Finite Group Databasebeta

← #72313868

Subgroups — #72313868

Order 1024.

2900 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623358C211yesmaximal, characteristic
2#6389901C211yesmaximal, characteristic, complemented
3#6382990C211yesmaximal, characteristic, complemented
4#498621C214yesmaximal, complemented
5#498578C214yesmaximal, complemented
6#498120C218yesmaximal, complemented
7#496984C214yesmaximal, complemented
8#496605C211yesmaximal, characteristic, complemented
9#495845C214yesmaximal, complemented
10#495476C211yesmaximal, characteristic, complemented
11C2×#13255C211yesmaximal, characteristic, complemented
12#493301C211yesmaximal, characteristic, complemented
13C2×#3169C2211yescharacteristic
14C2×#3147C2211yescharacteristic
15#60237—21no—
16#34236—21no—
17#33780C414yescomplemented
18#33779C414yescomplemented
19#33773C414yescomplemented
20#33772C412yescomplemented
21#33771C412yescomplemented
22#33717C2212yes—
23#33707C2212yes—
24#33580C2214yes—
25#33520C2214yes—
26C2×AGL(1,ℤ/16)C2218yescomplemented
27#33418C2211yescharacteristic
28C2×#2150C2211yescharacteristic
29C22×#360C2214yes—
30#23215—22no—
31#23188C2212yescomplemented
32#23180C2214yes—
33#23179—22no—
34#23162C2212yescomplemented
35#23127—22no—
36#23029C2214yes—
37#22454—22no—
38#22452C2214yes—
39#22282—22no—
40#21816—21no—
41#21707C2214yes—
42#21395—21no—
43#21284C2212yescomplemented
44#21134—22no—
45#20826C2211yescharacteristic
46#20503C2212yescomplemented
47#20476C2211yescharacteristic
48C2×C4×#106C2211yescharacteristic
49#13279C2212yescomplemented
50#13257C2212yescomplemented
51#13255C2212yes—
52#13255C2214yes—
53#13255C2212yes—
54#13249C2218yescomplemented
55#13185C2212yescomplemented
56#13185C2212yescomplemented
57#13153C2218yescomplemented
58#13143C2218yescomplemented
59#13067C2214yes—
60#13040C2218yescomplemented
61#13037C2218yescomplemented
62#12955C2218yescomplemented
63#12929C2214yes—
64#12818C2214yescomplemented
65C4×#365C2214yescomplemented
66#12666C2214yescomplemented
67#12657C2214yescomplemented
68#12650C2218yescomplemented
69#12616C2214yes—
70C22×#135—21no—
71C22×#135C2312yes—
72C2×#532—21no—
73C2×#532—21no—
74C2×#509C2318yes—
75C22×M32C2312yes—
76#3169—21no—
77#3169—21no—
78#3169—21no—
79#3169—21no—
80#3169C2×C412yes—
81#3169C2×C412yes—
82#3169C2×C412yes—
83#3169C2×C412yes—
84C2×#500C2311yescharacteristic
85#3147—21no—
86#3147—21no—
87#3147—21no—
88#3147—21no—
89#3147C2×C412yescomplemented
90#3147C2×C412yescomplemented
91#3147C2312yes—
92#3147C2312yes—
93C2×#495—21no—
94C2×#495C2×C412yescomplemented
95C2×#494C2×C411yescharacteristic, complemented
96C2×#493C2×C411yescharacteristic, complemented
97C2×#493C2311yescharacteristic
98C2×#492—21no—
99C2×#486—21no—
100C2×#466—21no—
101C2×#466C2312yes—
102#2981—42no—
103#2980—42no—
104#2974—42no—
105#2973—42no—
106C2×#444C2318yes—
107C2×#443—24no—
108C2×#442C2314yes—
109C2×C4×D8—21no—
110C2×C4×D8C2312yes—
111#2935—24no—
112#2932—24no—
113#2920—21no—
114C2×#432D411yescharacteristic
115C22×#106C2312yes—
116#2880—24no—
117C22×C4×C8C2311yescharacteristic
118#2369—22no—
119#2366—22no—
120#2361—24no—
121#2357—41no—
122#2349—41no—
123#2339—42no—
124#2337—42no—
125#2319—22no—
126C4×#121—42no—
127#2283D411yescharacteristic
128#2275—22no—
129C2×C4×C4⋊C4—21no—
130#2250C2×C418yescomplemented
131#2248C2×C414yescomplemented
132#2246C2×C414yescomplemented
133#2243C2×C418yescomplemented
134#2241C2×C414yescomplemented
135#2240C2×C414yescomplemented
136#2210C2×C4116yescomplemented
137#2208C2×C418yescomplemented
138#2206C2×C418yescomplemented
139#2186C2×C4116yescomplemented
140#2185C2×C418yescomplemented
141#2184C2×C418yescomplemented
142AGL(1,ℤ/16)—416no—
143#2163C2×C412yescomplemented
144#2163C2×C412yescomplemented
145#2162C2×C412yescomplemented
146#2162C2×C412yescomplemented
147C2×#365C2314yes—
148C2×#365C2314yes—
149#2150—21no—
150#2150—21no—
151#2150C2312yes—
152#2150C2312yes—
153#2150C2312yes—
154C2×C4⋊C16—21no—
155C2×C4⋊C16—21no—
156C2×#361C2318yes—
157C2×#360—48no—
158C2×#360C2318yes—
159C2×#360C2318yes—
160#2139C2318yes—
161#2112C2312yes—
162C2×#347C2318yes—
163C4×M32C2312yes—
164#1987—22no—
165#1982—22no—
166#1980—24no—
167#1975C2318yes—
168#1974—24no—
169#1972C2314yes—
170#1963—24no—
171#1943C2314yes—
172#1934—24no—
173#1926—24no—
174#1918—24no—
175#1879—24no—
176#1876—28no—
177#1876—28no—
178#1874—24no—
179#1864—24no—
180#1848C2312yes—
181#1837—21no—
182#1810—21no—
183#1810C2312yes—
184#1789—24no—
185C4×#108—21no—
186C4×#108C2312yes—
187#1776C2314yes—
188C4×#106—21no—
189C4×#106—21no—
190C4×#106C2311yescharacteristic
191C4×#106C2311yescharacteristic
192C4×#106C2312yes—
193#1770C2312yes—
194C8×C4⋊C4D412yes—
195#1762—22no—
196#1762—22no—
197C4×#102—24no—
198#1752C2312yes—
199C8×C22⋊C4D412yes—
200#1746D412yes—
201C2×#340—21no—
202#1726C2312yes—
203#1387C2318yes—
204#1383C2314yes—
205#1383C2314yes—
206#1375C2318yes—
207C22×#41—22no—
208C22×#41—41no—
209C2×#135—22no—
210C2×#135—22no—
211C2×#135—22no—
212C2×#135—22no—
213C2×#135—22no—
214C2×#135—22no—
215C2×#135—44no—
216C2×#135—44no—
217C2×#135—84no—
218C2×#135C22×C414yes—
219C2×#135C2414yes—
220C22×Q16—21no—
221C22×Q16C22×C412yes—
222C22×SD16—22no—
223C22×SD16—22no—
224C22×D8—21no—
225C22×D8—21no—
226C22×D8C22×C412yes—
227C22×D8C2412yes—
228C2×#131—28no—
229C23×C8C2×D411yescharacteristic
230C23×C8C2411yescharacteristic
231#532—22no—
232#532—22no—
233#532—22no—
234#532—22no—
235#532—22no—
236#532—22no—
237#532—22no—
238#532—22no—
239#532—41no—
240#532—41no—
241#532—41no—
242#532—41no—
243#532—41no—
244#532—41no—
245#532—41no—
246#532—41no—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—21no—
249C2×#127—21no—
250C2×#127—21no—
251C2×#124—22no—
252C2×#124—41no—
253C2×#121—22no—
254C2×#121—41no—
255C2×#121—41no—
256C2×#121—41no—
257C2×C4×D4—22no—
258C2×C4×D4—24no—
259C2×C4×D4—44no—
260C2×C4×D4—42no—
261C2×C4×D4—41no—
262C2×C4×D4—41no—
263C2×C4×D4—41no—
264C22×C4⋊C4—22no—
265C22×C42—41no—
266C22×C42C2×D411yescharacteristic
267#509—48no—
268#509—48no—
269C2×SD32C22×C4116yes—
270C2×D16C22×C4116yes—
271C2×M32—22no—
272C2×M32—44no—
273C2×M32C2414yes—
274C2×M32C2414yes—
275C22×C16—22no—
276#500—21no—
277#500—21no—
278#500C22×C412yes—
279#500C22×C412yes—
280#495—22no—
281#495—22no—
282#495—22no—
283#495—22no—
284#495—22no—
285#495—22no—
286#495C22×C414yes—
287#495C22×C414yes—
288#494—21no—
289#494—21no—
290#494C22×C412yes—
291#494C22×C412yes—
292#493—21no—
293#493—21no—
294#493—21no—
295#493—21no—
296#493C22×C412yes—
297#493C22×C412yes—
298#493C22×C412yes—
299#493C22×C412yes—
300#492—22no—
301#492—22no—
302#492—22no—
303#492—22no—
304#486—22no—
305#486—22no—
306#486—22no—
307#486—22no—
308#466—22no—
309#466—22no—
310#466—22no—
311#466—22no—
312#466—22no—
313#466—22no—
314#466C22×C414yes—
315#466C22×C414yes—
316#444—48no—
317#444—48no—
318#443—88no—
319#442—28no—
320#442—44no—
321C4×D8—22no—
322C4×D8—22no—
323C4×D8—22no—
324C4×D8—22no—
325C4×D8—22no—
326C4×D8—22no—
327C4×D8C22×C414yes—
328C4×D8C22×C414yes—
329#436—44no—
330#435—48no—
331#435—48no—
332#435—48no—
333C8×D4—44no—
334#432—21no—
335#432—21no—
336#432—21no—
337#432—21no—
338#432—41no—
339#432—41no—
340#431—41no—
341#431—41no—
342C2×#108—22no—
343C2×#108C2414yes—
344C2×#107—21no—
345C2×#107C2412yes—
346C2×#106—24no—
347C2×#106—22no—
348C2×#106—42no—
349C2×#106C2412yes—
350C2×#106C2412yes—
351#423—22no—
352C2×C4⋊C8C2×D412yes—
353C2×#104—28no—
354C2×#104—28no—
355C2×#102—22no—
356C2×#102—22no—
357C2×#102—24no—
358C2×#102—24no—
359#408—28no—
360#408—48no—
361#407—22no—
362#407—44no—
363C2×C22⋊C8—44no—
364C2×C22⋊C8C2×D412yes—
365C4×M16—22no—
366C2×#97C2×D412yes—
367C2×#97C2414yes—
368C2×C4×C8C22×C411yescharacteristic
369C2×C4×C8C22×C411yescharacteristic
370C2×C4×C8C22×C411yescharacteristic
371C2×C4×C8C22×C411yescharacteristic
372C2×C4×C8C2×D414yes—
373C2×C4×C8C2×D411yescharacteristic
374C2×C4×C8C2×D411yescharacteristic
375C2×C4×C8#4111yescharacteristic
376C2×C4×C8#4111yescharacteristic
377C2×C4×C8#4111yescharacteristic
378C2×C4×C8#4111yescharacteristic
379C2×C4×C8C2411yescharacteristic
380C2×C4×C8C2411yescharacteristic
381#391—44no—
382#390—24no—
383#390—42no—
384#389—24no—
385#389—42no—
386#388—44no—
387#388—44no—
388#386—44no—
389#386—44no—
390#385—44no—
391#383—21no—
392#382—21no—
393#381—21no—
394#381—42no—
395#380—21no—
396#380—42no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—24no—
399C4×C4⋊C4—22no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—42no—
402C4×C4⋊C4—41no—
403C4×C4⋊C4—41no—
404C4×C4⋊C4C2×D412yes—
405C4×C22⋊C4—44no—
406C4×C22⋊C4—42no—
407C4×C22⋊C4C2×D412yes—
408#376C2×D412yes—
409C2×#95—42no—
410C2×#95—41no—
411#365—28no—
412#365—44no—
413C4⋊C16—22no—
414C4⋊C16—22no—
415C4⋊C16—22no—
416C4⋊C16—22no—
417C4⋊C16C22×C414yes—
418C4⋊C16C22×C414yes—
419#361—48no—
420#360—216no—
421#360—48no—
422#358C22×C4116yes—
423#357C22×C4116yes—
424C22⋊C16C22×C414yes—
425C22⋊C16C22×C414yes—
426#347—48no—
427#346C22×C414yes—
428C4×C16C22×C414yes—
429#341—22no—
430#341—22no—
431#340—24no—
432#340—24no—
433#340—22no—
434#340—21no—
435#340—21no—
436#336C2×D414yes—
437#336C2×D414yes—
438C2×#41—24no—
439C2×#41—24no—
440C2×#41—42no—
441C2×#41—42no—
442C2×#41—42no—
443C2×#41—42no—
444C2×#41—42no—
445C2×#41—42no—
446C2×#41—84no—
447C2×#41—84no—
448C2×#41—164no—
449C22×Q8—22no—
450C22×Q8—41no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4—41no—
458C22×D4—41no—
459C23×C4—44no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4AGL(1,ℤ/8)11yescharacteristic
464C23×C4AGL(1,ℤ/8)11yescharacteristic
465C23×C4C22×D411yescharacteristic
466#135—28no—
467#135—28no—
468#135—48no—
469#135—48no—
470#135—82no—
471#135—82no—
472#135—84no—
473#135—84no—
474#135—84no—
475#135—84no—
476C2×Q16—22no—
477C2×Q16—22no—
478C2×Q16—22no—
479C2×Q16—44no—
480C2×Q16—82no—
481C2×Q16C23×C414yes—
482C2×SD16—24no—
483C2×SD16—24no—
484C2×SD16—24no—
485C2×SD16—24no—
486C2×SD16—82no—
487C2×SD16—82no—
488C2×SD16—84no—
489C2×D8—22no—
490C2×D8—22no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—22no—
495C2×D8—24no—
496C2×D8—24no—
497C2×D8—44no—
498C2×D8—82no—
499C2×D8—82no—
500C2×D8C23×C414yes—
501C2×D8C23×C414yes—
502#131—88no—
503#131—88no—
504C2×M16—24no—
505C2×M16—48no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—42no—
509C22×C8—48no—
510C22×C8C4×D411yescharacteristic
511C22×C8C4×D411yescharacteristic
512C22×C8C4×D411yescharacteristic
513C22×C8C4×D411yescharacteristic
514C22×C8C23×C411yescharacteristic
515C22×C8C23×C411yescharacteristic
516C22×C8C22×D414yes—
517C22×C8C22×D411yescharacteristic
518C22×C8C22×D411yescharacteristic
519C22×C8C22×D411yescharacteristic
520C22×C8C2×#4111yescharacteristic
521C22×C8C2×#4111yescharacteristic
522C22×C8C2511yescharacteristic
523C4⋊Q8—22no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531#127—22no—
532#127—22no—
533#127—22no—
534#127—22no—
535#127—41no—
536#127—41no—
537#127—41no—
538#127—41no—
539#124—24no—
540#124—24no—
541#124—42no—
542#124—42no—
543#124—42no—
544#124—42no—
545#124—42no—
546#124—42no—
547#121—24no—
548#121—24no—
549#121—42no—
550#121—42no—
551#121—42no—
552#121—42no—
553#121—42no—
554#121—42no—
555#121—42no—
556#121—42no—
557#121—42no—
558#121—42no—
559#121—42no—
560#121—42no—
561#121—42no—
562#121—42no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—48no—
566C4×D4—42no—
567C4×D4—42no—
568C4×D4—42no—
569C4×D4—42no—
570C4×D4—42no—
571C4×D4—42no—
572C4×D4—42no—
573C4×D4—42no—
574C4×D4—42no—
575C4×D4—42no—
576C4×D4—42no—
577C4×D4—42no—
578C4×D4—42no—
579C4×D4—42no—
580C4×D4—84no—
581C4×D4—164no—
582C4×D4—168no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—82no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—44no—
600C2×C22⋊C4—44no—
601C2×C22⋊C4—44no—
602C2×C42—42no—
603C2×C42—44no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—162no—
607C2×C42C4×D411yescharacteristic
608C2×C42C4×D411yescharacteristic
609C2×C42C4×D411yescharacteristic
610C2×C42C4×D411yescharacteristic
611C2×C42AGL(1,ℤ/8)11yescharacteristic
612C2×C42AGL(1,ℤ/8)11yescharacteristic
613C2×C42AGL(1,ℤ/8)11yescharacteristic
614C2×C42AGL(1,ℤ/8)11yescharacteristic
615C2×C42AGL(1,ℤ/8)11yescharacteristic
616C2×C42AGL(1,ℤ/8)11yescharacteristic
617C2×C42C22×D414yes—
618C2×C42C22×D411yescharacteristic
619C2×C42C22×D411yescharacteristic
620SD32—416no—
621D16—416no—
622M32—24no—
623M32—24no—
624M32—28no—
625M32—82no—
626C2×C16—24no—
627C2×C16—82no—
628C2×C16C23×C418yes—
629#108—24no—
630#108—24no—
631#108—44no—
632#107—22no—
633#107—22no—
634#107—22no—
635#107C23×C414yes—
636#106—22no—
637#106—22no—
638#106—22no—
639#106—44no—
640#106H(5,𝔽2)14yes—
641C4⋊C8—22no—
642C4⋊C8—22no—
643C4⋊C8—42no—
644C4⋊C8—42no—
645#104—88no—
646#104—88no—
647#102—24no—
648#102—24no—
649#102—24no—
650#102—24no—
651#102—48no—
652#102—84no—
653C22⋊C8—22no—
654C22⋊C8—22no—
655C22⋊C8—48no—
656C22⋊C8—48no—
657C22⋊C8—42no—
658C22⋊C8—42no—
659#97—24no—
660#97—24no—
661#97—22no—
662#97—22no—
663#97—42no—
664C4×C8—44no—
665C4×C8—42no—
666C4×C8C4×D411yescharacteristic
667C4×C8C4×D411yescharacteristic
668C4×C8C4×D411yescharacteristic
669C4×C8C4×D411yescharacteristic
670C4×C8C4×D411yescharacteristic
671C4×C8C4×D411yescharacteristic
672C4×C8C4×D411yescharacteristic
673C4×C8C4×D411yescharacteristic
674C4×C8C23×C411yescharacteristic
675C4×C8C23×C411yescharacteristic
676C4×C8C23×C411yescharacteristic
677C4×C8C23×C411yescharacteristic
678C4×C8C2×#4111yescharacteristic
679C4×C8C2×#4111yescharacteristic
680C4×C8C2×#4111yescharacteristic
681C4×C8C2×#4111yescharacteristic
682#95—22no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—44no—
687#95—44no—
688#95—41no—
689#95—41no—
690#95—42no—
691C24—42no—
692C24—42no—
693C24C2×AGL(1,ℤ/8)11yescharacteristic
694#41—48no—
695#41—48no—
696#41—84no—
697#41—84no—
698#41—164no—
699#41—164no—
700#41—164no—
701#41—164no—
702#41—164no—
703#41—164no—
704C2×Q8—24no—
705C2×Q8—42no—
706C2×Q8—42no—
707C2×Q8—42no—
708C2×Q8—82no—
709C2×Q8—82no—
710C2×Q8—162no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—82no—
730C2×D4—82no—
731C2×D4—82no—
732C2×D4—82no—
733C2×D4—88no—
734C2×D4—162no—
735C2×D4—162no—
736C2×D4—162no—
737C2×D4—164no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—24no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—42no—
751C22×C4—88no—
752C22×C4—84no—
753C22×C4—84no—
754C22×C4—164no—
755C22×C4—164no—
756C22×C4—164no—
757C22×C4—164no—
758C22×C4—162no—
759C22×C4#44211yescharacteristic
760C22×C4#44211yescharacteristic
761C22×C4#44211yescharacteristic
762C22×C4#44211yescharacteristic
763C22×C4#44211yescharacteristic
764C22×C4#44211yescharacteristic
765C22×C4#44211yescharacteristic
766C22×C4#44211yescharacteristic
767C22×C4C2×C4×D411yescharacteristic
768C22×C4C2×C4×D411yescharacteristic
769C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
770C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
771C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
772C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
773C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
774C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
775C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
776C22×C4C23×D411yescharacteristic
777Q16—28no—
778Q16—44no—
779Q16—82no—
780Q16—82no—
781SD16—48no—
782SD16—44no—
783SD16—44no—
784SD16—84no—
785SD16—84no—
786D8—28no—
787D8—28no—
788D8—44no—
789D8—42no—
790D8—42no—
791D8—82no—
792D8—82no—
793D8—82no—
794D8—82no—
795M16—44no—
796M16—44no—
797M16—168no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8—22no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—24no—
808C2×C8—24no—
809C2×C8—24no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—41no—
814C2×C8—44no—
815C2×C8—168no—
816C2×C8C2×C4×D411yescharacteristic
817C2×C8C2×C4×D411yescharacteristic
818C2×C8C2×C4×D411yescharacteristic
819C2×C8C2×C4×D411yescharacteristic
820C2×C8C2×C4×D411yescharacteristic
821C2×C8C2×C4×D411yescharacteristic
822C2×C8C24×C411yescharacteristic
823C2×C8C22×#4111yescharacteristic
824C2×C8C2×H(5,𝔽2)12yes—
825C2×C8#58512yes—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—44no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—84no—
840C4⋊C4—164no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—88no—
851C22⋊C4—164no—
852C22⋊C4—164no—
853C42—24no—
854C42—24no—
855C42—84no—
856C42—161no—
857C42—161no—
858C42—164no—
859C42#44211yescharacteristic
860C42#44211yescharacteristic
861C42#44211yescharacteristic
862C42#44211yescharacteristic
863C42#44211yescharacteristic
864C42#44211yescharacteristic
865C42#44211yescharacteristic
866C42#44211yescharacteristic
867C42C2×C4×D411yescharacteristic
868C42C2×C4×D411yescharacteristic
869C42C2×C4×D411yescharacteristic
870C42C2×C4×D411yescharacteristic
871C42C2×AGL(1,ℤ/8)11yescharacteristic
872C42C2×AGL(1,ℤ/8)11yescharacteristic
873C42C2×AGL(1,ℤ/8)11yescharacteristic
874C42C2×AGL(1,ℤ/8)11yescharacteristic
875C16—28no—
876C16—44no—
877C23—22no—
878C23—22no—
879C23—41no—
880C23—44no—
881C23—44no—
882C23—82no—
883C23—84no—
884C23—82no—
885C23—84no—
886C23—84no—
887C23—162no—
888C23—162no—
889C23C2×#44211yescharacteristic
890C23C2×#44211yescharacteristic
891C23C22×AGL(1,ℤ/8)11yescharacteristic
892Q8—44no—
893Q8—44no—
894Q8—162no—
895Q8—162no—
896Q8—162no—
897D4—44no—
898D4—44no—
899D4—44no—
900D4—44no—
901D4—84no—
902D4—88no—
903D4—88no—
904D4—88no—
905D4—84no—
906D4—84no—
907D4—84no—
908D4—162no—
909D4—162no—
910D4—162no—
911D4—162no—
912D4—162no—
913D4—162no—
914D4—164no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—44no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4—82no—
941C2×C4—82no—
942C2×C4—84no—
943C2×C4—88no—
944C2×C4—82no—
945C2×C4—82no—
946C2×C4—82no—
947C2×C4—164no—
948C2×C4—164no—
949C2×C4—164no—
950C2×C4—162no—
951C2×C4—168no—
952C2×C4—328no—
953C2×C4C2×#44211yescharacteristic
954C2×C4C2×#44211yescharacteristic
955C2×C4C2×#44211yescharacteristic
956C2×C4C2×#44211yescharacteristic
957C2×C4C2×#44211yescharacteristic
958C2×C4C2×#44211yescharacteristic
959C2×C4C2×#44211yescharacteristic
960C2×C4C2×#44211yescharacteristic
961C2×C4C2×#44211yescharacteristic
962C2×C4C2×#44211yescharacteristic
963C2×C4C22×C4×D411yescharacteristic
964C2×C4#348812yes—
965C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
966C2×C4#358512yes—
967C8—21no—
968C8—21no—
969C8—21no—
970C8—21no—
971C8—21no—
972C8—21no—
973C8—44no—
974C8—84no—
975C8C4×H(5,𝔽2)12yes—
976C8#350811yescharacteristic
977C8#351011yescharacteristic
978C22—21no—
979C22—21no—
980C22—21no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—21no—
985C22—44no—
986C22—84no—
987C22—84no—
988C22—84no—
989C22—84no—
990C22—84no—
991C22—84no—
992C22—164no—
993C22—164no—
994C22—324no—
995C22#3347112yes—
996C22C22×#44211yescharacteristic
997C22#6196112yes—
998C4—21no—
999C4—21no—
1000C4—21no—
1001C4—21no—
1002C4—21no—
1003C4—21no—
1004C4—21no—
1005C4—21no—
1006C4—21no—
1007C4—84no—
1008C4—84no—
1009C4—84no—
1010C4—84no—
1011C4—162no—
1012C4#3346912yes—
1013C4#3426911yescharacteristic
1014C4#6016811yescharacteristic
1015C4#6196312yes—
1016C2—22no—
1017C2—22no—
1018C2—41no—
1019C2—164no—
1020C2—164no—
1021C2#639569811yescharacteristic
1022C2C2×#3346911yescharacteristic
1023C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radical#7623358C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ #20476 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6389901C2semidirect
3. #6382990C2semidirect
4. #498621C2semidirect
5. #498578C2semidirect
6. #498120C2semidirect
7. #496984C2semidirect
8. #496605C2semidirect
9. #495845C2semidirect
10. #495476C2semidirect
11. C2×#13255C2semidirect
12. #493301C2semidirect
17. #33780C4semidirect
18. #33779C4semidirect
19. #33773C4semidirect
20. #33772C4semidirect
21. #33771C4semidirect
26. C2×AGL(1,ℤ/16)C22semidirect
31. #23188C22semidirect
34. #23162C22semidirect
43. #21284C22semidirect
46. #20503C22semidirect
49. #13279C22semidirect
50. #13257C22semidirect
54. #13249C22semidirect
55. #13185C22semidirect
56. #13185C22semidirect
57. #13153C22semidirect
58. #13143C22semidirect
60. #13040C22semidirect
61. #13037C22semidirect
62. #12955C22semidirect
64. #12818C22semidirect
65. C4×#365C22semidirect
66. #12666C22semidirect
67. #12657C22semidirect
68. #12650C22semidirect
89. #3147C2×C4semidirect
90. #3147C2×C4semidirect
94. C2×#495C2×C4semidirect
95. C2×#494C2×C4semidirect
96. C2×#493C2×C4semidirect
130. #2250C2×C4semidirect
131. #2248C2×C4semidirect
132. #2246C2×C4semidirect
133. #2243C2×C4semidirect
134. #2241C2×C4semidirect
135. #2240C2×C4semidirect
136. #2210C2×C4semidirect
137. #2208C2×C4semidirect
138. #2206C2×C4semidirect
139. #2186C2×C4semidirect
140. #2185C2×C4semidirect
141. #2184C2×C4semidirect
143. #2163C2×C4semidirect
144. #2163C2×C4semidirect
145. #2162C2×C4semidirect
146. #2162C2×C4semidirect

Maximal subgroups

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

subgroupindex
#76233582
#63899012
#63829902
#4986212
#4985782
#4981202
#4969842
#4966052
#4958452
#4954762
C2×#132552
#4933012