Finite Group Databasebeta

← #626826

Subgroups — #626826

Order 512.

5122 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C2×#2315C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic
5#15439C214yesmaximal, complemented
6#15429C214yesmaximal, complemented
7#15324C214yesmaximal, complemented
8#15323C214yesmaximal, complemented
9#14920C212yesmaximal, complemented
10#14726C212yesmaximal, complemented
11#14680C211yesmaximal, characteristic, complemented
12#14281C211yesmaximal, characteristic, complemented
13#14275C211yesmaximal, characteristic, complemented
14#13877C212yesmaximal, complemented
15#13867C212yesmaximal
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yescomplemented
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C23×C22⋊C4C2211yescharacteristic
24#2848—28no—
25#2626—28no—
26C2×#399C2212yescomplemented
27C2×#396C2212yescomplemented
28C2×#396C2212yescomplemented
29C2×#396C2214yescomplemented
30C2×#393C2212yescomplemented
31#2315—28no—
32C2×#386—28no—
33C2×#386C2214yes—
34C2×#386C2214yes—
35C2×#386C2214yes—
36C2×#386C2214yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2214yescomplemented
41C2×#385C2214yescomplemented
42C2×#385C2214yescomplemented
43C2×#380C2212yes—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2212yescomplemented
48C2×#380C2214yescomplemented
49C2×#380C2212yescomplemented
50C2×#380C2212yescomplemented
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×#379C2212yes—
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1446C2212yescomplemented
57#1445C2214yescomplemented
58#1445C2212yescomplemented
59#1444C2212yescomplemented
60#1442C2214yescomplemented
61#1442C2212yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2214yescomplemented
65#1441C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1438C2214yes—
72#1438C2214yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2214yescomplemented
78C22⋊#95C2214yescomplemented
79C26C2311yescharacteristic
80C26C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—44no—
85C23×D4—44no—
86C23×D4Q818yescomplemented
87C23×D4C2314yes—
88C24×C4—24no—
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2314yes—
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—28no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—28no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4—44no—
126C22×C22⋊C4—44no—
127C22×C22⋊C4D418yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145#399—28no—
146#396—28no—
147#396—28no—
148#396—48no—
149#393—28no—
150#386—216no—
151#386—216no—
152#386—48no—
153#386—48no—
154#385—28no—
155#385—216no—
156#385—28no—
157#385—216no—
158#385—216no—
159#385—44no—
160#380—24no—
161#380—24no—
162#380—28no—
163#380—28no—
164#380—44no—
165#380—48no—
166#380—44no—
167#380D418yescomplemented
168#379—28no—
169#379—28no—
170#379—44no—
171C2×#95—24no—
172C2×#95—24no—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C25—22no—
193C25—22no—
194C25—24no—
195C25—24no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—42no—
205C25—42no—
206C25—42no—
207C25—42no—
208C25—42no—
209C25—42no—
210C25C2×D414yes—
211C25C2×Q814yes—
212C25C2×Q814yes—
213C25#4114yes—
214C25C2412yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—42no—
221C22×Q8—42no—
222C22×D4—232no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—432no—
230C22×D4—416no—
231C22×D4—416no—
232C22×D4—432no—
233C22×D4C2×Q8116yes—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—28no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—28no—
257C23×C4—42no—
258C23×C4—42no—
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—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—44no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—416no—
276C23×C4—432no—
277C23×C4—432no—
278C23×C4—416no—
279C23×C4—416no—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×Q814yes—
284C23×C4#4114yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2414yes—
291C23×C4C2412yes—
292C23×C4C2414yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C22⋊Q8—432no—
298C22⋊Q8—416no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4C2×D418yescomplemented
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—232no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
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—432no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—416no—
367C2×C22⋊C4—416no—
368C2×C22⋊C4—44no—
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—44no—
376C2×C22⋊C4C2×D418yes—
377C2×C22⋊C4C2×D418yes—
378C2×C22⋊C4C2×D418yes—
379#95—28no—
380#95—24no—
381#95—24no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95C2×D418yescomplemented
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—28no—
403C24—28no—
404C24—216no—
405C24—28no—
406C24—216no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—48no—
436C24—44no—
437C24—44no—
438C24—44no—
439C24—48no—
440C24—48no—
441C24—44no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—44no—
453C24—48no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—84no—
464C24—84no—
465C24—84no—
466C24—84no—
467C24C22⋊Q8116yescomplemented
468C24C22×D414yes—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C22×Q814yes—
472C24C22×Q814yes—
473C24C22×Q812yes—
474C24C2×#4114yes—
475C24C2×#4112yes—
476C24C2×#4112yes—
477C24H(5,𝔽2)14yes—
478C24H(5,𝔽2)14yes—
479C24H(5,𝔽2)12yes—
480C242−1+412yes—
481C24C2511yescharacteristic
482C2×Q8—48no—
483C2×Q8—44no—
484C2×Q8—82no—
485C2×Q8—82no—
486C2×Q8—84no—
487C2×D4—232no—
488C2×D4—232no—
489C2×D4—416no—
490C2×D4—416no—
491C2×D4—416no—
492C2×D4—416no—
493C2×D4—416no—
494C2×D4—4128no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—28no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—28no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—416no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—4128no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—416no—
587C22×C4—44no—
588C22×C4—88no—
589C22×C4—88no—
590C22×C4—84no—
591C22×C4—88no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—88no—
596C22×C4—88no—
597C22×C4#121116yes—
598C22×C4C22×D414yes—
599C22×C4C22×D418yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×Q814yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C4⋊C4—48no—
609C4⋊C4—416no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—82no—
613C4⋊C4—82no—
614C4⋊C4—84no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C4⋊C4—88no—
618C4⋊C4—88no—
619C22⋊C4—216no—
620C22⋊C4—216no—
621C22⋊C4—216no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—232no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—28no—
657C23—24no—
658C23—28no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—28no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—28no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—232no—
686C23—416no—
687C23—416no—
688C23—432no—
689C23—432no—
690C23—416no—
691C23—432no—
692C23—416no—
693C23—416no—
694C23—432no—
695C23—416no—
696C23—416no—
697C23—42no—
698C23—416no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23—42no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—88no—
723C23—816no—
724C23—816no—
725C23—88no—
726C23—88no—
727C23—816no—
728C23—88no—
729C23—816no—
730C23C2×#12114yes—
731C23C2×C22⋊Q818yes—
732C23C2×C22⋊Q814yes—
733C23#53714yes—
734C23#54318yes—
735C23#54614yes—
736C23D4×Q814yes—
737C23#55214yes—
738C23#55414yes—
739C23C23×D411yescharacteristic
740C23C23×D411yescharacteristic
741C23C23×Q811yescharacteristic
742C23C22×#4111yescharacteristic
743C23C22×#4111yescharacteristic
744C23C2×H(5,𝔽2)11yescharacteristic
745C23C2×H(5,𝔽2)12yes—
746C23C2×H(5,𝔽2)12yes—
747C23C2×H(5,𝔽2)12yes—
748C23C2×2−1+411yescharacteristic
749C23#58512yes—
750Q8—88no—
751D4—464no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—416no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—416no—
775C2×C4—416no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—88no—
822C2×C4—832no—
823C2×C4—88no—
824C2×C4C2×#12114yes—
825C2×C4C2×#12114yes—
826C22—24no—
827C22—28no—
828C22—28no—
829C22—24no—
830C22—24no—
831C22—28no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—28no—
842C22—464no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—48no—
848C22—44no—
849C22—48no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—48no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—48no—
863C22—832no—
864C22#241718yes—
865C22C22×#12111yescharacteristic
866C22C22×C22⋊Q811yescharacteristic
867C22C2×#53711yescharacteristic
868C22C2×#54312yes—
869C22#345912yes—
870C22C2×#54611yescharacteristic
871C22C2×D4×Q811yescharacteristic
872C22C2×#55211yescharacteristic
873C22C2×#55411yescharacteristic
874C22#348412yes—
875C22#348411yescharacteristic
876C22#348411yescharacteristic
877C22#348411yescharacteristic
878C22#348511yescharacteristic
879C22#348812yes—
880C22#349012yes—
881C22#349012yes—
882C22#349412yes—
883C22#350112yes—
884C22#353412yes—
885C22#353512yes—
886C22#353612yes—
887C22#353712yes—
888C4—24no—
889C4—24no—
890C4—44no—
891C4—48no—
892C4—44no—
893C4—44no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—84no—
899C4—82no—
900C2—28no—
901C2—48no—
902C2—48no—
903C2C2×#241711yescharacteristic
904C2#3498211yescharacteristic
905C2#3498511yescharacteristic
906C2#3534811yescharacteristic
907C2#3551411yescharacteristic
908C2#3670611yescharacteristic
909C2#3670911yescharacteristic
910C2#3768412yes—
911C2#3774412yes—
912C2#3787212yes—
913C2#3793212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2848C2semidirect
2. C2×#2626C2semidirect
3. C2×#2315C2semidirect
5. #15439C2semidirect
6. #15429C2semidirect
7. #15324C2semidirect
8. #15323C2semidirect
9. #14920C2semidirect
10. #14726C2semidirect
11. #14680C2semidirect
12. #14281C2semidirect
13. #14275C2semidirect
14. #13877C2semidirect
19. C22×C22⋊Q8C22semidirect
26. C2×#399C22semidirect
27. C2×#396C22semidirect
28. C2×#396C22semidirect
29. C2×#396C22semidirect
30. C2×#393C22semidirect
40. C2×#385C22semidirect
41. C2×#385C22semidirect
42. C2×#385C22semidirect
47. C2×#380C22semidirect
48. C2×#380C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
56. #1446C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1444C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
77. C22⋊#95C22semidirect
78. C22⋊#95C22semidirect
86. C23×D4Q8semidirect
167. #380D4semidirect
327. C2×C4⋊C4C2×D4semidirect
397. #95C2×D4semidirect
467. C24C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26262
C2×#23152
C22×#3862
#154392
#154292
#153242
#153232
#149202
#147262
#146802
#142812
#142752
#138772
#138672