Finite Group Databasebeta

← #627787

Subgroups — #627787

Order 512.

4846 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×#2312C211yesmaximal, characteristic, complemented
4C22×#386C211yesmaximal, characteristic
5#15613C214yesmaximal, complemented
6#15394C214yesmaximal, complemented
7#15308C214yesmaximal, complemented
8#15303C214yesmaximal, complemented
9#14727C212yesmaximal, complemented
10#14724C212yesmaximal
11#14680C211yesmaximal, characteristic, complemented
12#14281C211yesmaximal, characteristic, complemented
13#14275C211yesmaximal, characteristic, complemented
14#14044C212yesmaximal, complemented
15#13971C212yesmaximal, 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×#397C2214yescomplemented
27C2×#396C2212yescomplemented
28C2×#396C2212yescomplemented
29C2×#394C2214yes—
30C2×#394C2214yes—
31C2×#393C2212yescomplemented
32#2312—28no—
33C2×#388C2214yescomplemented
34C2×#388C2214yescomplemented
35C2×#388C2214yescomplemented
36C2×#386—28no—
37C2×#386C2214yes—
38C2×#386C2214yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2214yescomplemented
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2212yescomplemented
47C2×#380C2212yescomplemented
48C2×#380C2212yescomplemented
49C2×#379C2212yes—
50C2×#379C2212yes—
51C2×#379C2212yes—
52C2×#379C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56#1446C2212yescomplemented
57#1445C2212yescomplemented
58#1444C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2214yescomplemented
63#1441C2214yescomplemented
64#1440C2214yescomplemented
65#1440C2214yescomplemented
66#1440C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1438C2214yes—
70#1438C2214yes—
71#1437C2214yescomplemented
72#1436C2214yescomplemented
73C4⋊#95C2214yescomplemented
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—24no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C22⋊C4—24no—
117C22×C22⋊C4—24no—
118C22×C22⋊C4—24no—
119C22×C22⋊C4—24no—
120C22×C22⋊C4—44no—
121C22×C22⋊C4—44no—
122C22×C22⋊C4D418yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C42C2314yes—
142#399—28no—
143#397—48no—
144#396—28no—
145#396—28no—
146#394—48no—
147#394—48no—
148#393—28no—
149#388—216no—
150#388—216no—
151#388—48no—
152#386—216no—
153#386—216no—
154#385—28no—
155#385—28no—
156#385—28no—
157#385—216no—
158#380—24no—
159#380—24no—
160#380—28no—
161#380—44no—
162#380—44no—
163#380D418yescomplemented
164#379—28no—
165#379—28no—
166#379—28no—
167#379—28no—
168C4×C22⋊C4—28no—
169C2×#95—24no—
170C2×#95—24no—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C25—22no—
191C25—22no—
192C25—24no—
193C25—24no—
194C25—22no—
195C25—22no—
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—
211C25#4114yes—
212C25C2412yes—
213C25C2412yes—
214C25C2411yescharacteristic
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—42no—
219C22×Q8—42no—
220C22×D4—232no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—432no—
229C22×D4—416no—
230C22×D4—416no—
231C22×D4—432no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—42no—
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—416no—
267C23×C4—432no—
268C23×C4—432no—
269C23×C4—416no—
270C23×C4—416no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C22⋊Q8—432no—
289C22⋊Q8—416no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—44no—
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×D418yescomplemented
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—232no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
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—416no—
355C2×C22⋊C4—416no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
367C2×C22⋊C4C2×D418yes—
368C2×C22⋊C4C2×D418yes—
369C2×C42—28no—
370C2×C42—44no—
371C2×C42—44no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
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×D418yescomplemented
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—28no—
396C24—28no—
397C24—216no—
398C24—28no—
399C24—216no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—28no—
413C24—28no—
414C24—28no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—28no—
426C24—28no—
427C24—48no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—48no—
433C24—48no—
434C24—48no—
435C24—48no—
436C24—48no—
437C24—48no—
438C24—48no—
439C24—48no—
440C24—44no—
441C24—48no—
442C24—44no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—44no—
448C24—44no—
449C24—44no—
450C24—44no—
451C24—44no—
452C24—44no—
453C24—44no—
454C24—44no—
455C24—84no—
456C24—84no—
457C24—84no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24C22×D414yes—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4114yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24H(5,𝔽2)14yes—
471C24H(5,𝔽2)14yes—
472C242−1+412yes—
473C242−1+412yes—
474C24C2511yescharacteristic
475C2×Q8—48no—
476C2×Q8—44no—
477C2×Q8—82no—
478C2×Q8—82no—
479C2×Q8—84no—
480C2×D4—232no—
481C2×D4—416no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—4128no—
486C2×D4—416no—
487C2×D4—416no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—28no—
493C22×C4—216no—
494C22×C4—216no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
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—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—44no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
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×D418yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C2×#4114yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)14yes—
594C4⋊C4—48no—
595C4⋊C4—416no—
596C4⋊C4—44no—
597C4⋊C4—48no—
598C4⋊C4—84no—
599C4⋊C4—82no—
600C4⋊C4—82no—
601C4⋊C4—84no—
602C4⋊C4—84no—
603C4⋊C4—88no—
604C22⋊C4—216no—
605C22⋊C4—216no—
606C22⋊C4—216no—
607C22⋊C4—416no—
608C22⋊C4—416no—
609C22⋊C4—416no—
610C22⋊C4—416no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—416no—
614C22⋊C4—48no—
615C22⋊C4—88no—
616C22⋊C4—88no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—88no—
622C42—88no—
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—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—432no—
666C23—432no—
667C23—416no—
668C23—416no—
669C23—432no—
670C23—416no—
671C23—416no—
672C23—432no—
673C23—416no—
674C23—416no—
675C23—416no—
676C23—42no—
677C23—416no—
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—42no—
691C23—42no—
692C23—42no—
693C23—416no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—88no—
711C23—88no—
712C23—88no—
713C23—88no—
714C23—816no—
715C23—816no—
716C23—816no—
717C23—816no—
718C23C2×#12114yes—
719C23#52514yes—
720C23#53614yes—
721C23#53818yes—
722C23#54714yes—
723C23#54814yes—
724C23#55214yes—
725C23#55614yes—
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—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—416no—
759C2×C4—432no—
760C2×C4—432no—
761C2×C4—416no—
762C2×C4—416no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—24no—
814C22—28no—
815C22—28no—
816C22—24no—
817C22—24no—
818C22—28no—
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—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—832no—
846C22—84no—
847C22—84no—
848C22—84no—
849C22—84no—
850C22#241518yes—
851C22C22×#12111yescharacteristic
852C22C2×#52511yescharacteristic
853C22C2×#53611yescharacteristic
854C22C2×#53812yes—
855C22#346012yes—
856C22C2×#54711yescharacteristic
857C22C2×#54811yescharacteristic
858C22C2×#55211yescharacteristic
859C22C2×#55611yescharacteristic
860C22#348411yescharacteristic
861C22#348412yes—
862C22#348411yescharacteristic
863C22#348411yescharacteristic
864C22#348511yescharacteristic
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—48no—
878C4—44no—
879C4—44no—
880C4—82no—
881C4—82no—
882C4—84no—
883C4—82no—
884C4—82no—
885C4—82no—
886C2—28no—
887C2—48no—
888C2—84no—
889C2C2×#241511yescharacteristic
890C2#3498811yescharacteristic
891C2#3509111yescharacteristic
892C2#3534811yescharacteristic
893C2#3551411yescharacteristic
894C2#3671811yescharacteristic
895C2#3672011yescharacteristic
896C2#3770312yes—
897C2#3776112yes—
898C2#3788112yes—
899C2#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×#2312C2semidirect
5. #15613C2semidirect
6. #15394C2semidirect
7. #15308C2semidirect
8. #15303C2semidirect
9. #14727C2semidirect
11. #14680C2semidirect
12. #14281C2semidirect
13. #14275C2semidirect
14. #14044C2semidirect
15. #13971C2semidirect
19. C22×C22⋊Q8C22semidirect
25. C2×#399C22semidirect
26. C2×#397C22semidirect
27. C2×#396C22semidirect
28. C2×#396C22semidirect
31. C2×#393C22semidirect
33. C2×#388C22semidirect
34. C2×#388C22semidirect
35. C2×#388C22semidirect
42. C2×#385C22semidirect
46. C2×#380C22semidirect
47. C2×#380C22semidirect
48. C2×#380C22semidirect
56. #1446C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1440C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
71. #1437C22semidirect
72. #1436C22semidirect
73. C4⋊#95C22semidirect
78. C22⋊#95C22semidirect
163. #380D4semidirect
315. C2×C4⋊C4C2×D4semidirect
390. #95C2×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×#23122
C22×#3862
#156132
#153942
#153082
#153032
#147272
#147242
#146802
#142812
#142752
#140442
#139712