Finite Group Databasebeta

← #627915

Subgroups — #627915

Order 512.

4854 conjugacy classes of subgroups.

The subgroup lattice has 901 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#15452C214yesmaximal, complemented
6#15380C214yesmaximal, complemented
7#15302C214yesmaximal, complemented
8#15275C214yesmaximal, complemented
9#14955C212yesmaximal, complemented
10#14724C212yesmaximal
11#14680C211yesmaximal, characteristic, complemented
12#14347C211yesmaximal, characteristic, complemented
13#14338C211yesmaximal, characteristic, complemented
14#13991C212yesmaximal, complemented
15#13991C212yesmaximal, complemented
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×#394C2214yes—
28C2×#394C2214yes—
29C2×#393C2212yescomplemented
30#2329—28no—
31C2×#391C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#388C2214yescomplemented
34C2×#388C2214yescomplemented
35C2×#387C2212yescomplemented
36C2×#387C2212yescomplemented
37C2×#386—28no—
38C2×#386C2214yes—
39C2×#386C2214yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2214yescomplemented
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2212yescomplemented
48C2×#380C2212yescomplemented
49C2×#380C2212yescomplemented
50C2×#379C2212yes—
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×#379C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57#1442C2214yescomplemented
58#1442C2214yescomplemented
59#1442C2214yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1440C2214yescomplemented
64#1440C2214yescomplemented
65#1439C2214yescomplemented
66#1439C2212yescomplemented
67#1439C2212yescomplemented
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1438C2214yes—
71#1438C2214yes—
72#1437C2214yescomplemented
73#1437C2214yescomplemented
74C22⋊#95C2212yes—
75C22⋊#95C2212yes—
76C22⋊#95C2212yes—
77C22⋊#95C2212yes—
78C22⋊#95C2214yescomplemented
79C26C2311yescharacteristic
80C26C2311yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×D4—24no—
83C23×D4—24no—
84C23×D4—24no—
85C23×D4—44no—
86C23×D4—44no—
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⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2314yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—24no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4—44no—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C42C2312yes—
140C22×C42C2312yes—
141#399—28no—
142#396—216no—
143#394—48no—
144#394—48no—
145#393—28no—
146#391—28no—
147#389—28no—
148#388—48no—
149#388—48no—
150#387—28no—
151#387—28no—
152#386—216no—
153#386—216no—
154#385—28no—
155#385—216no—
156#385—28no—
157#385—28no—
158#380—24no—
159#380—24no—
160#380—24no—
161#380—28no—
162#380—44no—
163#380—44no—
164#379—28no—
165#379—28no—
166#379—28no—
167#379—28no—
168C4×C22⋊C4—28no—
169C2×#95—24no—
170C2×#95D418yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C25—22no—
192C25—22no—
193C25—24no—
194C25—24no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25—22no—
203C25—22no—
204C25—22no—
205C25—42no—
206C25—42no—
207C25—42no—
208C25—42no—
209C25—42no—
210C25—42no—
211C25#4114yes—
212C25#4114yes—
213C25C2412yes—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×Q8C2×D414yescomplemented
221C22×D4—232no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—416no—
230C22×D4—416no—
231C22×D4—432no—
232C22×D4—432no—
233C23×C4—22no—
234C23×C4—22no—
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×C4#4114yes—
277C23×C4C2412yes—
278C23×C4C2414yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C22⋊Q8—232no—
290C22⋊Q8—432no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C2×D414yescomplemented
316C2×C4⋊C4C2×D418yescomplemented
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—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—416no—
357C2×C22⋊C4—416no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—44no—
371C2×C42—44no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—28no—
382#95—28no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95C2×D418yes—
391#95C2×D418yes—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—28no—
397C24—28no—
398C24—216no—
399C24—28no—
400C24—216no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—28no—
414C24—28no—
415C24—28no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—24no—
426C24—28no—
427C24—28no—
428C24—48no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—44no—
440C24—48no—
441C24—44no—
442C24—44no—
443C24—48no—
444C24—44no—
445C24—44no—
446C24—44no—
447C24—48no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—84no—
457C24—84no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—84no—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2×#4114yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24C2×#4112yes—
471C24H(5,𝔽2)14yes—
472C24H(5,𝔽2)14yes—
473C242−1+412yes—
474C242−1+412yes—
475C24C2511yescharacteristic
476C2×Q8—28no—
477C2×Q8—48no—
478C2×Q8—82no—
479C2×Q8—82no—
480C2×Q8—84no—
481C2×D4—232no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—4128no—
487C2×D4—416no—
488C2×D4—416no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—216no—
495C22×C4—216no—
496C22×C4—28no—
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—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
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—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—4128no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4#121116yes—
584C22×C4C22×D414yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)14yes—
595C4⋊C4—28no—
596C4⋊C4—216no—
597C4⋊C4—416no—
598C4⋊C4—48no—
599C4⋊C4—82no—
600C4⋊C4—84no—
601C4⋊C4—82no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C4⋊C4—88no—
605C22⋊C4—216no—
606C22⋊C4—416no—
607C22⋊C4—416no—
608C22⋊C4—416no—
609C22⋊C4—416no—
610C22⋊C4—416no—
611C22⋊C4—48no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—88no—
618C22⋊C4—88no—
619C22⋊C4—88no—
620C22⋊C4—88no—
621C42—84no—
622C42—84no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—232no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—24no—
661C23—24no—
662C23—28no—
663C23—432no—
664C23—432no—
665C23—416no—
666C23—432no—
667C23—416no—
668C23—416no—
669C23—432no—
670C23—416no—
671C23—416no—
672C23—416no—
673C23—416no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—416no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—416no—
710C23—816no—
711C23—816no—
712C23—88no—
713C23—816no—
714C23—88no—
715C23—88no—
716C23—88no—
717C23—816no—
718C23C2×#12114yes—
719C23#52514yes—
720C23#53614yes—
721C23#53818yes—
722C23#54814yes—
723C23#54814yes—
724C23#55214yes—
725C23#55214yes—
726C23C23×D411yescharacteristic
727C23C23×D411yescharacteristic
728C23C22×#4111yescharacteristic
729C23C22×#4111yescharacteristic
730C23C22×#4111yescharacteristic
731C23C2×H(5,𝔽2)12yes—
732C23C2×H(5,𝔽2)12yes—
733C23C2×H(5,𝔽2)12yes—
734C23C2×2−1+411yescharacteristic
735C23C2×2−1+411yescharacteristic
736C23#58512yes—
737Q8—88no—
738D4—464no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—416no—
761C2×C4—432no—
762C2×C4—432no—
763C2×C4—416no—
764C2×C4—416no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—88no—
809C2×C4—88no—
810C2×C4C2×#12114yes—
811C2×C4C2×#12114yes—
812C22—24no—
813C22—28no—
814C22—28no—
815C22—24no—
816C22—24no—
817C22—28no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—28no—
822C22—28no—
823C22—28no—
824C22—28no—
825C22—464no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—48no—
839C22—44no—
840C22—48no—
841C22—44no—
842C22—44no—
843C22—832no—
844C22—82no—
845C22—84no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—84no—
850C22#253618yes—
851C22C22×#12111yescharacteristic
852C22C2×#52511yescharacteristic
853C22C2×#53611yescharacteristic
854C22C2×#53812yes—
855C22#345912yes—
856C22C2×#54811yescharacteristic
857C22C2×#54811yescharacteristic
858C22C2×#55211yescharacteristic
859C22C2×#55211yescharacteristic
860C22#348412yes—
861C22#348411yescharacteristic
862C22#348411yescharacteristic
863C22#348411yescharacteristic
864C22#348711yescharacteristic
865C22#348812yes—
866C22#349012yes—
867C22#349012yes—
868C22#349412yes—
869C22#350512yes—
870C22#353512yes—
871C22#353512yes—
872C22#353612yes—
873C22#353612yes—
874C4—24no—
875C4—24no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—84no—
882C4—84no—
883C4—82no—
884C4—82no—
885C4—82no—
886C2—28no—
887C2—48no—
888C2—84no—
889C2C2×#253611yescharacteristic
890C2#3498711yescharacteristic
891C2#3498811yescharacteristic
892C2#3534811yescharacteristic
893C2#3556311yescharacteristic
894C2#3671111yescharacteristic
895C2#3671811yescharacteristic
896C2#3770312yes—
897C2#3775212yes—
898C2#3788112yes—
899C2#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×#2329C2semidirect
5. #15452C2semidirect
6. #15380C2semidirect
7. #15302C2semidirect
8. #15275C2semidirect
9. #14955C2semidirect
11. #14680C2semidirect
12. #14347C2semidirect
13. #14338C2semidirect
14. #13991C2semidirect
15. #13991C2semidirect
19. C22×C22⋊Q8C22semidirect
25. C2×#399C22semidirect
26. C2×#396C22semidirect
29. C2×#393C22semidirect
31. C2×#391C22semidirect
32. C2×#389C22semidirect
33. C2×#388C22semidirect
34. C2×#388C22semidirect
35. C2×#387C22semidirect
36. C2×#387C22semidirect
43. C2×#385C22semidirect
47. C2×#380C22semidirect
48. C2×#380C22semidirect
49. C2×#380C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1440C22semidirect
64. #1440C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
72. #1437C22semidirect
73. #1437C22semidirect
78. C22⋊#95C22semidirect
105. C2×C22⋊Q8D4semidirect
220. C22×Q8C2×D4semidirect
315. C2×C4⋊C4C2×D4semidirect
316. C2×C4⋊C4C2×D4semidirect

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
#154522
#153802
#153022
#152752
#149552
#147242
#146802
#143472
#143382
#139912