Finite Group Databasebeta

← #627984

Subgroups — #627984

Order 512.

4514 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#540C211yesmaximal, characteristic, complemented
2C2×#2629C211yesmaximal, characteristic, complemented
3C2×#2619C211yesmaximal, characteristic, complemented
4C2×#2293C211yesmaximal, characteristic, complemented
5#15319C214yesmaximal, complemented
6#15315C214yesmaximal, complemented
7#15272C214yesmaximal, complemented
8#15271C214yesmaximal, complemented
9#15126C212yesmaximal, complemented
10#15123C212yesmaximal, complemented
11#14713C211yesmaximal, characteristic, complemented
12#14709C211yesmaximal, characteristic, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14018C212yesmaximal, complemented
15#13970C212yesmaximal, complemented
16C2×#540—28no—
17C2×#540—28no—
18C2×#540—28no—
19C22×#127C2211yescharacteristic
20C22×#125C2211yescharacteristic
21C22×#123C2214yes—
22C22×#121C2212yes—
23C22×#121C2214yes—
24C22×#121C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2212yes—
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2629—28no—
30#2619—28no—
31C2×#398C2214yes—
32C2×#396C2214yes—
33C2×#394C2214yes—
34C2×#394C2214yes—
35C2×#392C2214yes—
36C2×#392C2214yes—
37#2293—28no—
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2214yes—
43C2×#390C2214yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#386C2214yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C43C2211yescharacteristic
58#1441C2214yes—
59#1440C2214yes—
60#1440C2214yes—
61#1439C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1438C2214yes—
67#1438C2214yes—
68#1438C2214yes—
69#1438C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C22⋊#95C2214yes—
76C22⋊#95C2214yes—
77C23×D4C2312yes—
78C23×D4C2311yescharacteristic
79C23×D4C2314yes—
80C23×D4C2314yes—
81C23×D4C2314yes—
82C24×C4C2311yescharacteristic
83C24×C4C2311yescharacteristic
84C24×C4C2314yes—
85#540—2128no—
86C2×#127—24no—
87C2×#127—24no—
88C2×#127D418yescomplemented
89C2×#125—24no—
90C2×#125—24no—
91C2×#125D418yescomplemented
92C2×#123—216no—
93C2×#123—216no—
94C2×#123—216no—
95C2×#121—216no—
96C2×#121—28no—
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—216no—
101C2×#121—28no—
102C2×#121—216no—
103C2×#121—44no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—24no—
110C2×#117—24no—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117D418yescomplemented
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#398—216no—
151#396—216no—
152#394—216no—
153#394—48no—
154#392—216no—
155#392—48no—
156#390—28no—
157#390—28no—
158#390—28no—
159#390—48no—
160#390—48no—
161#390—44no—
162#389—28no—
163#389—28no—
164#388—28no—
165#388—28no—
166#386—48no—
167#385—48no—
168#384—24no—
169#382—24no—
170#380—28no—
171#380—44no—
172C4×C4⋊C4—24no—
173C4×C22⋊C4—24no—
174C4×C22⋊C4—24no—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C43—24no—
189C25C2414yes—
190C25C2411yescharacteristic
191C25C2411yescharacteristic
192C22×D4—22no—
193C22×D4—22no—
194C22×D4—28no—
195C22×D4—28no—
196C22×D4—28no—
197C22×D4—28no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—28no—
201C22×D4—28no—
202C22×D4—28no—
203C22×D4—22no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—42no—
210C22×D4—44no—
211C22×D4—44no—
212C22×D4—44no—
213C22×D4—44no—
214C22×D4—44no—
215C22×D4—44no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4C2×D418yes—
224C22×D4C2×D4116yes—
225C23×C4—28no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4—44no—
243C23×C4—44no—
244C23×C4C2×D414yes—
245C23×C4#4114yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2414yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2414yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258#127—232no—
259#125—232no—
260#123—2128no—
261#121—2128no—
262#121—264no—
263#121—432no—
264C4×D4—232no—
265C4×D4—264no—
266#117—232no—
267#117—416no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C2×D418yes—
296C2×C4⋊C4C2×D418yes—
297C2×C4⋊C4C2×D4116yes—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D418yes—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42C2×D414yes—
366C2×C42C2×D414yes—
367C2×C42C2×D414yes—
368C2×C42C2×D414yes—
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—28no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383C24—21no—
384C24—21no—
385C24—24no—
386C24—21no—
387C24—21no—
388C24—24no—
389C24—21no—
390C24—24no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—21no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—24no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24C22×D418yes—
418C24C22×D412yes—
419C24C2×#4112yes—
420C24C2511yescharacteristic
421C2×D4—28no—
422C2×D4—232no—
423C2×D4—216no—
424C2×D4—232no—
425C2×D4—216no—
426C2×D4—216no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—44no—
430C2×D4—416no—
431C2×D4—416no—
432C2×D4—416no—
433C2×D4—416no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—44no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—88no—
440C2×D4—88no—
441C2×D4—88no—
442C2×D4—88no—
443C2×D4—88no—
444C2×D4—88no—
445C2×D4—88no—
446C2×D4—88no—
447C2×D4—88no—
448C2×D4—88no—
449C2×D4—88no—
450C2×D4—88no—
451C2×D4—88no—
452C2×D4—88no—
453C2×D4—88no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—232no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—88no—
532C22×C4—88no—
533C22×C4—88no—
534C22×C4—88no—
535C22×C4—88no—
536C22×C4—88no—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D418yes—
540C22×C4C22×D414yes—
541C22×C4C22×D414yes—
542C22×C4C22×D414yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4H(5,𝔽2)14yes—
552C22×C4H(5,𝔽2)14yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C42−1+412yes—
555C4⋊C4—28no—
556C4⋊C4—216no—
557C4⋊C4—216no—
558C4⋊C4—232no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—88no—
564C4⋊C4—88no—
565C22⋊C4—28no—
566C22⋊C4—28no—
567C22⋊C4—232no—
568C22⋊C4—232no—
569C22⋊C4—216no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—416no—
573C22⋊C4—48no—
574C22⋊C4—416no—
575C22⋊C4—88no—
576C22⋊C4—88no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C22⋊C4—88no—
581C22⋊C4—88no—
582C42—28no—
583C42—28no—
584C42—48no—
585C42—48no—
586C42—44no—
587C42—44no—
588C42#120116yes—
589C23—22no—
590C23—28no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—28no—
596C23—22no—
597C23—28no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—28no—
606C23—41no—
607C23—44no—
608C23—41no—
609C23—44no—
610C23—44no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—44no—
616C23—44no—
617C23—42no—
618C23—44no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—44no—
624C23—41no—
625C23—41no—
626C23—44no—
627C23—42no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—44no—
632C23—44no—
633C23—42no—
634C23—44no—
635C23—44no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—44no—
642C23—44no—
643C23—42no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—44no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—44no—
654C23—42no—
655C23—44no—
656C23—44no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—44no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—44no—
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C23×D411yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×H(5,𝔽2)12yes—
677C23C2×H(5,𝔽2)12yes—
678C23C2×2−1+411yescharacteristic
679C23#58512yes—
680C23#58512yes—
681D4—416no—
682D4—432no—
683D4—832no—
684D4—832no—
685D4—832no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—28no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—832no—
760C2×C4C2×#12018yes—
761C2×C4C2×#12014yes—
762C2×C4#52514yes—
763C2×C4#53714yes—
764C2×C4#54014yescomplemented
765C2×C4#54614yes—
766C2×C4#54714yes—
767C2×C4#54814yes—
768C2×C4#55014yes—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—48no—
773C22—44no—
774C22—48no—
775C22—48no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—48no—
782C22—48no—
783C22—44no—
784C22—48no—
785C22—48no—
786C22—84no—
787C22—82no—
788C22—84no—
789C22—82no—
790C22—84no—
791C22—84no—
792C22—82no—
793C22—84no—
794C22—84no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—84no—
802C22—84no—
803C22—81no—
804C22—81no—
805C22—82no—
806C22C22×#12011yescharacteristic
807C22C2×#52511yescharacteristic
808C22C2×#53711yescharacteristic
809C22C2×#54011yescharacteristic
810C22#345511yescharacteristic
811C22#346012yes—
812C22C2×#54611yescharacteristic
813C22C2×#54711yescharacteristic
814C22C2×#54811yescharacteristic
815C22C2×#55011yescharacteristic
816C22#348812yes—
817C22#348812yes—
818C22#349412yes—
819C22#349612yes—
820C22#349612yes—
821C22#349812yes—
822C22#350012yes—
823C22#350811yescharacteristic
824C22#351211yescharacteristic
825C22#354312yes—
826C22#354712yes—
827C22#355912yes—
828C22#356212yes—
829C4—28no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—44no—
835C4—48no—
836C4—42no—
837C4—82no—
838C4—84no—
839C4—84no—
840C4#240718yes—
841C2—82no—
842C2—82no—
843C2—88no—
844C2C2×#240711yescharacteristic
845C2#3525911yescharacteristic
846C2#3526111yescharacteristic
847C2#3551312yes—
848C2#3727612yes—
849C2#3937211yescharacteristic
850C2#3937811yescharacteristic
851C2#3938211yescharacteristic
852C2#3938611yescharacteristic
853C2#3941612yes—
854C2#3942612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#540C2semidirect
2. C2×#2629C2semidirect
3. C2×#2619C2semidirect
4. C2×#2293C2semidirect
5. #15319C2semidirect
6. #15315C2semidirect
7. #15272C2semidirect
8. #15271C2semidirect
9. #15126C2semidirect
10. #15123C2semidirect
11. #14713C2semidirect
12. #14709C2semidirect
13. #14340C2semidirect
14. #14018C2semidirect
15. #13970C2semidirect
88. C2×#127D4semidirect
91. C2×#125D4semidirect
115. C2×#117D4semidirect
764. C2×C4#540semidirect

Maximal subgroups

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

subgroupindex
C22×#5402
C2×#26292
C2×#26192
C2×#22932
#153192
#153152
#152722
#152712
#151262
#151232
#147132
#147092
#143402
#140182
#139702