Finite Group Databasebeta

← #72313211

Subgroups — #72313211

Order 1024.

3586 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#33717C211yesmaximal, characteristic
2#6389899C211yesmaximal, characteristic, complemented
3#6389853C211yesmaximal, characteristic, complemented
4#498578C218yesmaximal, complemented
5#497422C218yesmaximal, complemented
6#497146C214yesmaximal, complemented
7#496366C211yesmaximal, characteristic, complemented
8#496363C211yesmaximal, characteristic, complemented
9#496124C214yesmaximal, complemented
10#494192C211yesmaximal, characteristic, complemented
11#493201C211yesmaximal, characteristic, complemented
12C22×#509C2214yes—
13C2×#3147C2211yescharacteristic
14C22×#493C2211yescharacteristic
15#60236—21no—
16#34210—21no—
17#33717C414yescomplemented
18#33717C414yescomplemented
19#33717C2214yes—
20#33717C2212yes—
21#33717C2212yes—
22C2×#2250C414yescomplemented
23C2×#2248C412yescomplemented
24C2×#2246C412yescomplemented
25C2×AGL(1,ℤ/16)C22116yescomplemented
26#33418C2211yescharacteristic
27C2×C4×M32C2211yescharacteristic
28#23188—22no—
29#23188C2214yescomplemented
30#23180—22no—
31#23180C2214yescomplemented
32#22452—22no—
33#22452C2214yes—
34#22436—22no—
35#22436C2214yes—
36#22280—22no—
37#22269—22no—
38#21815—21no—
39#21803—21no—
40#21706C2214yescomplemented
41#21690C2214yescomplemented
42#20826C2211yescharacteristic
43#20816C2211yescharacteristic
44#20473C2211yescharacteristic
45#13257C2214yescomplemented
46#13255C2214yescomplemented
47#13249C22116yescomplemented
48#13213C2214yescomplemented
49#13210C2214yescomplemented
50#13040C22116yescomplemented
51#13037C22116yescomplemented
52#12903C2212yescomplemented
53#12886C2212yescomplemented
54#12831C2214yes—
55#12736C2214yes—
56#12735C2214yes—
57C4×#365C2214yescomplemented
58#12666C2214yescomplemented
59#12616C2214yes—
60#12594C2212yescomplemented
61C4×#347C2212yescomplemented
62C22×#135—21no—
63C22×#135C2312yes—
64C23×D8—21no—
65C23×D8C2312yes—
66C2×#532—21no—
67C22×#127—21no—
68C2×#518—41no—
69C2×#509—416no—
70C2×#509C2×C4116yescomplemented
71C2×#509C2318yes—
72C2×#509C2318yes—
73C22×SD32C2×C418yescomplemented
74C22×D16C2×C418yescomplemented
75C22×M32C2312yes—
76#3147—21no—
77#3147—21no—
78#3147—21no—
79#3147—21no—
80#3147C2×C412yescomplemented
81#3147C2×C412yescomplemented
82#3147C2312yes—
83#3147C2312yes—
84C2×#495—21no—
85C2×#495C2×C412yescomplemented
86C2×#494C2×C411yescharacteristic, complemented
87C2×#493—21no—
88C2×#493—21no—
89C2×#493—21no—
90C2×#493—21no—
91C2×#493—21no—
92C2×#493—21no—
93C2×#493C2×C412yes—
94C2×#493C2×C412yes—
95C2×#493C2×C412yes—
96C2×#493C2×C412yes—
97C2×#493C2×C411yescharacteristic, complemented
98C2×#493C2312yes—
99C2×#493C2312yes—
100C2×#492—21no—
101#2981—42no—
102#2979—42no—
103#2975—41no—
104#2974—42no—
105#2972—41no—
106C2×#444—24no—
107C2×#444C2318yes—
108C2×#442—24no—
109C2×#442C2318yes—
110#2935—24no—
111#2931—24no—
112#2920—21no—
113C2×#431D411yescharacteristic
114#2880—24no—
115C22×C4×C8C2311yescharacteristic
116#2366—24no—
117#2366—42no—
118D4×C22⋊C4—24no—
119D4×C22⋊C4—42no—
120#2328—42no—
121#2309—41no—
122C4×#127—24no—
123#2285—21no—
124C4×#117D411yescharacteristic
125#2250C2×C418yescomplemented
126#2250C2×C4116yescomplemented
127#2250C2×C418yescomplemented
128#2248C2×C414yescomplemented
129#2248C2×C418yescomplemented
130#2248C2×C414yescomplemented
131#2246C2×C414yescomplemented
132#2246C2×C418yescomplemented
133#2246C2×C414yescomplemented
134AGL(1,ℤ/16)—432no—
135#2163—21no—
136#2163—21no—
137#2162—21no—
138#2162—21no—
139C2×#365C2318yes—
140#2150C2312yes—
141C2×#361C23116yes—
142C2×#360C23116yes—
143#2112C2312yes—
144C2×#347C2318yes—
145C4×M32C2×C412yescomplemented
146C4×M32C2×C412yescomplemented
147C4×M32C2312yes—
148C4×M32C2311yescharacteristic
149C4×M32C2311yescharacteristic
150C4×M32C2312yes—
151C2×#346C2×C412yescomplemented
152C2×C4×C16C2×C412yescomplemented
153#1982—24no—
154#1980—24no—
155#1975—24no—
156#1975C2318yes—
157#1972—24no—
158#1972C2318yes—
159#1962—24no—
160#1957—24no—
161#1879—28no—
162#1879—28no—
163#1876—28no—
164#1876—28no—
165#1848C2312yes—
166#1844C2312yes—
167#1837—21no—
168#1834—21no—
169#1810—21no—
170#1810C2312yes—
171#1807—21no—
172#1807C2312yes—
173#1789—24no—
174#1786—24no—
175C4×#108—21no—
176C4×#108C2312yes—
177C4×#106—21no—
178C4×#106C2312yes—
179#1770D412yes—
180#1770C2312yes—
181#1752D412yes—
182#1752C2312yes—
183#1744D412yes—
184C4×#97C2312yes—
185#1383C2318yes—
186#1375C2318yes—
187C22×#41—22no—
188C23×D4—22no—
189C23×D4—41no—
190C23×D4—41no—
191C2×#135—22no—
192C2×#135—22no—
193C2×#135—22no—
194C2×#135—22no—
195C2×#135—22no—
196C2×#135—22no—
197C2×#135—48no—
198C2×#135—84no—
199C2×#135C22×C414yes—
200C2×#135C2414yes—
201C22×Q16—21no—
202C22×Q16C22×C412yes—
203C22×SD16—22no—
204C22×SD16—22no—
205C22×D8—22no—
206C22×D8—22no—
207C22×D8—22no—
208C22×D8—22no—
209C22×D8—21no—
210C22×D8—22no—
211C22×D8—22no—
212C22×D8—22no—
213C22×D8—22no—
214C22×D8—22no—
215C22×D8—48no—
216C22×D8—84no—
217C22×D8C22×C414yes—
218C22×D8C22×C414yes—
219C22×D8C22×C412yes—
220C22×D8C2414yes—
221C2×#131—28no—
222C23×C8C2×D411yescharacteristic
223C23×C8C2411yescharacteristic
224#532—22no—
225#532—22no—
226#532—22no—
227#532—22no—
228#532—41no—
229#532—41no—
230#532—41no—
231#532—41no—
232C2×C4⋊Q8—21no—
233C2×#127—21no—
234C2×#127—22no—
235C2×#127—22no—
236C2×#127—22no—
237C2×#127—22no—
238C2×#127—22no—
239C2×#127—22no—
240C2×#127—41no—
241C2×#127—41no—
242C2×#127—41no—
243C2×#127—41no—
244C2×#127—41no—
245C2×#127—41no—
246C2×#124—22no—
247C2×#121—41no—
248C2×#121—41no—
249#518—88no—
250C2×C4×D4—28no—
251C2×C4×D4—44no—
252C2×C4×D4—44no—
253C2×C4×D4—44no—
254C2×C4×D4—41no—
255C2×C4×D4—41no—
256C2×#117—21no—
257C2×#117—41no—
258C22×C22⋊C4—44no—
259C22×C42C2×D411yescharacteristic
260#509—232no—
261#509—432no—
262#509—416no—
263C2×SD32—416no—
264C2×SD32C22×C4116yes—
265C2×SD32C22×C4116yes—
266C2×D16—416no—
267C2×D16C22×C4116yes—
268C2×D16C22×C4116yes—
269C2×M32—28no—
270C2×M32C22×C414yes—
271C2×M32C2414yes—
272C2×M32C2412yes—
273C2×M32C2412yes—
274C22×C16C22×C414yes—
275#495—22no—
276#495—22no—
277#495—22no—
278#495—22no—
279#495—22no—
280#495—22no—
281#495C22×C414yes—
282#495C22×C414yes—
283#494—21no—
284#494—21no—
285#494C22×C412yes—
286#494C22×C412yes—
287#493—22no—
288#493—22no—
289#493—22no—
290#493—22no—
291#493—22no—
292#493—22no—
293#493—22no—
294#493—22no—
295#493—21no—
296#493—21no—
297#493—22no—
298#493—22no—
299#493—22no—
300#493—22no—
301#493C22×C414yes—
302#493C22×C414yes—
303#493C22×C414yes—
304#493C22×C414yes—
305#493C22×C412yes—
306#493C22×C412yes—
307#492—22no—
308#492—22no—
309#492—22no—
310#492—22no—
311#444—416no—
312#444—88no—
313#442—416no—
314#442—88no—
315#436—44no—
316#436—44no—
317#436—44no—
318#435—48no—
319C8×D4—44no—
320C8×D4—44no—
321C8×D4—44no—
322#432—41no—
323#432—41no—
324#431—21no—
325#431—21no—
326#431—21no—
327#431—21no—
328#431—41no—
329#431—41no—
330C2×#108—22no—
331C2×#108C2414yes—
332C2×#106—22no—
333C2×#106C2414yes—
334#423—22no—
335C2×C4⋊C8C2×D412yes—
336C2×#104—28no—
337C2×#104—28no—
338C2×#102—28no—
339C2×#102—28no—
340#408—28no—
341#408—48no—
342#407—22no—
343#407—44no—
344C2×C22⋊C8—44no—
345C2×C22⋊C8C2×D412yes—
346C4×M16—22no—
347C2×#97C2×D414yes—
348C2×#97C2414yes—
349C2×C4×C8C22×C411yescharacteristic
350C2×C4×C8C22×C411yescharacteristic
351C2×C4×C8C22×C411yescharacteristic
352C2×C4×C8C22×C411yescharacteristic
353C2×C4×C8C2×D412yes—
354C2×C4×C8C2×D411yescharacteristic
355C2×C4×C8C2×D411yescharacteristic
356C2×C4×C8#4111yescharacteristic
357C2×C4×C8#4111yescharacteristic
358C2×C4×C8#4111yescharacteristic
359C2×C4×C8#4111yescharacteristic
360C2×C4×C8C2411yescharacteristic
361C2×C4×C8C2411yescharacteristic
362#390—28no—
363#390—44no—
364#390—44no—
365#390—44no—
366#386—48no—
367#386—48no—
368#384—22no—
369#382—41no—
370#380—22no—
371#380—41no—
372#379—44no—
373C4×C4⋊C4—21no—
374C4×C4⋊C4—22no—
375C4×C4⋊C4—41no—
376C4×C4⋊C4C2×D412yes—
377C4×C22⋊C4—21no—
378C4×C22⋊C4C2×D412yes—
379#376—21no—
380C43C2×D412yes—
381#365—216no—
382C4⋊C16—22no—
383C4⋊C16—22no—
384#361—416no—
385#360—416no—
386C22⋊C16—22no—
387C22⋊C16—22no—
388#347—216no—
389#346—22no—
390#346C22×C412yes—
391#346C22×C414yes—
392#346C22×C412yes—
393C4×C16—22no—
394C4×C16C22×C412yes—
395C4×C16C22×C414yes—
396C4×C16C22×C412yes—
397#341—22no—
398#341—22no—
399#340—22no—
400#340—22no—
401#336C2×D414yes—
402#336C2×D414yes—
403C25—42no—
404C2×#41—24no—
405C2×#41—24no—
406C2×#41—42no—
407C2×#41—42no—
408C2×#41—84no—
409C2×#41—84no—
410C22×Q8—22no—
411C22×D4—22no—
412C22×D4—24no—
413C22×D4—24no—
414C22×D4—24no—
415C22×D4—42no—
416C22×D4—42no—
417C22×D4—42no—
418C22×D4—42no—
419C22×D4—42no—
420C22×D4—42no—
421C22×D4—42no—
422C22×D4—42no—
423C22×D4—41no—
424C22×D4—42no—
425C22×D4—42no—
426C22×D4—42no—
427C22×D4—42no—
428C22×D4—41no—
429C22×D4—42no—
430C22×D4—42no—
431C22×D4—42no—
432C22×D4—42no—
433C22×D4—84no—
434C22×D4—84no—
435C22×D4—84no—
436C22×D4—84no—
437C22×D4—164no—
438C23×C4—48no—
439C23×C4—42no—
440C23×C4AGL(1,ℤ/8)11yescharacteristic
441C23×C4AGL(1,ℤ/8)11yescharacteristic
442C23×C4C22×D411yescharacteristic
443#135—216no—
444#135—48no—
445#135—48no—
446#135—84no—
447#135—84no—
448#135—84no—
449#135—84no—
450#135—84no—
451C2×Q16—22no—
452C2×Q16—22no—
453C2×Q16—22no—
454C2×Q16—44no—
455C2×Q16—82no—
456C2×Q16C23×C414yes—
457C2×SD16—24no—
458C2×SD16—24no—
459C2×SD16—24no—
460C2×SD16—24no—
461C2×SD16—84no—
462C2×SD16—84no—
463C2×D8—24no—
464C2×D8—24no—
465C2×D8—22no—
466C2×D8—24no—
467C2×D8—24no—
468C2×D8—24no—
469C2×D8—24no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—24no—
473C2×D8—216no—
474C2×D8—48no—
475C2×D8—48no—
476C2×D8—44no—
477C2×D8—48no—
478C2×D8—84no—
479C2×D8—84no—
480C2×D8—84no—
481C2×D8—84no—
482C2×D8—84no—
483C2×D8—84no—
484C2×D8—82no—
485C2×D8—84no—
486C2×D8—84no—
487C2×D8C23×C418yes—
488C2×D8C23×C414yes—
489#131—88no—
490#131—88no—
491C2×M16—24no—
492C2×M16—48no—
493C22×C8—24no—
494C22×C8—24no—
495C22×C8—48no—
496C22×C8C4×D411yescharacteristic
497C22×C8C4×D411yescharacteristic
498C22×C8C4×D411yescharacteristic
499C22×C8C4×D411yescharacteristic
500C22×C8C23×C411yescharacteristic
501C22×C8C23×C411yescharacteristic
502C22×C8C22×D414yes—
503C22×C8C22×D411yescharacteristic
504C22×C8C22×D411yescharacteristic
505C22×C8C22×D411yescharacteristic
506C22×C8C2×#4111yescharacteristic
507C22×C8C2×#4111yescharacteristic
508C22×C8C2511yescharacteristic
509C4⋊Q8—22no—
510C4⋊Q8—22no—
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513#127—24no—
514#127—24no—
515#127—24no—
516#127—24no—
517#127—22no—
518#127—22no—
519#127—42no—
520#127—42no—
521#127—42no—
522#127—42no—
523#127—42no—
524#127—42no—
525#127—42no—
526#127—42no—
527#127—42no—
528#127—42no—
529#127—42no—
530#127—42no—
531#127—41no—
532#127—41no—
533#124—24no—
534#124—24no—
535#124—42no—
536#124—42no—
537#121—42no—
538#121—42no—
539#121—42no—
540#121—42no—
541#121—42no—
542#121—42no—
543#121—42no—
544#121—42no—
545C4×D4—42no—
546C4×D4—42no—
547C4×D4—42no—
548C4×D4—42no—
549C4×D4—42no—
550C4×D4—42no—
551C4×D4—42no—
552C4×D4—42no—
553C4×D4—88no—
554C4×D4—88no—
555C4×D4—816no—
556C4×D4—816no—
557C4×D4—168no—
558#117—44no—
559#117—84no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—42no—
565C2×C4⋊C4—42no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—48no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—48no—
572C2×C22⋊C4—48no—
573C2×C22⋊C4—816no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—42no—
577C2×C42C4×D411yescharacteristic
578C2×C42C4×D411yescharacteristic
579C2×C42C4×D411yescharacteristic
580C2×C42C4×D411yescharacteristic
581C2×C42AGL(1,ℤ/8)11yescharacteristic
582C2×C42AGL(1,ℤ/8)11yescharacteristic
583C2×C42AGL(1,ℤ/8)11yescharacteristic
584C2×C42AGL(1,ℤ/8)11yescharacteristic
585C2×C42AGL(1,ℤ/8)11yescharacteristic
586C2×C42AGL(1,ℤ/8)11yescharacteristic
587C2×C42C22×D414yes—
588C2×C42C22×D411yescharacteristic
589C2×C42C22×D411yescharacteristic
590SD32—232no—
591SD32—416no—
592D16—232no—
593D16—416no—
594M32—24no—
595M32—28no—
596M32—28no—
597M32H(5,𝔽2)18yes—
598C2×C16—28no—
599C2×C16—24no—
600C2×C16C23×C414yes—
601C2×C16C23×C414yes—
602#108—28no—
603#108—44no—
604#106—28no—
605#106—44no—
606C4⋊C8—22no—
607C4⋊C8—22no—
608C4⋊C8—42no—
609C4⋊C8—42no—
610#104—88no—
611#104—88no—
612#102—88no—
613#102—88no—
614C22⋊C8—22no—
615C22⋊C8—22no—
616C22⋊C8—48no—
617C22⋊C8—48no—
618C22⋊C8—42no—
619C22⋊C8—42no—
620#97—28no—
621#97—28no—
622#97—42no—
623C4×C8—22no—
624C4×C8—22no—
625C4×C8—42no—
626C4×C8C4×D411yescharacteristic
627C4×C8C4×D411yescharacteristic
628C4×C8C4×D411yescharacteristic
629C4×C8C4×D411yescharacteristic
630C4×C8C4×D411yescharacteristic
631C4×C8C4×D411yescharacteristic
632C4×C8C4×D411yescharacteristic
633C4×C8C4×D411yescharacteristic
634C4×C8C23×C411yescharacteristic
635C4×C8C23×C411yescharacteristic
636C4×C8C23×C411yescharacteristic
637C4×C8C23×C411yescharacteristic
638C4×C8C2×#4111yescharacteristic
639C4×C8C2×#4111yescharacteristic
640C4×C8C2×#4111yescharacteristic
641C4×C8C2×#4111yescharacteristic
642#95—22no—
643#95—22no—
644#95—42no—
645#95—42no—
646C24—44no—
647C24—42no—
648C24—44no—
649C24—44no—
650C24—84no—
651C24—84no—
652C24—164no—
653C24—164no—
654C24C2×AGL(1,ℤ/8)11yescharacteristic
655#41—48no—
656#41—48no—
657#41—84no—
658#41—84no—
659#41—164no—
660#41—164no—
661C2×Q8—24no—
662C2×Q8—42no—
663C2×Q8—82no—
664C2×Q8—82no—
665C2×D4—24no—
666C2×D4—28no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—48no—
685C2×D4—44no—
686C2×D4—48no—
687C2×D4—84no—
688C2×D4—84no—
689C2×D4—82no—
690C2×D4—84no—
691C2×D4—84no—
692C2×D4—82no—
693C2×D4—84no—
694C2×D4—84no—
695C2×D4—88no—
696C2×D4—88no—
697C2×D4—84no—
698C2×D4—84no—
699C2×D4—88no—
700C2×D4—88no—
701C2×D4—84no—
702C2×D4—88no—
703C2×D4—162no—
704C2×D4—164no—
705C2×D4—164no—
706C2×D4—164no—
707C2×D4—164no—
708C2×D4—164no—
709C2×D4—164no—
710C2×D4—164no—
711C2×D4—164no—
712C2×D4—164no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—24no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—816no—
723C22×C4—164no—
724C22×C4—168no—
725C22×C4—168no—
726C22×C4#44211yescharacteristic
727C22×C4#44211yescharacteristic
728C22×C4#44211yescharacteristic
729C22×C4#44211yescharacteristic
730C22×C4#44211yescharacteristic
731C22×C4#44211yescharacteristic
732C22×C4#44211yescharacteristic
733C22×C4#44211yescharacteristic
734C22×C4C2×C4×D411yescharacteristic
735C22×C4C2×C4×D411yescharacteristic
736C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
737C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
738C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
739C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
740C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
741C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
742C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
743C22×C4C23×D411yescharacteristic
744Q16—28no—
745Q16—44no—
746Q16—82no—
747Q16—82no—
748SD16—48no—
749SD16—48no—
750SD16—84no—
751SD16—84no—
752D8—28no—
753D8—216no—
754D8—48no—
755D8—48no—
756D8—44no—
757D8—48no—
758D8—84no—
759D8—84no—
760D8—82no—
761D8—84no—
762D8—84no—
763D8—82no—
764M16—44no—
765M16—44no—
766M16—168no—
767C2×C8—22no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—22no—
774C2×C8—22no—
775C2×C8—22no—
776C2×C8—22no—
777C2×C8—24no—
778C2×C8—24no—
779C2×C8—24no—
780C2×C8—44no—
781C2×C8—168no—
782C2×C8C2×C4×D411yescharacteristic
783C2×C8C2×C4×D411yescharacteristic
784C2×C8C2×C4×D411yescharacteristic
785C2×C8C2×C4×D411yescharacteristic
786C2×C8C2×C4×D411yescharacteristic
787C2×C8C2×C4×D411yescharacteristic
788C2×C8#57614yes—
789C2×C8C24×C411yescharacteristic
790C2×C8C22×#4111yescharacteristic
791C2×C8C2×H(5,𝔽2)14yes—
792C4⋊C4—44no—
793C4⋊C4—42no—
794C4⋊C4—42no—
795C4⋊C4—42no—
796C4⋊C4—42no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—84no—
800C4⋊C4—84no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—816no—
807C22⋊C4—84no—
808C22⋊C4—168no—
809C22⋊C4—168no—
810C42—24no—
811C42—24no—
812C42—44no—
813C42—44no—
814C42—84no—
815C42#44211yescharacteristic
816C42#44211yescharacteristic
817C42#44211yescharacteristic
818C42#44211yescharacteristic
819C42#44211yescharacteristic
820C42#44211yescharacteristic
821C42#44211yescharacteristic
822C42#44211yescharacteristic
823C42C2×C4×D411yescharacteristic
824C42C2×C4×D411yescharacteristic
825C42C2×C4×D411yescharacteristic
826C42C2×C4×D411yescharacteristic
827C42C2×AGL(1,ℤ/8)11yescharacteristic
828C42C2×AGL(1,ℤ/8)11yescharacteristic
829C42C2×AGL(1,ℤ/8)11yescharacteristic
830C42C2×AGL(1,ℤ/8)11yescharacteristic
831C16—24no—
832C16—44no—
833C16#51818yescomplemented
834C23—22no—
835C23—22no—
836C23—41no—
837C23—44no—
838C23—48no—
839C23—84no—
840C23—88no—
841C23—84no—
842C23—88no—
843C23—88no—
844C23—88no—
845C23—84no—
846C23—162no—
847C23—164no—
848C23—164no—
849C23—164no—
850C23—164no—
851C23—162no—
852C23—328no—
853C23—328no—
854C23C2×#44211yescharacteristic
855C23C2×#44211yescharacteristic
856C23C22×AGL(1,ℤ/8)11yescharacteristic
857Q8—44no—
858Q8—44no—
859Q8—162no—
860D4—48no—
861D4—44no—
862D4—48no—
863D4—44no—
864D4—88no—
865D4—88no—
866D4—88no—
867D4—88no—
868D4—84no—
869D4—84no—
870D4—88no—
871D4—88no—
872D4—88no—
873D4—84no—
874D4—88no—
875D4—164no—
876D4—164no—
877D4—162no—
878D4—162no—
879D4—164no—
880D4—164no—
881D4—164no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—88no—
905C2×C4—84no—
906C2×C4—84no—
907C2×C4—84no—
908C2×C4—164no—
909C2×C4—162no—
910C2×C4—3216no—
911C2×C4AGL(1,ℤ/16)14yescomplemented
912C2×C4C2×#44211yescharacteristic
913C2×C4C2×#44211yescharacteristic
914C2×C4C2×#44211yescharacteristic
915C2×C4C2×#44211yescharacteristic
916C2×C4C2×#44211yescharacteristic
917C2×C4C2×#44211yescharacteristic
918C2×C4C2×#44211yescharacteristic
919C2×C4C2×#44211yescharacteristic
920C2×C4C2×#44211yescharacteristic
921C2×C4C2×#44211yescharacteristic
922C2×C4C22×C4×D411yescharacteristic
923C2×C4#349812yes—
924C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
925C2×C4C2×#57612yes—
926C8—21no—
927C8—21no—
928C8—21no—
929C8—21no—
930C8—44no—
931C8—84no—
932C8#294812yes—
933C8#294812yes—
934C8C2×#51812yes—
935C8#350812yes—
936C22—21no—
937C22—21no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—21no—
942C22—21no—
943C22—44no—
944C22—84no—
945C22—88no—
946C22—88no—
947C22—84no—
948C22—88no—
949C22—84no—
950C22—168no—
951C22—168no—
952C22—324no—
953C22—328no—
954C22—328no—
955C22C2×AGL(1,ℤ/16)12yes—
956C22C22×#44211yescharacteristic
957C22#6242312yes—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—21no—
965C4—84no—
966C4—84no—
967C4—164no—
968C4C2×AGL(1,ℤ/16)12yes—
969C4C2×AGL(1,ℤ/16)12yes—
970C4#3347112yes—
971C4#3421011yescharacteristic
972C4C2×#294811yescharacteristic
973C4#6242312yes—
974C2—22no—
975C2—22no—
976C2—41no—
977C2—168no—
978C2—164no—
979C2#638985311yescharacteristic
980C2C22×AGL(1,ℤ/16)11yescharacteristic
981C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC22×C8C25
prime radicalC2×#33717C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ #20473 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6389899C2semidirect
3. #6389853C2semidirect
4. #498578C2semidirect
5. #497422C2semidirect
6. #497146C2semidirect
7. #496366C2semidirect
8. #496363C2semidirect
9. #496124C2semidirect
10. #494192C2semidirect
11. #493201C2semidirect
17. #33717C4semidirect
18. #33717C4semidirect
22. C2×#2250C4semidirect
23. C2×#2248C4semidirect
24. C2×#2246C4semidirect
25. C2×AGL(1,ℤ/16)C22semidirect
29. #23188C22semidirect
31. #23180C22semidirect
40. #21706C22semidirect
41. #21690C22semidirect
45. #13257C22semidirect
46. #13255C22semidirect
47. #13249C22semidirect
48. #13213C22semidirect
49. #13210C22semidirect
50. #13040C22semidirect
51. #13037C22semidirect
52. #12903C22semidirect
53. #12886C22semidirect
57. C4×#365C22semidirect
58. #12666C22semidirect
60. #12594C22semidirect
61. C4×#347C22semidirect
70. C2×#509C2×C4semidirect
73. C22×SD32C2×C4semidirect
74. C22×D16C2×C4semidirect
80. #3147C2×C4semidirect
81. #3147C2×C4semidirect
85. C2×#495C2×C4semidirect
86. C2×#494C2×C4semidirect
97. C2×#493C2×C4semidirect
125. #2250C2×C4semidirect
126. #2250C2×C4semidirect
127. #2250C2×C4semidirect
128. #2248C2×C4semidirect
129. #2248C2×C4semidirect
130. #2248C2×C4semidirect
131. #2246C2×C4semidirect
132. #2246C2×C4semidirect
133. #2246C2×C4semidirect
145. C4×M32C2×C4semidirect
146. C4×M32C2×C4semidirect
151. C2×#346C2×C4semidirect
152. C2×C4×C16C2×C4semidirect
833. C16#518semidirect
911. C2×C4AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
C2×#337172
#63898992
#63898532
#4985782
#4974222
#4971462
#4963662
#4963632
#4961242
#4941922
#4932012