Finite Group Databasebeta

← #360141

Subgroups — #360141

Order 512.

1974 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×SD16C211yesmaximal, characteristic
2C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#1880C212yesmaximal
4C2×#1803C211yesmaximal, characteristic, complemented
5C2×#1802C211yesmaximal, characteristic
6#13906C211yesmaximal, characteristic
7#11220C212yesmaximal, complemented
8#11066C212yesmaximal
9#10841C211yesmaximal, characteristic, complemented
10#10834C211yesmaximal, characteristic, complemented
11#10789C212yesmaximal, complemented
12C23×SD16C2211yescharacteristic
13C22×C4×Q8C2212yes—
14C22×C4×Q8C2211yescharacteristic
15C22×C4×D4C2211yescharacteristic
16C2×C4×SD16—24no—
17C2×C4×SD16—24no—
18C2×C4×SD16C418yescomplemented
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2212yes—
22C22×#103C2211yescharacteristic
23C22×#102C2212yes—
24C22×#102C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26Q8×C4⋊C4—24no—
27Q8×C4⋊C4—24no—
28C2×#390C2212yes—
29C2×#389—22no—
30C2×#389C2212yes—
31C2×#384—21no—
32C2×#384C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#380—21no—
35C2×#380—21no—
36C2×C4×C4⋊C4—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1880—28no—
39#1803—24no—
40#1802—24no—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#340C2212yes—
45C2×#336C2212yes—
46C2×#336C2212yes—
47#1439—22no—
48C4⋊#95C2212yes—
49C23×Q8C2311yescharacteristic
50C23×D4C2311yescharacteristic
51C24×C4—21no—
52C22×SD16—22no—
53C22×SD16—22no—
54C22×SD16—22no—
55C22×SD16—22no—
56C22×SD16C2×C414yes—
57C22×SD16D414yes—
58C22×SD16Q814yes—
59C23×C8C2312yes—
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C2×C4×Q8—24no—
63C2×C4×Q8—24no—
64C2×C4×Q8—22no—
65C2×C4×Q8—22no—
66C2×C4×Q8—22no—
67C2×C4×Q8—24no—
68C2×C4×Q8—24no—
69C2×C4×Q8—42no—
70C2×C4×Q8—42no—
71C2×C4×Q8C2×C414yes—
72C2×C4×Q8D414yes—
73C2×C4×Q8D414yes—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4C2×C414yes—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4D411yescharacteristic
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2311yescharacteristic
93C22×C22⋊C4—21no—
94C22×C22⋊C4—22no—
95C22×C22⋊C4—22no—
96C22×C42—21no—
97C22×C42—22no—
98C22×C42C2312yes—
99C22×C42C2311yescharacteristic
100C4×SD16—232no—
101C2×#106—22no—
102C2×#106—22no—
103C2×#106C2×C414yes—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—24no—
110C2×#103—24no—
111C2×#103—24no—
112C2×#103C2×C414yes—
113C2×#102—22no—
114C2×#102—22no—
115C2×#102—24no—
116C2×#102—24no—
117C2×#102—42no—
118C2×#102C2×C414yes—
119C2×C4×C8—22no—
120C2×C4×C8—22no—
121C2×C4×C8C2×C414yes—
122#390—24no—
123#390—42no—
124#389—216no—
125#389—24no—
126#389—24no—
127#384—28no—
128#384—22no—
129#384—22no—
130#384—22no—
131#384D414yes—
132#380—44no—
133#380—44no—
134C4×C4⋊C4—28no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—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×Q8C22×C412yes—
156C22×Q8C2×D412yes—
157C22×Q8C2×D412yes—
158C22×Q8C2×D412yes—
159C22×Q8C2×Q812yes—
160C22×Q8#4112yes—
161C22×Q8#4112yes—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C22×C412yes—
174C22×D4C2×D412yes—
175C22×D4C2×Q812yes—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—24no—
181C23×C4—22no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4C2×D412yes—
189C23×C4C2×D412yes—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2411yescharacteristic
193C2×SD16—28no—
194C2×SD16—28no—
195C2×SD16—28no—
196C2×SD16—28no—
197C2×SD16—28no—
198C2×SD16—28no—
199C2×SD16C4⋊C4116yescomplemented
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—22no—
211C22×C8—22no—
212C22×C8—22no—
213C22×C8—22no—
214C22×C8—22no—
215C22×C8—22no—
216C22×C8—22no—
217C22×C8C22×C412yes—
218C22×C8C22×C412yes—
219C22×C8C2×D412yes—
220C22×C8C2×Q812yes—
221C4×Q8—28no—
222C4×Q8—28no—
223C4×Q8—28no—
224C4×Q8—48no—
225C4×Q8—48no—
226C4×Q8—48no—
227C4×Q8—48no—
228C4×Q8C22⋊C4116yescomplemented
229C4×D4—28no—
230C4×D4—28no—
231C4×D4—44no—
232C4×D4—44no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—42no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4—81no—
274C2×C4⋊C4—81no—
275C2×C4⋊C4—81no—
276C2×C4⋊C4—82no—
277C2×C4⋊C4—82no—
278C2×C4⋊C4SD1614yescomplemented
279C2×C4⋊C4C22×C412yes—
280C2×C4⋊C4C22×C412yes—
281C2×C4⋊C4C2×D414yes—
282C2×C4⋊C4C2×D412yes—
283C2×C4⋊C4C2×D412yes—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—44no—
288C2×C22⋊C4—44no—
289C2×C22⋊C4—44no—
290C2×C22⋊C4—44no—
291C2×C22⋊C4—82no—
292C2×C22⋊C4—82no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—24no—
296C2×C42—28no—
297C2×C42—22no—
298C2×C42—22no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42—44no—
304C2×C42—44no—
305C2×C42C22×C412yes—
306C2×C42C2×D412yes—
307C2×C42C2×D412yes—
308C2×C42C2×D412yes—
309C2×C42#4112yes—
310C2×C42#4112yes—
311#106—28no—
312C4⋊C8—44no—
313#103—28no—
314#103—48no—
315#102—28no—
316#102—48no—
317C4×C8—28no—
318#95—28no—
319#95—24no—
320#95—44no—
321#95—44no—
322C24—22no—
323C24—22no—
324C24—22no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24—41no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24C22×D411yescharacteristic
338C2×Q8—22no—
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—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8C2×C22⋊C414yes—
360C2×Q8C2×C4⋊C414yes—
361C2×Q8#11714yes—
362C2×Q8#12114yes—
363C2×Q8#12114yes—
364C2×Q8C22⋊Q814yes—
365C2×Q8C22⋊Q814yes—
366C2×D4—22no—
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—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4C2×C4⋊C414yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—42no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—41no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—48no—
440C22×C4—48no—
441C22×C4—48no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—84no—
450C22×C4—84no—
451C22×C4—84no—
452C22×C4—84no—
453C22×C4C4×D412yes—
454C22×C4C4×D412yes—
455C22×C4#12012yes—
456C22×C4#12012yes—
457C22×C4#12112yes—
458C22×C4#12112yes—
459C22×C4C2×SD1614yes—
460C22×C4C2×SD1612yes—
461C22×C4#13512yes—
462C22×C4AGL(1,ℤ/8)12yes—
463C22×C4#13712yes—
464C22×C4C23×C411yescharacteristic
465C22×C4C22×D411yescharacteristic
466C22×C4C22×D411yescharacteristic
467C22×C4C22×D411yescharacteristic
468C22×C4C22×D411yescharacteristic
469C22×C4C22×Q811yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4H(5,𝔽2)11yescharacteristic
475C22×C4H(5,𝔽2)11yescharacteristic
476C22×C42−1+411yescharacteristic
477C22×C42−1+411yescharacteristic
478SD16—232no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8C2×C4⋊C414yes—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—216no—
504C4⋊C4—28no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—416no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—41no—
513C4⋊C4—42no—
514C4⋊C4—44no—
515C4⋊C4—48no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—84no—
521C4⋊C4—84no—
522C4⋊C4—88no—
523C4⋊C4—84no—
524C4⋊C4C2×C22⋊C414yes—
525C22⋊C4—48no—
526C22⋊C4—88no—
527C22⋊C4—88no—
528C42—216no—
529C42—416no—
530C42—42no—
531C42—42no—
532C42—42no—
533C42—42no—
534C42C2×C22⋊C414yes—
535C42C4×D414yes—
536C42#12114yes—
537C42#12314yes—
538C23—24no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—81no—
558C23—81no—
559C23—81no—
560C23—81no—
561C23—81no—
562C23—81no—
563C23—81no—
564C23—81no—
565C23—81no—
566C23—81no—
567C23—81no—
568C23—81no—
569C23—81no—
570C23—81no—
571C23—81no—
572C23—81no—
573C23C2×C4×D411yescharacteristic
574C23C2×#12011yescharacteristic
575C23C2×#12111yescharacteristic
576C23D4211yescharacteristic
577C23#54611yescharacteristic
578C23#54811yescharacteristic
579C23D4×Q811yescharacteristic
580C23C22×SD1611yescharacteristic
581C23C2×#13511yescharacteristic
582C23C2×AGL(1,ℤ/8)11yescharacteristic
583C23C2×#13711yescharacteristic
584C23#57611yescharacteristic
585C23#57711yescharacteristic
586C23#57711yescharacteristic
587C23#57811yescharacteristic
588Q8—24no—
589Q8—24no—
590Q8—24no—
591Q8—24no—
592Q8—24no—
593Q8—24no—
594Q8—24no—
595Q8#38018yescomplemented
596D4—24no—
597D4—24no—
598D4—42no—
599D4—42no—
600D4—42no—
601D4—42no—
602D4—42no—
603D4—42no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
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—44no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—44no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—82no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—82no—
648C2×C4—82no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—82no—
652C2×C4—816no—
653C2×C4—82no—
654C2×C4—82no—
655C2×C4—82no—
656C2×C4—82no—
657C2×C4—82no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4#38614yes—
661C2×C4#38614yes—
662C2×C4C4×SD1614yes—
663C2×C4#44014yes—
664C2×C4#44814yes—
665C2×C4#44914yes—
666C2×C4#46014yes—
667C2×C4#46414yes—
668C2×C4C22×C22⋊C411yescharacteristic
669C2×C4C22×C4⋊C411yescharacteristic
670C2×C4C2×#11711yescharacteristic
671C2×C4C2×C4×D411yescharacteristic
672C2×C4#52011yescharacteristic
673C2×C4#52011yescharacteristic
674C2×C4C2×#12111yescharacteristic
675C2×C4C2×#12111yescharacteristic
676C2×C4C2×#12111yescharacteristic
677C2×C4C2×C22⋊Q811yescharacteristic
678C2×C4C2×C22⋊Q811yescharacteristic
679C2×C4C2×#12311yescharacteristic
680C2×C4#53511yescharacteristic
681C2×C4#53611yescharacteristic
682C2×C4#53711yescharacteristic
683C2×C4#53711yescharacteristic
684C2×C4D4211yescharacteristic
685C2×C4#54611yescharacteristic
686C2×C4#54711yescharacteristic
687C2×C4#54711yescharacteristic
688C2×C4#54811yescharacteristic
689C2×C4D4×Q811yescharacteristic
690C2×C4#55211yescharacteristic
691C2×C4#55211yescharacteristic
692C2×C4#55311yescharacteristic
693C2×C4#55311yescharacteristic
694C2×C4#55411yescharacteristic
695C2×C4#55411yescharacteristic
696C8—24no—
697C8—42no—
698C8—82no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—82no—
703C22—82no—
704C22—82no—
705C22—82no—
706C22—82no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22C2×#38611yescharacteristic
715C22D4×C4⋊C411yescharacteristic
716C22#235211yescharacteristic
717C22#240811yescharacteristic
718C22#240911yescharacteristic
719C22#241611yescharacteristic
720C22#241711yescharacteristic
721C22C2×C4×SD1611yescharacteristic
722C22C2×#44011yescharacteristic
723C22#295111yescharacteristic
724C22#295211yescharacteristic
725C22C2×#44811yescharacteristic
726C22C2×#44911yescharacteristic
727C22#301211yescharacteristic
728C22#301311yescharacteristic
729C22C2×#46011yescharacteristic
730C22C2×#46411yescharacteristic
731C22#304511yescharacteristic
732C22#304611yescharacteristic
733C22#327411yescharacteristic
734C22#327611yescharacteristic
735C22D4×SD1611yescharacteristic
736C22#328411yescharacteristic
737C22#329811yescharacteristic
738C22#330511yescharacteristic
739C22#332911yescharacteristic
740C22#333211yescharacteristic
741C22#336211yescharacteristic
742C22#336411yescharacteristic
743C22#336811yescharacteristic
744C22#336911yescharacteristic
745C22Q8×SD1611yescharacteristic
746C22#338111yescharacteristic
747C22#338511yescharacteristic
748C22#338611yescharacteristic
749C4—28no—
750C4—24no—
751C4—44no—
752C4—44no—
753C4—82no—
754C4—84no—
755C4—82no—
756C4—162no—
757C4#188018yescomplemented
758C4C2×#38011yescharacteristic
759C4#231111yescharacteristic
760C4D4×C4⋊C411yescharacteristic
761C4#235211yescharacteristic
762C4#241611yescharacteristic
763C4#241711yescharacteristic
764C4#248611yescharacteristic
765C4#248711yescharacteristic
766C2—84no—
767C2#1387211yescharacteristic
768C2C2×#188011yescharacteristic
769C2#2093711yescharacteristic
770C2#2267111yescharacteristic
771C2C4⋊C4×SD1611yescharacteristic
772C2#2275911yescharacteristic
773C2#2276711yescharacteristic
774C2#2423811yescharacteristic
775C2#2423911yescharacteristic
776C2#2432811yescharacteristic
777C2#2432911yescharacteristic
778C2#2472811yescharacteristic
779C2#2472911yescharacteristic
780C2#2481311yescharacteristic
781C2#2481411yescharacteristic
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
2. C2×Q8×C4⋊C4C2semidirect
4. C2×#1803C2semidirect
7. #11220C2semidirect
9. #10841C2semidirect
10. #10834C2semidirect
11. #10789C2semidirect
18. C2×C4×SD16C4semidirect
199. C2×SD16C4⋊C4semidirect
228. C4×Q8C22⋊C4semidirect
278. C2×C4⋊C4SD16semidirect
595. Q8#380semidirect
757. C4#1880semidirect

Maximal subgroups

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

subgroupindex
C22×C4×SD162
C2×Q8×C4⋊C42
C2×#18802
C2×#18032
C2×#18022
#139062
#112202
#110662
#108412
#108342
#107892