Finite Group Databasebeta

← #6345380

Subgroups — #6345380

Order 512.

1679 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60561C211yesmaximal, characteristic
2#60283C211yesmaximal, characteristic, complemented
3#60232C211yesmaximal, characteristic, complemented
4#18048C214yesmaximal, complemented
5#18046C214yesmaximal, complemented
6#18030C214yesmaximal, complemented
7#18026C214yesmaximal, complemented
8#17948C214yesmaximal, complemented
9#17920C214yesmaximal, complemented
10#17821C211yesmaximal, characteristic, complemented
11#17495C211yesmaximal, characteristic, complemented
12#17450C211yesmaximal, characteristic, complemented
13#17339C211yesmaximal, characteristic, complemented
14C2×#532C2211yescharacteristic
15C2×C4×#41C2211yescharacteristic
16#3115C412yes—
17#3115C412yes—
18#3112C412yes—
19#3109C412yes—
20#3106C2212yes—
21#3106C2212yes—
22#3103C2212yes—
23#3100C2212yes—
24#3094C412yes—
25#3079C411yescharacteristic
26#3079C411yescharacteristic
27#3038C411yescharacteristic
28#3038C411yescharacteristic
29#3006C412yes—
30#2989—22no—
31#2989C2212yescomplemented
32#2988C2212yescomplemented
33#2984C2212yescomplemented
34#2981—22no—
35#2981C2214yescomplemented
36#2980—21no—
37#2980—21no—
38#2979C2214yes—
39#2974—22no—
40#2974C2212yescomplemented
41#2971C2212yes—
42#2970—22no—
43#2970C2212yes—
44C4×AGL(1,ℤ/8)C2212yes—
45C4×AGL(1,ℤ/8)C2212yes—
46D4×M16—22no—
47D4×M16C2214yescomplemented
48#2920—21no—
49#2920C2211yescharacteristic
50#2920C2211yescharacteristic
51#2920C2211yescharacteristic
52#2920C2211yescharacteristic
53C2×#432—21no—
54C2×#432C2211yescharacteristic
55#2879—22no—
56#1594C2214yescomplemented
57#1592C2214yescomplemented
58#1590C2214yescomplemented
59#1589C2214yescomplemented
60#1588C2214yescomplemented
61#1586C2214yescomplemented
62#1586C2214yescomplemented
63#1585C2214yescomplemented
64#1583C2214yescomplemented
65#1582C2214yescomplemented
66#1581C2214yescomplemented
67#1581C2214yescomplemented
68#1580C2214yescomplemented
69SD16⋊C8C2214yescomplemented
70C8×SD16C2214yescomplemented
71C8×D8C2214yescomplemented
72#1573C2214yescomplemented
73#1572C2214yescomplemented
74#1569C2214yescomplemented
75#1496C2214yes—
76#1490C2214yescomplemented
77#1489C2212yes—
78#1489C2212yes—
79#1488C2212yescomplemented
80#1488C2212yescomplemented
81#1480C2214yescomplemented
82#1479C2212yescomplemented
83#1478C2212yescomplemented
84#1455C2214yescomplemented
85#1454C2214yescomplemented
86#1454C2214yescomplemented
87C22×#41—21no—
88C22×#41C2×C411yescharacteristic
89C2×AGL(1,ℤ/8)C2×C412yes—
90C2×AGL(1,ℤ/8)C2×C412yes—
91C22×M16—24no—
92#532—21no—
93#532—21no—
94#532—21no—
95#532—21no—
96#532C2×C412yes—
97#532C2×C412yes—
98#532C2312yes—
99#532C2312yes—
100C2×C4⋊Q8C2×C411yescharacteristic
101C2×#127C2×C411yescharacteristic
102C2×#124—21no—
103C2×#121—21no—
104C2×#121C2×C412yes—
105C4×#41—21no—
106C4×#41—21no—
107C4×#41—21no—
108C4×#41—21no—
109C4×#41C2×C411yescharacteristic
110C4×#41C2×C411yescharacteristic
111C4×#41C2×C411yescharacteristic
112C4×#41C2×C411yescharacteristic
113C4×#41C2311yescharacteristic
114C4×#41C2311yescharacteristic
115C4×#41C2311yescharacteristic
116C4×#41C2311yescharacteristic
117C2×C4×Q8C2×C411yescharacteristic
118C2×C4×Q8C2311yescharacteristic
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—21no—
122C2×C4×D4C2×C411yescharacteristic
123C2×C4×D4C2311yescharacteristic
124C2×C4×D4C2312yes—
125C2×#117—21no—
126C2×#117C2×C411yescharacteristic
127C22×C42—21no—
128C22×C42C2311yescharacteristic
129#482C2×C414yes—
130#482C2×C414yes—
131#481C2×C414yes—
132#480C2×C414yes—
133#477C2×C412yes—
134#477C2×C412yes—
135#476C2×C412yes—
136#476C2×C412yes—
137#475C2×C412yes—
138#475C2×C412yes—
139#474C2×C412yes—
140#474C2×C412yes—
141#460C2×C412yes—
142#460C2×C412yes—
143#460C2×C412yes—
144#460C2×C412yes—
145#459C2×C412yes—
146#459C2×C412yes—
147#459C2×C412yes—
148#459C2×C412yes—
149#449C2×C414yes—
150#449C2×C414yes—
151#448C2×C414yes—
152#447C2×C414yes—
153#446—24no—
154#446C2314yes—
155C8×Q8C2314yes—
156#442C2×C414yes—
157#442C2×C414yes—
158#440C2×C414yes—
159#440C2×C414yes—
160C4×SD16C2314yes—
161C4×SD16C2314yes—
162C4×D8C2314yes—
163C4×D8C2314yes—
164#436—24no—
165#436—24no—
166#436C2314yes—
167#436C2314yes—
168#436C2314yes—
169#435—24no—
170#435—24no—
171#435—24no—
172#435—24no—
173#435—24no—
174#435—24no—
175#435—24no—
176C8×D4—24no—
177C8×D4—24no—
178C8×D4C2314yes—
179C8×D4C2314yes—
180C8×D4C2314yes—
181#432—21no—
182#432—21no—
183#432—21no—
184#432—21no—
185#432—21no—
186#432—22no—
187#432—22no—
188#432—22no—
189#432—22no—
190#432C2×C412yes—
191#432C2×C412yes—
192#432D411yescharacteristic
193#432D411yescharacteristic
194#432D412yes—
195#432C2312yes—
196#432C2312yes—
197#432C2312yes—
198#431—21no—
199#431—22no—
200#431—22no—
201#431C2312yes—
202#431C2312yes—
203#431C2312yes—
204#431C2312yes—
205#431C2312yes—
206#431C2312yes—
207#431C2312yes—
208#428C2×C412yes—
209#428C2×C412yes—
210#423—21no—
211#423—22no—
212#423C2×C411yescharacteristic
213#423C2×C411yescharacteristic
214#423D412yes—
215#423C2312yes—
216C2×C4⋊C8—22no—
217C2×C4⋊C8C2312yes—
218#418C2×C412yes—
219#418C2×C412yes—
220#417C2×C412yes—
221#417C2×C412yes—
222#408—24no—
223#408—24no—
224#408—24no—
225#408—24no—
226#407—21no—
227#407—21no—
228#407—24no—
229#407—22no—
230#407C2×C412yes—
231#407D412yes—
232C2×C22⋊C8—21no—
233C2×C22⋊C8—22no—
234C4×M16—21no—
235C4×M16—22no—
236C4×M16C2312yes—
237C4×M16C2312yes—
238C4×M16C2312yes—
239C2×#97—21no—
240C2×#97—22no—
241#335C2314yes—
242#335C2314yes—
243#334C2314yes—
244#334C2314yes—
245Q8⋊C8C2314yes—
246Q8⋊C8C2314yes—
247D4⋊C8C2314yes—
248D4⋊C8C2314yes—
249D4⋊C8C2314yes—
250D4⋊C8C2314yes—
251D4⋊C8C2314yes—
252D4⋊C8C2314yes—
253#322C2314yes—
254#322C2314yes—
255#322C2314yes—
256C82C2314yes—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—22no—
263C2×#41—42no—
264C2×#41—42no—
265C2×#41—84no—
266C2×#41C22×C411yescharacteristic
267C2×#41C22×C411yescharacteristic
268C2×#41C22×C411yescharacteristic
269C2×#41C22×C411yescharacteristic
270C22×Q8—21no—
271C22×Q8C22×C411yescharacteristic
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4C22×C411yescharacteristic
277C22×D4C22×C412yes—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4C22×C411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4#4111yescharacteristic
285AGL(1,ℤ/8)—44no—
286AGL(1,ℤ/8)—44no—
287C2×SD16C22×C414yes—
288C2×SD16C22×C414yes—
289C2×D8C22×C414yes—
290C2×D8C22×C414yes—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16—88no—
297C2×M16C22×C412yes—
298C2×M16C22×C412yes—
299C2×M16C2×D414yes—
300C22×C8—22no—
301C22×C8—24no—
302C22×C8—24no—
303C22×C8—24no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C22×C412yes—
307C4⋊Q8C22×C412yes—
308#127—21no—
309#127—21no—
310#127C22×C412yes—
311#127C22×C412yes—
312#124—22no—
313#124—22no—
314#124—22no—
315#124—22no—
316#121—22no—
317#121—22no—
318#121—22no—
319#121—22no—
320#121—22no—
321#121—22no—
322#121C22×C414yes—
323#121C22×C414yes—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×Q8C22×C411yescharacteristic
329C4×Q8C22×C411yescharacteristic
330C4×Q8C22×C411yescharacteristic
331C4×Q8C22×C411yescharacteristic
332C4×Q8C22×C411yescharacteristic
333C4×Q8C22×C411yescharacteristic
334C4×Q8C2411yescharacteristic
335C4×Q8C2411yescharacteristic
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—21no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4—22no—
362C4×D4C22×C411yescharacteristic
363C4×D4C22×C411yescharacteristic
364C4×D4C22×C411yescharacteristic
365C4×D4C22×C411yescharacteristic
366C4×D4C22×C411yescharacteristic
367C4×D4C22×C411yescharacteristic
368C4×D4C22×C414yes—
369C4×D4C2411yescharacteristic
370C4×D4C2411yescharacteristic
371C4×D4C2414yes—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C22×C411yescharacteristic
383#117C22×C411yescharacteristic
384#117C22×C411yescharacteristic
385#117C22×C411yescharacteristic
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4C22×C411yescharacteristic
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C412yes—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42#4111yescharacteristic
415C2×C42#4111yescharacteristic
416C2×C42#4111yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420#107C22×C414yes—
421#107C22×C414yes—
422#106C22×C414yes—
423#106C22×C414yes—
424C4⋊C8—24no—
425C4⋊C8—24no—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8C22×C412yes—
431C4⋊C8C22×C412yes—
432C4⋊C8C22×C412yes—
433C4⋊C8C22×C412yes—
434C4⋊C8C2×D412yes—
435C4⋊C8C2×D412yes—
436C4⋊C8C2×D414yes—
437C4⋊C8C2414yes—
438C4⋊C8C2414yes—
439#103C22×C414yes—
440#103C22×C414yes—
441#102C22×C414yes—
442#102C22×C414yes—
443#102C22×C414yes—
444#102C22×C414yes—
445#102C22×C414yes—
446#102C22×C414yes—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8C22×C414yes—
460C22⋊C8C22×C414yes—
461C22⋊C8C2×D412yes—
462C22⋊C8C2×D412yes—
463C22⋊C8C2×D414yes—
464#97—24no—
465#97—22no—
466#97—22no—
467#97—22no—
468#97—22no—
469#97C22×C414yes—
470#97C2×D412yes—
471#97C2×D412yes—
472C4×C8—24no—
473C4×C8—22no—
474C4×C8C2414yes—
475C4×C8C2414yes—
476C4×C8C2414yes—
477C24—21no—
478C24—22no—
479C24C4×D411yescharacteristic
480#41—22no—
481#41—22no—
482#41—22no—
483#41—22no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—44no—
489#41—44no—
490#41—84no—
491#41—82no—
492#41—82no—
493#41—84no—
494#41—84no—
495C2×Q8—21no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—41no—
500C2×Q8—82no—
501C2×Q8C23×C411yescharacteristic
502C2×Q8C23×C411yescharacteristic
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—44no—
520C2×D4—82no—
521C2×D4—82no—
522C2×D4—84no—
523C2×D4C23×C411yescharacteristic
524C2×D4C23×C414yes—
525C2×D4C23×C411yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—48no—
548C22×C4—44no—
549C22×C4—82no—
550C22×C4—81no—
551C22×C4—82no—
552C22×C4C4×D411yescharacteristic
553C22×C4C4×D411yescharacteristic
554C22×C4C4×D411yescharacteristic
555C22×C4C4×D411yescharacteristic
556C22×C4C4×D411yescharacteristic
557C22×C4C4×D411yescharacteristic
558C22×C4C4×D411yescharacteristic
559C22×C4C4×D411yescharacteristic
560C22×C4C4×D411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C23×C411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C2×#4111yescharacteristic
568C22×C4C2×#4111yescharacteristic
569C22×C4C2×#4111yescharacteristic
570SD16—28no—
571SD16—44no—
572D8—28no—
573D8—44no—
574M16—44no—
575M16—42no—
576M16—42no—
577M16—44no—
578M16—84no—
579M16—84no—
580M16—84no—
581M16—82no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—84no—
586C2×C8—84no—
587C2×C8—84no—
588C2×C8—82no—
589C2×C8C23×C414yes—
590C2×C8C23×C414yes—
591C2×C8C22×D414yes—
592C2×C8C22×D414yes—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4C23×C411yescharacteristic
607C4⋊C4C23×C411yescharacteristic
608C4⋊C4C23×C411yescharacteristic
609C4⋊C4C23×C411yescharacteristic
610C4⋊C4C23×C414yes—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—24no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42C4×D411yescharacteristic
640C42C4×D411yescharacteristic
641C42C4×D411yescharacteristic
642C42C4×D411yescharacteristic
643C42C4×D411yescharacteristic
644C42C4×D411yescharacteristic
645C42C23×C411yescharacteristic
646C42C23×C411yescharacteristic
647C42C23×C411yescharacteristic
648C42C22×D411yescharacteristic
649C42C22×D411yescharacteristic
650C42C22×D411yescharacteristic
651C42C2×#4111yescharacteristic
652C42C2×#4111yescharacteristic
653C42C2×#4111yescharacteristic
654C42C2511yescharacteristic
655C23—21no—
656C23—21no—
657C23—24no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—81no—
665C23—82no—
666C23—82no—
667C23C2×C4×D411yescharacteristic
668C23C2×C4×D411yescharacteristic
669C23C2×C4×D411yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—21no—
673Q8—42no—
674Q8—82no—
675Q8—82no—
676Q8#56812yes—
677D4—24no—
678D4—21no—
679D4—24no—
680D4—21no—
681D4—24no—
682D4—21no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—42no—
687D4—42no—
688D4—82no—
689D4—82no—
690D4—82no—
691D4—82no—
692D4—84no—
693D4—84no—
694D4#56812yes—
695C2×C4—24no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—24no—
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—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—48no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4C2×C4×D411yescharacteristic
743C2×C4C2×C4×D411yescharacteristic
744C2×C4C2×C4×D411yescharacteristic
745C2×C4C2×C4×D411yescharacteristic
746C2×C4C2×C4×D411yescharacteristic
747C2×C4C2×C4×D411yescharacteristic
748C2×C4C2×C4×D411yescharacteristic
749C2×C4C2×C4×D411yescharacteristic
750C2×C4C2×C4×D411yescharacteristic
751C2×C4C24×C411yescharacteristic
752C2×C4C23×D411yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C8—24no—
755C8—24no—
756C8—24no—
757C8—24no—
758C8—44no—
759C8—44no—
760C8—44no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—41no—
772C22—41no—
773C22—44no—
774C22—41no—
775C22—41no—
776C22—44no—
777C22—41no—
778C22—44no—
779C22—82no—
780C22—84no—
781C22—164no—
782C22C22×C4×D411yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—22no—
792C4—21no—
793C4—21no—
794C4—44no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4C2×#56811yescharacteristic
801C4C2×#56811yescharacteristic
802C4#358512yes—
803C2—41no—
804C2—41no—
805C2—41no—
806C2—42no—
807C2—81no—
808C2—84no—
809C2#6014111yescharacteristic
810C2#6016811yescharacteristic
811C2#6018211yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60561C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ #2920 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60283C2semidirect
3. #60232C2semidirect
4. #18048C2semidirect
5. #18046C2semidirect
6. #18030C2semidirect
7. #18026C2semidirect
8. #17948C2semidirect
9. #17920C2semidirect
10. #17821C2semidirect
11. #17495C2semidirect
12. #17450C2semidirect
13. #17339C2semidirect
31. #2989C22semidirect
32. #2988C22semidirect
33. #2984C22semidirect
35. #2981C22semidirect
40. #2974C22semidirect
47. D4×M16C22semidirect
56. #1594C22semidirect
57. #1592C22semidirect
58. #1590C22semidirect
59. #1589C22semidirect
60. #1588C22semidirect
61. #1586C22semidirect
62. #1586C22semidirect
63. #1585C22semidirect
64. #1583C22semidirect
65. #1582C22semidirect
66. #1581C22semidirect
67. #1581C22semidirect
68. #1580C22semidirect
69. SD16⋊C8C22semidirect
70. C8×SD16C22semidirect
71. C8×D8C22semidirect
72. #1573C22semidirect
73. #1572C22semidirect
74. #1569C22semidirect
76. #1490C22semidirect
79. #1488C22semidirect
80. #1488C22semidirect
81. #1480C22semidirect
82. #1479C22semidirect
83. #1478C22semidirect
84. #1455C22semidirect
85. #1454C22semidirect
86. #1454C22semidirect

Maximal subgroups

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

subgroupindex
#605612
#602832
#602322
#180482
#180462
#180302
#180262
#179482
#179202
#178212
#174952
#174502
#173392