Finite Group Databasebeta

← #72318660

Subgroups — #72318660

Order 1024.

2505 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623523C211yesmaximal, characteristic
2#6345722C211yesmaximal, characteristic, complemented
3#6345702C211yesmaximal, characteristic, complemented
4#484058C218yesmaximal, complemented
5#484040C218yesmaximal, complemented
6#483992C214yesmaximal, complemented
7#483961C214yesmaximal, complemented
8#483443C211yesmaximal, characteristic, complemented
9#481345C211yesmaximal, characteristic, complemented
10C2×#11680C211yesmaximal, characteristic, complemented
11#479962C211yesmaximal, characteristic, complemented
12C2×#3169C2211yescharacteristic
13C2×#3169C2211yescharacteristic
14#60236—21no—
15#60144—21no—
16#33819C414yes—
17#33793C412yes—
18#33793C412yes—
19#33771C412yes—
20#33771C412yes—
21#33758C414yes—
22#33748C2214yes—
23#33669C2214yes—
24#33669C2214yes—
25#33418C2211yescharacteristic
26C2×C4×M32C2211yescharacteristic
27#18091—22no—
28#18091C2214yes—
29#18073—22no—
30#18073C2214yes—
31#18064—22no—
32#18064C2214yescomplemented
33#18044—22no—
34#18044C2214yescomplemented
35#17981—22no—
36#17975—22no—
37#17962C2214yescomplemented
38#17962C2214yescomplemented
39#17793C2211yescharacteristic
40C2×#1566C2211yescharacteristic
41#17500—21no—
42#17485—21no—
43C2×#1451C2211yescharacteristic
44#12089C22116yescomplemented
45#12078C22116yescomplemented
46#12078C22116yescomplemented
47#12067C22116yescomplemented
48#12029C2214yescomplemented
49#12028C2214yescomplemented
50#12020C2214yescomplemented
51#11680C2214yes—
52#11680C2212yescomplemented
53#11680C2212yescomplemented
54#11680C2212yescomplemented
55#11680C2212yescomplemented
56#11678C2214yes—
57#11599C2214yescomplemented
58C2×#1333C2214yescomplemented
59#11414C2214yescomplemented
60#11413C2214yescomplemented
61#11404C2212yescomplemented
62#11404C2212yescomplemented
63C2×#568—41no—
64C2×#532—21no—
65C2×#532—21no—
66C22×M32—21no—
67#3169—21no—
68#3169—21no—
69#3169—21no—
70#3169—21no—
71#3169—21no—
72#3169—21no—
73#3169—21no—
74#3169—21no—
75#3169C2×C412yes—
76#3169C2×C412yes—
77#3169C2×C412yes—
78#3169C2×C412yes—
79#3169C2312yes—
80#3169C2312yes—
81#3169C2312yes—
82#3169C2312yes—
83C2×#500C2×C411yescharacteristic
84C2×#500C2×C411yescharacteristic
85C2×#493C2×C411yescharacteristic
86C2×#493C2×C411yescharacteristic
87C2×#486—21no—
88C2×#486—21no—
89C2×#466—21no—
90C2×#466—21no—
91C2×#466C2×C412yes—
92C2×#466C2×C412yes—
93#2981—42no—
94#2979—24no—
95#2975—41no—
96#2974—24no—
97#2972—41no—
98C2×C4×D8—21no—
99C2×C4×D8—21no—
100C2×C4×D8C2312yes—
101C2×C4×D8C2312yes—
102#2935—24no—
103#2935—42no—
104#2935—42no—
105D4×M16—24no—
106D4×M16—42no—
107#2932—42no—
108#2931—24no—
109#2931—24no—
110#2920—21no—
111C2×#431D411yescharacteristic
112C2×#423—21no—
113#2880—42no—
114#2879—41no—
115C2×C4×M16D411yescharacteristic
116C22×C4×C8C2311yescharacteristic
117#2254C2×C414yes—
118#2246C2×C414yes—
119#2240C2×C414yes—
120#2240C2×C414yes—
121#2233C2×C418yes—
122#2233C2×C418yes—
123#2226C2×C418yes—
124#2226C2×C418yes—
125#2218C2×C4116yes—
126#2206C2×C418yes—
127#2206C2×C418yes—
128#2184C2×C418yes—
129#2184C2×C418yes—
130#2177C23116yes—
131#2163C2312yes—
132#2163C2312yes—
133#2162C2×C412yes—
134#2162C2×C412yes—
135#2150C2×C412yes—
136#2112C2×C412yes—
137C4×M32—21no—
138C4×M32—21no—
139C4×M32C2312yes—
140C4×M32C2311yescharacteristic
141C4×M32C2311yescharacteristic
142C4×M32C2312yes—
143C2×#346C2312yes—
144C2×C4×C16—21no—
145#1594—24no—
146#1594—24no—
147#1594C2318yes—
148#1594C2318yes—
149#1586—28no—
150#1586—28no—
151#1581—28no—
152#1581—28no—
153#1580—24no—
154#1580—24no—
155#1580C2318yes—
156#1580C2318yes—
157#1568—21no—
158#1568C2312yes—
159#1567—21no—
160#1566—21no—
161#1566—21no—
162#1566C2312yes—
163#1566C2312yes—
164#1566C2312yes—
165#1564—21no—
166#1564C2312yes—
167C2×#334—21no—
168C2×#334C2312yes—
169#1492—24no—
170#1492—24no—
171#1490—24no—
172#1486—24no—
173#1484—24no—
174#1480—24no—
175#1451D412yes—
176#1451D412yes—
177#1451C2312yes—
178#1451C2312yes—
179C2×#322D412yes—
180C2×#322C2312yes—
181#1368C23116yes—
182#1333C2318yes—
183#1333C2318yes—
184#1333C2318yes—
185#1333C2318yes—
186#1313C2318yes—
187#1313C2318yes—
188C22×#41—41no—
189C22×#41—41no—
190C22×D8—21no—
191C22×D8—21no—
192C22×D8C22×C412yes—
193C22×D8C22×C412yes—
194#568—88no—
195C2×#131—44no—
196C2×#131—44no—
197C2×#131—44no—
198C22×M16—21no—
199C22×M16—44no—
200C22×M16—41no—
201C23×C8C22×C411yescharacteristic
202C23×C8#4111yescharacteristic
203#532—22no—
204#532—22no—
205#532—22no—
206#532—22no—
207#532—22no—
208#532—22no—
209#532—22no—
210#532—22no—
211#532—41no—
212#532—41no—
213#532—41no—
214#532—41no—
215#532—41no—
216#532—41no—
217#532—41no—
218#532—41no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×#127—21no—
222C2×#127—21no—
223C2×#124—41no—
224C2×#124—41no—
225C2×#121—22no—
226C2×#121—22no—
227C2×#121—41no—
228C2×#121—41no—
229C2×C4×D4—22no—
230C2×C4×D4—22no—
231C2×C4×D4—41no—
232C2×C4×D4—41no—
233C22×C42C2×D411yescharacteristic
234C2×D16C22×C4116yes—
235C2×M32—21no—
236C2×M32—22no—
237C2×M32—21no—
238C2×M32—44no—
239C2×M32C22×C414yes—
240C22×C16—22no—
241#500—21no—
242#500—21no—
243#500—21no—
244#500—21no—
245#500C22×C412yes—
246#500C22×C412yes—
247#500C22×C412yes—
248#500C22×C412yes—
249#493—21no—
250#493—21no—
251#493—21no—
252#493—21no—
253#493C22×C412yes—
254#493C22×C412yes—
255#493C22×C412yes—
256#493C22×C412yes—
257#486—22no—
258#486—22no—
259#486—22no—
260#486—22no—
261#486—22no—
262#486—22no—
263#486—22no—
264#486—22no—
265#466—22no—
266#466—22no—
267#466—22no—
268#466—22no—
269#466—22no—
270#466—22no—
271#466—22no—
272#466—22no—
273#466—22no—
274#466—22no—
275#466—22no—
276#466—22no—
277#466C22×C414yes—
278#466C22×C414yes—
279#466C22×C414yes—
280#466C22×C414yes—
281C4×D8—22no—
282C4×D8—22no—
283C4×D8—22no—
284C4×D8—22no—
285C4×D8—22no—
286C4×D8—22no—
287C4×D8—22no—
288C4×D8—22no—
289C4×D8—22no—
290C4×D8—22no—
291C4×D8—22no—
292C4×D8—22no—
293C4×D8C22×C414yes—
294C4×D8C22×C414yes—
295C4×D8C2414yes—
296C4×D8C2414yes—
297#436—28no—
298#436—28no—
299#436—44no—
300#436—44no—
301#436—44no—
302#435—48no—
303#435—48no—
304#435—48no—
305C8×D4—28no—
306C8×D4—28no—
307C8×D4—44no—
308C8×D4—44no—
309C8×D4—44no—
310#432—22no—
311#432—41no—
312#431—21no—
313#431—21no—
314#431—22no—
315#431—41no—
316#431C2×D412yes—
317#431C2×D412yes—
318C2×#107—21no—
319C2×#107—21no—
320C2×#107C22×C412yes—
321C2×#107C22×C412yes—
322#423—22no—
323#423—22no—
324#423—22no—
325#423—41no—
326#423—41no—
327C2×C4⋊C8—21no—
328C2×C4⋊C8—22no—
329C2×C4⋊C8—41no—
330C2×#102—22no—
331C2×#102—22no—
332C2×#102—22no—
333C2×#102—22no—
334#408—48no—
335#408—44no—
336#408—44no—
337#408—44no—
338#407—44no—
339#407—44no—
340#407—41no—
341C2×C22⋊C8—21no—
342C2×C22⋊C8—44no—
343C4×M16—21no—
344C4×M16—21no—
345C4×M16—41no—
346C4×M16C2×D412yes—
347C4×M16C2×D412yes—
348C2×#97—21no—
349C2×C4×C8C22×C411yescharacteristic
350C2×C4×C8C22×C411yescharacteristic
351C2×C4×C8C22×C411yescharacteristic
352C2×C4×C8C2×D412yes—
353C2×C4×C8C2×D412yes—
354C2×C4×C8C2×D411yescharacteristic
355C2×C4×C8C2×D411yescharacteristic
356C2×C4×C8C2×D411yescharacteristic
357C2×C4×C8#4111yescharacteristic
358C2×C4×C8#4111yescharacteristic
359C2×C4×C8#4111yescharacteristic
360C2×C4×C8C2411yescharacteristic
361C2×C4×C8C2411yescharacteristic
362C2×C4×C8C2411yescharacteristic
363#367C22×C4116yes—
364C4⋊C16C22×C414yes—
365C4⋊C16C22×C414yes—
366#357C22×C4116yes—
367#357C22×C4116yes—
368C22⋊C16C22×C414yes—
369C22⋊C16C22×C414yes—
370#346—22no—
371#346C2412yes—
372#346C2412yes—
373#346C2414yes—
374C4×C16—22no—
375C4×C16—21no—
376C4×C16—21no—
377C4×C16C22×C414yes—
378#335—22no—
379#335—22no—
380#334—22no—
381#334—22no—
382#334—22no—
383#334—22no—
384#334C2414yes—
385#334C2414yes—
386D4⋊C8—28no—
387D4⋊C8—28no—
388D4⋊C8—28no—
389D4⋊C8—28no—
390#322C2×D414yes—
391#322C2×D414yes—
392#322C2×D414yes—
393#322C2414yes—
394C2×#41—42no—
395C2×#41—42no—
396C2×#41—42no—
397C2×#41—42no—
398C2×#41—42no—
399C2×#41—42no—
400C2×#41—42no—
401C2×#41—42no—
402C2×#41—84no—
403C2×#41—84no—
404C2×#41—164no—
405C22×Q8—41no—
406C22×Q8—41no—
407C22×D4—22no—
408C22×D4—22no—
409C22×D4—42no—
410C22×D4—42no—
411C22×D4—41no—
412C22×D4—41no—
413C22×D4—41no—
414C22×D4—41no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4C4×D411yescharacteristic
418C23×C4AGL(1,ℤ/8)11yescharacteristic
419C23×C4AGL(1,ℤ/8)11yescharacteristic
420C2×D8—22no—
421C2×D8—22no—
422C2×D8—22no—
423C2×D8—22no—
424C2×D8—22no—
425C2×D8—22no—
426C2×D8—44no—
427C2×D8—44no—
428C2×D8—82no—
429C2×D8—82no—
430C2×D8C23×C414yes—
431C2×D8C23×C414yes—
432#131—816no—
433#131—816no—
434#131—168no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—48no—
438C2×M16—48no—
439C2×M16—44no—
440C2×M16—42no—
441C2×M16—42no—
442C2×M16—42no—
443C2×M16—816no—
444C2×M16—84no—
445C22×C8—22no—
446C22×C8—22no—
447C22×C8—42no—
448C22×C8—42no—
449C22×C8—48no—
450C22×C8—48no—
451C22×C8—42no—
452C22×C8C4×D411yescharacteristic
453C22×C8C4×D411yescharacteristic
454C22×C8C4×D411yescharacteristic
455C22×C8C4×D411yescharacteristic
456C22×C8C4×D411yescharacteristic
457C22×C8C4×D411yescharacteristic
458C22×C8C23×C411yescharacteristic
459C22×C8C23×C411yescharacteristic
460C22×C8C23×C411yescharacteristic
461C22×C8C2×#4111yescharacteristic
462C22×C8C2×#4111yescharacteristic
463C22×C8C2×#4111yescharacteristic
464C4⋊Q8—22no—
465C4⋊Q8—22no—
466C4⋊Q8—22no—
467C4⋊Q8—22no—
468C4⋊Q8—41no—
469C4⋊Q8—41no—
470C4⋊Q8—41no—
471C4⋊Q8—41no—
472#127—22no—
473#127—22no—
474#127—22no—
475#127—22no—
476#127—41no—
477#127—41no—
478#127—41no—
479#127—41no—
480#124—42no—
481#124—42no—
482#124—42no—
483#124—42no—
484#124—42no—
485#124—42no—
486#124—42no—
487#124—42no—
488#121—24no—
489#121—24no—
490#121—24no—
491#121—24no—
492#121—42no—
493#121—42no—
494#121—42no—
495#121—42no—
496#121—42no—
497#121—42no—
498#121—42no—
499#121—42no—
500#121—42no—
501#121—42no—
502#121—42no—
503#121—42no—
504C4×D4—24no—
505C4×D4—24no—
506C4×D4—24no—
507C4×D4—24no—
508C4×D4—42no—
509C4×D4—42no—
510C4×D4—42no—
511C4×D4—42no—
512C4×D4—42no—
513C4×D4—42no—
514C4×D4—42no—
515C4×D4—42no—
516C4×D4—42no—
517C4×D4—42no—
518C4×D4—42no—
519C4×D4—42no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—41no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C42C4×D411yescharacteristic
529C2×C42C4×D411yescharacteristic
530C2×C42C4×D411yescharacteristic
531C2×C42AGL(1,ℤ/8)11yescharacteristic
532C2×C42AGL(1,ℤ/8)11yescharacteristic
533C2×C42AGL(1,ℤ/8)11yescharacteristic
534C2×C42AGL(1,ℤ/8)11yescharacteristic
535C2×C42AGL(1,ℤ/8)11yescharacteristic
536C2×C42AGL(1,ℤ/8)11yescharacteristic
537C2×C42C22×D411yescharacteristic
538C2×C42C22×D411yescharacteristic
539C2×C42C22×D411yescharacteristic
540D16—416no—
541M32—24no—
542M32—44no—
543M32—44no—
544M32—42no—
545C2×C16—22no—
546C2×C16—22no—
547C2×C16—44no—
548C2×C16C23×C418yes—
549#107—22no—
550#107—22no—
551#107—22no—
552#107—22no—
553#107—22no—
554#107—22no—
555#107C23×C414yes—
556#107C23×C414yes—
557C4⋊C8—22no—
558C4⋊C8—22no—
559C4⋊C8—24no—
560C4⋊C8—24no—
561C4⋊C8—42no—
562C4⋊C8—42no—
563C4⋊C8—42no—
564C4⋊C8—42no—
565#102—24no—
566#102—24no—
567#102—24no—
568#102—24no—
569#102—24no—
570#102—24no—
571#102—24no—
572#102—24no—
573C22⋊C8—22no—
574C22⋊C8—22no—
575C22⋊C8—48no—
576C22⋊C8—48no—
577C22⋊C8—48no—
578C22⋊C8—48no—
579C22⋊C8—42no—
580C22⋊C8—42no—
581#97—22no—
582#97—22no—
583#97—42no—
584C4×C8—22no—
585C4×C8—22no—
586C4×C8—42no—
587C4×C8C4×D411yescharacteristic
588C4×C8C4×D411yescharacteristic
589C4×C8C4×D411yescharacteristic
590C4×C8C4×D411yescharacteristic
591C4×C8C4×D411yescharacteristic
592C4×C8C4×D411yescharacteristic
593C4×C8C23×C411yescharacteristic
594C4×C8C23×C411yescharacteristic
595C4×C8C23×C411yescharacteristic
596C4×C8C22×D414yes—
597C4×C8C22×D414yes—
598C4×C8C22×D411yescharacteristic
599C4×C8C22×D411yescharacteristic
600C4×C8C22×D411yescharacteristic
601C4×C8C2×#4111yescharacteristic
602C4×C8C2×#4111yescharacteristic
603C4×C8C2×#4111yescharacteristic
604C4×C8C2511yescharacteristic
605C24—42no—
606C24—42no—
607C24#44211yescharacteristic
608#41—84no—
609#41—84no—
610#41—88no—
611#41—84no—
612#41—84no—
613#41—88no—
614#41—88no—
615#41—164no—
616#41—164no—
617#41—164no—
618C2×Q8—42no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8—42no—
622C2×Q8—84no—
623C2×Q8—162no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—82no—
641C2×D4—82no—
642C2×D4—82no—
643C2×D4—82no—
644C2×D4—84no—
645C2×D4—88no—
646C2×D4—84no—
647C2×D4—162no—
648C2×D4—162no—
649C2×D4—164no—
650C22×C4—24no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—84no—
661C22×C4—84no—
662C22×C4—164no—
663C22×C4#44211yescharacteristic
664C22×C4#44211yescharacteristic
665C22×C4#44211yescharacteristic
666C22×C4#44211yescharacteristic
667C22×C4#44211yescharacteristic
668C22×C4#44211yescharacteristic
669C22×C4#44211yescharacteristic
670C22×C4#44211yescharacteristic
671C22×C4#44211yescharacteristic
672C22×C4C2×C4×D411yescharacteristic
673C22×C4C2×C4×D411yescharacteristic
674C22×C4C2×C4×D411yescharacteristic
675C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
676C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
677C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
678C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
679C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
680C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
681D8—28no—
682D8—28no—
683D8—44no—
684D8—44no—
685D8—82no—
686D8—82no—
687D8—82no—
688D8—82no—
689M16—44no—
690M16—44no—
691M16—816no—
692M16—84no—
693M16—84no—
694M16—84no—
695M16—168no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—22no—
699C2×C8—22no—
700C2×C8—22no—
701C2×C8—22no—
702C2×C8—24no—
703C2×C8—24no—
704C2×C8—41no—
705C2×C8—41no—
706C2×C8—41no—
707C2×C8—41no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—44no—
711C2×C8—44no—
712C2×C8—44no—
713C2×C8—44no—
714C2×C8—816no—
715C2×C8—84no—
716C2×C8—168no—
717C2×C8C2×C4×D411yescharacteristic
718C2×C8C2×C4×D411yescharacteristic
719C2×C8C2×C4×D411yescharacteristic
720C2×C8C2×C4×D411yescharacteristic
721C2×C8C2×C4×D411yescharacteristic
722C2×C8C2×C4×D411yescharacteristic
723C2×C8C24×C411yescharacteristic
724C2×C8C22×#4111yescharacteristic
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—42no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—44no—
739C22⋊C4—44no—
740C22⋊C4—44no—
741C42#44211yescharacteristic
742C42#44211yescharacteristic
743C42#44211yescharacteristic
744C42#44211yescharacteristic
745C42#44211yescharacteristic
746C42#44211yescharacteristic
747C42C2×C4×D411yescharacteristic
748C42C2×C4×D411yescharacteristic
749C42C2×C4×D411yescharacteristic
750C42C2×AGL(1,ℤ/8)11yescharacteristic
751C42C2×AGL(1,ℤ/8)11yescharacteristic
752C42C2×AGL(1,ℤ/8)11yescharacteristic
753C42C2×AGL(1,ℤ/8)11yescharacteristic
754C42C2×AGL(1,ℤ/8)11yescharacteristic
755C42C2×AGL(1,ℤ/8)11yescharacteristic
756C42C23×D411yescharacteristic
757C16—24no—
758C16—28no—
759C16—42no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—44no—
764C23—44no—
765C23—84no—
766C23—84no—
767C23—162no—
768C23—162no—
769C23—162no—
770C23—162no—
771C23C2×#44211yescharacteristic
772C23C2×#44211yescharacteristic
773C23C2×#44211yescharacteristic
774Q8—84no—
775Q8—84no—
776Q8—84no—
777Q8—162no—
778D4—44no—
779D4—44no—
780D4—44no—
781D4—44no—
782D4—84no—
783D4—88no—
784D4—88no—
785D4—88no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—162no—
792D4—162no—
793D4—162no—
794D4—162no—
795D4—164no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—84no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—88no—
823C2×C4—164no—
824C2×C4—162no—
825C2×C4AGL(1,ℤ/16)14yes—
826C2×C4C2×#44211yescharacteristic
827C2×C4C2×#44211yescharacteristic
828C2×C4C2×#44211yescharacteristic
829C2×C4C2×#44211yescharacteristic
830C2×C4C2×#44211yescharacteristic
831C2×C4C2×#44211yescharacteristic
832C2×C4C2×#44211yescharacteristic
833C2×C4C2×#44211yescharacteristic
834C2×C4C2×#44211yescharacteristic
835C2×C4C22×C4×D411yescharacteristic
836C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
837C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
838C8—21no—
839C8—21no—
840C8—21no—
841C8—21no—
842C8—21no—
843C8—21no—
844C8—44no—
845C8—44no—
846C8—84no—
847C8—84no—
848C8#295612yes—
849C8#357312yes—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—82no—
859C22—84no—
860C22—84no—
861C22—84no—
862C22—84no—
863C22—84no—
864C22—84no—
865C22—324no—
866C22—324no—
867C22C2×AGL(1,ℤ/16)12yes—
868C22C22×#44211yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—84no—
878C4—84no—
879C4C2×AGL(1,ℤ/16)12yes—
880C4C2×AGL(1,ℤ/16)12yes—
881C4#3347112yes—
882C4#6014311yescharacteristic
883C4C2×#295611yescharacteristic
884C2—22no—
885C2—41no—
886C2—41no—
887C2—164no—
888C2—164no—
889C2#634561211yescharacteristic
890C2C22×AGL(1,ℤ/16)11yescharacteristic
891C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623523C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#1451 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6345722C2semidirect
3. #6345702C2semidirect
4. #484058C2semidirect
5. #484040C2semidirect
6. #483992C2semidirect
7. #483961C2semidirect
8. #483443C2semidirect
9. #481345C2semidirect
10. C2×#11680C2semidirect
11. #479962C2semidirect
32. #18064C22semidirect
34. #18044C22semidirect
37. #17962C22semidirect
38. #17962C22semidirect
44. #12089C22semidirect
45. #12078C22semidirect
46. #12078C22semidirect
47. #12067C22semidirect
48. #12029C22semidirect
49. #12028C22semidirect
50. #12020C22semidirect
52. #11680C22semidirect
53. #11680C22semidirect
54. #11680C22semidirect
55. #11680C22semidirect
57. #11599C22semidirect
58. C2×#1333C22semidirect
59. #11414C22semidirect
60. #11413C22semidirect
61. #11404C22semidirect
62. #11404C22semidirect

Maximal subgroups

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

subgroupindex
#76235232
#63457222
#63457022
#4840582
#4840402
#4839922
#4839612
#4834432
#4813452
C2×#116802
#4799622