Finite Group Databasebeta

← #713046

Subgroups — #713046

Order 512.

2682 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2427C211yesmaximal, characteristic
2C2×#2345C211yesmaximal, characteristic, complemented
3#16498C214yesmaximal, complemented
4#15960C214yesmaximal, complemented
5#15958C214yesmaximal, complemented
6#15234C211yesmaximal, characteristic, complemented
7#15226C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic
9#15182C211yesmaximal, characteristic, complemented
10#14798C214yesmaximal, complemented
11#14261C211yesmaximal, characteristic, complemented
12#14153C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14137C211yesmaximal, characteristic
15#14049C211yesmaximal, characteristic, complemented
16#14003C211yesmaximal, characteristic, complemented
17#13977C211yesmaximal, characteristic, complemented
18#13842C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2427—28no—
26C2×#397C2212yes—
27C2×#394C2212yes—
28#2345—28no—
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#385C2214yes—
47C2×#384C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×#376C2211yescharacteristic
60#1445C2214yes—
61#1443C2212yes—
62#1443C2214yes—
63#1443C2214yes—
64#1442C2212yes—
65#1442C2214yes—
66#1442C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1440C2212yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2212yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1437C2214yes—
81#1437C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C2×#124—24no—
100C2×#124—24no—
101C2×#124—42no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—42no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—42no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—42no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2312yes—
149#397—28no—
150#394—28no—
151#391—24no—
152#391—24no—
153#391—24no—
154#391—42no—
155#391—42no—
156#390—24no—
157#390—24no—
158#390—24no—
159#390—42no—
160#389—24no—
161#389—24no—
162#389—24no—
163#387—28no—
164#387—28no—
165#387—48no—
166#386—28no—
167#386—48no—
168#385—48no—
169#384—24no—
170#382—42no—
171#380—24no—
172#380—28no—
173#380—28no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—42no—
177C4×C22⋊C4—28no—
178C4×C22⋊C4—42no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4D418yes—
181#376—42no—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C25C2412yes—
213C25C2411yescharacteristic
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—28no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—42no—
231C22×D4—44no—
232C22×D4#4114yes—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—42no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—44no—
249C23×C4C2×D414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267#124—416no—
268C22⋊Q8—416no—
269#121—416no—
270C4×D4—416no—
271C2×C4⋊C4—232no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4#4114yes—
306C2×C4⋊C4#4114yes—
307C2×C4⋊C4#4114yes—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
346C2×C22⋊C4C2×D414yes—
347C2×C42—22no—
348C2×C42—22no—
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—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42C2×D414yes—
368C2×C42C2×D414yes—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—28no—
379#95—24no—
380#95—28no—
381#95—24no—
382#95—42no—
383#95—42no—
384#95—44no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95C2×D414yes—
398#95C2×D414yes—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24C22×D412yes—
419C24C2×#4114yes—
420C242−1+414yes—
421C24C2511yescharacteristic
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—48no—
433C2×D4—416no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—84no—
440C2×D4—88no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—216no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
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—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—84no—
535C22×C4—88no—
536C22×C4—88no—
537C22×C4—88no—
538C22×C4—84no—
539C22×C4—84no—
540C22×C4—88no—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C2×#4114yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4H(5,𝔽2)14yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)12yes—
557C4⋊C4—216no—
558C4⋊C4—28no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—416no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—84no—
568C4⋊C4—84no—
569C4⋊C4—84no—
570C22⋊C4—28no—
571C22⋊C4—44no—
572C22⋊C4—416no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C42—28no—
585C42—28no—
586C42—44no—
587C42—44no—
588C42—44no—
589C42—44no—
590C42—84no—
591C42—84no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—28no—
608C23—28no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
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—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23#53614yes—
638C23C23×D411yescharacteristic
639C23C22×#4111yescharacteristic
640C23C22×#4111yescharacteristic
641C23C22×#4111yescharacteristic
642C23C22×#4111yescharacteristic
643C23C2×H(5,𝔽2)11yescharacteristic
644C23C2×H(5,𝔽2)11yescharacteristic
645C23C2×H(5,𝔽2)12yes—
646C23C2×2−1+412yes—
647C23#58512yes—
648C23#58512yes—
649Q8—88no—
650D4—416no—
651D4—816no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—416no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—816no—
746C2×C4—816no—
747C2×C4#52514yes—
748C2×C4#52914yes—
749C2×C4#54014yes—
750C2×C4#54614yes—
751C2×C4#54614yes—
752C2×C4#55314yes—
753C2×C4#55514yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—44no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—48no—
766C22—48no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—84no—
771C22—82no—
772C22—84no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#52511yescharacteristic
777C22C2×#52911yescharacteristic
778C22C2×#53611yescharacteristic
779C22#344911yescharacteristic
780C22C2×#54011yescharacteristic
781C22C2×#54611yescharacteristic
782C22C2×#54611yescharacteristic
783C22C2×#55311yescharacteristic
784C22C2×#55511yescharacteristic
785C22#349811yescharacteristic
786C22#350011yescharacteristic
787C22#351312yes—
788C22#351312yes—
789C22#351412yes—
790C22#351612yes—
791C22#351612yes—
792C22#351612yes—
793C22#352012yes—
794C22#352112yes—
795C22#353612yes—
796C22#353912yes—
797C22#354112yes—
798C22#354612yes—
799C4—44no—
800C4—42no—
801C4—44no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—44no—
807C4—44no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4#247618yes—
816C2—44no—
817C2—84no—
818C2C2×#247611yescharacteristic
819C2#3524611yescharacteristic
820C2#3553611yescharacteristic
821C2#3588512yes—
822C2#3807811yescharacteristic
823C2#3808311yescharacteristic
824C2#3809211yescharacteristic
825C2#3894511yescharacteristic
826C2#4275212yes—
827C2#4520312yes—
828C2#4538212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2345C2semidirect
3. #16498C2semidirect
4. #15960C2semidirect
5. #15958C2semidirect
6. #15234C2semidirect
7. #15226C2semidirect
9. #15182C2semidirect
10. #14798C2semidirect
11. #14261C2semidirect
12. #14153C2semidirect
13. #14139C2semidirect
15. #14049C2semidirect
16. #14003C2semidirect
17. #13977C2semidirect
18. #13842C2semidirect
19. #13785C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24272
C2×#23452
#164982
#159602
#159582
#152342
#152262
#152192
#151822
#147982
#142612
#141532
#141392
#141372
#140492
#140032
#139772
#138422
#137852