Finite Group Databasebeta

← #6345293

Subgroups — #6345293

Order 512.

1899 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60558C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic, complemented
3C2×D4×M16C211yesmaximal, characteristic, complemented
4#18048C214yesmaximal, complemented
5#18046C214yesmaximal, complemented
6#18008C214yesmaximal, complemented
7#18006C214yesmaximal, complemented
8#17935C211yesmaximal, characteristic, complemented
9#17933C211yesmaximal, characteristic, complemented
10#17930C211yesmaximal, characteristic, complemented
11#17928C211yesmaximal, characteristic, complemented
12#17907C211yesmaximal, characteristic, complemented
13#17905C211yesmaximal, characteristic, complemented
14#17902C211yesmaximal, characteristic, complemented
15#17900C211yesmaximal, characteristic, complemented
16#17820C211yesmaximal, characteristic, complemented
17#17498C211yesmaximal, characteristic, complemented
18#17448C211yesmaximal, characteristic, complemented
19#17334C211yesmaximal, characteristic, complemented
20C23×M16—21no—
21#3444C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23#3114C412yes—
24#3114C412yes—
25#3110C412yes—
26#3109C412yes—
27#3105C2214yes—
28#3101C2211yescharacteristic
29#3101C2211yescharacteristic
30#3100C2211yescharacteristic
31#3100C2211yescharacteristic
32#3092C412yes—
33#3077C412yes—
34#3036C412yes—
35#3003C412yes—
36#2971—21no—
37#2971C2212yescomplemented
38#2970—21no—
39#2970C2212yescomplemented
40#2969—21no—
41#2969—21no—
42#2969C2212yescomplemented
43#2969C2212yescomplemented
44#2960C2211yescharacteristic, complemented
45#2960C2211yescharacteristic, complemented
46C4×AGL(1,ℤ/8)C2214yes—
47D4×M16—21no—
48D4×M16—21no—
49D4×M16—21no—
50D4×M16—21no—
51D4×M16C2212yes—
52D4×M16C2212yes—
53D4×M16C2212yes—
54D4×M16C2212yes—
55#2931C2211yescharacteristic, complemented
56#2931C2211yescharacteristic, complemented
57#2930—21no—
58#2930—21no—
59C2×#436C2211yescharacteristic
60C2×#436C2211yescharacteristic
61C2×#435—21no—
62C2×#435—21no—
63C2×C8×D4C2211yescharacteristic
64C2×C8×D4C2211yescharacteristic
65#2923—21no—
66#2920C2211yescharacteristic
67#2920C2211yescharacteristic
68#2920C2211yescharacteristic
69C2×#423C2211yescharacteristic
70C2×#407—21no—
71#2875—21no—
72C2×C4×M16C2211yescharacteristic
73#1594C2214yescomplemented
74#1592C2214yescomplemented
75#1590C2214yescomplemented
76#1589C2214yescomplemented
77#1588C2214yescomplemented
78#1586C2214yescomplemented
79#1586C2214yescomplemented
80#1585C2214yescomplemented
81#1583C2214yescomplemented
82#1582C2214yescomplemented
83#1581C2214yescomplemented
84#1581C2214yescomplemented
85#1580C2214yescomplemented
86SD16⋊C8C2214yescomplemented
87C8×SD16C2214yescomplemented
88C8×D8C2214yescomplemented
89#1574C2214yescomplemented
90#1571C2211yescharacteristic, complemented
91#1571C2211yescharacteristic, complemented
92#1570C2211yescharacteristic, complemented
93#1570C2211yescharacteristic, complemented
94#1569C2214yescomplemented
95#1495C2214yescomplemented
96#1490C2214yes—
97#1489C2214yescomplemented
98#1486C2211yescharacteristic
99#1486C2211yescharacteristic
100#1486C2211yescharacteristic
101#1486C2211yescharacteristic
102#1481C2211yescharacteristic, complemented
103#1481C2211yescharacteristic, complemented
104#1480C2211yescharacteristic, complemented
105#1480C2211yescharacteristic, complemented
106#1478C2214yes—
107#1455C2212yescomplemented
108#1455C2212yescomplemented
109#1453C2212yescomplemented
110#1453C2212yescomplemented
111#1452C2211yescharacteristic, complemented
112#1452C2211yescharacteristic, complemented
113#1450C2211yescharacteristic, complemented
114#1450C2211yescharacteristic, complemented
115C23×D4C2×C411yescharacteristic
116C24×C4—21no—
117C2×AGL(1,ℤ/8)C2×C414yes—
118C2×#131—21no—
119C2×#131—21no—
120C22×M16—21no—
121C22×M16—22no—
122C22×M16—22no—
123C22×M16—22no—
124C22×M16—22no—
125C22×M16—21no—
126C22×M16—21no—
127C22×M16—48no—
128C22×M16D411yescharacteristic
129C22×M16D411yescharacteristic
130C23×C8—21no—
131C23×C8—21no—
132#533C2×C411yescharacteristic
133#533C2×C411yescharacteristic
134#533C2311yescharacteristic
135#532C2×C411yescharacteristic
136#532C2×C411yescharacteristic
137#532C2311yescharacteristic
138#529—21no—
139#529—21no—
140#529—21no—
141#529—21no—
142#529C2×C412yes—
143#529C2312yes—
144#525—21no—
145#525—21no—
146#525C2×C412yes—
147C4×#41—21no—
148C4×#41—21no—
149C4×#41C2312yes—
150C2×C4×D4—21no—
151C2×C4×D4—21no—
152C2×C4×D4—21no—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4—21no—
156C2×C4×D4C2×C412yes—
157C2×C4×D4C2×C412yes—
158C2×C4×D4C2×C411yescharacteristic
159C2×C4×D4C2×C411yescharacteristic
160C2×C4×D4C2311yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×C4×D4C2312yes—
163C2×C4×D4C2312yes—
164C22×C4⋊C4C2×C411yescharacteristic
165C22×C22⋊C4—21no—
166C22×C42C2311yescharacteristic
167#484C2×C414yes—
168#483C2×C412yes—
169#483C2×C412yes—
170#481C2×C414yes—
171#480C2×C412yes—
172#480C2×C412yes—
173#478C2×C414yes—
174#478C2×C414yes—
175#476C2×C412yes—
176#476C2×C412yes—
177#474C2×C412yes—
178#474C2×C412yes—
179#463C2×C414yes—
180#463C2×C414yes—
181#461C2×C412yes—
182#461C2×C412yes—
183#459C2×C412yes—
184#459C2×C412yes—
185#450C2×C412yes—
186#450C2×C412yes—
187#450C2×C414yes—
188#447C2×C412yes—
189#447C2×C412yes—
190#447C2×C414yes—
191#446—21no—
192#446—21no—
193#446C2312yescomplemented
194#446C2312yescomplemented
195C8×Q8—21no—
196C8×Q8—21no—
197C8×Q8C2312yescomplemented
198C8×Q8C2312yescomplemented
199#442C2×C414yes—
200#442C2×C414yes—
201#440C2×C414yes—
202#440C2×C414yes—
203C4×SD16C2314yes—
204C4×SD16C2314yes—
205C4×D8C2314yes—
206C4×D8C2314yes—
207#436—22no—
208#436—22no—
209#436—22no—
210#436—22no—
211#436—21no—
212#436—21no—
213#436—21no—
214#436—21no—
215#436—21no—
216#436—21no—
217#436C2312yes—
218#436C2312yes—
219#436C2312yes—
220#436C2312yes—
221#436C2312yescomplemented
222#436C2312yescomplemented
223#435—22no—
224#435—22no—
225#435—22no—
226#435—22no—
227#435—22no—
228#435—22no—
229#435—22no—
230#435—22no—
231#435—22no—
232#435—22no—
233#435—22no—
234#435—22no—
235C8×D4—21no—
236C8×D4—21no—
237C8×D4—21no—
238C8×D4—21no—
239C8×D4—21no—
240C8×D4—21no—
241C8×D4C2312yes—
242C8×D4C2312yes—
243C8×D4C2312yes—
244C8×D4C2312yes—
245C8×D4C2312yescomplemented
246C8×D4C2312yescomplemented
247#433—22no—
248#433—22no—
249#432—21no—
250#432—21no—
251#432—21no—
252#432—22no—
253#432—22no—
254#432C2×C412yes—
255#432C2×C412yes—
256#432C2312yes—
257#431—21no—
258#431C2312yes—
259#431C2311yescharacteristic
260#431C2311yescharacteristic
261#431C2312yes—
262#431C2311yescharacteristic
263#431C2311yescharacteristic
264#431C2312yes—
265#428C2×C414yes—
266#424—21no—
267#424—21no—
268#423—21no—
269#423—21no—
270#423—21no—
271#423C2×C412yes—
272#423C2312yes—
273#423C2311yescharacteristic
274#423C2311yescharacteristic
275#423C2312yes—
276C2×C4⋊C8—21no—
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#418C2×C414yes—
280#417C2×C414yes—
281#408—21no—
282#408—21no—
283#407—21no—
284#407—21no—
285#407—22no—
286#407—22no—
287#407—22no—
288#407—22no—
289#407C2×C412yes—
290C2×C22⋊C8—21no—
291C2×C22⋊C8—21no—
292C2×C22⋊C8—21no—
293C2×C22⋊C8—21no—
294#405—21no—
295#405—21no—
296#405—22no—
297#405—22no—
298C4×M16—21no—
299C4×M16—22no—
300C4×M16D411yescharacteristic
301C4×M16D411yescharacteristic
302C4×M16D411yescharacteristic
303C4×M16D411yescharacteristic
304C4×M16C2312yes—
305C4×M16C2312yes—
306C4×M16C2311yescharacteristic
307C4×M16C2311yescharacteristic
308C4×M16C2311yescharacteristic
309C4×M16C2311yescharacteristic
310C2×#97—22no—
311C2×#97D411yescharacteristic
312C2×#97D411yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#335C2314yescomplemented
316#335C2314yescomplemented
317#334C2314yescomplemented
318#334C2314yescomplemented
319Q8⋊C8C2314yescomplemented
320Q8⋊C8C2314yescomplemented
321D4⋊C8C2314yes—
322D4⋊C8C2314yes—
323D4⋊C8C2314yes—
324D4⋊C8C2314yes—
325D4⋊C8C2314yescomplemented
326D4⋊C8C2314yescomplemented
327#322C2312yescomplemented
328#322C2312yescomplemented
329#322C2312yescomplemented
330#322C2312yescomplemented
331#322C2312yescomplemented
332#322C2312yescomplemented
333C82C2312yescomplemented
334C82C2312yescomplemented
335C25—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41C22×C412yes—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—44no—
343C22×D4C22×C411yescharacteristic
344C22×D4C22×C412yes—
345C22×D4C22×C412yes—
346C22×D4C22×C411yescharacteristic
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—44no—
357C23×C4—44no—
358C23×C4C22×C411yescharacteristic
359C23×C4C2×D411yescharacteristic
360C23×C4#4111yescharacteristic
361AGL(1,ℤ/8)—48no—
362C2×SD16C22×C414yes—
363C2×SD16C22×C414yes—
364C2×D8C22×C414yes—
365C2×D8C22×C414yes—
366#131—44no—
367#131—44no—
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—22no—
373C2×M16—24no—
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C2×M16—22no—
379C2×M16—22no—
380C2×M16—42no—
381C2×M16—44no—
382C2×M16—48no—
383C2×M16—48no—
384C2×M16—48no—
385C2×M16—48no—
386C2×M16—44no—
387C2×M16—44no—
388C2×M16C22×C414yes—
389C2×M16C2×D411yescharacteristic
390C2×M16C2×D411yescharacteristic
391C2×M16C2×D411yescharacteristic
392C2×M16C2×D411yescharacteristic
393C2×M16C2×D411yescharacteristic
394C2×M16C2×D411yescharacteristic
395C2×M16C2×D411yescharacteristic
396C2×M16C2×D411yescharacteristic
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—22no—
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—44no—
406C22×C8—44no—
407C22×C8C2×D411yescharacteristic
408C22×C8C2×D411yescharacteristic
409C22×C8C2×D411yescharacteristic
410C22×C8C2×D411yescharacteristic
411C4⋊Q8C22×C411yescharacteristic
412C4⋊Q8C22×C411yescharacteristic
413C4⋊Q8C22×C411yescharacteristic
414#127C22×C411yescharacteristic
415#126—22no—
416#126—22no—
417#125—21no—
418#125—21no—
419#125C22×C412yes—
420#124—21no—
421#124—21no—
422#124C22×C412yes—
423#123—22no—
424#123—22no—
425#123—22no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8C22×C412yes—
431C22⋊Q8C22×C412yes—
432#121—21no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121C22×C412yes—
437#121C22×C412yes—
438#120—22no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8C22×C412yes—
444C4×Q8C2412yes—
445C4×D4—22no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—22no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4—21no—
460C4×D4—21no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—22no—
464C4×D4—22no—
465C4×D4—21no—
466C4×D4—21no—
467C4×D4—22no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—22no—
471C4×D4C22×C412yes—
472C4×D4C22×C412yes—
473C4×D4C22×C412yes—
474C4×D4C22×C412yes—
475C4×D4C22×C412yes—
476C4×D4C22×C412yes—
477C4×D4C22×C412yes—
478C4×D4C2412yes—
479C4×D4C2412yes—
480C4×D4C2412yes—
481#117—21no—
482#117—21no—
483#117—22no—
484#117—22no—
485#117—22no—
486#117C22×C412yes—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C22×C412yes—
491C2×C4⋊C4C22×C411yescharacteristic
492C2×C4⋊C4C22×C411yescharacteristic
493C2×C4⋊C4C22×C412yes—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C42—22no—
503C2×C42C22×C411yescharacteristic
504C2×C42C22×C411yescharacteristic
505C2×C42C22×C411yescharacteristic
506C2×C42C2×D411yescharacteristic
507C2×C42C2×D411yescharacteristic
508C2×C42C2×D411yescharacteristic
509C2×C42#4111yescharacteristic
510C2×C42#4111yescharacteristic
511C2×C42#4111yescharacteristic
512C2×C42C2411yescharacteristic
513C2×C42C2411yescharacteristic
514C2×C42C2411yescharacteristic
515#107C22×C414yes—
516#107C22×C414yes—
517#106C22×C414yes—
518#106C22×C414yes—
519C4⋊C8—22no—
520C4⋊C8—22no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523C4⋊C8—22no—
524C4⋊C8—22no—
525C4⋊C8—21no—
526C4⋊C8—21no—
527C4⋊C8—21no—
528C4⋊C8—21no—
529C4⋊C8—21no—
530C4⋊C8—21no—
531C4⋊C8—22no—
532C4⋊C8C22×C412yes—
533C4⋊C8C22×C412yes—
534C4⋊C8C22×C414yes—
535C4⋊C8C2412yes—
536C4⋊C8C2412yes—
537C4⋊C8C2412yes—
538C4⋊C8C2412yes—
539#103C22×C414yes—
540#103C22×C414yes—
541#102C22×C414yes—
542#102C22×C414yes—
543#102C22×C414yes—
544#102C22×C414yes—
545#102C22×C414yes—
546#102C22×C414yes—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—22no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8C22×C412yes—
565C22⋊C8C22×C412yes—
566C22⋊C8C22×C414yes—
567#97—22no—
568#97—22no—
569#97—22no—
570#97—22no—
571#97C22×C414yes—
572#97C2×D411yescharacteristic
573#97C2×D411yescharacteristic
574#97C2×D411yescharacteristic
575#97C2×D411yescharacteristic
576#97C2×D411yescharacteristic
577#97C2×D411yescharacteristic
578#97C2×D411yescharacteristic
579#97C2×D411yescharacteristic
580C4×C8—22no—
581C4×C8—22no—
582C4×C8—22no—
583C4×C8C2×D411yescharacteristic
584C4×C8C2×D411yescharacteristic
585C4×C8C2×D411yescharacteristic
586C4×C8C2×D411yescharacteristic
587C4×C8C2412yes—
588C4×C8C2412yes—
589C4×C8C2412yes—
590C4×C8C2412yes—
591C4×C8C2411yescharacteristic
592C4×C8C2411yescharacteristic
593C4×C8C2411yescharacteristic
594C4×C8C2411yescharacteristic
595C24—21no—
596C24—21no—
597C24—22no—
598C24—22no—
599C24—44no—
600C24—44no—
601C24—82no—
602C24C4×D411yescharacteristic
603#41—44no—
604#41—42no—
605#41—42no—
606#41—82no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8C23×C412yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4C23×C412yes—
629C2×D4C23×C412yes—
630C2×D4C23×C412yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—42no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—81no—
663C22×C4C4×D411yescharacteristic
664C22×C4C4×D411yescharacteristic
665C22×C4C4×D411yescharacteristic
666C22×C4C4×D411yescharacteristic
667C22×C4C4×D411yescharacteristic
668C22×C4C4×D411yescharacteristic
669C22×C4C4×D411yescharacteristic
670C22×C4C4×D411yescharacteristic
671C22×C4C4×D411yescharacteristic
672C22×C4C23×C411yescharacteristic
673C22×C4C23×C411yescharacteristic
674C22×C4C23×C411yescharacteristic
675C22×C4C22×D411yescharacteristic
676C22×C4C22×D411yescharacteristic
677C22×C4C22×D411yescharacteristic
678C22×C4C2×#4111yescharacteristic
679C22×C4C2×#4111yescharacteristic
680C22×C4C2×#4111yescharacteristic
681SD16—28no—
682SD16—44no—
683D8—28no—
684D8—44no—
685M16—22no—
686M16—22no—
687M16—22no—
688M16—22no—
689M16—41no—
690M16—41no—
691M16—41no—
692M16—41no—
693M16—44no—
694M16—44no—
695M16—44no—
696M16—44no—
697M16—44no—
698M16—44no—
699M16—42no—
700M16—42no—
701M16—44no—
702M16—44no—
703M16—44no—
704M16—82no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—44no—
715C2×C8—44no—
716C2×C8—44no—
717C2×C8—42no—
718C2×C8—42no—
719C2×C8—44no—
720C2×C8—44no—
721C2×C8—44no—
722C2×C8AGL(1,ℤ/8)14yescomplemented
723C2×C8C23×C414yes—
724C2×C8C23×C414yes—
725C2×C8C22×D411yescharacteristic
726C2×C8C22×D411yescharacteristic
727C2×C8C22×D411yescharacteristic
728C2×C8C22×D411yescharacteristic
729C2×C8C22×D411yescharacteristic
730C2×C8C22×D411yescharacteristic
731C2×C8C22×D411yescharacteristic
732C2×C8C22×D411yescharacteristic
733C4⋊C4—22no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—22no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—22no—
745C4⋊C4—22no—
746C4⋊C4—22no—
747C4⋊C4C23×C412yes—
748C4⋊C4C23×C412yes—
749C4⋊C4C23×C412yes—
750C4⋊C4C23×C412yes—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—22no—
758C22⋊C4—22no—
759C22⋊C4—22no—
760C22⋊C4—22no—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C42—22no—
769C42—22no—
770C42—22no—
771C42C4×D411yescharacteristic
772C42C4×D411yescharacteristic
773C42C4×D411yescharacteristic
774C42C4×D411yescharacteristic
775C42C4×D411yescharacteristic
776C42C4×D411yescharacteristic
777C42C23×C411yescharacteristic
778C42C23×C411yescharacteristic
779C42C23×C411yescharacteristic
780C42C22×D411yescharacteristic
781C42C22×D411yescharacteristic
782C42C22×D411yescharacteristic
783C42C2×#4111yescharacteristic
784C42C2×#4111yescharacteristic
785C42C2×#4111yescharacteristic
786C42C2511yescharacteristic
787C23—24no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—41no—
793C23—41no—
794C23—44no—
795C23—44no—
796C23—42no—
797C23—44no—
798C23—44no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—82no—
804C23—82no—
805C23—816no—
806C23C2×C4×D411yescharacteristic
807C23C2×C4×D411yescharacteristic
808C23C2×C4×D411yescharacteristic
809Q8—24no—
810Q8—42no—
811Q8—42no—
812D4—24no—
813D4—22no—
814D4—24no—
815D4—22no—
816D4—22no—
817D4—44no—
818D4—44no—
819D4—42no—
820D4—42no—
821D4—44no—
822D4—42no—
823D4—82no—
824D4—82no—
825D4#56814yes—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—82no—
867C2×C4—82no—
868C2×C4C2×C4×D411yescharacteristic
869C2×C4C2×C4×D411yescharacteristic
870C2×C4C2×C4×D411yescharacteristic
871C2×C4C2×C4×D411yescharacteristic
872C2×C4C2×C4×D411yescharacteristic
873C2×C4C2×C4×D411yescharacteristic
874C2×C4C2×C4×D411yescharacteristic
875C2×C4C2×C4×D411yescharacteristic
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C2×AGL(1,ℤ/8)12yes—
878C2×C4#57512yes—
879C2×C4C24×C411yescharacteristic
880C2×C4C23×D411yescharacteristic
881C2×C4C22×#4111yescharacteristic
882C8—24no—
883C8—24no—
884C8—21no—
885C8—21no—
886C8—21no—
887C8—21no—
888C8—21no—
889C8—21no—
890C8—42no—
891C8—42no—
892C8—42no—
893C8—42no—
894C8—42no—
895C8—42no—
896C8C2×AGL(1,ℤ/8)12yes—
897C8C2×AGL(1,ℤ/8)12yes—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—24no—
905C22—21no—
906C22—21no—
907C22—48no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—84no—
918C22—88no—
919C22—88no—
920C22C4×AGL(1,ℤ/8)12yes—
921C22C22×C4×D411yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—21no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4C4×AGL(1,ℤ/8)12yes—
937C4C2×#56812yes—
938C4C22×AGL(1,ℤ/8)11yescharacteristic
939C4C2×#57511yescharacteristic
940C2—22no—
941C2—41no—
942C2—41no—
943C2—44no—
944C2—82no—
945C2—82no—
946C2#6014111yescharacteristic
947C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
948C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60558C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×M16 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60208C2semidirect
3. C2×D4×M16C2semidirect
4. #18048C2semidirect
5. #18046C2semidirect
6. #18008C2semidirect
7. #18006C2semidirect
8. #17935C2semidirect
9. #17933C2semidirect
10. #17930C2semidirect
11. #17928C2semidirect
12. #17907C2semidirect
13. #17905C2semidirect
14. #17902C2semidirect
15. #17900C2semidirect
16. #17820C2semidirect
17. #17498C2semidirect
18. #17448C2semidirect
19. #17334C2semidirect
37. #2971C22semidirect
39. #2970C22semidirect
42. #2969C22semidirect
43. #2969C22semidirect
44. #2960C22semidirect
45. #2960C22semidirect
55. #2931C22semidirect
56. #2931C22semidirect
73. #1594C22semidirect
74. #1592C22semidirect
75. #1590C22semidirect
76. #1589C22semidirect
77. #1588C22semidirect
78. #1586C22semidirect
79. #1586C22semidirect
80. #1585C22semidirect
81. #1583C22semidirect
82. #1582C22semidirect
83. #1581C22semidirect
84. #1581C22semidirect
85. #1580C22semidirect
86. SD16⋊C8C22semidirect
87. C8×SD16C22semidirect
88. C8×D8C22semidirect
89. #1574C22semidirect
90. #1571C22semidirect
91. #1571C22semidirect
92. #1570C22semidirect
93. #1570C22semidirect
94. #1569C22semidirect
95. #1495C22semidirect
97. #1489C22semidirect
102. #1481C22semidirect
103. #1481C22semidirect
104. #1480C22semidirect
105. #1480C22semidirect
107. #1455C22semidirect
108. #1455C22semidirect
109. #1453C22semidirect
110. #1453C22semidirect
111. #1452C22semidirect
112. #1452C22semidirect
113. #1450C22semidirect
114. #1450C22semidirect
193. #446C23semidirect
194. #446C23semidirect
197. C8×Q8C23semidirect
198. C8×Q8C23semidirect
221. #436C23semidirect
222. #436C23semidirect
245. C8×D4C23semidirect
246. C8×D4C23semidirect
315. #335C23semidirect
316. #335C23semidirect
317. #334C23semidirect
318. #334C23semidirect
319. Q8⋊C8C23semidirect
320. Q8⋊C8C23semidirect
325. D4⋊C8C23semidirect
326. D4⋊C8C23semidirect
327. #322C23semidirect
328. #322C23semidirect
329. #322C23semidirect
330. #322C23semidirect
331. #322C23semidirect
332. #322C23semidirect
333. C82C23semidirect
334. C82C23semidirect
722. C2×C8AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#605582
#602082
C2×D4×M162
#180482
#180462
#180082
#180062
#179352
#179332
#179302
#179282
#179072
#179052
#179022
#179002
#178202
#174982
#174482
#173342