#55211yescharacteristic
697C2×C4#55211yescharacteristic
698C2×C4#55311yescharacteristic
699C2×C4#55311yescharacteristic
700C2×C4#55411yescharacteristic
701C2×C4#55411yescharacteristic
702C8—24no—
703C8—42no—
704C8—82no—
705C22—28no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—44no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22C2×#38611yescharacteristic
721C22D4×C4⋊C411yescharacteristic
722C22#235211yescharacteristic
723C22#240811yescharacteristic
724C22#240911yescharacteristic
725C22#241611yescharacteristic
726C22#241711yescharacteristic
727C22C2×C4×SD1611yescharacteristic
728C22C2×#44011yescharacteristic
729C22#295111yescharacteristic
730C22#295211yescharacteristic
731C22C2×#45011yescharacteristic
732C22C2×#45211yescharacteristic
733C22#301211yescharacteristic
734C22#301311yescharacteristic
735C22C2×#46111yescharacteristic
736C22C2×#46311yescharacteristic
737C22#304511yescharacteristic
738C22#304611yescharacteristic
739C22#327411yescharacteristic
740C22#327611yescharacteristic
741C22D4×SD1611yescharacteristic
742C22#328411yescharacteristic
743C22#329511yescharacteristic
744C22#330211yescharacteristic
745C22#332411yescharacteristic
746C22#333111yescharacteristic
747C22#335911yescharacteristic
748C22#336111yescharacteristic
749C22#337211yescharacteristic
750C22#337311yescharacteristic
751C22Q8×SD1611yescharacteristic
752C22#338111yescharacteristic
753C22#338511yescharacteristic
754C22#338611yescharacteristic
755C4—24no—
756C4—44no—
757C4—44no—
758C4—44no—
759C4—84no—
760C4—82no—
761C4—82no—
762C4—162no—
763C4#187718yescomplemented
764C4C2×#38011yescharacteristic
765C4#231111yescharacteristic
766C4D4×C4⋊C411yescharacteristic
767C4#235211yescharacteristic
768C4#241611yescharacteristic
769C4#241711yescharacteristic
770C4#248611yescharacteristic
771C4#248711yescharacteristic
772C2—48no—
773C2#1387211yescharacteristic
774C2C2×#187711yescharacteristic
775C2#2093711yescharacteristic
776C2#2267111yescharacteristic
777C2C4⋊C4×SD1611yescharacteristic
778C2#2276211yescharacteristic
779C2#2277011yescharacteristic
780C2#2424011yescharacteristic
781C2#2424111yescharacteristic
782C2#2433011yescharacteristic
783C2#2433111yescharacteristic
784C2#2473011yescharacteristic
785C2#2473111yescharacteristic
786C2#2481511yescharacteristic
787C2#2481611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1803C2semidirect
6. #13926C2semidirect
7. #11220C2semidirect
8. #11067C2semidirect
9. #10841C2semidirect
10. #10834C2semidirect
19. C2×C4×SD16C4semidirect
68. C2×C4×Q8C2×C4semidirect
104. C2×#106C2×C4semidirect
113. C2×#103C2×C4semidirect
122. C2×C4×C8C2×C4semidirect
206. C2×SD16C4⋊C4semidirect
283. C2×C4⋊C4SD16semidirect
366. C2×Q8C2×C4⋊C4semidirect
507. C2×C8C2×C4⋊C4semidirect
763. C4#1877semidirect

Maximal subgroups

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

subgroupindex
C22×C4×SD162
C2×D4×C4⋊C42
C2×#18772
C2×#18032
C2×#18022
#139262
#112202
#110672
#108412
#108342
#107882