Finite Group Databasebeta

← #764799

Subgroups — #764799

Order 512.

4730 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic, complemented
2C2×#2561C211yesmaximal, characteristic, complemented
3C2×#2539C211yesmaximal, characteristic
4C22×#396C211yesmaximal, characteristic, complemented
5#15913C214yesmaximal, complemented
6#15846C214yesmaximal, complemented
7#15280C214yesmaximal, complemented
8#15272C214yesmaximal, complemented
9#15069C212yesmaximal, complemented
10#14911C212yesmaximal, complemented
11#14139C211yesmaximal, characteristic, complemented
12#14137C211yesmaximal, characteristic, complemented
13#13968C212yesmaximal, complemented
14#13967C212yesmaximal, complemented
15#13776C211yesmaximal, characteristic, complemented
16C2×#539—28no—
17C2×#539—28no—
18C2×#539—28no—
19C22×#126C2212yescomplemented
20C22×#125C2212yescomplemented
21C22×#123C2212yes—
22C22×#123C2212yes—
23C22×#123C2212yescomplemented
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yescomplemented
26C22×#121C2211yescharacteristic
27C22×#120C2212yes—
28C22×C4×D4C2212yes—
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35#2561—28no—
36#2539—28no—
37C2×#399C2212yes—
38C2×#397C2212yes—
39C2×#396—28no—
40C2×#396C2214yes—
41C2×#396C2214yes—
42C2×#393C2212yes—
43C2×#392C2212yes—
44C2×#391C2212yescomplemented
45C2×#390C2214yes—
46C2×#390C2212yescomplemented
47C2×#388C2214yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2214yes—
51C2×#381C2212yes—
52C2×#381C2212yes—
53C2×#379C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C22×#95C2211yescharacteristic
57#1444C2214yescomplemented
58#1444C2214yescomplemented
59#1441C2214yescomplemented
60#1441C2214yescomplemented
61#1440C2214yescomplemented
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1438C2214yes—
69#1438C2214yes—
70#1438C2214yes—
71#1437C2214yes—
72#1436C2214yescomplemented
73#1436C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C22⋊#95C2212yes—
78C22⋊#95C2212yes—
79C22⋊#95C2212yes—
80C22⋊#95C2214yescomplemented
81C26C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4C2312yes—
84C23×D4C2314yes—
85C23×D4C2311yescharacteristic
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93#539—2128no—
94C2×#126—28no—
95C2×#126—28no—
96C2×#126—28no—
97C2×#125—28no—
98C2×#125—28no—
99C2×#125—28no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—28no—
105C2×#123—28no—
106C2×#123—28no—
107C2×#123—28no—
108C2×#123—44no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8D418yescomplemented
115C2×#121—24no—
116C2×#121—24no—
117C2×#121D418yes—
118C2×#120—28no—
119C2×#120—28no—
120C2×#120—44no—
121C2×C4×D4—28no—
122C2×C4×D4—28no—
123C2×C4×D4—28no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—44no—
129C22×C4⋊C4—44no—
130C22×C4⋊C4D418yescomplemented
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C22⋊C4—24no—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—24no—
148C22×C22⋊C4—44no—
149C22×C22⋊C4—44no—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2312yes—
170#399—28no—
171#397—28no—
172#396—216no—
173#396—216no—
174#393—28no—
175#392—28no—
176#391—44no—
177#390—216no—
178#390—44no—
179#388—216no—
180#386—48no—
181#386—44no—
182#386—44no—
183#381—28no—
184#381—28no—
185#379—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—24no—
188C2×#95—24no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C25—22no—
205C25—24no—
206C25—22no—
207C25—22no—
208C25—24no—
209C25—24no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25C2412yes—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8C2×D414yes—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—28no—
232C22×D4—44no—
233C22×D4—42no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4—42no—
237C22×D4—44no—
238C22×D4C2×D418yes—
239C22×D4C2×D414yes—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4C2×D414yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285#126—264no—
286#125—264no—
287#123—264no—
288#123—264no—
289#123—432no—
290C22⋊Q8—264no—
291C22⋊Q8—232no—
292#121—232no—
293#120—432no—
294C4×D4—264no—
295C2×C4⋊C4—232no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—416no—
328C2×C4⋊C4—416no—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D418yes—
333C2×C4⋊C4C2×D414yes—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—416no—
376C2×C22⋊C4—416no—
377C2×C22⋊C4—416no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4C2×D418yes—
386C2×C22⋊C4C2×D418yes—
387C2×C22⋊C4#4118yes—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—28no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—24no—
433C24—22no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—48no—
438C24—48no—
439C24—416no—
440C24—416no—
441C24—44no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—48no—
448C24—48no—
449C24—84no—
450C24—84no—
451C24—88no—
452C24—88no—
453C24C22×D414yes—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C2×#4114yes—
458C24H(5,𝔽2)14yes—
459C242−1+414yes—
460C24C2511yescharacteristic
461C2×Q8—28no—
462C2×Q8—48no—
463C2×Q8—82no—
464C2×Q8—82no—
465C2×Q8—84no—
466C2×D4—216no—
467C2×D4—216no—
468C2×D4—216no—
469C2×D4—28no—
470C2×D4—48no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—416no—
478C2×D4—82no—
479C2×D4—82no—
480C2×D4—84no—
481C2×D4—88no—
482C2×D4—88no—
483C2×D4—88no—
484C2×D4—88no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—24no—
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—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—216no—
528C22×C4—28no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—416no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—84no—
566C22×C4—84no—
567C22×C4—88no—
568C22×C4—84no—
569C22×C4—84no—
570C22×C4—88no—
571C22×C4—88no—
572C22×C4#120116yes—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D414yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C2×#4118yes—
585C22×C4H(5,𝔽2)14yes—
586C4⋊C4—216no—
587C4⋊C4—216no—
588C4⋊C4—216no—
589C4⋊C4—216no—
590C4⋊C4—216no—
591C4⋊C4—28no—
592C4⋊C4—216no—
593C4⋊C4—28no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—416no—
597C4⋊C4—416no—
598C22⋊C4—216no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—216no—
602C22⋊C4—216no—
603C22⋊C4—216no—
604C22⋊C4—416no—
605C22⋊C4—416no—
606C22⋊C4—416no—
607C22⋊C4—416no—
608C22⋊C4—416no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—88no—
613C22⋊C4—88no—
614C22⋊C4—88no—
615C42—216no—
616C42—84no—
617C42—84no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—416no—
641C23—416no—
642C23—416no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—44no—
649C23—42no—
650C23—42no—
651C23—44no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—832no—
680C23—832no—
681C23—88no—
682C23—88no—
683C23—88no—
684C23—88no—
685C23C2×#12014yes—
686C23#53214yes—
687C23#53514yes—
688C23#54618yes—
689C23#55018yes—
690C23C23×D411yescharacteristic
691C23C23×D411yescharacteristic
692C23C23×D411yescharacteristic
693C23C22×#4112yes—
694C23C2×H(5,𝔽2)12yes—
695C23C2×H(5,𝔽2)12yes—
696C23C2×2−1+412yes—
697C23#58512yes—
698C23#58512yes—
699Q8—88no—
700D4—432no—
701D4—88no—
702D4—832no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—416no—
730C2×C4—416no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—88no—
773C2×C4—816no—
774C2×C4—88no—
775C2×C4—88no—
776C2×C4C2×#12014yes—
777C2×C4C2×#12014yes—
778C22—216no—
779C22—24no—
780C22—216no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—48no—
787C22—48no—
788C22—48no—
789C22—44no—
790C22—48no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—832no—
797C22—84no—
798C22—82no—
799C22—84no—
800C22—84no—
801C22—84no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#243118yes—
810C22C22×#12011yescharacteristic
811C22C2×#53211yescharacteristic
812C22C2×#53511yescharacteristic
813C22C2×#54612yes—
814C22C2×#55012yes—
815C22#348411yescharacteristic
816C22#348511yescharacteristic
817C22#348611yescharacteristic
818C22#348711yescharacteristic
819C22#348912yes—
820C22#348912yes—
821C22#349612yes—
822C22#349612yes—
823C22#352014yes—
824C22#352114yes—
825C22#353414yes—
826C22#353514yes—
827C4—24no—
828C4—24no—
829C4—48no—
830C4—44no—
831C4—44no—
832C4—44no—
833C4—44no—
834C4—44no—
835C4—44no—
836C4—84no—
837C4—82no—
838C4—82no—
839C2—28no—
840C2—84no—
841C2—84no—
842C2C2×#243111yescharacteristic
843C2#3534711yescharacteristic
844C2#3539711yescharacteristic
845C2#3546911yescharacteristic
846C2#3565911yescharacteristic
847C2#3711811yescharacteristic
848C2#3718511yescharacteristic
849C2#4302614yes—
850C2#4302914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2539C2
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×#539C2semidirect
2. C2×#2561C2semidirect
4. C22×#396C2semidirect
5. #15913C2semidirect
6. #15846C2semidirect
7. #15280C2semidirect
8. #15272C2semidirect
9. #15069C2semidirect
10. #14911C2semidirect
11. #14139C2semidirect
12. #14137C2semidirect
13. #13968C2semidirect
14. #13967C2semidirect
15. #13776C2semidirect
19. C22×#126C22semidirect
20. C22×#125C22semidirect
23. C22×#123C22semidirect
25. C22×C22⋊Q8C22semidirect
44. C2×#391C22semidirect
46. C2×#390C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
61. #1440C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
72. #1436C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
80. C22⋊#95C22semidirect
114. C2×C22⋊Q8D4semidirect
130. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#25612
C2×#25392
C22×#3962
#159132
#158462
#152802
#152722
#150692
#149112
#141392
#141372
#139682
#139672
#137762