Finite Group Databasebeta

← #6345707

Subgroups — #6345707

Order 512.

1836 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60700C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic, complemented
3#60144C211yesmaximal, characteristic, complemented
4#18078C214yesmaximal, complemented
5#18076C214yesmaximal, complemented
6#18048C214yesmaximal, complemented
7#18046C214yesmaximal, complemented
8#17981C211yesmaximal, characteristic, complemented
9#17979C211yesmaximal, characteristic, complemented
10#17976C211yesmaximal, characteristic, complemented
11#17975C211yesmaximal, characteristic, complemented
12#17962C211yesmaximal, characteristic, complemented
13#17960C211yesmaximal, characteristic, complemented
14#17957C211yesmaximal, characteristic, complemented
15#17956C211yesmaximal, characteristic, complemented
16#17796C211yesmaximal, characteristic, complemented
17#17504C211yesmaximal, characteristic, complemented
18#17500C211yesmaximal, characteristic, complemented
19C2×#1455C211yesmaximal, characteristic, complemented
20C2×#568—21no—
21#3444C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3184C411yescharacteristic
24#3184C411yescharacteristic
25#3182C411yescharacteristic
26#3182C411yescharacteristic
27#3180C414yes—
28#3171C2214yes—
29#3169C2211yescharacteristic
30#3169C2211yescharacteristic
31#3167C2211yescharacteristic
32#3167C2211yescharacteristic
33#3165C411yescharacteristic
34#3151C411yescharacteristic
35#3141C411yescharacteristic
36#3138C411yescharacteristic
37#3055C414yes—
38#2971—21no—
39#2971C2212yes—
40#2970—21no—
41#2970C2212yes—
42#2969—21no—
43#2969—21no—
44#2969C2212yescomplemented
45#2969C2212yescomplemented
46#2960C2211yescharacteristic, complemented
47#2960C2211yescharacteristic, complemented
48C4×AGL(1,ℤ/8)C2214yes—
49#2935—21no—
50#2935—21no—
51#2935C2212yes—
52#2935C2212yes—
53D4×M16—21no—
54D4×M16—21no—
55D4×M16C2212yes—
56D4×M16C2212yes—
57#2932—21no—
58#2932—21no—
59#2931C2211yescharacteristic
60#2931C2211yescharacteristic
61#2931C2211yescharacteristic
62#2931C2211yescharacteristic
63#2931C2211yescharacteristic, complemented
64#2931C2211yescharacteristic, complemented
65#2930—21no—
66#2930—21no—
67#2923—21no—
68#2920C2211yescharacteristic
69C2×#423C2211yescharacteristic
70#2879—21no—
71#2875—21no—
72C2×C4×M16C2211yescharacteristic
73C2×C4×M16C2211yescharacteristic
74C2×C4×M16C2211yescharacteristic
75#1594C2214yescomplemented
76#1592C2214yescomplemented
77#1590C2214yescomplemented
78#1589C2214yescomplemented
79#1588C2214yescomplemented
80#1586C2214yescomplemented
81#1586C2214yescomplemented
82#1585C2214yescomplemented
83#1583C2214yescomplemented
84#1582C2214yescomplemented
85#1581C2214yescomplemented
86#1581C2214yescomplemented
87#1580C2214yescomplemented
88SD16⋊C8C2214yescomplemented
89C8×SD16C2214yescomplemented
90C8×D8C2214yescomplemented
91#1569C2214yes—
92#1567C2211yescharacteristic, complemented
93#1567C2211yescharacteristic, complemented
94#1566C2211yescharacteristic, complemented
95#1566C2211yescharacteristic, complemented
96#1565C2214yescomplemented
97#1493C2211yescharacteristic, complemented
98#1493C2211yescharacteristic, complemented
99#1492C2211yescharacteristic
100#1492C2211yescharacteristic
101#1492C2211yescharacteristic
102#1492C2211yescharacteristic
103#1492C2211yescharacteristic, complemented
104#1492C2211yescharacteristic, complemented
105#1490C2214yes—
106#1489C2214yes—
107#1484C2214yes—
108#1483C2214yescomplemented
109#1455C2212yes—
110#1455C2212yes—
111#1455C2212yescomplemented
112#1455C2212yescomplemented
113C2×#322C2211yescharacteristic, complemented
114C2×#322C2211yescharacteristic, complemented
115C2×#322C2211yescharacteristic, complemented
116C2×C82C2211yescharacteristic, complemented
117C22×#41—21no—
118C2×AGL(1,ℤ/8)C2×C414yes—
119#568—48no—
120C2×#131—22no—
121C2×#131—22no—
122C2×#131—21no—
123C2×#131—21no—
124C2×#131—21no—
125C2×#131—21no—
126C2×#131—21no—
127C2×#131—21no—
128C22×M16—21no—
129C22×M16—21no—
130C22×M16—22no—
131C22×M16—22no—
132C22×M16C2×C412yes—
133C22×M16D411yescharacteristic
134C22×M16D411yescharacteristic
135#533C2×C411yescharacteristic
136#533C2×C411yescharacteristic
137#533C2311yescharacteristic
138#532—21no—
139#532—21no—
140#532—21no—
141#532—21no—
142#532C2×C411yescharacteristic
143#532C2×C412yes—
144#532C2×C411yescharacteristic
145#532C2×C411yescharacteristic
146#532C2×C411yescharacteristic
147#532C2311yescharacteristic
148#532C2311yescharacteristic
149#532C2311yescharacteristic
150#532C2312yes—
151C2×C4⋊Q8C2×C411yescharacteristic
152C2×#127C2×C411yescharacteristic
153#529—21no—
154#529—21no—
155#529—21no—
156#529—21no—
157#529C2×C412yes—
158#529C2312yes—
159C2×#124—21no—
160#525—21no—
161#525—21no—
162#525C2×C412yes—
163C2×#121—21no—
164C2×#121C2×C412yes—
165C4×#41—21no—
166C4×#41—21no—
167C4×#41C2312yes—
168C2×C4×D4—21no—
169C2×C4×D4C2312yes—
170C22×C42C2311yescharacteristic
171#501C2×C414yes—
172#500C2×C411yescharacteristic
173#500C2×C411yescharacteristic
174#498C2×C411yescharacteristic
175#498C2×C411yescharacteristic
176#496C2×C414yes—
177#493C2×C411yescharacteristic
178#493C2×C411yescharacteristic
179#492C2×C411yescharacteristic
180#492C2×C411yescharacteristic
181#490C2×C414yes—
182#489C2×C414yes—
183#487C2×C411yescharacteristic
184#487C2×C411yescharacteristic
185#486C2×C411yescharacteristic
186#486C2×C411yescharacteristic
187#486C2×C411yescharacteristic
188#486C2×C411yescharacteristic
189#486C2×C411yescharacteristic
190#486C2×C411yescharacteristic
191#469C2×C414yes—
192#469C2×C414yes—
193#468C2×C414yes—
194#468C2×C414yes—
195#466C2×C414yes—
196#466C2×C414yes—
197#465C2×C414yes—
198#465C2×C414yes—
199#446—21no—
200#446—21no—
201#446C2312yes—
202#446C2312yes—
203C8×Q8—21no—
204C8×Q8—21no—
205C8×Q8C2312yes—
206C8×Q8C2312yes—
207#442C2×C414yes—
208#442C2×C414yes—
209#440C2×C414yes—
210#440C2×C414yes—
211C4×SD16C2314yes—
212C4×SD16C2314yes—
213C4×D8C2314yes—
214C4×D8C2314yes—
215#436—22no—
216#436—22no—
217#436—22no—
218#436—22no—
219#436—21no—
220#436—21no—
221#436—21no—
222#436—21no—
223#436—21no—
224#436—21no—
225#436C2312yes—
226#436C2312yes—
227#436C2312yes—
228#436C2312yes—
229#436C2312yes—
230#436C2312yes—
231#435—22no—
232#435—22no—
233#435—22no—
234#435—22no—
235#435—22no—
236#435—22no—
237#435—22no—
238#435—22no—
239#435—22no—
240#435—22no—
241#435—22no—
242#435—22no—
243C8×D4—21no—
244C8×D4—21no—
245C8×D4—21no—
246C8×D4—21no—
247C8×D4—21no—
248C8×D4—21no—
249C8×D4C2312yes—
250C8×D4C2312yes—
251C8×D4C2312yes—
252C8×D4C2312yes—
253C8×D4C2312yes—
254C8×D4C2312yes—
255#433—22no—
256#433—22no—
257#432—21no—
258#432—22no—
259#432—22no—
260#432C2312yes—
261#431—21no—
262#431C2312yes—
263#428C2×C414yes—
264#424—21no—
265#424—21no—
266#423—21no—
267#423—21no—
268#423C2311yescharacteristic
269#423C2311yescharacteristic
270#423C2311yescharacteristic
271#423C2311yescharacteristic
272#423C2312yes—
273C2×C4⋊C8—21no—
274C2×C4⋊C8C2312yes—
275#418C2×C414yes—
276#417C2×C414yes—
277#408—22no—
278#408—22no—
279#408—21no—
280#408—21no—
281#408—21no—
282#408—21no—
283#408—21no—
284#408—21no—
285#407—21no—
286#407—22no—
287#407—22no—
288#405—21no—
289#405—21no—
290#405—22no—
291#405—22no—
292C4×M16—21no—
293C4×M16—21no—
294C4×M16—21no—
295C4×M16—22no—
296C4×M16C2×C411yescharacteristic
297C4×M16C2×C411yescharacteristic
298C4×M16C2×C411yescharacteristic
299C4×M16C2×C411yescharacteristic
300C4×M16D411yescharacteristic
301C4×M16D411yescharacteristic
302C4×M16D411yescharacteristic
303C4×M16D411yescharacteristic
304C4×M16C2312yes—
305C4×M16C2312yes—
306C4×M16C2312yes—
307C4×M16C2312yes—
308C4×M16C2311yescharacteristic
309C4×M16C2311yescharacteristic
310C4×M16C2311yescharacteristic
311C4×M16C2311yescharacteristic
312C2×#97—21no—
313C2×#97—22no—
314C2×#97C2×C412yes—
315C2×#97D411yescharacteristic
316C2×#97D411yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#335C2314yes—
324#335C2314yes—
325#334C2314yes—
326#334C2314yes—
327Q8⋊C8C2314yes—
328Q8⋊C8C2314yes—
329D4⋊C8C2314yes—
330D4⋊C8C2314yes—
331D4⋊C8C2314yes—
332D4⋊C8C2314yes—
333D4⋊C8C2314yes—
334D4⋊C8C2314yes—
335#322C2312yes—
336#322C2312yes—
337#322C2312yes—
338#322C2312yes—
339#322C2312yes—
340#322C2312yes—
341C82C2312yes—
342C82C2312yes—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—22no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—22no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—44no—
352C2×#41—44no—
353C2×#41C22×C412yes—
354C22×Q8—21no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4C22×C412yes—
359C23×C4—22no—
360C23×C4C22×C411yescharacteristic
361C23×C4C2×D411yescharacteristic
362C23×C4#4111yescharacteristic
363AGL(1,ℤ/8)—48no—
364C2×SD16C22×C414yes—
365C2×SD16C22×C414yes—
366C2×D8C22×C414yes—
367C2×D8C22×C414yes—
368#131—44no—
369#131—44no—
370#131—44no—
371#131—48no—
372#131—48no—
373#131—44no—
374#131—44no—
375#131—44no—
376C2×M16—22no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—24no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—42no—
391C2×M16—44no—
392C2×M16—44no—
393C2×M16—48no—
394C2×M16—48no—
395C2×M16—44no—
396C2×M16C22×C412yes—
397C2×M16C22×C412yes—
398C2×M16C22×C412yes—
399C2×M16C22×C412yes—
400C2×M16C2×D411yescharacteristic
401C2×M16C2×D411yescharacteristic
402C2×M16C2×D411yescharacteristic
403C2×M16C2×D411yescharacteristic
404C2×M16C2×D411yescharacteristic
405C2×M16C2×D411yescharacteristic
406C2×M16C2×D411yescharacteristic
407C2×M16C2×D411yescharacteristic
408C22×C8—21no—
409C22×C8—22no—
410C22×C8—21no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—22no—
417C22×C8C22×C412yes—
418C22×C8C22×C412yes—
419C22×C8C2×D411yescharacteristic
420C22×C8C2×D411yescharacteristic
421C22×C8C2×D411yescharacteristic
422C22×C8C2×D411yescharacteristic
423C4⋊Q8—21no—
424C4⋊Q8—21no—
425C4⋊Q8C22×C411yescharacteristic
426C4⋊Q8C22×C411yescharacteristic
427C4⋊Q8C22×C411yescharacteristic
428C4⋊Q8C22×C412yes—
429C4⋊Q8C22×C411yescharacteristic
430C4⋊Q8C22×C411yescharacteristic
431#127—21no—
432#127—21no—
433#127C22×C411yescharacteristic
434#127C22×C411yescharacteristic
435#127C22×C412yes—
436#127C22×C411yescharacteristic
437#126—22no—
438#126—22no—
439#125—21no—
440#125—21no—
441#125C22×C412yes—
442#124—22no—
443#124—21no—
444#124—21no—
445#124—21no—
446#124—21no—
447#124—21no—
448#124—22no—
449#124—21no—
450#124C22×C412yes—
451#123—22no—
452#123—22no—
453#123—22no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8C22×C412yes—
459C22⋊Q8C22×C412yes—
460#121—21no—
461#121—21no—
462#121—22no—
463#121—22no—
464#121—22no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121C22×C412yes—
473#121C22×C412yes—
474#121C22×C412yes—
475#121C22×C412yes—
476#121C22×C412yes—
477#121C22×C412yes—
478#120—22no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8C22×C412yes—
484C4×Q8C2412yes—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—21no—
502C4×D4—22no—
503C4×D4C22×C412yes—
504C4×D4C22×C412yes—
505C4×D4C22×C412yes—
506C4×D4C2412yes—
507C4×D4C2412yes—
508C4×D4C2412yes—
509#117—21no—
510#117—21no—
511#117—22no—
512#117—22no—
513#117—22no—
514#117C22×C412yes—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C22×C412yes—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C42—22no—
520C2×C42C22×C411yescharacteristic
521C2×C42C22×C411yescharacteristic
522C2×C42C22×C411yescharacteristic
523C2×C42C2×D411yescharacteristic
524C2×C42C2×D411yescharacteristic
525C2×C42C2×D411yescharacteristic
526C2×C42#4111yescharacteristic
527C2×C42#4111yescharacteristic
528C2×C42#4111yescharacteristic
529C2×C42C2411yescharacteristic
530C2×C42C2411yescharacteristic
531C2×C42C2411yescharacteristic
532#107C22×C414yes—
533#107C22×C414yes—
534#106C22×C414yes—
535#106C22×C414yes—
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—22no—
539C4⋊C8—22no—
540C4⋊C8—21no—
541C4⋊C8—21no—
542C4⋊C8—22no—
543C4⋊C8—22no—
544C4⋊C8—21no—
545C4⋊C8—21no—
546C4⋊C8C2412yes—
547C4⋊C8C2412yes—
548C4⋊C8C2412yes—
549C4⋊C8C2412yes—
550#103C22×C414yes—
551#103C22×C414yes—
552#102C22×C414yes—
553#102C22×C414yes—
554#102C22×C414yes—
555#102C22×C414yes—
556#102C22×C414yes—
557#102C22×C414yes—
558C22⋊C8—22no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563C22⋊C8—22no—
564C22⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—22no—
570C22⋊C8—22no—
571C22⋊C8—22no—
572#97—22no—
573#97—22no—
574#97—22no—
575#97—22no—
576#97—22no—
577#97C22×C412yes—
578#97C22×C412yes—
579#97C22×C412yes—
580#97C22×C412yes—
581#97C2×D411yescharacteristic
582#97C2×D411yescharacteristic
583#97C2×D411yescharacteristic
584#97C2×D411yescharacteristic
585#97C2×D411yescharacteristic
586#97C2×D411yescharacteristic
587#97C2×D411yescharacteristic
588#97C2×D411yescharacteristic
589C4×C8—22no—
590C4×C8—22no—
591C4×C8—22no—
592C4×C8—21no—
593C4×C8—21no—
594C4×C8C22×C411yescharacteristic
595C4×C8C22×C411yescharacteristic
596C4×C8C22×C411yescharacteristic
597C4×C8C22×C411yescharacteristic
598C4×C8C2×D411yescharacteristic
599C4×C8C2×D411yescharacteristic
600C4×C8C2×D411yescharacteristic
601C4×C8C2×D411yescharacteristic
602C4×C8C2412yes—
603C4×C8C2412yes—
604C4×C8C2412yes—
605C4×C8C2412yes—
606C4×C8C2411yescharacteristic
607C4×C8C2411yescharacteristic
608C4×C8C2411yescharacteristic
609C4×C8C2411yescharacteristic
610C24—22no—
611C24C4×D411yescharacteristic
612#41—44no—
613#41—48no—
614#41—44no—
615#41—44no—
616#41—44no—
617#41—44no—
618#41—42no—
619#41—42no—
620#41—42no—
621#41—42no—
622#41—42no—
623#41—42no—
624#41—82no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—44no—
631C2×Q8C23×C412yes—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—48no—
651C2×D4—82no—
652C2×D4C23×C412yes—
653C2×D4C23×C412yes—
654C2×D4C23×C412yes—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4C4×D411yescharacteristic
670C22×C4C4×D411yescharacteristic
671C22×C4C4×D411yescharacteristic
672C22×C4C4×D411yescharacteristic
673C22×C4C4×D411yescharacteristic
674C22×C4C4×D411yescharacteristic
675C22×C4C4×D411yescharacteristic
676C22×C4C4×D411yescharacteristic
677C22×C4C4×D411yescharacteristic
678C22×C4C23×C411yescharacteristic
679C22×C4C23×C411yescharacteristic
680C22×C4C23×C411yescharacteristic
681C22×C4C22×D411yescharacteristic
682C22×C4C22×D411yescharacteristic
683C22×C4C22×D411yescharacteristic
684C22×C4C2×#4111yescharacteristic
685C22×C4C2×#4111yescharacteristic
686C22×C4C2×#4111yescharacteristic
687SD16—28no—
688SD16—44no—
689D8—28no—
690D8—44no—
691M16—24no—
692M16—24no—
693M16—22no—
694M16—22no—
695M16—22no—
696M16—22no—
697M16—42no—
698M16—42no—
699M16—41no—
700M16—41no—
701M16—41no—
702M16—41no—
703M16—44no—
704M16—44no—
705M16—44no—
706M16—44no—
707M16—44no—
708M16—44no—
709M16—42no—
710M16—42no—
711M16—42no—
712M16—42no—
713M16—44no—
714M16—44no—
715M16—44no—
716C2×C8—24no—
717C2×C8—22no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—24no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—42no—
728C2×C8—44no—
729C2×C8—44no—
730C2×C8—44no—
731C2×C8—42no—
732C2×C8—44no—
733C2×C8—44no—
734C2×C8—44no—
735C2×C8—44no—
736C2×C8AGL(1,ℤ/8)14yescomplemented
737C2×C8C23×C412yes—
738C2×C8C23×C412yes—
739C2×C8C23×C412yes—
740C2×C8C23×C412yes—
741C2×C8C22×D411yescharacteristic
742C2×C8C22×D411yescharacteristic
743C2×C8C22×D411yescharacteristic
744C2×C8C22×D411yescharacteristic
745C2×C8C22×D411yescharacteristic
746C2×C8C22×D411yescharacteristic
747C2×C8C22×D411yescharacteristic
748C2×C8C22×D411yescharacteristic
749C4⋊C4—22no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—22no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—22no—
763C4⋊C4C23×C412yes—
764C4⋊C4C23×C412yes—
765C4⋊C4C23×C412yes—
766C4⋊C4C23×C412yes—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—22no—
783C22⋊C4—22no—
784C42—22no—
785C42—22no—
786C42—22no—
787C42C4×D411yescharacteristic
788C42C4×D411yescharacteristic
789C42C4×D411yescharacteristic
790C42C4×D411yescharacteristic
791C42C4×D411yescharacteristic
792C42C4×D411yescharacteristic
793C42C23×C411yescharacteristic
794C42C23×C411yescharacteristic
795C42C23×C411yescharacteristic
796C42C22×D411yescharacteristic
797C42C22×D411yescharacteristic
798C42C22×D411yescharacteristic
799C42C2×#4111yescharacteristic
800C42C2×#4111yescharacteristic
801C42C2×#4111yescharacteristic
802C42C2511yescharacteristic
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—41no—
808C23—41no—
809C23—44no—
810C23—82no—
811C23—82no—
812C23C2×C4×D411yescharacteristic
813C23C2×C4×D411yescharacteristic
814C23C2×C4×D411yescharacteristic
815Q8—24no—
816Q8—44no—
817Q8—42no—
818Q8—42no—
819Q8—42no—
820Q8—42no—
821D4—24no—
822D4—24no—
823D4—24no—
824D4—44no—
825D4—44no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—44no—
830D4—42no—
831D4—42no—
832D4—42no—
833D4—42no—
834D4—42no—
835D4—42no—
836D4—82no—
837D4—82no—
838D4—82no—
839D4—82no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—82no—
874C2×C4—82no—
875C2×C4C2×C4×D411yescharacteristic
876C2×C4C2×C4×D411yescharacteristic
877C2×C4C2×C4×D411yescharacteristic
878C2×C4C2×C4×D411yescharacteristic
879C2×C4C2×C4×D411yescharacteristic
880C2×C4C2×C4×D411yescharacteristic
881C2×C4C2×C4×D411yescharacteristic
882C2×C4C2×C4×D411yescharacteristic
883C2×C4C2×C4×D411yescharacteristic
884C2×C4C2×AGL(1,ℤ/8)12yes—
885C2×C4#57512yes—
886C2×C4C24×C411yescharacteristic
887C2×C4C23×D411yescharacteristic
888C2×C4C22×#4111yescharacteristic
889C8—24no—
890C8—22no—
891C8—22no—
892C8—22no—
893C8—21no—
894C8—21no—
895C8—21no—
896C8—21no—
897C8—21no—
898C8—21no—
899C8—42no—
900C8—42no—
901C8—42no—
902C8—42no—
903C8—42no—
904C8#56814yescomplemented
905C8C2×AGL(1,ℤ/8)12yes—
906C8C2×AGL(1,ℤ/8)12yes—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—82no—
925C22—164no—
926C22C4×AGL(1,ℤ/8)12yes—
927C22C22×C4×D411yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4C4×AGL(1,ℤ/8)12yes—
942C4#295612yes—
943C4C2×#56812yes—
944C4C22×AGL(1,ℤ/8)11yescharacteristic
945C4C2×#57511yescharacteristic
946C2—22no—
947C2—41no—
948C2—41no—
949C2—82no—
950C2—82no—
951C2—82no—
952C2#6014411yescharacteristic
953C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
954C2C2×#295611yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60700C2
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. #60144C2semidirect
4. #18078C2semidirect
5. #18076C2semidirect
6. #18048C2semidirect
7. #18046C2semidirect
8. #17981C2semidirect
9. #17979C2semidirect
10. #17976C2semidirect
11. #17975C2semidirect
12. #17962C2semidirect
13. #17960C2semidirect
14. #17957C2semidirect
15. #17956C2semidirect
16. #17796C2semidirect
17. #17504C2semidirect
18. #17500C2semidirect
19. C2×#1455C2semidirect
44. #2969C22semidirect
45. #2969C22semidirect
46. #2960C22semidirect
47. #2960C22semidirect
63. #2931C22semidirect
64. #2931C22semidirect
75. #1594C22semidirect
76. #1592C22semidirect
77. #1590C22semidirect
78. #1589C22semidirect
79. #1588C22semidirect
80. #1586C22semidirect
81. #1586C22semidirect
82. #1585C22semidirect
83. #1583C22semidirect
84. #1582C22semidirect
85. #1581C22semidirect
86. #1581C22semidirect
87. #1580C22semidirect
88. SD16⋊C8C22semidirect
89. C8×SD16C22semidirect
90. C8×D8C22semidirect
92. #1567C22semidirect
93. #1567C22semidirect
94. #1566C22semidirect
95. #1566C22semidirect
96. #1565C22semidirect
97. #1493C22semidirect
98. #1493C22semidirect
103. #1492C22semidirect
104. #1492C22semidirect
108. #1483C22semidirect
111. #1455C22semidirect
112. #1455C22semidirect
113. C2×#322C22semidirect
114. C2×#322C22semidirect
115. C2×#322C22semidirect
116. C2×C82C22semidirect
736. C2×C8AGL(1,ℤ/8)semidirect
904. C8#568semidirect

Maximal subgroups

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

subgroupindex
#607002
#602082
#601442
#180782
#180762
#180482
#180462
#179812
#179792
#179762
#179752
#179622
#179602
#179572
#179562
#177962
#175042
#175002
C2×#14552