Finite Group Databasebeta

← #626951

Subgroups — #626951

Order 512.

4926 conjugacy classes of subgroups.

The subgroup lattice has 909 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×#2329C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic
5#15355C214yesmaximal, complemented
6#15335C214yesmaximal, complemented
7#15309C214yesmaximal, complemented
8#15280C214yesmaximal, complemented
9#14726C212yesmaximal, complemented
10#14726C212yesmaximal, complemented
11#14680C211yesmaximal, characteristic, complemented
12#14353C211yesmaximal, characteristic, complemented
13#14338C211yesmaximal, characteristic, complemented
14#14149C212yesmaximal, complemented
15#13902C212yesmaximal
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yescomplemented
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2848—28no—
24#2626—28no—
25C2×#399C2212yescomplemented
26C2×#396C2214yescomplemented
27C2×#396C2214yescomplemented
28C2×#396C2214yescomplemented
29C2×#393C2212yescomplemented
30#2329—28no—
31C2×#391C2212yescomplemented
32C2×#390C2214yes—
33C2×#390C2214yes—
34C2×#389C2212yescomplemented
35C2×#387C2212yescomplemented
36C2×#387C2212yescomplemented
37C2×#386—28no—
38C2×#386C2214yes—
39C2×#386C2214yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2214yescomplemented
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yescomplemented
50C2×#380C2212yescomplemented
51C2×#380C2212yescomplemented
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59#1444C2214yescomplemented
60#1444C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1439C2214yescomplemented
64#1439C2212yescomplemented
65#1439C2212yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1438C2214yes—
73#1438C2214yes—
74#1436C2214yescomplemented
75#1436C2214yescomplemented
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
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×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—44no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8D418yescomplemented
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—24no—
122C22×C22⋊C4—24no—
123C22×C22⋊C4—44no—
124C22×C22⋊C4—44no—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C42C2312yes—
142C22×C42C2312yes—
143#399—28no—
144#396—216no—
145#396—48no—
146#396—48no—
147#393—28no—
148#391—28no—
149#390—48no—
150#390—48no—
151#389—28no—
152#387—28no—
153#387—28no—
154#386—216no—
155#386—216no—
156#385—28no—
157#385—216no—
158#385—28no—
159#385—28no—
160#380—24no—
161#380—24no—
162#380—24no—
163#380—28no—
164#380—28no—
165#380—44no—
166#380—44no—
167#380—44no—
168#379—28no—
169#379—28no—
170#379—44no—
171#379—44no—
172C4×C22⋊C4—28no—
173C2×#95—24no—
174C2×#95D418yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C25—22no—
194C25—22no—
195C25—24no—
196C25—24no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—22no—
206C25—22no—
207C25—42no—
208C25—42no—
209C25—42no—
210C25—42no—
211C25—42no—
212C25—42no—
213C25C2×Q814yes—
214C25C2×Q814yes—
215C25C2412yes—
216C25C2412yes—
217C25C2411yescharacteristic
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—42no—
221C22×Q8—42no—
222C22×Q8C2×D414yescomplemented
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—232no—
226C22×D4—28no—
227C22×D4—28no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4—432no—
231C22×D4—416no—
232C22×D4—416no—
233C22×D4—432no—
234C22×D4C2×Q8116yes—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
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—42no—
267C23×C4—416no—
268C23×C4—432no—
269C23×C4—432no—
270C23×C4—416no—
271C23×C4—416no—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×Q814yes—
277C23×C4#4114yes—
278C23×C4#4114yes—
279C23×C4C2414yes—
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C22⋊Q8—232no—
292C22⋊Q8—432no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2×D414yescomplemented
324C2×C4⋊C4C2×D418yescomplemented
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
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—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—416no—
360C2×C22⋊C4—416no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—44no—
379C2×C42—44no—
380#95—28no—
381#95—24no—
382#95—24no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95C2×D418yes—
397#95C2×D418yes—
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—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—28no—
420C24—28no—
421C24—28no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—24no—
432C24—28no—
433C24—28no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—44no—
446C24—48no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—48no—
452C24—48no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—84no—
463C24—84no—
464C24—84no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24C22×D412yes—
471C24C22×D412yes—
472C24C22×Q814yes—
473C24C22×Q814yes—
474C24C22×Q812yes—
475C24C2×#4112yes—
476C24C2×#4112yes—
477C24H(5,𝔽2)14yes—
478C24H(5,𝔽2)14yes—
479C24H(5,𝔽2)12yes—
480C242−1+412yes—
481C24C2511yescharacteristic
482C2×Q8—28no—
483C2×Q8—48no—
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—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—28no—
502C22×C4—216no—
503C22×C4—216no—
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—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—28no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—4128no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4#121116yes—
587C22×C4C22⋊Q8116yescomplemented
588C22×C4C22×D414yes—
589C22×C4C22×D414yes—
590C22×C4C22×D414yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×Q814yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4114yes—
600C22×C4H(5,𝔽2)14yes—
601C4⋊C4—28no—
602C4⋊C4—216no—
603C4⋊C4—416no—
604C4⋊C4—48no—
605C4⋊C4—82no—
606C4⋊C4—84no—
607C4⋊C4—82no—
608C4⋊C4—88no—
609C4⋊C4—84no—
610C4⋊C4—84no—
611C4⋊C4—88no—
612C4⋊C4—88no—
613C22⋊C4—216no—
614C22⋊C4—416no—
615C22⋊C4—416no—
616C22⋊C4—416no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C42—84no—
630C42—84no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—232no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—24no—
669C23—24no—
670C23—28no—
671C23—432no—
672C23—432no—
673C23—416no—
674C23—432no—
675C23—416no—
676C23—416no—
677C23—416no—
678C23—432no—
679C23—416no—
680C23—416no—
681C23—416no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—416no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—416no—
718C23—816no—
719C23—816no—
720C23—88no—
721C23—816no—
722C23—88no—
723C23—88no—
724C23—816no—
725C23—88no—
726C23C2×#12114yes—
727C23C2×C22⋊Q814yes—
728C23#53714yes—
729C23#54318yes—
730C23D4×Q814yes—
731C23#55014yes—
732C23#55414yes—
733C23#55614yes—
734C23C23×D411yescharacteristic
735C23C23×D411yescharacteristic
736C23C23×Q811yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4111yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)12yes—
741C23C2×H(5,𝔽2)12yes—
742C23C2×H(5,𝔽2)12yes—
743C23C2×2−1+411yescharacteristic
744C23#58512yes—
745Q8—88no—
746D4—464no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—24no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—432no—
772C2×C4—432no—
773C2×C4—416no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—88no—
816C2×C4—88no—
817C2×C4C2×#12114yes—
818C2×C4C2×#12114yes—
819C2×C4C2×C22⋊Q818yes—
820C22—24no—
821C22—28no—
822C22—28no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—28no—
827C22—24no—
828C22—24no—
829C22—28no—
830C22—28no—
831C22—28no—
832C22—28no—
833C22—464no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—48no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—48no—
851C22—832no—
852C22—82no—
853C22—84no—
854C22—82no—
855C22—82no—
856C22—84no—
857C22—82no—
858C22#253818yes—
859C22C22×#12111yescharacteristic
860C22C22×C22⋊Q811yescharacteristic
861C22C2×#53711yescharacteristic
862C22C2×#54312yes—
863C22#346012yes—
864C22C2×D4×Q811yescharacteristic
865C22C2×#55011yescharacteristic
866C22C2×#55411yescharacteristic
867C22C2×#55611yescharacteristic
868C22#348412yes—
869C22#348411yescharacteristic
870C22#348411yescharacteristic
871C22#348411yescharacteristic
872C22#348711yescharacteristic
873C22#348812yes—
874C22#349012yes—
875C22#349012yes—
876C22#349412yes—
877C22#350112yes—
878C22#353412yes—
879C22#353512yes—
880C22#353612yes—
881C22#353712yes—
882C4—24no—
883C4—24no—
884C4—28no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—44no—
889C4—82no—
890C4—82no—
891C4—84no—
892C4—84no—
893C4—82no—
894C2—28no—
895C2—48no—
896C2—84no—
897C2C2×#253811yescharacteristic
898C2#3498211yescharacteristic
899C2#3517411yescharacteristic
900C2#3534811yescharacteristic
901C2#3556311yescharacteristic
902C2#3670611yescharacteristic
903C2#3672211yescharacteristic
904C2#3768412yes—
905C2#3776912yes—
906C2#3787212yes—
907C2#3795712yes—
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×#2329C2semidirect
5. #15355C2semidirect
6. #15335C2semidirect
7. #15309C2semidirect
8. #15280C2semidirect
9. #14726C2semidirect
10. #14726C2semidirect
11. #14680C2semidirect
12. #14353C2semidirect
13. #14338C2semidirect
14. #14149C2semidirect
19. C22×C22⋊Q8C22semidirect
25. C2×#399C22semidirect
26. C2×#396C22semidirect
27. C2×#396C22semidirect
28. C2×#396C22semidirect
29. C2×#393C22semidirect
31. C2×#391C22semidirect
34. C2×#389C22semidirect
35. C2×#387C22semidirect
36. C2×#387C22semidirect
43. C2×#385C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
51. C2×#380C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
74. #1436C22semidirect
75. #1436C22semidirect
78. C22⋊#95C22semidirect
86. C23×D4Q8semidirect
105. C2×C22⋊Q8D4semidirect
222. C22×Q8C2×D4semidirect
323. C2×C4⋊C4C2×D4semidirect
324. C2×C4⋊C4C2×D4semidirect
587. C22×C4C22⋊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×#23292
C22×#3862
#153552
#153352
#153092
#152802
#147262
#146802
#143532
#143382
#141492
#139022