Finite Group Databasebeta

← #72319189

Subgroups — #72319189

Order 1024.

2395 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623097C211yesmaximal, characteristic
2#6345117C211yesmaximal, characteristic, complemented
3C2×#18065C211yesmaximal, characteristic, complemented
4#484053C214yesmaximal, complemented
5#484052C214yesmaximal, complemented
6#484041C218yesmaximal, complemented
7#483838C212yesmaximal, complemented
8#483805C212yesmaximal, complemented
9#483803C212yesmaximal, complemented
10#483590C212yesmaximal, complemented
11#483424C211yesmaximal, characteristic, complemented
12#481347C211yesmaximal, characteristic, complemented
13#481065C211yesmaximal, characteristic, complemented
14#479962C211yesmaximal, characteristic, complemented
15#60673C2211yescharacteristic
16C2×#2990—21no—
17#60210—21no—
18C2×C4×#135C2211yescharacteristic
19#33676C2212yes—
20#33675C2212yes—
21#33671C2214yes—
22#33667C412yes—
23#33666C412yes—
24#33662C414yes—
25#33647C412yes—
26#33628C411yescharacteristic
27#33627C411yescharacteristic
28#33581C411yescharacteristic
29#33580C411yescharacteristic
30#33519C412yes—
31C4×#510C2212yes—
32C4×#509C2212yes—
33#33418C2211yescharacteristic
34C2×C4×M32C2211yescharacteristic
35#18075C2214yescomplemented
36#18074—22no—
37#18073C2212yescomplemented
38#18072C2212yescomplemented
39#18071—22no—
40#18065—22no—
41#18065—22no—
42#18065C2214yes—
43#18065C2214yes—
44#17890C2212yes—
45C2×#1593C2212yes—
46#17868—22no—
47C2×#1582—22no—
48#17849C2212yes—
49C2×#1580C2212yes—
50C2×#1566C2211yescharacteristic
51C2×#1564C2211yescharacteristic
52#17458—21no—
53C2×#1489—21no—
54C2×#1451C2211yescharacteristic
55#12088C2218yescomplemented
56#12087C2218yescomplemented
57#12079C2218yescomplemented
58#12078C2218yescomplemented
59#12077C2218yescomplemented
60#12077C2218yescomplemented
61#12067C2218yescomplemented
62#12065C2218yescomplemented
63#12030C2214yescomplemented
64#12029C2214yescomplemented
65#12000C2212yes—
66#12000C2212yes—
67#11681C2212yescomplemented
68#11680C2212yescomplemented
69#11677C2214yescomplemented
70#11600C2211yescharacteristic
71#11600C2211yescharacteristic
72#11599C2211yescharacteristic
73#11599C2211yescharacteristic
74#11598C2212yes—
75#11598C2214yes—
76#11598C2212yes—
77#11597C2214yes—
78#11414C2214yescomplemented
79#11413C2214yescomplemented
80#11404C2212yes—
81#11404C2212yes—
82C22×#135C2×C411yescharacteristic
83#3444—21no—
84C2×C4×#41—21no—
85C2×#510C2×C412yes—
86C2×#509C2×C412yes—
87C22×M32—21no—
88#3170C2×C411yescharacteristic
89#3170C2311yescharacteristic
90#3169C2×C411yescharacteristic
91#3169C2311yescharacteristic
92#3168—21no—
93#3168—21no—
94#3168C2×C412yes—
95#3168C2312yes—
96#3167—21no—
97#3167—21no—
98#3160C2×C411yescharacteristic
99#3147C2×C411yescharacteristic
100#3131—21no—
101#3050—21no—
102#3050C2×C412yes—
103#2990—24no—
104#2990—24no—
105#2990—42no—
106#2990—42no—
107#2969—24no—
108#2968—42no—
109#2965—22no—
110#2965—42no—
111C8×#41—22no—
112#2962—22no—
113C2×#446—22no—
114C4×#135—21no—
115C4×#135—21no—
116C4×#135—21no—
117C4×#135—21no—
118C4×#135—21no—
119C4×#135C2×C412yes—
120C4×#135C2×C412yes—
121C4×#135C2312yes—
122C4×#135C2312yes—
123C4×#135C2312yes—
124C2×C4×Q16C2×C411yescharacteristic
125C2×C4×Q16C2311yescharacteristic
126C2×C4×SD16—21no—
127C2×C4×SD16—21no—
128C2×C4×D8C2×C411yescharacteristic
129C2×C4×D8C2311yescharacteristic
130#2935—22no—
131#2933—42no—
132C2×#435—42no—
133C2×C8×D4—22no—
134#2922—41no—
135C2×#432—41no—
136C2×#431—21no—
137C2×#431D411yescharacteristic
138C2×#427C2×C411yescharacteristic
139C2×#423—21no—
140C22×C4⋊C8—41no—
141C2×#416—21no—
142C4×#131—41no—
143C2×C4×M16D411yescharacteristic
144C22×C4×C8C2311yescharacteristic
145#2237C2×C414yes—
146#2237C2×C414yes—
147#2234C2×C414yes—
148#2234C2×C414yes—
149#2229C2×C414yes—
150#2228C2×C414yes—
151#2227C2×C412yes—
152#2226C2×C412yes—
153#2225C2×C412yes—
154#2224C2×C412yes—
155#2211C2×C414yes—
156#2210C2×C414yes—
157#2209C2×C412yes—
158#2208C2×C412yes—
159#2207C2×C412yes—
160#2206C2×C412yes—
161#2189C2×C414yes—
162#2189C2×C414yes—
163#2186C2×C414yes—
164#2186C2×C414yes—
165#2177C2314yes—
166#2176C2314yes—
167#2175C2314yes—
168#2175C2314yes—
169C4×Q32C2×C414yes—
170C4×SD32C2×C414yes—
171C4×SD32C2×C414yes—
172C4×D16C2×C414yes—
173#2163C2312yes—
174#2163C2312yes—
175#2162C2×C412yes—
176#2162C2×C412yes—
177#2159C2×C412yes—
178#2159C2×C412yes—
179#2150C2×C411yescharacteristic
180#2150C2×C411yescharacteristic
181#2141C2×C412yes—
182#2140C2×C412yes—
183#2139C2×C412yes—
184#2139C2×C412yes—
185#2112C2×C412yes—
186C4×M32—21no—
187C4×M32—21no—
188C4×M32C2311yescharacteristic
189C4×M32C2311yescharacteristic
190C4×M32C2312yes—
191C4×M32C2312yes—
192C2×#346C2312yes—
193C2×C4×C16—21no—
194#1594C2314yes—
195#1593—24no—
196#1593C2314yes—
197#1593C2318yes—
198#1592—24no—
199#1588—24no—
200#1587—24no—
201#1586—24no—
202#1585—24no—
203#1582—28no—
204#1582—28no—
205#1580—24no—
206#1580C2318yes—
207#1580C2314yes—
208#1579C2314yes—
209SD16⋊C8—24no—
210#1566—21no—
211#1566—21no—
212#1566C2312yes—
213#1566C2312yes—
214#1564—21no—
215#1564—21no—
216#1564C2312yes—
217#1564C2311yescharacteristic
218#1564C2311yescharacteristic
219C2×#335—21no—
220C2×#334—21no—
221C2×#334C2312yes—
222C2×#334C2312yes—
223#1489—24no—
224#1489—24no—
225#1482—24no—
226#1481—22no—
227#1480—22no—
228#1476—22no—
229#1476—22no—
230C2×Q8⋊C8—22no—
231C2×D4⋊C8—22no—
232#1451D412yes—
233#1451D412yes—
234#1451C2312yes—
235#1451C2312yes—
236C2×#322D412yes—
237C2×#322C2312yes—
238#1368C2318yes—
239#1368C2318yes—
240#1334C2314yes—
241#1334C2314yes—
242#1334C2314yes—
243#1334C2314yes—
244#1333C2314yes—
245#1333C2314yes—
246#1333C2314yes—
247#1333C2314yes—
248#1313C2318yes—
249#1313C2318yes—
250C22×#41—21no—
251C2×#135—24no—
252C2×#135—21no—
253C2×#135—21no—
254C2×#135—21no—
255C2×#135—42no—
256C2×#135C22×C412yes—
257C2×#135C22×C412yes—
258C2×#135C22×C412yes—
259C22×Q16C22×C411yescharacteristic
260C22×SD16—21no—
261C22×D8C22×C411yescharacteristic
262C2×#131—42no—
263C22×M16—21no—
264C22×M16—41no—
265C23×C8—42no—
266C23×C8C22×C411yescharacteristic
267C23×C8#4111yescharacteristic
268#533—21no—
269#533—21no—
270#533—21no—
271#532—21no—
272#532—21no—
273#532—21no—
274#529—22no—
275#529—22no—
276#529—41no—
277#529—41no—
278#529—41no—
279#529—41no—
280#525—22no—
281#525—41no—
282#525—41no—
283C4×#41—22no—
284C4×#41—22no—
285C4×#41—22no—
286C4×#41—22no—
287C4×#41—22no—
288C4×#41—41no—
289C4×#41—41no—
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—41no—
299C2×C4×D4—41no—
300C2×#117—21no—
301C2×#117—41no—
302C22×C42—41no—
303C22×C42C2×D411yescharacteristic
304#510—44no—
305#509—28no—
306C2×Q32C22×C414yes—
307C2×SD32C22×C414yes—
308C2×SD32C22×C414yes—
309C2×D16C22×C414yes—
310C2×M32—21no—
311C2×M32—22no—
312C2×M32—21no—
313C2×M32—44no—
314C2×M32C22×C412yes—
315C2×M32C22×C412yes—
316C22×C16—22no—
317#500C22×C411yescharacteristic
318#500C22×C411yescharacteristic
319#499—21no—
320#499C22×C412yes—
321#498—21no—
322#495—21no—
323#495C22×C412yes—
324#494C22×C411yescharacteristic
325#493C22×C411yescharacteristic
326#492—21no—
327#488—22no—
328#488—22no—
329#487—21no—
330#487—21no—
331#486—21no—
332#486—21no—
333#467—21no—
334#467—21no—
335#467C22×C412yes—
336#467C22×C412yes—
337#466—21no—
338#466—21no—
339#466C22×C412yes—
340#466C22×C412yes—
341#465—22no—
342#465—22no—
343#465—22no—
344#465—22no—
345#446—28no—
346#446—24no—
347#446—44no—
348#446—44no—
349C8×Q8—24no—
350C4×Q16—21no—
351C4×Q16—21no—
352C4×Q16—21no—
353C4×Q16—21no—
354C4×Q16—21no—
355C4×Q16—21no—
356C4×Q16C22×C412yes—
357C4×Q16C22×C412yes—
358C4×Q16C22×C412yes—
359C4×Q16C22×C412yes—
360C4×Q16C2412yes—
361C4×Q16C2412yes—
362C4×SD16—22no—
363C4×SD16—22no—
364C4×SD16—22no—
365C4×SD16—22no—
366C4×SD16—22no—
367C4×SD16—22no—
368C4×SD16—22no—
369C4×SD16—22no—
370C4×SD16—22no—
371C4×SD16—22no—
372C4×SD16—22no—
373C4×SD16—22no—
374C4×D8—21no—
375C4×D8—21no—
376C4×D8—21no—
377C4×D8—21no—
378C4×D8—21no—
379C4×D8—21no—
380C4×D8C22×C412yes—
381C4×D8C22×C412yes—
382C4×D8C22×C412yes—
383C4×D8C22×C412yes—
384C4×D8C2412yes—
385C4×D8C2412yes—
386#436—24no—
387#436—44no—
388#435—44no—
389#435—48no—
390#435—48no—
391#435—44no—
392#435—44no—
393C8×D4—24no—
394C8×D4—28no—
395C8×D4—44no—
396C8×D4—44no—
397#433—44no—
398#432—44no—
399#432—44no—
400#431—21no—
401#431—21no—
402#431—21no—
403#431—21no—
404#431—22no—
405#431—42no—
406#431—42no—
407#431—41no—
408#431—41no—
409#431C2×D412yes—
410#431C2×D412yes—
411#427—21no—
412#427—21no—
413#427—21no—
414#427C22×C412yes—
415#427C22×C412yes—
416#427C22×C412yes—
417C2×#107C22×C411yescharacteristic
418C2×#107C22×C411yescharacteristic
419C2×#106—21no—
420#424—42no—
421#423—22no—
422#423—22no—
423#423—41no—
424#423—41no—
425C2×C4⋊C8—21no—
426C2×C4⋊C8—22no—
427C2×C4⋊C8—22no—
428C2×C4⋊C8—44no—
429C2×C4⋊C8—44no—
430C2×C4⋊C8—42no—
431C2×C4⋊C8—41no—
432#416—22no—
433#416—22no—
434#416—22no—
435#416—22no—
436#416—22no—
437#416—22no—
438C2×#103—21no—
439C2×#103—21no—
440C2×#102—21no—
441C2×#102—21no—
442#408—42no—
443C2×C22⋊C8—21no—
444C2×C22⋊C8—42no—
445C2×C22⋊C8—41no—
446#405—44no—
447#405—42no—
448C4×M16—21no—
449C4×M16—21no—
450C4×M16—42no—
451C4×M16C2×D412yes—
452C4×M16C2×D412yes—
453C2×#97—21no—
454C2×#97—42no—
455C2×C4×C8—42no—
456C2×C4×C8—41no—
457C2×C4×C8C22×C411yescharacteristic
458C2×C4×C8C22×C411yescharacteristic
459C2×C4×C8C22×C411yescharacteristic
460C2×C4×C8C2×D412yes—
461C2×C4×C8C2×D412yes—
462C2×C4×C8C2×D411yescharacteristic
463C2×C4×C8C2×D411yescharacteristic
464C2×C4×C8C2×D411yescharacteristic
465C2×C4×C8#4111yescharacteristic
466C2×C4×C8#4111yescharacteristic
467C2×C4×C8#4111yescharacteristic
468C2×C4×C8C2411yescharacteristic
469C2×C4×C8C2411yescharacteristic
470C2×C4×C8C2411yescharacteristic
471#367C22×C414yes—
472#367C22×C414yes—
473#366C22×C414yes—
474#366C22×C414yes—
475C4⋊C16C22×C412yes—
476C4⋊C16C22×C412yes—
477C4⋊C16C22×C412yes—
478C4⋊C16C22×C412yes—
479#358C22×C414yes—
480#358C22×C414yes—
481#358C22×C414yes—
482#358C22×C414yes—
483#357C22×C414yes—
484#357C22×C414yes—
485#357C22×C414yes—
486#357C22×C414yes—
487C22⋊C16C22×C414yes—
488C22⋊C16C22×C414yes—
489#346—22no—
490#346C2412yes—
491#346C2412yes—
492#346C2414yes—
493C4×C16—21no—
494C4×C16—21no—
495C4×C16—22no—
496C4×C16C22×C414yes—
497#335—21no—
498#335—22no—
499#335—21no—
500#334—22no—
501#334—22no—
502#334—22no—
503#334—22no—
504#334C2412yes—
505#334C2412yes—
506#334C2414yes—
507Q8⋊C8—24no—
508Q8⋊C8—28no—
509Q8⋊C8—24no—
510D4⋊C8—24no—
511D4⋊C8—28no—
512D4⋊C8—24no—
513#322C2×D414yes—
514#322C2×D414yes—
515#322C2×D414yes—
516#322C2414yes—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—44no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—82no—
526C22×Q8—21no—
527C22×D4—21no—
528C22×D4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4C4×D411yescharacteristic
533C23×C4AGL(1,ℤ/8)11yescharacteristic
534C23×C4AGL(1,ℤ/8)11yescharacteristic
535#135—24no—
536#135—24no—
537#135—24no—
538#135—24no—
539#135—42no—
540#135—42no—
541#135—44no—
542#135—44no—
543#135—82no—
544C2×Q16—21no—
545C2×Q16—21no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16C23×C412yes—
549C2×Q16C23×C412yes—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—44no—
555C2×D8—21no—
556C2×D8—21no—
557C2×D8—22no—
558C2×D8#13114yescomplemented
559C2×D8C23×C412yes—
560C2×D8C23×C412yes—
561#131—88no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—44no—
565C2×M16—42no—
566C2×M16—42no—
567C2×M16—82no—
568C2×M16—162no—
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8—22no—
573C22×C8—42no—
574C22×C8—44no—
575C22×C8—48no—
576C22×C8—42no—
577C22×C8—42no—
578C22×C8—164no—
579C22×C8C4×D411yescharacteristic
580C22×C8C4×D411yescharacteristic
581C22×C8C4×D411yescharacteristic
582C22×C8C4×D411yescharacteristic
583C22×C8C4×D411yescharacteristic
584C22×C8C4×D411yescharacteristic
585C22×C8C23×C411yescharacteristic
586C22×C8C23×C411yescharacteristic
587C22×C8C23×C411yescharacteristic
588C22×C8C2×#4111yescharacteristic
589C22×C8C2×#4111yescharacteristic
590C22×C8C2×#4111yescharacteristic
591C4⋊Q8—21no—
592C4⋊Q8—21no—
593C4⋊Q8—21no—
594#127—21no—
595#126—42no—
596#126—42no—
597#125—22no—
598#125—41no—
599#125—41no—
600#124—22no—
601#124—41no—
602#124—41no—
603#123—42no—
604#123—42no—
605#123—42no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—41no—
609C22⋊Q8—41no—
610C22⋊Q8—41no—
611C22⋊Q8—41no—
612#121—22no—
613#121—22no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#120—42no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—22no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×Q8—41no—
632C4×Q8—41no—
633C4×D4—22no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—42no—
640C4×D4—42no—
641C4×D4—42no—
642C4×D4—42no—
643C4×D4—42no—
644C4×D4—42no—
645C4×D4—42no—
646C4×D4—42no—
647C4×D4—42no—
648C4×D4—42no—
649C4×D4—42no—
650C4×D4—42no—
651C4×D4—42no—
652C4×D4—42no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—41no—
660C4×D4—41no—
661#117—22no—
662#117—22no—
663#117—22no—
664#117—41no—
665#117—41no—
666#117—41no—
667#117—41no—
668#117—42no—
669#117—42no—
670#117—42no—
671#117—42no—
672#117—42no—
673#117—42no—
674#117—42no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42—42no—
686C2×C42—42no—
687C2×C42—42no—
688C2×C42—42no—
689C2×C42—42no—
690C2×C42C4×D411yescharacteristic
691C2×C42C4×D411yescharacteristic
692C2×C42C4×D411yescharacteristic
693C2×C42AGL(1,ℤ/8)11yescharacteristic
694C2×C42AGL(1,ℤ/8)11yescharacteristic
695C2×C42AGL(1,ℤ/8)11yescharacteristic
696C2×C42AGL(1,ℤ/8)11yescharacteristic
697C2×C42AGL(1,ℤ/8)11yescharacteristic
698C2×C42AGL(1,ℤ/8)11yescharacteristic
699C2×C42C22×D411yescharacteristic
700C2×C42C22×D411yescharacteristic
701C2×C42C22×D411yescharacteristic
702Q32—44no—
703SD32—28no—
704SD32—44no—
705D16—28no—
706M32—24no—
707M32—24no—
708M32—24no—
709M32—44no—
710M32—42no—
711C2×C16—22no—
712C2×C16—22no—
713C2×C16—44no—
714C2×C16C23×C414yes—
715C2×C16C23×C414yes—
716#107—21no—
717#107—21no—
718#107—21no—
719#107—21no—
720#107C23×C412yes—
721#107C23×C412yes—
722#107C23×C412yes—
723#107C23×C412yes—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—24no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—48no—
734C4⋊C8—44no—
735C4⋊C8—44no—
736C4⋊C8—42no—
737C4⋊C8—42no—
738C4⋊C8—42no—
739C4⋊C8—42no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—48no—
759C22⋊C8—44no—
760C22⋊C8—44no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—42no—
764#97—22no—
765#97—22no—
766#97—48no—
767#97—44no—
768C4×C8—22no—
769C4×C8—22no—
770C4×C8—44no—
771C4×C8—41no—
772C4×C8—41no—
773C4×C8—42no—
774C4×C8C4×D411yescharacteristic
775C4×C8C4×D411yescharacteristic
776C4×C8C4×D411yescharacteristic
777C4×C8C4×D411yescharacteristic
778C4×C8C4×D411yescharacteristic
779C4×C8C4×D411yescharacteristic
780C4×C8C23×C411yescharacteristic
781C4×C8C23×C411yescharacteristic
782C4×C8C23×C411yescharacteristic
783C4×C8C22×D414yes—
784C4×C8C22×D414yes—
785C4×C8C22×D411yescharacteristic
786C4×C8C22×D411yescharacteristic
787C4×C8C22×D411yescharacteristic
788C4×C8C2×#4111yescharacteristic
789C4×C8C2×#4111yescharacteristic
790C4×C8C2×#4111yescharacteristic
791C4×C8C2511yescharacteristic
792C24—41no—
793C24#44211yescharacteristic
794#41—44no—
795#41—44no—
796#41—44no—
797#41—44no—
798#41—82no—
799#41—82no—
800#41—84no—
801#41—84no—
802#41—84no—
803#41—162no—
804C2×Q8—22no—
805C2×Q8—22no—
806C2×Q8—41no—
807C2×Q8—41no—
808C2×Q8—41no—
809C2×Q8—42no—
810C2×Q8—42no—
811C2×D4—22no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—42no—
823C2×D4—84no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—84no—
841C22×C4—82no—
842C22×C4—84no—
843C22×C4—82no—
844C22×C4#44211yescharacteristic
845C22×C4#44211yescharacteristic
846C22×C4#44211yescharacteristic
847C22×C4#44211yescharacteristic
848C22×C4#44211yescharacteristic
849C22×C4#44211yescharacteristic
850C22×C4#44211yescharacteristic
851C22×C4#44211yescharacteristic
852C22×C4#44211yescharacteristic
853C22×C4C2×C4×D411yescharacteristic
854C22×C4C2×C4×D411yescharacteristic
855C22×C4C2×C4×D411yescharacteristic
856C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
857C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
858C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
859C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
860C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
861C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
862Q16—22no—
863Q16—22no—
864Q16—22no—
865Q16—22no—
866Q16—42no—
867Q16—81no—
868SD16—44no—
869SD16—44no—
870SD16—44no—
871SD16—82no—
872D8—24no—
873D8—22no—
874D8—22no—
875D8—22no—
876D8—81no—
877D8C2×#13114yes—
878M16—44no—
879M16—82no—
880M16—88no—
881M16—162no—
882M16—162no—
883C2×C8—22no—
884C2×C8—22no—
885C2×C8—22no—
886C2×C8—22no—
887C2×C8—22no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—24no—
893C2×C8—24no—
894C2×C8—41no—
895C2×C8—41no—
896C2×C8—41no—
897C2×C8—41no—
898C2×C8—44no—
899C2×C8—42no—
900C2×C8—42no—
901C2×C8—44no—
902C2×C8—82no—
903C2×C8—88no—
904C2×C8—84no—
905C2×C8—84no—
906C2×C8—168no—
907C2×C8C2×C4×D411yescharacteristic
908C2×C8C2×C4×D411yescharacteristic
909C2×C8C2×C4×D411yescharacteristic
910C2×C8C2×C4×D411yescharacteristic
911C2×C8C2×C4×D411yescharacteristic
912C2×C8C2×C4×D411yescharacteristic
913C2×C8C2×#13112yes—
914C2×C8#56812yes—
915C2×C8C24×C411yescharacteristic
916C2×C8C22×#4111yescharacteristic
917C4⋊C4—22no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—41no—
922C4⋊C4—41no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C42—42no—
953C42—42no—
954C42—42no—
955C42—42no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42#44211yescharacteristic
962C42#44211yescharacteristic
963C42#44211yescharacteristic
964C42#44211yescharacteristic
965C42#44211yescharacteristic
966C42#44211yescharacteristic
967C42C2×C4×D411yescharacteristic
968C42C2×C4×D411yescharacteristic
969C42C2×C4×D411yescharacteristic
970C42C2×AGL(1,ℤ/8)11yescharacteristic
971C42C2×AGL(1,ℤ/8)11yescharacteristic
972C42C2×AGL(1,ℤ/8)11yescharacteristic
973C42C2×AGL(1,ℤ/8)11yescharacteristic
974C42C2×AGL(1,ℤ/8)11yescharacteristic
975C42C2×AGL(1,ℤ/8)11yescharacteristic
976C42C23×D411yescharacteristic
977C16—24no—
978C16—24no—
979C16—24no—
980C16—42no—
981C23—22no—
982C23—41no—
983C23—41no—
984C23—44no—
985C23—42no—
986C23—42no—
987C23—82no—
988C23—82no—
989C23C2×#44211yescharacteristic
990C23C2×#44211yescharacteristic
991C23C2×#44211yescharacteristic
992Q8—42no—
993Q8—42no—
994Q8—42no—
995Q8—42no—
996Q8—82no—
997Q8—82no—
998Q8—161no—
999D4—24no—
1000D4—42no—
1001D4—42no—
1002D4—44no—
1003D4—42no—
1004D4—84no—
1005D4—84no—
1006D4—84no—
1007D4—84no—
1008D4—82no—
1009D4—161no—
1010D4—162no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—84no—
1037C2×C4—84no—
1038C2×C4—84no—
1039C2×C4—82no—
1040C2×C4—84no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4—82no—
1044C2×C4—82no—
1045C2×C4—84no—
1046C2×C4—84no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4#293312yes—
1050C2×C4C2×#44211yescharacteristic
1051C2×C4C2×#44211yescharacteristic
1052C2×C4C2×#44211yescharacteristic
1053C2×C4C2×#44211yescharacteristic
1054C2×C4C2×#44211yescharacteristic
1055C2×C4C2×#44211yescharacteristic
1056C2×C4C2×#44211yescharacteristic
1057C2×C4C2×#44211yescharacteristic
1058C2×C4C2×#44211yescharacteristic
1059C2×C4#295612yes—
1060C2×C4C22×C4×D411yescharacteristic
1061C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1062C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1063C8—21no—
1064C8—21no—
1065C8—21no—
1066C8—21no—
1067C8—21no—
1068C8—21no—
1069C8—44no—
1070C8—44no—
1071C8—82no—
1072C8—84no—
1073C8—82no—
1074C8#293312yes—
1075C8C22×#13111yescharacteristic
1076C8C2×#56811yescharacteristic
1077C22—21no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—21no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—44no—
1086C22—82no—
1087C22—88no—
1088C22—82no—
1089C22—82no—
1090C22—82no—
1091C22—82no—
1092C22—82no—
1093C22#1800112yes—
1094C22C22×#44211yescharacteristic
1095C4—21no—
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—21no—
1102C4—21no—
1103C4—82no—
1104C4—82no—
1105C4—82no—
1106C4—82no—
1107C4—82no—
1108C4—82no—
1109C4#1800112yes—
1110C4#3346812yes—
1111C4#3346912yes—
1112C4C2×#293311yescharacteristic
1113C4C2×#295611yescharacteristic
1114C2—22no—
1115C2—41no—
1116C2—41no—
1117C2—84no—
1118C2—162no—
1119C2C2×#1800111yescharacteristic
1120C2C2×#3346811yescharacteristic
1121C2C2×#3346911yescharacteristic
subgroupG/H
centerC2×C4C2×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
socleC22C22×#442
prime radical#7623097C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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. #6345117C2semidirect
3. C2×#18065C2semidirect
4. #484053C2semidirect
5. #484052C2semidirect
6. #484041C2semidirect
7. #483838C2semidirect
8. #483805C2semidirect
9. #483803C2semidirect
10. #483590C2semidirect
11. #483424C2semidirect
12. #481347C2semidirect
13. #481065C2semidirect
14. #479962C2semidirect
35. #18075C22semidirect
37. #18073C22semidirect
38. #18072C22semidirect
55. #12088C22semidirect
56. #12087C22semidirect
57. #12079C22semidirect
58. #12078C22semidirect
59. #12077C22semidirect
60. #12077C22semidirect
61. #12067C22semidirect
62. #12065C22semidirect
63. #12030C22semidirect
64. #12029C22semidirect
67. #11681C22semidirect
68. #11680C22semidirect
69. #11677C22semidirect
78. #11414C22semidirect
79. #11413C22semidirect
558. C2×D8#131semidirect

Maximal subgroups

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

subgroupindex
#76230972
#63451172
C2×#180652
#4840532
#4840522
#4840412
#4838382
#4838052
#4838032
#4835902
#4834242
#4813472
#4810652
#4799622