Finite Group Databasebeta

← #392932

Subgroups — #392932

Order 512.

2160 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×D4C211yesmaximal, characteristic
2C2×#1948C211yesmaximal, characteristic, complemented
3C2×#1864C212yesmaximal
4C2×#1802C211yesmaximal, characteristic
5C2×#1802C211yesmaximal, characteristic
6#14712C211yesmaximal, characteristic, complemented
7#10908C212yesmaximal, complemented
8#10885C212yesmaximal, complemented
9#10849C211yesmaximal, characteristic, complemented
10#10832C211yesmaximal, characteristic, complemented
11#10788C212yesmaximal
12C22×C4×D4C2211yescharacteristic
13C22×C4×D4C2211yescharacteristic
14C22×C4×D4C2211yescharacteristic
15C23×C42—21no—
16C22×#106C2212yes—
17C22×C4⋊C8C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#102C2212yes—
20C22×#102C2212yes—
21C2×#389—21no—
22C2×#389—21no—
23C2×#389C2212yes—
24C2×#384C2211yescharacteristic
25C2×#384C2211yescharacteristic
26C42×D4—24no—
27C42×D4—24no—
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4—21no—
32C2×C4×C22⋊C4—21no—
33C2×C4×C22⋊C4—21no—
34C2×C43C2211yescharacteristic
35#1948—24no—
36#1864—28no—
37#1802—24no—
38#1802C418yescomplemented
39C2×#340C2212yes—
40C2×#340C2212yes—
41C2×#340C2212yes—
42C2×#340C2212yes—
43C2×#340C2212yes—
44C2×#336C2212yes—
45C2×#336C2212yes—
46C4⋊#95—21no—
47C4⋊#95—21no—
48C4⋊#95C2212yes—
49C23×D4C2311yescharacteristic
50C24×C4—21no—
51C24×C4—21no—
52C24×C4—21no—
53C23×C8C2312yes—
54C23×C8C2312yes—
55C2×C4×D4—22no—
56C2×C4×D4—22no—
57C2×C4×D4—22no—
58C2×C4×D4—22no—
59C2×C4×D4—22no—
60C2×C4×D4—22no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4—22no—
64C2×C4×D4—22no—
65C2×C4×D4—22no—
66C2×C4×D4—22no—
67C2×C4×D4—22no—
68C2×C4×D4C2×C414yes—
69C2×C4×D4D414yes—
70C2×C4×D4D414yes—
71C2×C4×D4Q814yes—
72C2×C4×D4Q814yes—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C42—28no—
87C22×C42—21no—
88C22×C42—21no—
89C22×C42—21no—
90C22×C42—44no—
91C22×C42—44no—
92C22×C42D411yescharacteristic
93C22×C42D411yescharacteristic
94C22×C42D411yescharacteristic
95C22×C42D411yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C2×#106—24no—
100C2×#106—24no—
101C2×#106—24no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—22no—
107C2×C4⋊C8C2×C414yescomplemented
108C2×#102—24no—
109C2×#102—24no—
110C2×#102—24no—
111C2×#102—24no—
112C2×#102—24no—
113C2×#102C2×C418yes—
114#389—24no—
115#389—24no—
116#389—44no—
117#389—44no—
118#384—22no—
119#384—22no—
120#384—22no—
121#384C2×C414yescomplemented
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4D414yes—
128C4×C22⋊C4—28no—
129C4×C22⋊C4—28no—
130C4×C22⋊C4—28no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—22no—
135C2×#95—22no—
136C2×#95—22no—
137C43—22no—
138C43—22no—
139#340—24no—
140#340—24no—
141#340—24no—
142#340—24no—
143#340C2×C418yescomplemented
144#336—24no—
145#336—24no—
146C25—21no—
147C22×D4—21no—
148C22×D4—21no—
149C22×D4—21no—
150C22×D4—21no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—21no—
154C22×D4C22×C412yes—
155C22×D4C2×D412yes—
156C22×D4C2×D412yes—
157C22×D4C2×Q812yes—
158C22×D4C2×Q812yes—
159C22×D4#4112yes—
160C22×D4#4112yes—
161C23×C4—24no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—24no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—42no—
176C23×C4—42no—
177C23×C4—42no—
178C23×C4—42no—
179C23×C4—42no—
180C23×C4—42no—
181C23×C4—42no—
182C23×C4—42no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2411yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—22no—
198C22×C8—22no—
199C22×C8—22no—
200C22×C8—22no—
201C22×C8—22no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8—22no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8C22×C414yes—
208C4×D4—28no—
209C4×D4—28no—
210C4×D4—28no—
211C4×D4—28no—
212C4×D4—28no—
213C4×D4—28no—
214C4×D4—28no—
215C4×D4—28no—
216C4×D4—28no—
217C4×D4—28no—
218C4×D4—28no—
219C4×D4C4⋊C4116yescomplemented
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—44no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4C22×C414yes—
256C2×C4⋊C4C22×C412yes—
257C2×C4⋊C4C2×D412yes—
258C2×C4⋊C4C2×D412yes—
259C2×C4⋊C4C2×D412yes—
260C2×C4⋊C4C2×D412yes—
261C2×C4⋊C4C2×Q812yes—
262C2×C4⋊C4C2×Q812yes—
263C2×C4⋊C4#4112yes—
264C2×C4⋊C4#4112yes—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—24no—
268C2×C22⋊C4—24no—
269C2×C22⋊C4—24no—
270C2×C22⋊C4—24no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
274C2×C42—22no—
275C2×C42—22no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42—22no—
289C2×C42—24no—
290C2×C42—22no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—22no—
294C2×C42—432no—
295C2×C42—41no—
296C2×C42—41no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—42no—
301C2×C42—42no—
302C2×C42—42no—
303C2×C42SD1614yes—
304C2×C42C22×C412yes—
305C2×C42C2×D412yes—
306C2×C42C2×D412yes—
307C2×C42C2×D412yes—
308C2×C42C2×Q812yes—
309C2×C42C2×Q812yes—
310C2×C42#4112yes—
311C2×C42#4112yes—
312C2×C42#4112yes—
313C2×C42#4112yes—
314#106—48no—
315C4⋊C8—28no—
316C4⋊C8—44no—
317#102—216no—
318#102—48no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—44no—
323#95—44no—
324#95—44no—
325C24—22no—
326C24—22no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—41no—
333C24—41no—
334C24—41no—
335C24—41no—
336C24—41no—
337C24—41no—
338C24—41no—
339C24—41no—
340C24C22×D411yescharacteristic
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4C2×C4⋊C414yes—
363C2×D4C4×D414yes—
364C2×D4C4×Q814yes—
365C2×D4#12114yes—
366C2×D4C22⋊Q814yes—
367C2×D4#12514yes—
368C2×D4C4⋊Q814yes—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—216no—
382C22×C4—216no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—216no—
405C22×C4—24no—
406C22×C4—48no—
407C22×C4—48no—
408C22×C4—48no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—48no—
412C22×C4—48no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—48no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—48no—
429C22×C4—48no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—48no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4C4×D412yes—
450C22×C4C4×D412yes—
451C22×C4#12012yes—
452C22×C4#12012yes—
453C22×C4#12112yes—
454C22×C4#12112yes—
455C22×C4C22⋊Q812yes—
456C22×C4C22⋊Q812yes—
457C22×C4C22⋊Q812yes—
458C22×C4C22⋊Q812yes—
459C22×C4C2×SD1612yes—
460C22×C4C2×SD1612yes—
461C22×C4C2×SD1612yes—
462C22×C4#13512yes—
463C22×C4AGL(1,ℤ/8)12yes—
464C22×C4AGL(1,ℤ/8)12yes—
465C22×C4AGL(1,ℤ/8)12yes—
466C22×C4#13712yes—
467C22×C4C23×C411yescharacteristic
468C22×C4C22×D411yescharacteristic
469C22×C4C22×D411yescharacteristic
470C22×C4C22×D411yescharacteristic
471C22×C4C22×Q811yescharacteristic
472C22×C4C22×Q811yescharacteristic
473C22×C4C2×#4111yescharacteristic
474C22×C4C2×#4111yescharacteristic
475C22×C4C2×#4111yescharacteristic
476C22×C4C2×#4111yescharacteristic
477C22×C4C2×#4111yescharacteristic
478C22×C4C2×#4111yescharacteristic
479C22×C4C2×#4111yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C2×C8—24no—
482C2×C8—24no—
483C2×C8—24no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—42no—
490C2×C8—42no—
491C2×C8—42no—
492C2×C8—42no—
493C2×C8—42no—
494C2×C8—42no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—48no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—48no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—84no—
515C4⋊C4—88no—
516C4⋊C4—84no—
517C4⋊C4C2×C4⋊C414yes—
518C4⋊C4#12114yes—
519C4⋊C4C22⋊Q814yes—
520C22⋊C4—216no—
521C22⋊C4—216no—
522C22⋊C4—216no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—28no—
532C42—44no—
533C42—44no—
534C42—48no—
535C42—48no—
536C42—44no—
537C42—48no—
538C42C2×C4⋊C414yes—
539C42C4×D414yes—
540C42C22⋊Q814yes—
541C42#12314yes—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—42no—
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—
577C23C2×C4×D411yescharacteristic
578C23C2×#12011yescharacteristic
579C23C2×#12111yescharacteristic
580C23C2×C22⋊Q811yescharacteristic
581C23C2×C22⋊Q811yescharacteristic
582C23#52511yescharacteristic
583C23#52511yescharacteristic
584C23C22×SD1611yescharacteristic
585C23C2×#13511yescharacteristic
586C23C2×AGL(1,ℤ/8)11yescharacteristic
587C23C2×AGL(1,ℤ/8)11yescharacteristic
588C23C2×AGL(1,ℤ/8)11yescharacteristic
589C23C2×#13711yescharacteristic
590C23#57511yescharacteristic
591C23#57511yescharacteristic
592D4—24no—
593D4—24no—
594D4—24no—
595D4—24no—
596D4—24no—
597D4—24no—
598D4—24no—
599D4#38918yescomplemented
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—432no—
628C2×C4—432no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—432no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4#38514yes—
671C2×C4#38514yes—
672C2×C4C4×SD1614yes—
673C2×C4#44214yes—
674C2×C4#44914yes—
675C2×C4#45014yes—
676C2×C4#46114yes—
677C2×C4#47614yes—
678C2×C4#47614yes—
679C2×C4#47814yes—
680C2×C4C22×C4⋊C411yescharacteristic
681C2×C4C2×C4×D411yescharacteristic
682C2×C4C2×C4×D411yescharacteristic
683C2×C4C2×C4×Q811yescharacteristic
684C2×C4C4×#4111yescharacteristic
685C2×C4C4×#4111yescharacteristic
686C2×C4C2×#12111yescharacteristic
687C2×C4C2×#12111yescharacteristic
688C2×C4C2×C22⋊Q811yescharacteristic
689C2×C4C2×C22⋊Q811yescharacteristic
690C2×C4C2×C22⋊Q811yescharacteristic
691C2×C4C2×#12311yescharacteristic
692C2×C4#52511yescharacteristic
693C2×C4#52511yescharacteristic
694C2×C4#52511yescharacteristic
695C2×C4#52511yescharacteristic
696C2×C4C2×#12511yescharacteristic
697C2×C4#52911yescharacteristic
698C2×C4#52911yescharacteristic
699C2×C4#52911yescharacteristic
700C2×C4#52911yescharacteristic
701C2×C4C2×C4⋊Q811yescharacteristic
702C2×C4#53211yescharacteristic
703C2×C4#53211yescharacteristic
704C2×C4#53311yescharacteristic
705C2×C4#53311yescharacteristic
706C2×C4#53311yescharacteristic
707C2×C4#53311yescharacteristic
708C8—44no—
709C8—82no—
710C22—28no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—44no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22C2×#38511yescharacteristic
726C22C4×#12111yescharacteristic
727C22C4×C22⋊Q811yescharacteristic
728C22#284711yescharacteristic
729C22#284811yescharacteristic
730C22#285111yescharacteristic
731C22#285711yescharacteristic
732C22C2×C4×SD1611yescharacteristic
733C22C2×#44211yescharacteristic
734C22C4×AGL(1,ℤ/8)11yescharacteristic
735C22C4×#13711yescharacteristic
736C22C2×#45011yescharacteristic
737C22C2×#44911yescharacteristic
738C22#300611yescharacteristic
739C22#300711yescharacteristic
740C22C2×#46111yescharacteristic
741C22#303511yescharacteristic
742C22#303611yescharacteristic
743C22#303811yescharacteristic
744C22C2×#47611yescharacteristic
745C22C2×#47611yescharacteristic
746C22C2×#47811yescharacteristic
747C22#307611yescharacteristic
748C22#307711yescharacteristic
749C22#307911yescharacteristic
750C22#307911yescharacteristic
751C22#308011yescharacteristic
752C22#310111yescharacteristic
753C22#310111yescharacteristic
754C22#310611yescharacteristic
755C22#310711yescharacteristic
756C22#310911yescharacteristic
757C22#311011yescharacteristic
758C22#311511yescharacteristic
759C22#311511yescharacteristic
760C4—24no—
761C4—24no—
762C4—24no—
763C4—44no—
764C4—42no—
765C4—44no—
766C4—42no—
767C4—44no—
768C4—84no—
769C4—162no—
770C4#186418yescomplemented
771C4C2×#38911yescharacteristic
772C4#229611yescharacteristic
773C4C4×#12111yescharacteristic
774C4C4×C22⋊Q811yescharacteristic
775C4#285111yescharacteristic
776C4#285411yescharacteristic
777C4#285511yescharacteristic
778C4#285711yescharacteristic
779C2—48no—
780C2#1469711yescharacteristic
781C2C2×#186411yescharacteristic
782C2#2087511yescharacteristic
783C2C4×#46111yescharacteristic
784C2#2150311yescharacteristic
785C2C4×#47611yescharacteristic
786C2#2161311yescharacteristic
787C2#3290411yescharacteristic
788C2#3290511yescharacteristic
789C2#3295511yescharacteristic
790C2#3295611yescharacteristic
791C2#3306811yescharacteristic
792C2#3307211yescharacteristic
793C2#3319711yescharacteristic
794C2#3319911yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1948C2semidirect
6. #14712C2semidirect
7. #10908C2semidirect
8. #10885C2semidirect
9. #10849C2semidirect
10. #10832C2semidirect
38. #1802C4semidirect
107. C2×C4⋊C8C2×C4semidirect
121. #384C2×C4semidirect
143. #340C2×C4semidirect
219. C4×D4C4⋊C4semidirect
599. D4#389semidirect
770. C4#1864semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D42
C2×#19482
C2×#18642
C2×#18022
#147122
#109082
#108852
#108492
#108322
#107882