Finite Group Databasebeta

← #72319311

Subgroups — #72319311

Order 1024.

2400 conjugacy classes of subgroups.

The subgroup lattice has 1193 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623099C211yesmaximal, characteristic
2#6345722C211yesmaximal, characteristic, complemented
3#6345030C211yesmaximal, characteristic, complemented
4#484105C214yesmaximal, complemented
5#484103C214yesmaximal, complemented
6#484061C214yesmaximal, complemented
7#484058C214yesmaximal, complemented
8#483927C214yesmaximal, complemented
9#483881C214yesmaximal, complemented
10#483445C211yesmaximal, characteristic, complemented
11#481384C211yesmaximal, characteristic, complemented
12#481281C211yesmaximal, characteristic, complemented
13#479974C211yesmaximal, characteristic, complemented
14C2×#3169C2211yescharacteristic
15#60236—21no—
16M16×#41—21no—
17C2×C4×#135C2211yescharacteristic
18#33675C2212yes—
19#33675C2212yes—
20#33672C2212yes—
21#33669C2212yes—
22#33666C412yes—
23#33666C412yes—
24#33663C412yes—
25#33660C412yes—
26#33648C412yes—
27#33629C411yescharacteristic
28#33629C411yescharacteristic
29#33582C411yescharacteristic
30#33582C411yescharacteristic
31#33520C412yes—
32C4×#509C2212yes—
33C4×#509C2212yes—
34#33418C2211yescharacteristic
35#33418C2211yescharacteristic
36#18091—22no—
37#18091C2214yes—
38#18064—22no—
39#18064C2214yescomplemented
40#18045C2212yes—
41#18044C2212yescomplemented
42#18043C2212yes—
43#18042C2212yescomplemented
44#18041—22no—
45#18040—22no—
46#17975—22no—
47#17962C2214yescomplemented
48#17890C2212yescomplemented
49#17868—22no—
50#17849C2212yescomplemented
51#17793C2211yescharacteristic
52#17793C2211yescharacteristic
53#17500—21no—
54#17443—21no—
55C2×#1451C2211yescharacteristic
56#12089C2218yescomplemented
57#12087C2218yescomplemented
58#12080C2218yescomplemented
59#12078C2218yescomplemented
60#12078C2218yescomplemented
61#12077C2218yescomplemented
62#12067C2218yescomplemented
63#12065C2218yescomplemented
64#12029C2214yescomplemented
65#12029C2214yescomplemented
66#12021C2214yescomplemented
67#11680C2214yes—
68#11667C2214yescomplemented
69#11666C2212yescomplemented
70#11666C2212yescomplemented
71#11665C2212yes—
72#11665C2212yes—
73#11652C2214yescomplemented
74#11600C2212yescomplemented
75#11599C2212yescomplemented
76#11415C2214yescomplemented
77#11414C2214yescomplemented
78#11414C2214yescomplemented
79C22×#135C2×C411yescharacteristic
80C2×#532—21no—
81C2×C4×#41—21no—
82C2×#509C2×C412yes—
83C2×#509C2×C412yes—
84#3169—21no—
85#3169—21no—
86#3169—21no—
87#3169—21no—
88#3169C2×C412yes—
89#3169C2×C412yes—
90#3169C2312yes—
91#3169C2312yes—
92C2×#500C2×C411yescharacteristic
93C2×#493C2×C411yescharacteristic
94C2×#486—21no—
95C2×#466—21no—
96C2×#466C2×C412yes—
97#2981—42no—
98#2979—24no—
99#2975—41no—
100#2974—24no—
101#2972—41no—
102#2971—22no—
103#2970—22no—
104#2970—42no—
105#2965—22no—
106#2965—42no—
107C8×#41—22no—
108Q8×M16—22no—
109C4×#135—21no—
110C4×#135—21no—
111C4×#135—21no—
112C4×#135—21no—
113C4×#135C2×C411yescharacteristic
114C4×#135C2×C411yescharacteristic
115C4×#135C2×C411yescharacteristic
116C4×#135C2×C411yescharacteristic
117C4×#135C2311yescharacteristic
118C4×#135C2311yescharacteristic
119C4×#135C2311yescharacteristic
120C4×#135C2311yescharacteristic
121C2×C4×Q16C2×C411yescharacteristic
122C2×C4×Q16C2311yescharacteristic
123C2×C4×SD16—21no—
124C2×C4×SD16—21no—
125C2×C4×D8—21no—
126C2×C4×D8C2×C411yescharacteristic
127C2×C4×D8C2311yescharacteristic
128C2×C4×D8C2312yes—
129#2935—42no—
130D4×M16—22no—
131D4×M16—42no—
132#2931—24no—
133#2920—21no—
134#2920—21no—
135#2920—41no—
136C2×#431D411yescharacteristic
137C2×#427C2×C411yescharacteristic
138C2×#416—21no—
139#2880—42no—
140C2×C4×M16—41no—
141C2×C4×M16D411yescharacteristic
142C22×C4×C8C2311yescharacteristic
143#2234C2×C414yes—
144#2234C2×C414yes—
145#2233C2×C414yes—
146#2232C2×C414yes—
147#2227C2×C412yes—
148#2227C2×C412yes—
149#2226C2×C412yes—
150#2226C2×C412yes—
151#2225C2×C412yes—
152#2225C2×C412yes—
153#2224C2×C412yes—
154#2224C2×C412yes—
155#2207C2×C412yes—
156#2207C2×C412yes—
157#2207C2×C412yes—
158#2207C2×C412yes—
159#2206C2×C412yes—
160#2206C2×C412yes—
161#2206C2×C412yes—
162#2206C2×C412yes—
163#2186C2×C414yes—
164#2186C2×C414yes—
165#2185C2×C414yes—
166#2184C2×C414yes—
167#2177C2314yes—
168#2177C2314yes—
169#2175C2314yes—
170#2175C2314yes—
171C4×SD32C2×C414yes—
172C4×SD32C2×C414yes—
173C4×D16C2×C414yes—
174C4×D16C2×C414yes—
175#2163C2312yes—
176#2163C2312yes—
177#2163C2312yes—
178#2163C2312yes—
179#2162—21no—
180#2162—21no—
181#2162C2×C412yes—
182#2162C2×C412yes—
183#2159C2×C412yes—
184#2159C2×C412yes—
185#2150—21no—
186#2150C2×C411yescharacteristic
187#2150C2×C411yescharacteristic
188#2140C2×C412yes—
189#2140C2×C412yes—
190#2139C2×C412yes—
191#2139C2×C412yes—
192#2112—21no—
193#2112C2×C412yes—
194C4×M32C2312yes—
195C4×M32C2312yes—
196#1594—24no—
197#1594C2318yes—
198#1594C2314yes—
199#1593C2314yes—
200#1592—24no—
201#1588—24no—
202#1587—24no—
203#1586—24no—
204#1585—24no—
205#1581—28no—
206#1581—28no—
207#1580—24no—
208#1580C2318yes—
209#1580C2314yes—
210#1579C2314yes—
211SD16⋊C8—24no—
212#1568—21no—
213#1568—21no—
214#1568C2312yes—
215#1568C2312yes—
216#1567—21no—
217#1567—21no—
218#1566C2312yes—
219#1566C2312yes—
220#1564—21no—
221#1564—21no—
222#1564C2312yes—
223#1564C2312yes—
224#1492—24no—
225#1490—24no—
226#1488—22no—
227#1488—22no—
228#1487—22no—
229#1486—22no—
230#1484—24no—
231#1476—22no—
232#1476—22no—
233#1451D412yes—
234#1451D412yes—
235#1451C2312yes—
236#1451C2312yes—
237C2×#322D412yes—
238C2×#322C2312yes—
239#1368C2318yes—
240#1368C2318yes—
241#1334C2314yes—
242#1334C2314yes—
243#1333C2318yes—
244#1333C2314yes—
245#1333C2318yes—
246#1333C2314yes—
247#1313C2318yes—
248#1313C2318yes—
249C22×#41—21no—
250C22×#41—41no—
251C2×#135—21no—
252C2×#135—21no—
253C2×#135—42no—
254C2×#135—42no—
255C2×#135C22×C411yescharacteristic
256C2×#135C22×C411yescharacteristic
257C2×#135C22×C411yescharacteristic
258C2×#135C22×C411yescharacteristic
259C22×Q16C22×C411yescharacteristic
260C22×SD16—21no—
261C22×D8—21no—
262C22×D8C22×C411yescharacteristic
263C22×D8C22×C412yes—
264C2×#131—44no—
265C22×M16—21no—
266C22×M16—42no—
267C23×C8C22×C411yescharacteristic
268C23×C8#4111yescharacteristic
269#532—22no—
270#532—22no—
271#532—22no—
272#532—22no—
273#532—41no—
274#532—41no—
275#532—41no—
276#532—41no—
277C2×C4⋊Q8—21no—
278C2×#127—21no—
279C2×#124—41no—
280C2×#121—22no—
281C2×#121—41no—
282C4×#41—21no—
283C4×#41—21no—
284C4×#41—21no—
285C4×#41—21no—
286C4×#41—21no—
287C4×#41—21no—
288C4×#41—21no—
289C4×#41—21no—
290C4×#41—41no—
291C4×#41—41no—
292C4×#41—41no—
293C4×#41—41no—
294C2×C4×Q8—21no—
295C2×C4×Q8—21no—
296C2×C4×D4—21no—
297C2×C4×D4—21no—
298C2×C4×D4—22no—
299C2×C4×D4—41no—
300C2×C4×D4—41no—
301C2×C4×D4—41no—
302C2×#117—21no—
303C2×#117—41no—
304C22×C42—41no—
305C22×C42C2×D411yescharacteristic
306#509—44no—
307#509—44no—
308C2×SD32C22×C414yes—
309C2×SD32C22×C414yes—
310C2×D16C22×C414yes—
311C2×D16C22×C414yes—
312C2×M32—22no—
313C2×M32C22×C412yes—
314C2×M32C22×C412yes—
315#500—21no—
316#500—21no—
317#500C22×C412yes—
318#500C22×C412yes—
319#493—21no—
320#493—21no—
321#493C22×C412yes—
322#493C22×C412yes—
323#486—22no—
324#486—22no—
325#486—22no—
326#486—22no—
327#466—22no—
328#466—22no—
329#466—22no—
330#466—22no—
331#466—22no—
332#466—22no—
333#466C22×C414yes—
334#466C22×C414yes—
335#446—24no—
336#446—44no—
337C8×Q8—24no—
338C4×Q16—21no—
339C4×Q16—21no—
340C4×Q16—21no—
341C4×Q16—21no—
342C4×Q16C22×C411yescharacteristic
343C4×Q16C22×C411yescharacteristic
344C4×Q16C22×C411yescharacteristic
345C4×Q16C22×C411yescharacteristic
346C4×Q16C22×C411yescharacteristic
347C4×Q16C22×C411yescharacteristic
348C4×Q16C2411yescharacteristic
349C4×Q16C2411yescharacteristic
350C4×SD16—21no—
351C4×SD16—21no—
352C4×SD16—21no—
353C4×SD16—21no—
354C4×SD16—21no—
355C4×SD16—21no—
356C4×SD16—21no—
357C4×SD16—21no—
358C4×SD16—21no—
359C4×SD16—21no—
360C4×SD16—21no—
361C4×SD16—21no—
362C4×SD16—21no—
363C4×SD16—21no—
364C4×SD16—21no—
365C4×SD16—21no—
366C4×D8—22no—
367C4×D8—22no—
368C4×D8—21no—
369C4×D8—21no—
370C4×D8—22no—
371C4×D8—22no—
372C4×D8—22no—
373C4×D8—21no—
374C4×D8—22no—
375C4×D8—21no—
376C4×D8C22×C414yes—
377C4×D8C22×C411yescharacteristic
378C4×D8C22×C411yescharacteristic
379C4×D8C22×C411yescharacteristic
380C4×D8C22×C411yescharacteristic
381C4×D8C22×C411yescharacteristic
382C4×D8C22×C411yescharacteristic
383C4×D8C2411yescharacteristic
384C4×D8C2414yes—
385C4×D8C2411yescharacteristic
386#436—28no—
387#436—24no—
388#436—44no—
389#436—44no—
390#436—44no—
391#435—44no—
392#435—48no—
393#435—44no—
394#435—44no—
395C8×D4—24no—
396C8×D4—28no—
397C8×D4—44no—
398C8×D4—44no—
399C8×D4—44no—
400#432—22no—
401#432—22no—
402#432—42no—
403#432—42no—
404#432—41no—
405#432—41no—
406#431—21no—
407#431—21no—
408#431—22no—
409#431—22no—
410#431—42no—
411#431—42no—
412#431—41no—
413#431—41no—
414#431C2×D412yes—
415#431C2×D412yes—
416#427—21no—
417#427—21no—
418#427C22×C411yescharacteristic
419#427C22×C411yescharacteristic
420#427C22×C411yescharacteristic
421#427C22×C411yescharacteristic
422C2×#107—21no—
423C2×#107C22×C412yes—
424C2×#107C22×C411yescharacteristic
425C2×#107C22×C411yescharacteristic
426C2×#106—21no—
427#423—22no—
428#423—22no—
429#423—42no—
430C2×C4⋊C8—21no—
431#416—21no—
432#416—21no—
433#416—21no—
434#416—21no—
435#416—21no—
436#416—21no—
437#416—21no—
438#416—21no—
439C2×#103—21no—
440C2×#103—21no—
441C2×#102—22no—
442C2×#102—21no—
443C2×#102—22no—
444C2×#102—21no—
445#408—48no—
446#408—44no—
447#407—44no—
448#407—42no—
449#407—41no—
450#407—41no—
451C2×C22⋊C8—21no—
452C2×C22⋊C8—44no—
453C4×M16—21no—
454C4×M16—21no—
455C4×M16—42no—
456C4×M16—42no—
457C4×M16—42no—
458C4×M16—41no—
459C4×M16—41no—
460C4×M16C2×D412yes—
461C4×M16C2×D412yes—
462C2×#97—21no—
463C2×#97—42no—
464C2×C4×C8—42no—
465C2×C4×C8C22×C411yescharacteristic
466C2×C4×C8C22×C411yescharacteristic
467C2×C4×C8C22×C411yescharacteristic
468C2×C4×C8C2×D412yes—
469C2×C4×C8C2×D412yes—
470C2×C4×C8C2×D411yescharacteristic
471C2×C4×C8C2×D411yescharacteristic
472C2×C4×C8C2×D411yescharacteristic
473C2×C4×C8#4111yescharacteristic
474C2×C4×C8#4111yescharacteristic
475C2×C4×C8#4111yescharacteristic
476C2×C4×C8C2411yescharacteristic
477C2×C4×C8C2411yescharacteristic
478C2×C4×C8C2411yescharacteristic
479#367C22×C414yes—
480#367C22×C414yes—
481#366C22×C414yes—
482#366C22×C414yes—
483C4⋊C16—22no—
484C4⋊C16—22no—
485C4⋊C16C22×C412yes—
486C4⋊C16C22×C412yes—
487C4⋊C16C22×C412yes—
488C4⋊C16C22×C412yes—
489#358C22×C414yes—
490#358C22×C414yes—
491#357C22×C414yes—
492#357C22×C414yes—
493#357C22×C414yes—
494#357C22×C414yes—
495#357C22×C414yes—
496#357C22×C414yes—
497C22⋊C16—22no—
498C22⋊C16—22no—
499C22⋊C16C22×C414yes—
500C22⋊C16C22×C414yes—
501#346C2414yes—
502#346C2414yes—
503C4×C16—22no—
504C4×C16C22×C414yes—
505#335—22no—
506#335—22no—
507#335—22no—
508#335—22no—
509#334—22no—
510#334—22no—
511#334C2414yes—
512#334C2414yes—
513Q8⋊C8—24no—
514Q8⋊C8—24no—
515D4⋊C8—24no—
516D4⋊C8—28no—
517D4⋊C8—28no—
518D4⋊C8—24no—
519#322C2×D414yes—
520#322C2×D414yes—
521#322C2×D414yes—
522#322C2414yes—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41—21no—
526C2×#41—21no—
527C2×#41—42no—
528C2×#41—42no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—42no—
532C2×#41—42no—
533C2×#41—44no—
534C2×#41—82no—
535C2×#41—164no—
536C22×Q8—21no—
537C22×Q8—41no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—41no—
541C22×D4—42no—
542C22×D4—41no—
543C22×D4—41no—
544C23×C4—41no—
545C23×C4—41no—
546C23×C4—42no—
547C23×C4—41no—
548C23×C4C4×D411yescharacteristic
549C23×C4AGL(1,ℤ/8)11yescharacteristic
550C23×C4AGL(1,ℤ/8)11yescharacteristic
551#135—22no—
552#135—22no—
553#135—22no—
554#135—22no—
555#135—41no—
556#135—41no—
557#135—41no—
558#135—41no—
559#135—44no—
560#135—44no—
561C2×Q16—22no—
562C2×Q16—21no—
563C2×Q16—41no—
564C2×Q16C23×C411yescharacteristic
565C2×Q16C23×C411yescharacteristic
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—44no—
571C2×D8—22no—
572C2×D8—22no—
573C2×D8—21no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—41no—
577C2×D8—42no—
578C2×D8—42no—
579C2×D8—82no—
580C2×D8C23×C411yescharacteristic
581C2×D8C23×C414yes—
582C2×D8C23×C411yescharacteristic
583#131—168no—
584C2×M16—22no—
585C2×M16—22no—
586C2×M16—44no—
587C2×M16—48no—
588C2×M16—42no—
589C2×M16—42no—
590C2×M16—82no—
591C2×M16—88no—
592C22×C8—22no—
593C22×C8—22no—
594C22×C8—41no—
595C22×C8—41no—
596C22×C8—44no—
597C22×C8—48no—
598C22×C8—81no—
599C22×C8C4×D411yescharacteristic
600C22×C8C4×D411yescharacteristic
601C22×C8C4×D411yescharacteristic
602C22×C8C4×D411yescharacteristic
603C22×C8C4×D411yescharacteristic
604C22×C8C4×D411yescharacteristic
605C22×C8C23×C411yescharacteristic
606C22×C8C23×C411yescharacteristic
607C22×C8C23×C411yescharacteristic
608C22×C8C2×#4111yescharacteristic
609C22×C8C2×#4111yescharacteristic
610C22×C8C2×#4111yescharacteristic
611C4⋊Q8—22no—
612C4⋊Q8—22no—
613C4⋊Q8—41no—
614C4⋊Q8—41no—
615#127—22no—
616#127—22no—
617#127—41no—
618#127—41no—
619#124—42no—
620#124—42no—
621#124—42no—
622#124—42no—
623#121—24no—
624#121—24no—
625#121—42no—
626#121—42no—
627#121—42no—
628#121—42no—
629#121—42no—
630#121—42no—
631C4×Q8—21no—
632C4×Q8—21no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—21no—
637C4×Q8—21no—
638C4×Q8—21no—
639C4×Q8—41no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—21no—
648C4×D4—21no—
649C4×D4—24no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—24no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661C4×D4—41no—
662C4×D4—41no—
663C4×D4—41no—
664C4×D4—41no—
665C4×D4—41no—
666C4×D4—41no—
667C4×D4—41no—
668C4×D4—41no—
669C4×D4—41no—
670C4×D4—41no—
671C4×D4—42no—
672C4×D4—42no—
673C4×D4—42no—
674C4×D4—42no—
675C4×D4—41no—
676C4×D4—41no—
677C4×D4—42no—
678C4×D4—42no—
679#117—21no—
680#117—21no—
681#117—21no—
682#117—21no—
683#117—41no—
684#117—41no—
685#117—41no—
686#117—41no—
687#117—41no—
688#117—41no—
689#117—41no—
690#117—41no—
691#117—41no—
692#117—41no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—41no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—42no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—42no—
704C2×C42—41no—
705C2×C42—41no—
706C2×C42—41no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42C4×D411yescharacteristic
716C2×C42C4×D411yescharacteristic
717C2×C42C4×D411yescharacteristic
718C2×C42AGL(1,ℤ/8)11yescharacteristic
719C2×C42AGL(1,ℤ/8)11yescharacteristic
720C2×C42AGL(1,ℤ/8)11yescharacteristic
721C2×C42AGL(1,ℤ/8)11yescharacteristic
722C2×C42AGL(1,ℤ/8)11yescharacteristic
723C2×C42AGL(1,ℤ/8)11yescharacteristic
724C2×C42C22×D411yescharacteristic
725C2×C42C22×D411yescharacteristic
726C2×C42C22×D411yescharacteristic
727SD32—28no—
728SD32—44no—
729D16—28no—
730D16—44no—
731M32—42no—
732M32—42no—
733M32—82no—
734C2×C16—24no—
735C2×C16C23×C414yes—
736C2×C16C23×C414yes—
737#107—22no—
738#107—22no—
739#107—21no—
740#107—21no—
741#107—22no—
742#107C23×C411yescharacteristic
743#107C23×C411yescharacteristic
744#107C23×C411yescharacteristic
745#107C23×C411yescharacteristic
746#107C23×C414yes—
747#106—21no—
748#106—21no—
749#106—21no—
750#106—21no—
751C4⋊C8—22no—
752C4⋊C8—22no—
753C4⋊C8—24no—
754C4⋊C8—24no—
755C4⋊C8—44no—
756C4⋊C8—44no—
757C4⋊C8—42no—
758C4⋊C8—42no—
759#103—21no—
760#103—21no—
761#103—21no—
762#103—21no—
763#103—21no—
764#103—21no—
765#103—21no—
766#103—21no—
767#102—21no—
768#102—21no—
769#102—21no—
770#102—21no—
771#102—21no—
772#102—21no—
773#102—24no—
774#102—24no—
775#102—24no—
776#102—21no—
777#102—21no—
778#102—24no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781C22⋊C8—48no—
782C22⋊C8—48no—
783C22⋊C8—44no—
784C22⋊C8—44no—
785C22⋊C8—42no—
786C22⋊C8—42no—
787C22⋊C8—42no—
788C22⋊C8—42no—
789#97—22no—
790#97—22no—
791#97—44no—
792#97—42no—
793#97—42no—
794C4×C8—22no—
795C4×C8—22no—
796C4×C8—44no—
797C4×C8—42no—
798C4×C8—42no—
799C4×C8C4×D411yescharacteristic
800C4×C8C4×D411yescharacteristic
801C4×C8C4×D411yescharacteristic
802C4×C8C4×D411yescharacteristic
803C4×C8C4×D411yescharacteristic
804C4×C8C4×D411yescharacteristic
805C4×C8C23×C411yescharacteristic
806C4×C8C23×C411yescharacteristic
807C4×C8C23×C411yescharacteristic
808C4×C8C22×D414yes—
809C4×C8C22×D414yes—
810C4×C8C22×D411yescharacteristic
811C4×C8C22×D411yescharacteristic
812C4×C8C22×D411yescharacteristic
813C4×C8C2×#4111yescharacteristic
814C4×C8C2×#4111yescharacteristic
815C4×C8C2×#4111yescharacteristic
816C4×C8C2511yescharacteristic
817C24—41no—
818C24—42no—
819C24#44211yescharacteristic
820#41—24no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41—81no—
827#41—81no—
828#41—88no—
829#41—84no—
830#41—84no—
831#41—164no—
832#41—164no—
833#41—164no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—42no—
837C2×Q8—41no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—162no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—24no—
845C2×D4—42no—
846C2×D4—41no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—41no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—81no—
859C2×D4—82no—
860C2×D4—82no—
861C2×D4—84no—
862C2×D4—84no—
863C2×D4—162no—
864C2×D4—164no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—42no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—41no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—44no—
884C22×C4—41no—
885C22×C4—41no—
886C22×C4—44no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—162no—
890C22×C4—164no—
891C22×C4#44211yescharacteristic
892C22×C4#44211yescharacteristic
893C22×C4#44211yescharacteristic
894C22×C4#44211yescharacteristic
895C22×C4#44211yescharacteristic
896C22×C4#44211yescharacteristic
897C22×C4#44211yescharacteristic
898C22×C4#44211yescharacteristic
899C22×C4#44211yescharacteristic
900C22×C4C2×C4×D411yescharacteristic
901C22×C4C2×C4×D411yescharacteristic
902C22×C4C2×C4×D411yescharacteristic
903C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
904C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
905C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
906C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
907C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
908C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
909Q16—21no—
910Q16—21no—
911Q16—21no—
912Q16—42no—
913Q16#56812yes—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917SD16—42no—
918D8—21no—
919D8—24no—
920D8—21no—
921D8—24no—
922D8—21no—
923D8—42no—
924D8—44no—
925D8—82no—
926D8—82no—
927D8#56812yes—
928M16—44no—
929M16—82no—
930M16—88no—
931M16—84no—
932M16—84no—
933M16—168no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—24no—
941C2×C8—24no—
942C2×C8—41no—
943C2×C8—41no—
944C2×C8—41no—
945C2×C8—41no—
946C2×C8—41no—
947C2×C8—41no—
948C2×C8—41no—
949C2×C8—41no—
950C2×C8—41no—
951C2×C8—44no—
952C2×C8—44no—
953C2×C8—44no—
954C2×C8—82no—
955C2×C8—88no—
956C2×C8—168no—
957C2×C8C2×C4×D411yescharacteristic
958C2×C8C2×C4×D411yescharacteristic
959C2×C8C2×C4×D411yescharacteristic
960C2×C8C2×C4×D411yescharacteristic
961C2×C8C2×C4×D411yescharacteristic
962C2×C8C2×C4×D411yescharacteristic
963C2×C8C24×C411yescharacteristic
964C2×C8C22×#4111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—42no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—41no—
997C22⋊C4—41no—
998C22⋊C4—44no—
999C42—41no—
1000C42—41no—
1001C42—41no—
1002C42—41no—
1003C42—41no—
1004C42—41no—
1005C42—41no—
1006C42—41no—
1007C42—41no—
1008C42—41no—
1009C42—41no—
1010C42—41no—
1011C42#44211yescharacteristic
1012C42#44211yescharacteristic
1013C42#44211yescharacteristic
1014C42#44211yescharacteristic
1015C42#44211yescharacteristic
1016C42#44211yescharacteristic
1017C42C2×C4×D411yescharacteristic
1018C42C2×C4×D411yescharacteristic
1019C42C2×C4×D411yescharacteristic
1020C42C2×AGL(1,ℤ/8)11yescharacteristic
1021C42C2×AGL(1,ℤ/8)11yescharacteristic
1022C42C2×AGL(1,ℤ/8)11yescharacteristic
1023C42C2×AGL(1,ℤ/8)11yescharacteristic
1024C42C2×AGL(1,ℤ/8)11yescharacteristic
1025C42C2×AGL(1,ℤ/8)11yescharacteristic
1026C42C23×D411yescharacteristic
1027C16—24no—
1028C16—24no—
1029C16—44no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—44no—
1036C23—82no—
1037C23—82no—
1038C23—84no—
1039C23—161no—
1040C23—162no—
1041C23—162no—
1042C23C2×#44211yescharacteristic
1043C23C2×#44211yescharacteristic
1044C23C2×#44211yescharacteristic
1045Q8—22no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—82no—
1050Q8—84no—
1051Q8—162no—
1052D4—22no—
1053D4—44no—
1054D4—41no—
1055D4—44no—
1056D4—41no—
1057D4—41no—
1058D4—44no—
1059D4—82no—
1060D4—84no—
1061D4—82no—
1062D4—82no—
1063D4—82no—
1064D4—88no—
1065D4—84no—
1066D4—84no—
1067D4—162no—
1068D4—162no—
1069D4—164no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—44no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—44no—
1099C2×C4—82no—
1100C2×C4—82no—
1101C2×C4—82no—
1102C2×C4—88no—
1103C2×C4—82no—
1104C2×C4—82no—
1105C2×C4—82no—
1106C2×C4—82no—
1107C2×C4—82no—
1108C2×C4—82no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—161no—
1112C2×C4—161no—
1113C2×C4—164no—
1114C2×C4—161no—
1115C2×C4—162no—
1116C2×C4C2×#44211yescharacteristic
1117C2×C4C2×#44211yescharacteristic
1118C2×C4C2×#44211yescharacteristic
1119C2×C4C2×#44211yescharacteristic
1120C2×C4C2×#44211yescharacteristic
1121C2×C4C2×#44211yescharacteristic
1122C2×C4C2×#44211yescharacteristic
1123C2×C4C2×#44211yescharacteristic
1124C2×C4C2×#44211yescharacteristic
1125C2×C4C22×C4×D411yescharacteristic
1126C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1127C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1128C8—21no—
1129C8—21no—
1130C8—21no—
1131C8—21no—
1132C8—21no—
1133C8—21no—
1134C8—21no—
1135C8—44no—
1136C8—44no—
1137C8—84no—
1138C8—84no—
1139C8C2×#56811yescharacteristic
1140C8C2×#56811yescharacteristic
1141C22—21no—
1142C22—21no—
1143C22—21no—
1144C22—21no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—42no—
1151C22—82no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—84no—
1156C22—81no—
1157C22—84no—
1158C22—84no—
1159C22—81no—
1160C22—164no—
1161C22—324no—
1162C22C22×#44211yescharacteristic
1163C4—21no—
1164C4—21no—
1165C4—21no—
1166C4—21no—
1167C4—21no—
1168C4—21no—
1169C4—21no—
1170C4—21no—
1171C4—21no—
1172C4—42no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—84no—
1179C4#3346812yes—
1180C4#3347112yes—
1181C4#6014111yescharacteristic
1182C4#6018211yescharacteristic
1183C2—41no—
1184C2—41no—
1185C2—41no—
1186C2—82no—
1187C2—161no—
1188C2—164no—
1189C2#634528711yescharacteristic
1190C2C2×#3346811yescharacteristic
1191C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623099C2
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. #6345030C2semidirect
4. #484105C2semidirect
5. #484103C2semidirect
6. #484061C2semidirect
7. #484058C2semidirect
8. #483927C2semidirect
9. #483881C2semidirect
10. #483445C2semidirect
11. #481384C2semidirect
12. #481281C2semidirect
13. #479974C2semidirect
39. #18064C22semidirect
41. #18044C22semidirect
43. #18042C22semidirect
47. #17962C22semidirect
48. #17890C22semidirect
50. #17849C22semidirect
56. #12089C22semidirect
57. #12087C22semidirect
58. #12080C22semidirect
59. #12078C22semidirect
60. #12078C22semidirect
61. #12077C22semidirect
62. #12067C22semidirect
63. #12065C22semidirect
64. #12029C22semidirect
65. #12029C22semidirect
66. #12021C22semidirect
68. #11667C22semidirect
69. #11666C22semidirect
70. #11666C22semidirect
73. #11652C22semidirect
74. #11600C22semidirect
75. #11599C22semidirect
76. #11415C22semidirect
77. #11414C22semidirect
78. #11414C22semidirect

Maximal subgroups

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

subgroupindex
#76230992
#63457222
#63450302
#4841052
#4841032
#4840612
#4840582
#4839272
#4838812
#4834452
#4813842
#4812812
#4799742