Finite Group Databasebeta

← #719435

Subgroups — #719435

Order 512.

3866 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2536C211yesmaximal, characteristic, complemented
3C2×#2417C212yesmaximal, complemented
4C2×#2397C211yesmaximal, characteristic
5C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
6#16550C214yesmaximal, complemented
7#15419C214yesmaximal, complemented
8#15294C214yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14732C214yesmaximal, complemented
12#14276C211yesmaximal, characteristic, complemented
13#13905C211yesmaximal, characteristic, complemented
14#13872C212yesmaximal, complemented
15#13786C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8C2212yes—
17C22×C22⋊Q8C2212yes—
18C22×C4×Q8C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2212yes—
25#2538—28no—
26#2536—28no—
27#2417—216no—
28#2397—28no—
29C2×#399C2212yes—
30C2×#399C2212yes—
31C2×#398C2212yes—
32C2×#398C2214yes—
33C2×#396C2214yes—
34C2×#396C2214yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#392C2212yes—
38C2×#392C2212yes—
39D4×C4⋊C4—28no—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#390C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#388C2214yes—
47C2×#386C2214yes—
48C2×#386C2214yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2214yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×#376C2211yescharacteristic
60#1445C2212yes—
61#1444C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2212yes—
72#1438C2214yes—
73#1437C2214yes—
74#1436C2214yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78#1434C2214yes—
79C22⋊#95C2214yes—
80C23×Q8C2311yescharacteristic
81C23×D4C2311yescharacteristic
82C23×D4C2312yes—
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C24×C4C2312yes—
86C24×C4C2312yes—
87C24×C4C2314yes—
88C2×C22⋊Q8—28no—
89C2×C22⋊Q8—28no—
90C2×C22⋊Q8—28no—
91C2×C22⋊Q8—28no—
92C2×C22⋊Q8—44no—
93C2×C22⋊Q8—44no—
94C2×C4×Q8—24no—
95C2×C4×Q8—24no—
96C2×C4×Q8—24no—
97C2×C4×D4—28no—
98C2×C4×D4—28no—
99C2×C4×D4—28no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—28no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—28no—
106C2×C4×D4—24no—
107C2×C4×D4—44no—
108C2×C4×D4—44no—
109C2×C4×D4—48no—
110C2×C4×D4D418yes—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—44no—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148#399—28no—
149#399—28no—
150#398—28no—
151#398—216no—
152#396—216no—
153#396—216no—
154#394—28no—
155#394—48no—
156#392—28no—
157#392—28no—
158#391—24no—
159#391D418yescomplemented
160#390—28no—
161#389—28no—
162#389—28no—
163#389—28no—
164#388—216no—
165#386—216no—
166#386—48no—
167#385—216no—
168#384D418yescomplemented
169#382—24no—
170#380—28no—
171#380—28no—
172#380—28no—
173#380—28no—
174#380—216no—
175#380—44no—
176C4×C4⋊C4—24no—
177#376—24no—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C25C2412yes—
196C25C2412yes—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8C2×D414yes—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—22no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—42no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4C2×D414yes—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—28no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4C2×D418yes—
249C23×C4C2414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2414yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C22⋊Q8—432no—
263C22⋊Q8—432no—
264C4×Q8—416no—
265C4×D4—232no—
266C4×D4—432no—
267C4×D4—432no—
268C4×D4—432no—
269C4×D4—416no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—432no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4C2×D414yes—
313C2×C4⋊C4C2×D418yes—
314C2×C4⋊C4C2×D414yes—
315C2×C4⋊C4C2×D418yes—
316C2×C4⋊C4C2×D418yes—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4C2×D418yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—44no—
365C2×C42C2×D414yes—
366C2×C42C2×D414yes—
367C2×C42C2×D414yes—
368C2×C42#4114yes—
369C2×C42#4114yes—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—28no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95C2×D4116yes—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24C22×D414yes—
414C24H(5,𝔽2)14yes—
415C242−1+414yes—
416C242−1+414yes—
417C24C2511yescharacteristic
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—44no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—216no—
428C2×D4—216no—
429C2×D4—28no—
430C2×D4—216no—
431C2×D4—216no—
432C2×D4—28no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—44no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—44no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
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—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—216no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—416no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—88no—
529C22×C4—88no—
530C22×C4—88no—
531C22×C4—88no—
532C22×C4C22×D414yes—
533C22×C4C22×D414yes—
534C22×C4C22×D418yes—
535C22×C4C22×D414yes—
536C22×C4C22×D414yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C2×#4114yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C4H(5,𝔽2)12yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—216no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—416no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—416no—
560C4⋊C4—416no—
561C4⋊C4—44no—
562C4⋊C4—48no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—88no—
567C22⋊C4—216no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—416no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—416no—
574C22⋊C4—416no—
575C22⋊C4—416no—
576C22⋊C4—48no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C42—28no—
581C42—28no—
582C42—48no—
583C42—48no—
584C42#121116yes—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23#53718yes—
655C23C23×D411yescharacteristic
656C23C23×D411yescharacteristic
657C23C23×D411yescharacteristic
658C23C22×#4111yescharacteristic
659C23C22×#4111yescharacteristic
660C23C2×H(5,𝔽2)12yes—
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×2−1+412yes—
664C23C2×2−1+412yes—
665C23#58512yes—
666Q8—416no—
667D4—232no—
668D4—416no—
669D4—432no—
670D4—432no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—432no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—832no—
745C2×C4—816no—
746C2×C4C2×#12114yes—
747C2×C4C2×#12114yes—
748C2×C4C2×#12114yes—
749C2×C4#53214yes—
750C2×C4#54014yes—
751C2×C4D4214yes—
752C2×C4D4214yes—
753C2×C4#54614yes—
754C2×C4#55014yes—
755C22—28no—
756C22—28no—
757C22—28no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22C22×#12111yescharacteristic
786C22C2×#53211yescharacteristic
787C22C2×#53712yes—
788C22C2×#54011yescharacteristic
789C22C2×D4211yescharacteristic
790C22C2×D4211yescharacteristic
791C22C2×#54611yescharacteristic
792C22C2×#55011yescharacteristic
793C22#348411yescharacteristic
794C22#348511yescharacteristic
795C22#348612yes—
796C22#348611yescharacteristic
797C22#348611yescharacteristic
798C22#348812yes—
799C22#348912yes—
800C22#349212yes—
801C22#349212yes—
802C22#349512yes—
803C22#349512yes—
804C22#353612yes—
805C22#353812yes—
806C22#354112yes—
807C22#354212yes—
808C4—24no—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—44no—
813C4—48no—
814C4—44no—
815C4—44no—
816C4—84no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4#242818yes—
821C2—48no—
822C2—84no—
823C2C2×#242811yescharacteristic
824C2#3522311yescharacteristic
825C2#3563311yescharacteristic
826C2#3592612yes—
827C2#3764912yes—
828C2#3783712yes—
829C2#4251012yes—
830C2#4493211yescharacteristic
831C2#4513811yescharacteristic
832C2#4535611yescharacteristic
833C2#4541811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2397C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2538C2semidirect
2. C2×#2536C2semidirect
3. C2×#2417C2semidirect
5. C2×D4×C4⋊C4C2semidirect
6. #16550C2semidirect
7. #15419C2semidirect
8. #15294C2semidirect
9. #15177C2semidirect
10. #15129C2semidirect
11. #14732C2semidirect
12. #14276C2semidirect
13. #13905C2semidirect
14. #13872C2semidirect
15. #13786C2semidirect
159. #391D4semidirect
168. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#25362
C2×#24172
C2×#23972
C2×D4×C4⋊C42
#165502
#154192
#152942
#151772
#151292
#147322
#142762
#139052
#138722
#137862