Finite Group Databasebeta

← #6345615

Subgroups — #6345615

Order 512.

1784 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60946C211yesmaximal, characteristic
2#60208C211yesmaximal, characteristic, complemented
3#60144C211yesmaximal, characteristic, complemented
4#18011C214yesmaximal, complemented
5#18008C214yesmaximal, complemented
6#18007C214yesmaximal, complemented
7#18006C214yesmaximal, 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#17817C211yesmaximal, characteristic, complemented
17#17481C211yesmaximal, characteristic, complemented
18#17478C211yesmaximal, characteristic, complemented
19C2×#1453C211yesmaximal, characteristic, complemented
20C2×#568—21no—
21#3444C2211yescharacteristic
22C2×#532C2211yescharacteristic
23#3247C414yes—
24#3230C411yescharacteristic
25#3228C411yescharacteristic
26#3228C411yescharacteristic
27#3227C411yescharacteristic
28#3208C411yescharacteristic
29#3207C411yescharacteristic
30#3207C411yescharacteristic
31#3205C411yescharacteristic
32#3188C414yes—
33#3169C2211yescharacteristic
34#3169C2211yescharacteristic
35#3167C2211yescharacteristic
36#3167C2211yescharacteristic
37#3106C2214yes—
38#3105C2214yes—
39#2971—21no—
40#2971C2212yescomplemented
41#2970—21no—
42#2970C2212yescomplemented
43#2969—21no—
44#2969—21no—
45#2969C2212yes—
46#2969C2212yes—
47#2960C2211yescharacteristic, complemented
48#2960C2211yescharacteristic, complemented
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×#431C2211yescharacteristic
70C2×#431C2211yescharacteristic
71C2×#423C2211yescharacteristic
72#2879—21no—
73#2875—21no—
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#1574C2214yes—
92#1573C2214yescomplemented
93#1567C2211yescharacteristic, complemented
94#1567C2211yescharacteristic, complemented
95#1566C2211yescharacteristic, complemented
96#1566C2211yescharacteristic, complemented
97#1496C2214yes—
98#1495C2214yes—
99#1493C2211yescharacteristic, complemented
100#1493C2211yescharacteristic, complemented
101#1492C2211yescharacteristic
102#1492C2211yescharacteristic
103#1492C2211yescharacteristic
104#1492C2211yescharacteristic
105#1492C2211yescharacteristic, complemented
106#1492C2211yescharacteristic, complemented
107#1478C2214yes—
108#1477C2214yescomplemented
109#1453C2212yes—
110#1453C2212yes—
111#1453C2212yescomplemented
112#1453C2212yescomplemented
113C2×#322C2211yescharacteristic, complemented
114C2×#322C2211yescharacteristic, complemented
115C2×#322C2211yescharacteristic, complemented
116C2×C82C2211yescharacteristic, complemented
117C22×#41—21no—
118#568—48no—
119C2×#131—22no—
120C2×#131—22no—
121C2×#131—21no—
122C2×#131—21no—
123C2×#131—21no—
124C2×#131—21no—
125C2×#131—21no—
126C2×#131—21no—
127C22×M16—21no—
128C22×M16—22no—
129C22×M16—22no—
130C22×M16D411yescharacteristic
131C22×M16D411yescharacteristic
132#533C2×C411yescharacteristic
133#533C2×C411yescharacteristic
134#533C2311yescharacteristic
135#532—21no—
136#532—21no—
137#532—21no—
138#532—21no—
139#532C2×C411yescharacteristic
140#532C2×C411yescharacteristic
141#532C2×C411yescharacteristic
142#532C2×C412yes—
143#532C2×C411yescharacteristic
144#532C2312yes—
145#532C2311yescharacteristic
146#532C2311yescharacteristic
147#532C2311yescharacteristic
148C2×C4⋊Q8C2×C411yescharacteristic
149C2×#127C2×C411yescharacteristic
150#529—21no—
151#529—21no—
152#529—21no—
153#529—21no—
154#529C2×C412yes—
155#529C2312yes—
156C2×#124—21no—
157#525—21no—
158#525—21no—
159#525C2×C412yes—
160C2×#121—21no—
161C2×#121C2×C412yes—
162C4×#41—21no—
163C4×#41—21no—
164C4×#41C2312yes—
165C2×C4×D4—21no—
166C2×C4×D4C2312yes—
167C22×C42C2311yescharacteristic
168#500C2×C411yescharacteristic
169#500C2×C411yescharacteristic
170#498C2×C411yescharacteristic
171#498C2×C411yescharacteristic
172#493C2×C411yescharacteristic
173#493C2×C411yescharacteristic
174#492C2×C411yescharacteristic
175#492C2×C411yescharacteristic
176#487C2×C411yescharacteristic
177#487C2×C411yescharacteristic
178#486C2×C411yescharacteristic
179#486C2×C411yescharacteristic
180#486C2×C411yescharacteristic
181#486C2×C411yescharacteristic
182#486C2×C411yescharacteristic
183#486C2×C411yescharacteristic
184#484C2×C414yes—
185#482C2×C414yes—
186#482C2×C414yes—
187#481C2×C414yes—
188#478C2×C414yes—
189#478C2×C414yes—
190#477C2×C414yes—
191#476C2×C414yes—
192#466C2×C414yes—
193#466C2×C414yes—
194#465C2×C414yes—
195#465C2×C414yes—
196#463C2×C414yes—
197#463C2×C414yes—
198#460C2×C414yes—
199#459C2×C414yes—
200#450C2×C414yes—
201#449C2×C414yes—
202#449C2×C414yes—
203#447C2×C414yes—
204#446—21no—
205#446—21no—
206#446C2312yes—
207#446C2312yes—
208C8×Q8—21no—
209C8×Q8—21no—
210C8×Q8C2312yes—
211C8×Q8C2312yes—
212C4×SD16C2314yes—
213C4×SD16C2314yes—
214C4×D8C2314yes—
215C4×D8C2314yes—
216#436—22no—
217#436—22no—
218#436—22no—
219#436—22no—
220#436—21no—
221#436—21no—
222#436—21no—
223#436—21no—
224#436—21no—
225#436—21no—
226#436C2312yes—
227#436C2312yes—
228#436C2312yes—
229#436C2312yes—
230#436C2312yes—
231#436C2312yes—
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—
243#435—22no—
244C8×D4—21no—
245C8×D4—21no—
246C8×D4—21no—
247C8×D4—21no—
248C8×D4—21no—
249C8×D4—21no—
250C8×D4C2312yes—
251C8×D4C2312yes—
252C8×D4C2312yes—
253C8×D4C2312yes—
254C8×D4C2312yes—
255C8×D4C2312yes—
256#433—22no—
257#433—22no—
258#432—21no—
259#432—22no—
260#432—22no—
261#432C2312yes—
262#431—21no—
263#431—21no—
264#431—21no—
265#431C2×C411yescharacteristic
266#431C2×C411yescharacteristic
267#431C2×C411yescharacteristic
268#431C2×C411yescharacteristic
269#431C2312yes—
270#431C2312yes—
271#431C2312yes—
272#431C2312yes—
273#431C2312yes—
274#424—21no—
275#424—21no—
276#423—21no—
277#423—21no—
278#423C2311yescharacteristic
279#423C2311yescharacteristic
280#423C2311yescharacteristic
281#423C2311yescharacteristic
282#423C2312yes—
283C2×C4⋊C8—21no—
284C2×C4⋊C8—21no—
285C2×C4⋊C8C2×C412yes—
286C2×C4⋊C8C2312yes—
287#408—22no—
288#408—22no—
289#408—21no—
290#408—21no—
291#408—21no—
292#408—21no—
293#408—21no—
294#408—21no—
295#407—21no—
296#407—22no—
297#407—22no—
298C2×C22⋊C8—21no—
299C2×C22⋊C8C2×C412yes—
300#405—21no—
301#405—21no—
302#405—22no—
303#405—22no—
304C4×M16—21no—
305C4×M16—22no—
306C4×M16D411yescharacteristic
307C4×M16D411yescharacteristic
308C4×M16D411yescharacteristic
309C4×M16D411yescharacteristic
310C4×M16C2311yescharacteristic
311C4×M16C2311yescharacteristic
312C4×M16C2311yescharacteristic
313C4×M16C2311yescharacteristic
314C2×#97—22no—
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
363C2×SD16C22×C414yes—
364C2×SD16C22×C414yes—
365C2×D8C22×C414yes—
366C2×D8C22×C414yes—
367#131—44no—
368#131—44no—
369#131—44no—
370#131—48no—
371#131—48no—
372#131—44no—
373#131—44no—
374#131—44no—
375C2×M16—22no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—24no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—22no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—42no—
388C2×M16—48no—
389C2×M16—48no—
390C2×M16—44no—
391C2×M16C2×D411yescharacteristic
392C2×M16C2×D411yescharacteristic
393C2×M16C2×D411yescharacteristic
394C2×M16C2×D411yescharacteristic
395C2×M16C2×D411yescharacteristic
396C2×M16C2×D411yescharacteristic
397C2×M16C2×D411yescharacteristic
398C2×M16C2×D411yescharacteristic
399C22×C8—22no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8C22×C412yes—
409C22×C8C22×C412yes—
410C22×C8C2×D411yescharacteristic
411C22×C8C2×D411yescharacteristic
412C22×C8C2×D411yescharacteristic
413C22×C8C2×D411yescharacteristic
414C4⋊Q8—21no—
415C4⋊Q8—21no—
416C4⋊Q8C22×C411yescharacteristic
417C4⋊Q8C22×C412yes—
418C4⋊Q8C22×C411yescharacteristic
419C4⋊Q8C22×C411yescharacteristic
420C4⋊Q8C22×C411yescharacteristic
421C4⋊Q8C22×C411yescharacteristic
422#127—21no—
423#127—21no—
424#127C22×C412yes—
425#127C22×C411yescharacteristic
426#127C22×C411yescharacteristic
427#127C22×C411yescharacteristic
428#126—22no—
429#126—22no—
430#125—21no—
431#125—21no—
432#125C22×C412yes—
433#124—21no—
434#124—21no—
435#124—22no—
436#124—21no—
437#124—21no—
438#124—21no—
439#124—22no—
440#124—21no—
441#124C22×C412yes—
442#123—22no—
443#123—22no—
444#123—22no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8C22×C412yes—
450C22⋊Q8C22×C412yes—
451#121—21no—
452#121—21no—
453#121—22no—
454#121—22no—
455#121—22no—
456#121—21no—
457#121—21no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121—22no—
462#121—21no—
463#121C22×C412yes—
464#121C22×C412yes—
465#121C22×C412yes—
466#121C22×C412yes—
467#121C22×C412yes—
468#121C22×C412yes—
469#120—22no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8C22×C412yes—
475C4×Q8C2412yes—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4C22×C412yes—
495C4×D4C22×C412yes—
496C4×D4C22×C412yes—
497C4×D4C2412yes—
498C4×D4C2412yes—
499C4×D4C2412yes—
500#117—21no—
501#117—21no—
502#117—22no—
503#117—22no—
504#117—22no—
505#117C22×C412yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4C22×C412yes—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C42—22no—
511C2×C42C22×C411yescharacteristic
512C2×C42C22×C411yescharacteristic
513C2×C42C22×C411yescharacteristic
514C2×C42C2×D411yescharacteristic
515C2×C42C2×D411yescharacteristic
516C2×C42C2×D411yescharacteristic
517C2×C42#4111yescharacteristic
518C2×C42#4111yescharacteristic
519C2×C42#4111yescharacteristic
520C2×C42C2411yescharacteristic
521C2×C42C2411yescharacteristic
522C2×C42C2411yescharacteristic
523#107C22×C414yes—
524#107C22×C414yes—
525#106C22×C414yes—
526#106C22×C414yes—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—22no—
530C4⋊C8—22no—
531C4⋊C8—21no—
532C4⋊C8—21no—
533C4⋊C8—22no—
534C4⋊C8—22no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537C4⋊C8—22no—
538C4⋊C8—22no—
539C4⋊C8C22×C412yes—
540C4⋊C8C22×C412yes—
541C4⋊C8C22×C412yes—
542C4⋊C8C22×C412yes—
543C4⋊C8C2412yes—
544C4⋊C8C2412yes—
545C4⋊C8C2412yes—
546C4⋊C8C2412yes—
547#103C22×C414yes—
548#103C22×C414yes—
549#102C22×C414yes—
550#102C22×C414yes—
551#102C22×C414yes—
552#102C22×C414yes—
553#102C22×C414yes—
554#102C22×C414yes—
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⋊C8—22no—
565C22⋊C8—22no—
566C22⋊C8—22no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—22no—
570C22⋊C8—22no—
571C22⋊C8C22×C412yes—
572C22⋊C8C22×C412yes—
573C22⋊C8C22×C412yes—
574C22⋊C8C22×C412yes—
575#97—22no—
576#97—22no—
577#97—22no—
578#97C2×D411yescharacteristic
579#97C2×D411yescharacteristic
580#97C2×D411yescharacteristic
581#97C2×D411yescharacteristic
582#97C2×D411yescharacteristic
583#97C2×D411yescharacteristic
584#97C2×D411yescharacteristic
585#97C2×D411yescharacteristic
586C4×C8—22no—
587C4×C8—22no—
588C4×C8—22no—
589C4×C8—21no—
590C4×C8—21no—
591C4×C8C22×C411yescharacteristic
592C4×C8C22×C411yescharacteristic
593C4×C8C22×C411yescharacteristic
594C4×C8C22×C411yescharacteristic
595C4×C8C2×D411yescharacteristic
596C4×C8C2×D411yescharacteristic
597C4×C8C2×D411yescharacteristic
598C4×C8C2×D411yescharacteristic
599C4×C8C2412yes—
600C4×C8C2412yes—
601C4×C8C2412yes—
602C4×C8C2412yes—
603C4×C8C2411yescharacteristic
604C4×C8C2411yescharacteristic
605C4×C8C2411yescharacteristic
606C4×C8C2411yescharacteristic
607C24—22no—
608C24C4×D411yescharacteristic
609#41—44no—
610#41—48no—
611#41—44no—
612#41—44no—
613#41—44no—
614#41—44no—
615#41—42no—
616#41—42no—
617#41—42no—
618#41—42no—
619#41—42no—
620#41—42no—
621#41—82no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—44no—
628C2×Q8C23×C412yes—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—82no—
649C2×D4C23×C412yes—
650C2×D4C23×C412yes—
651C2×D4C23×C412yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4C4×D411yescharacteristic
667C22×C4C4×D411yescharacteristic
668C22×C4C4×D411yescharacteristic
669C22×C4C4×D411yescharacteristic
670C22×C4C4×D411yescharacteristic
671C22×C4C4×D411yescharacteristic
672C22×C4C4×D411yescharacteristic
673C22×C4C4×D411yescharacteristic
674C22×C4C4×D411yescharacteristic
675C22×C4C23×C411yescharacteristic
676C22×C4C23×C411yescharacteristic
677C22×C4C23×C411yescharacteristic
678C22×C4C22×D411yescharacteristic
679C22×C4C22×D411yescharacteristic
680C22×C4C22×D411yescharacteristic
681C22×C4C2×#4111yescharacteristic
682C22×C4C2×#4111yescharacteristic
683C22×C4C2×#4111yescharacteristic
684SD16—44no—
685SD16—44no—
686D8—44no—
687D8—44no—
688M16—22no—
689M16—22no—
690M16—22no—
691M16—22no—
692M16—41no—
693M16—41no—
694M16—41no—
695M16—41no—
696M16—44no—
697M16—44no—
698M16—44no—
699M16—44no—
700M16—42no—
701M16—42no—
702M16—42no—
703M16—42no—
704M16—44no—
705M16—44no—
706M16—44no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—22no—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—42no—
717C2×C8—42no—
718C2×C8—44no—
719C2×C8—44no—
720C2×C8—44no—
721C2×C8—42no—
722C2×C8—42no—
723C2×C8—44no—
724C2×C8—44no—
725C2×C8—44no—
726C2×C8—44no—
727C2×C8AGL(1,ℤ/8)14yes—
728C2×C8C23×C412yes—
729C2×C8C23×C412yes—
730C2×C8C23×C412yes—
731C2×C8C23×C412yes—
732C2×C8C22×D411yescharacteristic
733C2×C8C22×D411yescharacteristic
734C2×C8C22×D411yescharacteristic
735C2×C8C22×D411yescharacteristic
736C2×C8C22×D411yescharacteristic
737C2×C8C22×D411yescharacteristic
738C2×C8C22×D411yescharacteristic
739C2×C8C22×D411yescharacteristic
740C4⋊C4—22no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—22no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—22no—
749C4⋊C4—22no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—22no—
753C4⋊C4—22no—
754C4⋊C4C23×C412yes—
755C4⋊C4C23×C412yes—
756C4⋊C4C23×C412yes—
757C4⋊C4C23×C412yes—
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—
768C22⋊C4—22no—
769C22⋊C4—22no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C42—22no—
776C42—22no—
777C42—22no—
778C42C4×D411yescharacteristic
779C42C4×D411yescharacteristic
780C42C4×D411yescharacteristic
781C42C4×D411yescharacteristic
782C42C4×D411yescharacteristic
783C42C4×D411yescharacteristic
784C42C23×C411yescharacteristic
785C42C23×C411yescharacteristic
786C42C23×C411yescharacteristic
787C42C22×D411yescharacteristic
788C42C22×D411yescharacteristic
789C42C22×D411yescharacteristic
790C42C2×#4111yescharacteristic
791C42C2×#4111yescharacteristic
792C42C2×#4111yescharacteristic
793C42C2511yescharacteristic
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—44no—
801C23—82no—
802C23—82no—
803C23C2×C4×D411yescharacteristic
804C23C2×C4×D411yescharacteristic
805C23C2×C4×D411yescharacteristic
806Q8—24no—
807Q8—44no—
808Q8—42no—
809Q8—42no—
810Q8—42no—
811Q8—42no—
812D4—24no—
813D4—24no—
814D4—24no—
815D4—44no—
816D4—44no—
817D4—44no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—42no—
822D4—42no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—82no—
828D4—82no—
829D4—82no—
830D4—82no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C2×C4×D411yescharacteristic
867C2×C4C2×C4×D411yescharacteristic
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×AGL(1,ℤ/8)12yes—
876C2×C4#57512yes—
877C2×C4C24×C411yescharacteristic
878C2×C4C23×D411yescharacteristic
879C2×C4C22×#4111yescharacteristic
880C8—22no—
881C8—22no—
882C8—22no—
883C8—22no—
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—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—82no—
916C22—164no—
917C22C4×AGL(1,ℤ/8)12yes—
918C22C22×C4×D411yescharacteristic
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4C4×AGL(1,ℤ/8)12yes—
933C4#295712yes—
934C4#357312yes—
935C4C22×AGL(1,ℤ/8)11yescharacteristic
936C4C2×#57511yescharacteristic
937C2—22no—
938C2—41no—
939C2—41no—
940C2—82no—
941C2—82no—
942C2—82no—
943C2#6014311yescharacteristic
944C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
945C2C2×#295711yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC42C25
socleC22C22×C4×D4
prime radical#60946C2
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. #18011C2semidirect
5. #18008C2semidirect
6. #18007C2semidirect
7. #18006C2semidirect
8. #17981C2semidirect
9. #17979C2semidirect
10. #17976C2semidirect
11. #17975C2semidirect
12. #17962C2semidirect
13. #17960C2semidirect
14. #17957C2semidirect
15. #17956C2semidirect
16. #17817C2semidirect
17. #17481C2semidirect
18. #17478C2semidirect
19. C2×#1453C2semidirect
40. #2971C22semidirect
42. #2970C22semidirect
47. #2960C22semidirect
48. #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. #1573C22semidirect
93. #1567C22semidirect
94. #1567C22semidirect
95. #1566C22semidirect
96. #1566C22semidirect
99. #1493C22semidirect
100. #1493C22semidirect
105. #1492C22semidirect
106. #1492C22semidirect
108. #1477C22semidirect
111. #1453C22semidirect
112. #1453C22semidirect
113. C2×#322C22semidirect
114. C2×#322C22semidirect
115. C2×#322C22semidirect
116. C2×C82C22semidirect

Maximal subgroups

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

subgroupindex
#609462
#602082
#601442
#180112
#180082
#180072
#180062
#179812
#179792
#179762
#179752
#179622
#179602
#179572
#179562
#178172
#174812
#174782
C2×#14532