Finite Group Databasebeta

← #6497527

Subgroups — #6497527

Order 512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3240C212yesmaximal
2#36645C211yesmaximal, characteristic, complemented
3C4×#529C211yesmaximal, characteristic
4#33200C212yesmaximal, complemented
5#33199C212yesmaximal, complemented
6#29871C212yesmaximal, complemented
7#29870C212yesmaximal, complemented
8#28727C212yesmaximal, complemented
9#28726C211yesmaximal, characteristic, complemented
10#28726C211yesmaximal, characteristic, complemented
11#28695C212yesmaximal, complemented
12#28694C211yesmaximal, characteristic, complemented
13#28694C211yesmaximal, characteristic, complemented
14#27652C212yesmaximal, complemented
15#27650C212yesmaximal
16#27649C212yesmaximal, complemented
17#27646C212yesmaximal
18#21842C212yesmaximal, complemented
19#20810C211yesmaximal, characteristic, complemented
20C2×#533C2212yes—
21C2×#529C2211yescharacteristic
22#3240—216no—
23C2×#501C2212yes—
24C2×#501C2212yes—
25C2×#489C2212yes—
26C2×#489C2212yes—
27C2×#485C2214yes—
28C2×#482C2214yes—
29C2×#479C2214yes—
30C2×#478C2214yes—
31C2×#432C2212yes—
32#2868C2211yescharacteristic
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2859C2212yes—
36#2859C2212yes—
37#2857—21no—
38#2857—21no—
39#2857—21no—
40#2857—21no—
41C4×C4⋊Q8—21no—
42C4×C4⋊Q8—21no—
43C4×C4⋊Q8—21no—
44C4×C4⋊Q8—21no—
45C4×#125C2211yescharacteristic
46C4×#125C2211yescharacteristic
47C4×#126—21no—
48C4×#126—21no—
49C4×#124C2211yescharacteristic
50C4×#124C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52C4×C22⋊Q8C2211yescharacteristic
53C4×#123—21no—
54C4×#123—21no—
55C4×#121C2211yescharacteristic
56C4×#121C2211yescharacteristic
57#2298—21no—
58#2295C2211yescharacteristic
59#2293C2211yescharacteristic
60#2290—21no—
61#2285C2212yes—
62#2285C2212yes—
63#2283C2211yescharacteristic
64C42×Q8C2211yescharacteristic
65C42×D4—21no—
66C42×D4C2211yescharacteristic
67C4×#117—21no—
68C2×C43C2211yescharacteristic
69#2085C2214yes—
70#2085C2214yes—
71#2084C2212yes—
72#2084C2212yes—
73#2083C2212yes—
74#2083C2212yes—
75#2074C2214yes—
76#2073C2214yes—
77#2072C2212yes—
78#2072C2212yes—
79#2071C2212yes—
80#2071C2212yes—
81#1993C2212yes—
82#1993C2212yes—
83#1993C2212yes—
84#1993C2212yes—
85#1989C2214yes—
86#1989C2214yes—
87#1949C2214yes—
88#1949C2214yes—
89#1948C2212yes—
90#1948C2212yes—
91#1947C2212yes—
92#1947C2212yes—
93#1842C2212yes—
94#1831C2212yes—
95#1825C2214yes—
96#1825C2214yes—
97#1805C2214yes—
98#1804C2214yes—
99#1803C2212yes—
100#1803C2212yes—
101#1802C2212yes—
102#1802C2212yes—
103#1797C2212yes—
104#1797C2212yes—
105#1767C2211yescharacteristic
106#1767C2211yescharacteristic
107#1767C2212yes—
108#533—28no—
109#533—28no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8C2312yes—
115C2×C4⋊Q8C2312yes—
116#529—24no—
117#529D418yes—
118C2×#126—21no—
119C2×#125C2314yes—
120C2×#125C2311yescharacteristic
121C2×#124C2311yescharacteristic
122C2×#123—21no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8C2311yescharacteristic
126C2×#121C2311yescharacteristic
127C2×C4×Q8—22no—
128C2×C4×Q8—22no—
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×Q8C2311yescharacteristic
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×#117—21no—
139C2×#117—21no—
140C2×#117C2314yes—
141C22×C42—21no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#501—28no—
150#501—28no—
151#489—28no—
152#489—28no—
153#485—216no—
154#482—216no—
155#479—216no—
156#478—216no—
157#432—28no—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162C2×C4⋊C8C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×C22⋊C8C2314yes—
171C2×#97C2312yes—
172C2×#97C2312yes—
173#391—22no—
174#391—22no—
175#391—22no—
176#391—22no—
177#391C2311yescharacteristic
178#391C2311yescharacteristic
179#390C2311yescharacteristic
180#390C2311yescharacteristic
181#389—22no—
182#389—22no—
183#389—22no—
184#389—22no—
185#389—22no—
186#389—22no—
187#389—22no—
188#389—22no—
189#389C2311yescharacteristic
190#389C2311yescharacteristic
191#389C2311yescharacteristic
192#389C2311yescharacteristic
193#388—21no—
194#388—21no—
195#388—21no—
196#388—21no—
197#388—21no—
198#388—21no—
199#388—21no—
200#388—21no—
201#387—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205#387—21no—
206#387—21no—
207#387—21no—
208#387—21no—
209#386—21no—
210#386—21no—
211#385—21no—
212#385—21no—
213#384—21no—
214#384—21no—
215#384—21no—
216#384—21no—
217#384C2312yes—
218#384C2312yes—
219#384C2312yes—
220#384C2312yes—
221#383—21no—
222#382C2311yescharacteristic
223#382C2311yescharacteristic
224#382C2314yes—
225#382C2314yes—
226#381—21no—
227#380—22no—
228#380—22no—
229#380—22no—
230#380—22no—
231#380C2311yescharacteristic
232#380C2311yescharacteristic
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C2311yescharacteristic
248C4×C4⋊C4C2311yescharacteristic
249C4×C4⋊C4C2311yescharacteristic
250C4×C4⋊C4C2311yescharacteristic
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266#376—21no—
267#376—21no—
268C43—21no—
269C43D411yescharacteristic
270C43D411yescharacteristic
271C43D411yescharacteristic
272C43D411yescharacteristic
273C43C2311yescharacteristic
274C43C2311yescharacteristic
275C43C2311yescharacteristic
276C43C2311yescharacteristic
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#336C2312yes—
286#336C2312yes—
287#336C2314yes—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8C2411yescharacteristic
291C22×D4—21no—
292C22×D4C2411yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C22×C8C2414yes—
304C22×C8C2414yes—
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8—24no—
308C4⋊Q8—24no—
309C4⋊Q8—44no—
310C4⋊Q8—44no—
311C4⋊Q8—44no—
312C4⋊Q8—44no—
313#126—28no—
314#125—28no—
315#125—22no—
316#125—28no—
317#125C2×D414yes—
318#124—22no—
319#124C2×D414yes—
320#123—28no—
321C22⋊Q8—22no—
322C22⋊Q8—48no—
323C22⋊Q8—48no—
324C22⋊Q8C2×D414yes—
325#121—22no—
326#121C2×D414yes—
327C4×Q8—22no—
328C4×Q8—24no—
329C4×Q8—24no—
330C4×Q8—48no—
331C4×Q8—48no—
332C4×Q8C2×D414yes—
333C4×D4—28no—
334C4×D4—22no—
335C4×D4—24no—
336C4×D4—24no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4C2×D414yes—
340#117—28no—
341#117—28no—
342#117—28no—
343#117—44no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4C2414yes—
367C2×C4⋊C4C2414yes—
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2411yescharacteristic
372C2×C4⋊C4C2411yescharacteristic
373C2×C4⋊C4C2411yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—44no—
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D414yes—
428C2×C42#4114yes—
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435#107—28no—
436#107—28no—
437#106—28no—
438#106—28no—
439C4⋊C8—28no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—28no—
443#103—28no—
444#103—28no—
445#102—28no—
446#102—28no—
447C22⋊C8—28no—
448#97—24no—
449#97—24no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474C24—21no—
475C24C22×D411yescharacteristic
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8C22×D412yes—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C22×D412yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—24no—
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—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4#12114yes—
530C22×C4#12114yes—
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D412yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C2×#4112yes—
546C22×C4C2511yescharacteristic
547C2×C8—24no—
548C2×C8—24no—
549C2×C8—24no—
550C2×C8—24no—
551C2×C8—24no—
552C2×C8—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4C22×D412yes—
586C4⋊C4C22×D412yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—48no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C42—24no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—41no—
623C42—41no—
624C42—42no—
625C42—42no—
626C42—42no—
627C42—42no—
628C42—48no—
629C42—42no—
630C42—42no—
631C42—42no—
632C42—42no—
633C42#12114yes—
634C42#12114yes—
635C42C22×D412yes—
636C42C22×D412yes—
637C42C2×#4112yes—
638C42C2×#4112yes—
639C422−1+414yes—
640C422−1+414yes—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23C2×#12112yes—
655C23C23×D411yescharacteristic
656Q8—24no—
657Q8—42no—
658Q8—88no—
659Q8—88no—
660D4—24no—
661D4—48no—
662D4—42no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4C2×#12112yes—
728C2×C4C2×#12112yes—
729C2×C4C2×#12112yes—
730C2×C4C2×#12112yes—
731C2×C4C2×#12112yes—
732C2×C4#53612yes—
733C2×C4#53612yes—
734C2×C4#53612yes—
735C2×C4#53612yes—
736C2×C4#57512yes—
737C2×C4#57512yes—
738C2×C4#57512yes—
739C2×C4#57512yes—
740C2×C4C23×D411yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C2×2−1+412yes—
743C2×C4C2×2−1+412yes—
744C8—44no—
745C8—44no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22C22×#12111yescharacteristic
761C22C2×#53611yescharacteristic
762C22C2×#53611yescharacteristic
763C22C2×#57511yescharacteristic
764C22C2×#57511yescharacteristic
765C22C2×#57511yescharacteristic
766C22C2×#57511yescharacteristic
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4—84no—
787C4—84no—
788C4#324014yescomplemented
789C4#349912yes—
790C4#350912yes—
791C2—42no—
792C2—82no—
793C2#3531611yescharacteristic
794C2#6041511yescharacteristic
795C2#6041511yescharacteristic
796C2C2×#324011yescharacteristic
797C2#6085411yescharacteristic
798C2#6086211yescharacteristic
799C2#6086611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36645C2semidirect
4. #33200C2semidirect
5. #33199C2semidirect
6. #29871C2semidirect
7. #29870C2semidirect
8. #28727C2semidirect
9. #28726C2semidirect
10. #28726C2semidirect
11. #28695C2semidirect
12. #28694C2semidirect
13. #28694C2semidirect
14. #27652C2semidirect
16. #27649C2semidirect
18. #21842C2semidirect
19. #20810C2semidirect
788. C4#3240semidirect

Maximal subgroups

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

subgroupindex
C2×#32402
#366452
C4×#5292
#332002
#331992
#298712
#298702
#287272
#287262
#286952
#286942
#276522
#276502
#276492
#276462
#218422
#208102