Finite Group Databasebeta

← #6517044

Subgroups — #6517044

Order 512.

2482 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3215C211yesmaximal, characteristic, complemented
2C2×#2973C211yesmaximal, characteristic, complemented
3#35172C211yesmaximal, characteristic, complemented
4C2×#2540C211yesmaximal, characteristic
5#28612C214yesmaximal, complemented
6#28492C214yesmaximal, complemented
7#25403C214yesmaximal, complemented
8#25399C214yesmaximal, complemented
9#24386C212yesmaximal, complemented
10#24385C212yesmaximal, complemented
11#24380C212yesmaximal, complemented
12#24379C212yesmaximal, complemented
13#21808C211yesmaximal, characteristic, complemented
14#21394C211yesmaximal, characteristic, complemented
15#21365C211yesmaximal, characteristic, complemented
16C2×#533C2211yescharacteristic
17C22×#124C2211yescharacteristic
18C22×C22⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#3215—28no—
24C2×#497C2212yescomplemented
25C2×#489C2212yescomplemented
26C2×#470C2214yescomplemented
27C2×#468C2214yescomplemented
28C2×#467C2214yescomplemented
29C2×#465C2214yescomplemented
30C2×#464C2214yescomplemented
31C2×#451C2212yes—
32C2×#450C2212yes—
33#2973—28no—
34C2×#435C2214yescomplemented
35C2×#435C2214yescomplemented
36C2×#432C2211yescharacteristic
37C2×#432C2211yescharacteristic
38C2×#407C2212yes—
39C22×C22⋊C8C2212yes—
40#2848C2212yes—
41#2848C2212yes—
42#2626—21no—
43#2626—21no—
44#2580—22no—
45#2566—22no—
46#2563C2212yescomplemented
47#2542C2212yescomplemented
48#2540—22no—
49#2540—22no—
50#2540C2214yes—
51#2540C2214yes—
52#2538C2212yescomplemented
53#2538C2212yescomplemented
54C2×#399—21no—
55C2×#392—21no—
56#2317—21no—
57#2309—21no—
58C2×#390—21no—
59C2×#390—21no—
60#2285C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62#2036C2214yescomplemented
63#2035C2214yescomplemented
64#2034C2214yescomplemented
65#2033C2214yescomplemented
66#2001C2214yescomplemented
67#2001C2214yescomplemented
68#2000C2214yescomplemented
69#2000C2214yescomplemented
70#1988C2212yescomplemented
71#1983C2214yescomplemented
72#1981C2212yescomplemented
73#1959C2212yescomplemented
74#1959C2212yescomplemented
75#1948C2212yescomplemented
76#1947C2212yescomplemented
77#1895C2214yescomplemented
78#1894C2214yescomplemented
79#1893C2214yescomplemented
80#1892C2214yescomplemented
81#1872C2212yes—
82#1872C2212yes—
83#1853C2212yes—
84#1852C2212yes—
85#1787C2212yes—
86#1786C2212yes—
87#1776C2214yescomplemented
88#1763C2214yescomplemented
89C23×Q8C2311yescharacteristic
90C23×D4—21no—
91C23×D4—21no—
92C23×D4D411yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C22×Q16C2314yes—
97C22×SD16C2314yes—
98C22×M16C2314yes—
99C23×C8C2314yes—
100#533—24no—
101#533—24no—
102C2×C4⋊Q8C2311yescharacteristic
103C2×C4⋊Q8C2311yescharacteristic
104C2×#125—21no—
105C2×#124—21no—
106C2×#124—21no—
107C2×#124—24no—
108C2×#124—24no—
109C2×#124C2312yes—
110C2×#124C2312yes—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—44no—
115C2×C22⋊Q8—44no—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2314yes—
118C2×C22⋊Q8C2314yes—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×#121—22no—
124C2×#121—22no—
125C2×#121—44no—
126C2×#121—44no—
127C2×#121C2314yes—
128C2×#121C2314yes—
129C2×C4×Q8—21no—
130C2×C4×Q8C2312yes—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4D412yes—
134C2×C4×D4D412yes—
135C2×C4×D4C2312yes—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4D411yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4D411yescharacteristic
151C22×C22⋊C4D411yescharacteristic
152C22×C42—21no—
153C22×C42C2311yescharacteristic
154#497—28no—
155#489—28no—
156#470—48no—
157#468—48no—
158#467—48no—
159#465—48no—
160#464—216no—
161#451—28no—
162#450—28no—
163#435—216no—
164#435—216no—
165#432—24no—
166#432D418yescomplemented
167C2×#107C2314yes—
168C2×#106C2314yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#103C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179#407—28no—
180C2×C22⋊C8—28no—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2314yes—
183C2×C22⋊C8C2314yes—
184C2×C22⋊C8C2312yes—
185C2×#97C2312yes—
186C2×#97C2312yes—
187#399—24no—
188#399—24no—
189#399—22no—
190#399—22no—
191#396—22no—
192#396—22no—
193#396—22no—
194#396—22no—
195#393—22no—
196#393—22no—
197#392—24no—
198#392—24no—
199#390—22no—
200#390—22no—
201#390—22no—
202#390—22no—
203#390—24no—
204#390—24no—
205#390—24no—
206#390—24no—
207#389—22no—
208#389—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#384—22no—
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#382—22no—
219#382—21no—
220#380—21no—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#379—22no—
227#379—22no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2312yes—
233C4×C4⋊C4C2312yes—
234C2×#95—21no—
235#340C2314yes—
236#340C2314yes—
237#340C2314yes—
238#340C2314yes—
239C25—21no—
240C25C2×D411yescharacteristic
241C25C2×D411yescharacteristic
242C22×Q8—21no—
243C22×Q8—21no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—42no—
247C22×Q8—42no—
248C22×Q8C2412yes—
249C22×Q8C2412yes—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—22no—
255C22×D4—21no—
256C22×D4—22no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—82no—
265C22×D4—82no—
266C22×D4C2×D412yes—
267C22×D4C2×D412yes—
268C22×D4C2412yes—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×D412yes—
285C23×C4C2×D411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C2×Q16—28no—
290C2×Q16—44no—
291C2×Q16—44no—
292C2×SD16—28no—
293C2×SD16—44no—
294C2×SD16—44no—
295C2×M16—28no—
296C2×M16—44no—
297C2×M16—44no—
298C22×C8—28no—
299C22×C8—44no—
300C22×C8—44no—
301C22×C8C2414yes—
302C22×C8C2414yes—
303C4⋊Q8—22no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307#125—44no—
308#124—24no—
309#124—24no—
310#124—24no—
311#124—24no—
312#124—44no—
313#124—44no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—28no—
317C22⋊Q8—28no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—48no—
321C22⋊Q8—48no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327#121—28no—
328#121—28no—
329#121—44no—
330#121—44no—
331#121—48no—
332#121—48no—
333C4×Q8—24no—
334C4×Q8—24no—
335C4×Q8—44no—
336C4×D4—28no—
337C4×D4—28no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—24no—
342#117—44no—
343#117—44no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D412yes—
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4C2×D412yes—
400C2×C22⋊C4C2×D412yes—
401C2×C22⋊C4C2×D412yes—
402C2×C22⋊C4C2×D412yes—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—82no—
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414#107—28no—
415#106—28no—
416C4⋊C8—24no—
417C4⋊C8C2×D418yescomplemented
418#103—28no—
419#103—28no—
420#103—28no—
421#103—44no—
422#103—44no—
423#102—28no—
424#102—44no—
425#102—44no—
426C22⋊C8—24no—
427C22⋊C8—28no—
428C22⋊C8—28no—
429C22⋊C8C2×D418yes—
430#97—24no—
431#97C2×D418yescomplemented
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—41no—
447C24—41no—
448C24—41no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24#13714yes—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C22×D411yescharacteristic
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—24no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—81no—
478C2×Q8—81no—
479C2×Q8—84no—
480C2×Q8—84no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—24no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—416no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—42no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—84no—
503C2×D4—816no—
504C2×D4—816no—
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—22no—
514C22×C4—22no—
515C22×C4—22no—
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—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—84no—
548C22×C4—84no—
549C22×C4—84no—
550C22×C4—84no—
551C22×C4#12114yes—
552C22×C4#12114yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D412yes—
561C22×C4C2×#4112yes—
562C22×C4C2511yescharacteristic
563Q16—88no—
564SD16—88no—
565M16—88no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—88no—
572C2×C8C22×D418yes—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—81no—
593C4⋊C4—81no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4H(5,𝔽2)14yes—
599C4⋊C4H(5,𝔽2)14yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C42—44no—
623C42—44no—
624C42—82no—
625C42—82no—
626C42#12114yes—
627C42#12114yes—
628C42C22×D412yes—
629C42C22×D412yes—
630C42C2×#4112yes—
631C42C2×#4112yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—28no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—82no—
663C23—82no—
664C23—82no—
665C23—82no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23C2×#12112yes—
678C23C2×#13714yes—
679C23C2×#13712yes—
680C23#57512yes—
681C23C23×D411yescharacteristic
682Q8—44no—
683Q8—44no—
684Q8—44no—
685Q8—44no—
686Q8—84no—
687Q8—84no—
688D4—48no—
689D4—48no—
690D4—44no—
691D4—44no—
692D4—84no—
693D4—816no—
694D4—816no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—82no—
745C2×C4—82no—
746C2×C4—84no—
747C2×C4C2×#12112yes—
748C2×C4C2×#12112yes—
749C2×C4C2×#12112yes—
750C2×C4C2×#12112yes—
751C2×C4C2×#12112yes—
752C2×C4C23×D411yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C2×C4C2×H(5,𝔽2)12yes—
755C2×C4C2×H(5,𝔽2)12yes—
756C8—28no—
757C8—44no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—88no—
779C22—88no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—168no—
788C22#305614yes—
789C22C22×#12111yescharacteristic
790C22#348411yescharacteristic
791C22#348411yescharacteristic
792C22C22×#13711yescharacteristic
793C22C2×#57511yescharacteristic
794C22#358511yescharacteristic
795C22#358611yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—44no—
802C4—44no—
803C4—42no—
804C4—42no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4#349812yes—
811C4#350812yes—
812C2—24no—
813C2—44no—
814C2—82no—
815C2—162no—
816C2#3552811yescharacteristic
817C2C2×#305611yescharacteristic
818C2#6045611yescharacteristic
819C2#6157011yescharacteristic
820C2#6157311yescharacteristic
821C2#6157611yescharacteristic
822C2#6157811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#3215C2semidirect
2. C2×#2973C2semidirect
3. #35172C2semidirect
5. #28612C2semidirect
6. #28492C2semidirect
7. #25403C2semidirect
8. #25399C2semidirect
9. #24386C2semidirect
10. #24385C2semidirect
11. #24380C2semidirect
12. #24379C2semidirect
13. #21808C2semidirect
14. #21394C2semidirect
15. #21365C2semidirect
24. C2×#497C22semidirect
25. C2×#489C22semidirect
26. C2×#470C22semidirect
27. C2×#468C22semidirect
28. C2×#467C22semidirect
29. C2×#465C22semidirect
30. C2×#464C22semidirect
34. C2×#435C22semidirect
35. C2×#435C22semidirect
46. #2563C22semidirect
47. #2542C22semidirect
52. #2538C22semidirect
53. #2538C22semidirect
62. #2036C22semidirect
63. #2035C22semidirect
64. #2034C22semidirect
65. #2033C22semidirect
66. #2001C22semidirect
67. #2001C22semidirect
68. #2000C22semidirect
69. #2000C22semidirect
70. #1988C22semidirect
71. #1983C22semidirect
72. #1981C22semidirect
73. #1959C22semidirect
74. #1959C22semidirect
75. #1948C22semidirect
76. #1947C22semidirect
77. #1895C22semidirect
78. #1894C22semidirect
79. #1893C22semidirect
80. #1892C22semidirect
87. #1776C22semidirect
88. #1763C22semidirect
166. #432D4semidirect
417. C4⋊C8C2×D4semidirect
431. #97C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32152
C2×#29732
#351722
C2×#25402
#286122
#284922
#254032
#253992
#243862
#243852
#243802
#243792
#218082
#213942
#213652