Finite Group Databasebeta

← #6467743

Subgroups — #6467743

Order 512.

2016 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3181C212yesmaximal
2#36645C211yesmaximal, characteristic, complemented
3C4×#529C211yesmaximal, characteristic
4#28755C211yesmaximal, characteristic, complemented
5#28726C211yesmaximal, characteristic, complemented
6#28694C211yesmaximal, characteristic, complemented
7#28660C212yesmaximal, complemented
8#28620C212yesmaximal, complemented
9#28575C212yesmaximal, complemented
10#28571C212yesmaximal
11#28449C211yesmaximal, characteristic, complemented
12#24752C212yesmaximal, complemented
13#24751C212yesmaximal
14#23685C212yesmaximal, complemented
15#23683C212yesmaximal, complemented
16#21506C212yesmaximal, complemented
17#21504C212yesmaximal, complemented
18#21407C212yesmaximal, complemented
19C2×#1767C211yesmaximal, characteristic, complemented
20C2×#533C2212yes—
21C2×#529C2211yescharacteristic
22#3181—216no—
23C2×#501C2212yes—
24C2×#497C2212yes—
25C2×#491C2212yes—
26C2×#489C2212yes—
27C2×#467C2214yes—
28C2×#465C2214yes—
29C2×#462C2212yes—
30C2×#461C2212yes—
31C2×#441C2214yes—
32C2×#440C2214yes—
33C22×C4⋊C8C2212yes—
34C22×#97C2212yes—
35#2868C2211yescharacteristic
36#2868C2211yescharacteristic
37#2862C2212yes—
38#2859—21no—
39#2859—21no—
40#2857—21no—
41#2857—21no—
42#2857C2212yes—
43#2857C2212yes—
44C4×C4⋊Q8—21no—
45C4×C4⋊Q8—21no—
46C4×C4⋊Q8C2212yes—
47C4×C4⋊Q8C2212yes—
48C4×#125C2211yescharacteristic
49C4×#125C2211yescharacteristic
50C4×#126—21no—
51C4×#126—21no—
52C4×#124C2211yescharacteristic
53C4×#124C2211yescharacteristic
54C4×C22⋊Q8C2211yescharacteristic
55C4×C22⋊Q8C2211yescharacteristic
56C4×#123—21no—
57C4×#123—21no—
58C4×#121C2211yescharacteristic
59C4×#121C2211yescharacteristic
60#2298—21no—
61#2295C2211yescharacteristic
62#2293C2211yescharacteristic
63#2290—21no—
64#2285—21no—
65#2285—21no—
66#2283C2211yescharacteristic
67C42×Q8C2211yescharacteristic
68C42×D4—21no—
69C42×D4C2211yescharacteristic
70C4×#117—21no—
71C2×C43C2211yescharacteristic
72#2084C2212yes—
73#2083C2212yes—
74#2072C2212yes—
75#2071C2212yes—
76#2068C2214yes—
77#2066C2214yes—
78#2056C2214yes—
79#2055C2214yes—
80#2043C2212yes—
81#2043C2212yes—
82#2016C2212yes—
83#2013C2212yes—
84#1993C2212yes—
85#1993C2212yes—
86#1981C2212yes—
87#1981C2212yes—
88#1960C2212yes—
89#1960C2212yes—
90#1948C2212yes—
91#1947C2212yes—
92#1928C2214yes—
93#1927C2214yes—
94#1892C2214yes—
95#1892C2214yes—
96#1878C2214yes—
97#1877C2214yes—
98#1803C2212yes—
99#1802C2212yes—
100#1767C2212yes—
101#1767C2211yescharacteristic
102#1767C2211yescharacteristic
103#1767C2212yes—
104#1767C2212yes—
105#1763C2214yes—
106#1763C2214yes—
107C2×#336C2212yes—
108C22×Q16C2314yes—
109C22×SD16C2314yes—
110C23×C8C2314yes—
111#533—28no—
112#533—28no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8C2312yes—
116C2×C4⋊Q8C2312yes—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2312yes—
119#529—24no—
120#529D418yes—
121C2×#126—21no—
122C2×#125—22no—
123C2×#125C2311yescharacteristic
124C2×#124C2311yescharacteristic
125C2×#123—21no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8C2314yes—
128C2×C22⋊Q8C2311yescharacteristic
129C2×#121C2311yescharacteristic
130C2×C4×Q8—22no—
131C2×C4×Q8C2314yes—
132C2×C4×Q8C2311yescharacteristic
133C2×C4×Q8C2311yescharacteristic
134C2×C4×Q8C2311yescharacteristic
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C2311yescharacteristic
139C2×C4×D4C2311yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×#117—22no—
142C2×#117—21no—
143C2×#117—21no—
144C22×C42—21no—
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#501—28no—
153#497—28no—
154#491—28no—
155#489—28no—
156#467—216no—
157#465—216no—
158#462—28no—
159#461—28no—
160#441—216no—
161#440—216no—
162C2×#107C2314yes—
163C2×#106C2314yes—
164C2×C4⋊C8—28no—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#97—28no—
177C2×#97C2312yes—
178C2×#97C2312yes—
179C2×#97C2314yes—
180#391—22no—
181#391—22no—
182#391C2314yes—
183#391C2314yes—
184#391C2311yescharacteristic
185#391C2311yescharacteristic
186#390C2311yescharacteristic
187#390C2311yescharacteristic
188#389—22no—
189#389—22no—
190#389—22no—
191#389—22no—
192#389—22no—
193#389—22no—
194#389—22no—
195#389—22no—
196#389C2311yescharacteristic
197#389C2311yescharacteristic
198#389C2311yescharacteristic
199#389C2311yescharacteristic
200#388—21no—
201#388—21no—
202#388—21no—
203#388—21no—
204#388—21no—
205#388—21no—
206#388—21no—
207#388—21no—
208#387—21no—
209#387—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#387—21no—
214#387—21no—
215#387—21no—
216#386—21no—
217#386—21no—
218#385—21no—
219#385—21no—
220#384—21no—
221#384—21no—
222#384—21no—
223#384—21no—
224#384—21no—
225#384—21no—
226#384C2312yes—
227#384C2312yes—
228#383—21no—
229#382—22no—
230#382—22no—
231#382C2311yescharacteristic
232#382C2311yescharacteristic
233#381—21no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380C2311yescharacteristic
239#380C2311yescharacteristic
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—22no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4C2311yescharacteristic
255C4×C4⋊C4C2311yescharacteristic
256C4×C4⋊C4C2311yescharacteristic
257C4×C4⋊C4C2311yescharacteristic
258C4×C4⋊C4C2311yescharacteristic
259C4×C4⋊C4C2311yescharacteristic
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4—21no—
271C4×C22⋊C4—21no—
272C4×C22⋊C4—21no—
273#376—21no—
274#376—21no—
275C43—21no—
276C43D411yescharacteristic
277C43D411yescharacteristic
278C43D411yescharacteristic
279C43D411yescharacteristic
280C43C2311yescharacteristic
281C43C2311yescharacteristic
282C43C2311yescharacteristic
283C43C2311yescharacteristic
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#336C2312yes—
289#336C2312yes—
290#336C2314yes—
291C22×Q8—22no—
292C22×Q8C2414yes—
293C22×Q8C2411yescharacteristic
294C22×D4—21no—
295C22×D4C2411yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×Q16—28no—
307C2×Q16—28no—
308C2×Q16—44no—
309C2×SD16—28no—
310C2×SD16—28no—
311C2×SD16—44no—
312C22×C8—28no—
313C22×C8—28no—
314C22×C8—44no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—24no—
318C4⋊Q8—24no—
319C4⋊Q8—24no—
320C4⋊Q8—24no—
321C4⋊Q8—24no—
322C4⋊Q8—24no—
323C4⋊Q8—44no—
324C4⋊Q8—44no—
325C4⋊Q8—44no—
326#126—28no—
327#125—22no—
328#125—48no—
329#125C2×D414yes—
330#124—22no—
331#124C2×D414yes—
332#123—28no—
333C22⋊Q8—22no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—48no—
337C22⋊Q8C2×D414yes—
338#121—22no—
339#121C2×D414yes—
340C4×Q8—22no—
341C4×Q8—28no—
342C4×Q8—28no—
343C4×Q8—24no—
344C4×Q8—42no—
345C4×Q8—48no—
346C4×Q8C2×D414yes—
347C4×D4—28no—
348C4×D4—22no—
349C4×D4—24no—
350C4×D4—42no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4C2×D414yes—
354#117—28no—
355#117—44no—
356#117—48no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2411yescharacteristic
382C2×C4⋊C4C2414yes—
383C2×C4⋊C4C2411yescharacteristic
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—21no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—44no—
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×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D414yes—
441C2×C42#4114yes—
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—28no—
449#106—28no—
450C4⋊C8—28no—
451C4⋊C8—24no—
452C4⋊C8#4118yes—
453#103—28no—
454#103—28no—
455#103—28no—
456#103—28no—
457#103—28no—
458#103—44no—
459#103—44no—
460#102—28no—
461#97—28no—
462#97—24no—
463#97—24no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—24no—
485#95—24no—
486#95—24no—
487#95—24no—
488C24—21no—
489C24C22×D411yescharacteristic
490C2×Q8—21no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8C22×D412yes—
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C22×D412yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—24no—
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#12114yes—
545C22×C4#12114yes—
546C22×C4#13714yes—
547C22×C4#13714yes—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D412yes—
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C2×#4112yes—
563C22×C4C2511yescharacteristic
564Q16—416no—
565SD16—416no—
566C2×C8—24no—
567C2×C8—24no—
568C2×C8—24no—
569C2×C8—24no—
570C2×C8—24no—
571C2×C8—416no—
572C2×C8C2×#4118yes—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4C22×D412yes—
605C4⋊C4C22×D412yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—48no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C42—24no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C42—41no—
643C42—41no—
644C42—42no—
645C42—42no—
646C42—42no—
647C42—42no—
648C42—48no—
649C42—42no—
650C42—42no—
651C42—42no—
652C42—42no—
653C42#12114yes—
654C42#12114yes—
655C42C22×D412yes—
656C42C22×D412yes—
657C42C2×#4112yes—
658C42C2×#4112yes—
659C42C2×#4114yes—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C2×#12112yes—
672C23C2×#13712yes—
673C23C2×#13712yes—
674C23C23×D411yescharacteristic
675Q8—24no—
676Q8—42no—
677Q8—44no—
678Q8—44no—
679Q8—44no—
680Q8—44no—
681Q8—88no—
682D4—24no—
683D4—48no—
684D4—42no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—28no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—44no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—44no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4C2×#12112yes—
750C2×C4C2×#12112yes—
751C2×C4C2×#12112yes—
752C2×C4C2×#12112yes—
753C2×C4C2×#12112yes—
754C2×C4#53212yes—
755C2×C4#53212yes—
756C2×C4C2×#13712yes—
757C2×C4C2×#13712yes—
758C2×C4C2×#13712yes—
759C2×C4C2×#13712yes—
760C2×C4#57512yes—
761C2×C4#57512yes—
762C2×C4C23×D411yescharacteristic
763C2×C4C22×#4112yes—
764C2×C4C22×#4111yescharacteristic
765C2×C4#58512yes—
766C8—28no—
767C8—44no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22#303914yes—
782C22C22×#12111yescharacteristic
783C22C2×#53211yescharacteristic
784C22#344911yescharacteristic
785C22C22×#13711yescharacteristic
786C22C22×#13711yescharacteristic
787C22C2×#57511yescharacteristic
788C22C2×#57511yescharacteristic
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—41no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—84no—
809C4—84no—
810C4#318114yescomplemented
811C4D4×#4112yes—
812C4#348012yes—
813C2—24no—
814C2—82no—
815C2#3493711yescharacteristic
816C2C2×#303911yescharacteristic
817C2#6041511yescharacteristic
818C2C2×#318111yescharacteristic
819C2#6070111yescharacteristic
820C2#6096011yescharacteristic
821C2#6096311yescharacteristic
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. #28755C2semidirect
5. #28726C2semidirect
6. #28694C2semidirect
7. #28660C2semidirect
8. #28620C2semidirect
9. #28575C2semidirect
11. #28449C2semidirect
12. #24752C2semidirect
14. #23685C2semidirect
15. #23683C2semidirect
16. #21506C2semidirect
17. #21504C2semidirect
18. #21407C2semidirect
19. C2×#1767C2semidirect
810. C4#3181semidirect

Maximal subgroups

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

subgroupindex
C2×#31812
#366452
C4×#5292
#287552
#287262
#286942
#286602
#286202
#285752
#285712
#284492
#247522
#247512
#236852
#236832
#215062
#215042
#214072
C2×#17672