Finite Group Databasebeta

← #72287791

Subgroups — #72287791

Order 1024.

2418 conjugacy classes of subgroups.

The subgroup lattice has 1119 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#7623096C211yesmaximal, characteristic
2#6345776C211yesmaximal, characteristic, complemented
3#6345071C211yesmaximal, characteristic, complemented
4#484110C214yesmaximal, complemented
5#484106C214yesmaximal, complemented
6#484040C214yesmaximal, complemented
7#484039C214yesmaximal, complemented
8#483928C214yesmaximal, complemented
9#483882C214yesmaximal, complemented
10#483443C211yesmaximal, characteristic, complemented
11#481391C211yesmaximal, characteristic, complemented
12C2×#11663C211yesmaximal, characteristic, complemented
13#479971C211yesmaximal, characteristic, complemented
14#60673C2211yescharacteristic
15#60266—21no—
16#60230—21no—
17C22×C4×D8C2211yescharacteristic
18#33674C2212yes—
19#33674C2212yes—
20#33670C2212yes—
21#33669C2212yes—
22#33665C414yes—
23#33661C411yescharacteristic
24#33661C411yescharacteristic
25#33660C411yescharacteristic
26#33660C411yescharacteristic
27#33646C412yes—
28#33627C412yes—
29#33580C412yes—
30#33517C412yes—
31C4×#509C2214yes—
32#33418C2211yescharacteristic
33C2×#2163C2211yescharacteristic
34#18073C2212yescomplemented
35#18072C2212yescomplemented
36#18067—22no—
37#18065C2212yescomplemented
38#18064C2214yes—
39#18063C2212yescomplemented
40#18057—22no—
41#18054—22no—
42#18044C2214yes—
43M16×D8—22no—
44#17993—22no—
45#17974C2214yescomplemented
46#17895C2212yes—
47#17877—22no—
48#17854C2212yes—
49#17793C2211yescharacteristic
50C2×#1566C2211yescharacteristic
51#17498—21no—
52#17448—21no—
53#17323C2211yescharacteristic
54#12089C2218yescomplemented
55#12087C2218yescomplemented
56#12080C2218yescomplemented
57#12078C2218yescomplemented
58#12078C2218yescomplemented
59#12077C2218yescomplemented
60#12067C2218yescomplemented
61#12065C2218yescomplemented
62#12029C2214yescomplemented
63#12028C2214yescomplemented
64#12020C2212yescomplemented
65#12020C2212yescomplemented
66#11679C2212yescomplemented
67#11678C2212yescomplemented
68#11666C2214yescomplemented
69#11663C2212yes—
70#11663C2212yes—
71#11663C2212yes—
72#11663C2212yes—
73#11656C2214yescomplemented
74C2×#1333C2214yes—
75#11416C2214yescomplemented
76#11414C2214yescomplemented
77#11413C2214yescomplemented
78C23×D8C2×C411yescharacteristic
79#3444—21no—
80C22×C4×D4—21no—
81C2×#509C2×C414yes—
82#3170C2×C411yescharacteristic
83#3170C2311yescharacteristic
84#3169C2×C411yescharacteristic
85#3169C2311yescharacteristic
86#3168—21no—
87#3168—21no—
88#3168C2×C412yes—
89#3168C2312yes—
90#3167—21no—
91#3167—21no—
92#3160C2×C411yescharacteristic
93#3147C2×C411yescharacteristic
94#3131—21no—
95#3050—21no—
96#3050C2×C412yes—
97#2995—42no—
98#2993—24no—
99#2991—22no—
100#2990—22no—
101#2989—42no—
102#2975—22no—
103#2974—24no—
104#2974—42no—
105#2973—42no—
106#2972—22no—
107#2962—22no—
108C4×#135—21no—
109C4×#135C2312yes—
110C2×C4×D8—21no—
111C2×C4×D8—21no—
112C2×C4×D8—21no—
113C2×C4×D8—21no—
114C2×C4×D8—21no—
115C2×C4×D8—21no—
116C2×C4×D8C2×C412yes—
117C2×C4×D8C2×C411yescharacteristic
118C2×C4×D8C2×C411yescharacteristic
119C2×C4×D8C2×C412yes—
120C2×C4×D8C2312yes—
121C2×C4×D8C2312yes—
122C2×C4×D8C2311yescharacteristic
123C2×C4×D8C2311yescharacteristic
124#2935—22no—
125D4×M16—24no—
126D4×M16—42no—
127#2930—42no—
128#2925—41no—
129#2920—21no—
130#2920D411yescharacteristic
131#2920D411yescharacteristic
132C22×#107C2×C411yescharacteristic
133#2906—41no—
134C2×#423—21no—
135C22×#102—21no—
136C2×#407—42no—
137C22×C4×C8C2311yescharacteristic
138#2236C2×C414yes—
139#2235C2×C412yes—
140#2235C2×C412yes—
141#2233C2×C414yes—
142#2232C2×C412yes—
143#2232C2×C412yes—
144#2228C2×C414yes—
145#2228C2×C414yes—
146#2226C2×C412yes—
147#2226C2×C412yes—
148#2224C2×C412yes—
149#2224C2×C412yes—
150#2210C2×C414yes—
151#2210C2×C414yes—
152#2208C2×C412yes—
153#2208C2×C412yes—
154#2206C2×C412yes—
155#2206C2×C412yes—
156#2187C2×C412yes—
157#2187C2×C412yes—
158#2187C2×C414yes—
159#2184C2×C412yes—
160#2184C2×C412yes—
161#2184C2×C414yes—
162#2177C2314yes—
163#2177C2314yes—
164#2175C2314yes—
165#2175C2314yes—
166C4×SD32C2×C414yes—
167C4×SD32C2×C414yes—
168C4×D16C2×C414yes—
169C4×D16C2×C414yes—
170#2163—21no—
171#2163—21no—
172#2163C2312yes—
173#2163C2312yes—
174#2163C2312yes—
175#2163C2312yes—
176#2162C2×C411yescharacteristic
177#2162C2×C411yescharacteristic
178#2162C2×C412yes—
179#2159C2×C414yes—
180#2150C2×C412yes—
181C2×C4⋊C16—21no—
182#2140C2×C414yes—
183#2139C2×C414yes—
184#2112C2×C412yes—
185C2×C22⋊C16—21no—
186C4×M32C2312yes—
187C2×#346C2312yes—
188#1594C2318yes—
189#1594C2314yescomplemented
190#1593C2314yescomplemented
191#1590—24no—
192#1589—24no—
193#1587—24no—
194#1586—24no—
195#1586—28no—
196#1583—24no—
197#1582—24no—
198#1581—28no—
199#1580C2318yes—
200#1580C2314yescomplemented
201#1579C2314yescomplemented
202C8×SD16—24no—
203C8×D8—24no—
204#1568—21no—
205#1568C2312yes—
206#1567—21no—
207#1566—21no—
208#1566—21no—
209#1566C2312yes—
210#1566C2312yes—
211#1566C2311yescharacteristic
212#1566C2311yescharacteristic
213#1564—21no—
214#1564C2312yes—
215C2×#334—21no—
216C2×#334C2312yes—
217#1495—24no—
218#1490—24no—
219#1489—22no—
220#1489—22no—
221#1486—24no—
222#1481—22no—
223#1480—22no—
224#1478—22no—
225#1478—22no—
226#1452D412yes—
227#1451C2312yes—
228#1451C2312yes—
229#1450C2312yes—
230C8×M16D412yes—
231C8×M16D412yes—
232#1368C2318yescomplemented
233#1368C2318yescomplemented
234#1334C2318yescomplemented
235#1333C2314yes—
236#1333C2314yes—
237#1333C2314yes—
238#1333C2314yes—
239#1333C2318yescomplemented
240#1313C2318yescomplemented
241#1313C2318yescomplemented
242C23×D4—21no—
243C24×C4—41no—
244C2×#135—21no—
245C2×#135C22×C412yes—
246C22×D8—21no—
247C22×D8—21no—
248C22×D8—21no—
249C22×D8—44no—
250C22×D8C22×C411yescharacteristic
251C22×D8C22×C412yes—
252C22×D8C22×C412yes—
253C22×D8C22×C411yescharacteristic
254C2×#131—42no—
255C22×M16—44no—
256C22×M16—41no—
257C23×C8C22×C411yescharacteristic
258C23×C8#4111yescharacteristic
259#533—21no—
260#533—21no—
261#533—21no—
262#532—21no—
263#532—21no—
264#532—21no—
265#529—22no—
266#529—22no—
267#529—41no—
268#529—41no—
269#529—41no—
270#529—41no—
271#525—22no—
272#525—41no—
273#525—41no—
274C4×#41—22no—
275C4×#41—41no—
276C4×#41—41no—
277C2×C4×D4—22no—
278C2×C4×D4—21no—
279C2×C4×D4—21no—
280C2×C4×D4—22no—
281C2×C4×D4—22no—
282C2×C4×D4—21no—
283C2×C4×D4—22no—
284C2×C4×D4—21no—
285C2×C4×D4—41no—
286C2×C4×D4—41no—
287C2×C4×D4—41no—
288C2×C4×D4—41no—
289C2×C4×D4—41no—
290C2×C4×D4—41no—
291C22×C4⋊C4—21no—
292C22×C22⋊C4—41no—
293C22×C42C2×D411yescharacteristic
294#509—48no—
295C2×SD32C22×C414yes—
296C2×SD32C22×C414yes—
297C2×D16C22×C414yes—
298C2×D16C22×C414yes—
299C2×M32C22×C414yes—
300C22×C16—22no—
301#500C22×C411yescharacteristic
302#500C22×C411yescharacteristic
303#499—21no—
304#499C22×C412yes—
305#498—21no—
306#495—21no—
307#495C22×C412yes—
308#494C22×C411yescharacteristic
309#493C22×C411yescharacteristic
310#492—21no—
311#488—22no—
312#488—22no—
313#487—21no—
314#487—21no—
315#486—21no—
316#486—21no—
317#467—21no—
318#467—21no—
319#467C22×C412yes—
320#467C22×C412yes—
321#466—21no—
322#466—21no—
323#466C22×C412yes—
324#466C22×C412yes—
325#465—22no—
326#465—22no—
327#465—22no—
328#465—22no—
329#446—24no—
330#446—44no—
331C8×Q8—24no—
332C4×Q16—21no—
333C4×Q16—21no—
334C4×Q16C22×C412yes—
335C4×Q16C2412yes—
336C4×SD16—22no—
337C4×SD16—22no—
338C4×SD16—22no—
339C4×SD16—22no—
340C4×D8—21no—
341C4×D8—21no—
342C4×D8—21no—
343C4×D8—22no—
344C4×D8—21no—
345C4×D8—21no—
346C4×D8—22no—
347C4×D8—22no—
348C4×D8—22no—
349C4×D8—21no—
350C4×D8—22no—
351C4×D8—21no—
352C4×D8—22no—
353C4×D8—21no—
354C4×D8—22no—
355C4×D8—22no—
356C4×D8—21no—
357C4×D8—21no—
358C4×D8C22×C412yes—
359C4×D8C22×C412yes—
360C4×D8C22×C412yes—
361C4×D8C22×C412yes—
362C4×D8C22×C412yes—
363C4×D8C22×C412yes—
364C4×D8C22×C412yes—
365C4×D8C2412yes—
366C4×D8C2412yes—
367C4×D8C2412yes—
368#436—28no—
369#436—24no—
370#436—44no—
371#436—44no—
372#436—44no—
373#435—48no—
374#435—44no—
375#435—44no—
376#435—44no—
377#435—48no—
378C8×D4—28no—
379C8×D4—24no—
380C8×D4—44no—
381#433—44no—
382#432—21no—
383#432—21no—
384#432—21no—
385#432—21no—
386#432—22no—
387#432—42no—
388#432—41no—
389#431—22no—
390#431—42no—
391#431—41no—
392#431C2×D412yes—
393#431C2×D412yes—
394#431C2×D412yes—
395#431C2×D412yes—
396#427—21no—
397#427C22×C412yes—
398C2×#107—21no—
399C2×#107—21no—
400C2×#107—21no—
401C2×#107C22×C412yes—
402C2×#107C22×C411yescharacteristic
403C2×#107C22×C411yescharacteristic
404C2×#107C22×C412yes—
405#424—44no—
406#424—42no—
407#423—21no—
408#423—21no—
409#423—21no—
410#423—21no—
411#423—22no—
412#423—22no—
413#423—42no—
414#423—41no—
415#423—41no—
416C2×C4⋊C8—22no—
417C2×C4⋊C8—42no—
418C2×C4⋊C8—41no—
419#416—22no—
420#416—22no—
421C2×#102—22no—
422C2×#102—22no—
423C2×#102—21no—
424C2×#102—21no—
425C2×#102—22no—
426C2×#102—21no—
427C2×#102—21no—
428C2×#102—22no—
429#408—42no—
430#407—21no—
431#407—21no—
432#407—44no—
433#407—44no—
434#407—44no—
435#407—41no—
436C2×C22⋊C8—44no—
437C2×C22⋊C8—44no—
438#405—42no—
439C4×M16—41no—
440C4×M16C2×D412yes—
441C4×M16C2×D412yes—
442C2×C4×C8C22×C411yescharacteristic
443C2×C4×C8C22×C411yescharacteristic
444C2×C4×C8C22×C411yescharacteristic
445C2×C4×C8C2×D411yescharacteristic
446C2×C4×C8C2×D411yescharacteristic
447C2×C4×C8C2×D411yescharacteristic
448C2×C4×C8#4111yescharacteristic
449C2×C4×C8#4111yescharacteristic
450C2×C4×C8#4111yescharacteristic
451C2×C4×C8C2411yescharacteristic
452C2×C4×C8C2411yescharacteristic
453C2×C4×C8C2411yescharacteristic
454#367C22×C414yes—
455#367C22×C414yes—
456#366C22×C414yes—
457#366C22×C414yes—
458C4⋊C16—22no—
459C4⋊C16—22no—
460C4⋊C16C22×C412yes—
461C4⋊C16C22×C412yes—
462C4⋊C16C22×C414yes—
463#358C22×C414yes—
464#358C22×C414yes—
465#357C22×C414yes—
466#357C22×C414yes—
467#357C22×C414yes—
468#357C22×C414yes—
469#357C22×C414yes—
470#357C22×C414yes—
471C22⋊C16—22no—
472C22⋊C16—22no—
473C22⋊C16C22×C412yes—
474C22⋊C16C22×C412yes—
475C22⋊C16C22×C414yes—
476#346—22no—
477#346C2414yes—
478#346C2414yes—
479C4×C16C22×C412yes—
480C4×C16C22×C412yes—
481#335—22no—
482#335—22no—
483#334—22no—
484#334—21no—
485#334—21no—
486#334—22no—
487#334—22no—
488#334C2412yes—
489#334C2412yes—
490#334C2414yes—
491Q8⋊C8—24no—
492Q8⋊C8—24no—
493D4⋊C8—28no—
494D4⋊C8—24no—
495D4⋊C8—24no—
496D4⋊C8—28no—
497#322C2×D414yes—
498#322C2×D414yes—
499#322C2414yes—
500C82C2×D414yes—
501C25—41no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—44no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—82no—
514C23×C4—41no—
515C23×C4—42no—
516C23×C4—41no—
517C23×C4—42no—
518C23×C4—41no—
519C23×C4—42no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4—42no—
523C23×C4—164no—
524C23×C4C4×D411yescharacteristic
525C23×C4AGL(1,ℤ/8)11yescharacteristic
526C23×C4AGL(1,ℤ/8)11yescharacteristic
527#135—44no—
528#135—82no—
529C2×Q16—21no—
530C2×Q16C23×C412yes—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×D8—24no—
534C2×D8—24no—
535C2×D8—24no—
536C2×D8—21no—
537C2×D8—22no—
538C2×D8—21no—
539C2×D8—22no—
540C2×D8—21no—
541C2×D8—42no—
542C2×D8—42no—
543C2×D8—42no—
544C2×D8—44no—
545C2×D8—44no—
546C2×D8—44no—
547C2×D8C23×C412yes—
548C2×D8C23×C412yes—
549C2×D8C23×C412yes—
550#131—164no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—48no—
554C2×M16—44no—
555C2×M16—42no—
556C2×M16—41no—
557C2×M16—42no—
558C2×M16—41no—
559C2×M16—162no—
560C2×M16—168no—
561C22×C8—42no—
562C22×C8—48no—
563C22×C8—44no—
564C22×C8—42no—
565C22×C8—81no—
566C22×C8C4×D411yescharacteristic
567C22×C8C4×D411yescharacteristic
568C22×C8C4×D411yescharacteristic
569C22×C8C4×D411yescharacteristic
570C22×C8C4×D411yescharacteristic
571C22×C8C4×D411yescharacteristic
572C22×C8C23×C411yescharacteristic
573C22×C8C23×C411yescharacteristic
574C22×C8C23×C411yescharacteristic
575C22×C8C2×#4111yescharacteristic
576C22×C8C2×#4111yescharacteristic
577C22×C8C2×#4111yescharacteristic
578C4⋊Q8—21no—
579C4⋊Q8—21no—
580C4⋊Q8—21no—
581#127—21no—
582#126—42no—
583#126—42no—
584#125—22no—
585#125—41no—
586#125—41no—
587#124—22no—
588#124—41no—
589#124—41no—
590#123—42no—
591#123—42no—
592#123—42no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#120—42no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—42no—
623C4×D4—42no—
624C4×D4—42no—
625C4×D4—42no—
626C4×D4—42no—
627C4×D4—42no—
628C4×D4—42no—
629C4×D4—42no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—42no—
634C4×D4—42no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—42no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—42no—
641C4×D4—42no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—42no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648#117—22no—
649#117—41no—
650#117—41no—
651#117—42no—
652#117—42no—
653#117—42no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C22⋊C4—42no—
662C2×C22⋊C4—42no—
663C2×C22⋊C4—41no—
664C2×C22⋊C4—41no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C42—42no—
670C2×C42C4×D411yescharacteristic
671C2×C42C4×D411yescharacteristic
672C2×C42C4×D411yescharacteristic
673C2×C42AGL(1,ℤ/8)11yescharacteristic
674C2×C42AGL(1,ℤ/8)11yescharacteristic
675C2×C42AGL(1,ℤ/8)11yescharacteristic
676C2×C42AGL(1,ℤ/8)11yescharacteristic
677C2×C42AGL(1,ℤ/8)11yescharacteristic
678C2×C42AGL(1,ℤ/8)11yescharacteristic
679C2×C42C22×D411yescharacteristic
680C2×C42C22×D411yescharacteristic
681C2×C42C22×D411yescharacteristic
682SD32—28no—
683SD32—44no—
684D16—28no—
685D16—44no—
686M32—44no—
687C2×C16—24no—
688C2×C16—82no—
689C2×C16C23×C414yes—
690C2×C16C23×C414yes—
691#107—21no—
692#107—21no—
693#107—22no—
694#107—22no—
695#107—21no—
696#107—21no—
697#107C23×C412yes—
698#107C23×C412yes—
699#107C23×C412yes—
700#107C23×C412yes—
701#106—22no—
702#106—22no—
703C4⋊C8—22no—
704C4⋊C8—22no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—24no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—44no—
711C4⋊C8—44no—
712C4⋊C8—42no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—42no—
716C4⋊C8—42no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—48no—
738C22⋊C8—48no—
739C22⋊C8—44no—
740C22⋊C8—44no—
741C22⋊C8—42no—
742C22⋊C8—42no—
743#97—22no—
744#97—22no—
745#97—44no—
746#97—42no—
747C4×C8—44no—
748C4×C8—42no—
749C4×C8C4×D411yescharacteristic
750C4×C8C4×D411yescharacteristic
751C4×C8C4×D411yescharacteristic
752C4×C8C4×D411yescharacteristic
753C4×C8C4×D411yescharacteristic
754C4×C8C4×D411yescharacteristic
755C4×C8C23×C411yescharacteristic
756C4×C8C23×C411yescharacteristic
757C4×C8C23×C411yescharacteristic
758C4×C8C22×D414yes—
759C4×C8C22×D414yes—
760C4×C8C22×D411yescharacteristic
761C4×C8C22×D411yescharacteristic
762C4×C8C22×D411yescharacteristic
763C4×C8C2×#4111yescharacteristic
764C4×C8C2×#4111yescharacteristic
765C4×C8C2×#4111yescharacteristic
766C4×C8C2511yescharacteristic
767C24—41no—
768C24—42no—
769C24—42no—
770C24—41no—
771C24—84no—
772C24—162no—
773C24—162no—
774C24#44211yescharacteristic
775#41—82no—
776#41—82no—
777#41—82no—
778#41—82no—
779#41—162no—
780C2×Q8—22no—
781C2×Q8—41no—
782C2×Q8—41no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—42no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—82no—
802C2×D4—82no—
803C2×D4—84no—
804C2×D4—84no—
805C2×D4—84no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—88no—
826C22×C4—164no—
827C22×C4—162no—
828C22×C4—162no—
829C22×C4—162no—
830C22×C4—164no—
831C22×C4—162no—
832C22×C4—164no—
833C22×C4—162no—
834C22×C4#44211yescharacteristic
835C22×C4#44211yescharacteristic
836C22×C4#44211yescharacteristic
837C22×C4#44211yescharacteristic
838C22×C4#44211yescharacteristic
839C22×C4#44211yescharacteristic
840C22×C4#44211yescharacteristic
841C22×C4#44211yescharacteristic
842C22×C4#44211yescharacteristic
843C22×C4C2×C4×D411yescharacteristic
844C22×C4C2×C4×D411yescharacteristic
845C22×C4C2×C4×D411yescharacteristic
846C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
847C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
848C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
849C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
850C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
851C22×C4C2×AGL(1,ℤ/8)11yescharacteristic
852Q16—24no—
853Q16—81no—
854SD16—44no—
855SD16—82no—
856D8—24no—
857D8—22no—
858D8—24no—
859D8—22no—
860D8—22no—
861D8—44no—
862D8—44no—
863D8—42no—
864D8—81no—
865D8#56814yes—
866M16—44no—
867M16—44no—
868M16—84no—
869M16—168no—
870M16—164no—
871M16—161no—
872M16—162no—
873M16—161no—
874C2×C8—22no—
875C2×C8—22no—
876C2×C8—22no—
877C2×C8—24no—
878C2×C8—24no—
879C2×C8—41no—
880C2×C8—41no—
881C2×C8—41no—
882C2×C8—41no—
883C2×C8—41no—
884C2×C8—41no—
885C2×C8—41no—
886C2×C8—41no—
887C2×C8—41no—
888C2×C8—42no—
889C2×C8—44no—
890C2×C8—42no—
891C2×C8—84no—
892C2×C8—168no—
893C2×C8—164no—
894C2×C8C2×C4×D411yescharacteristic
895C2×C8C2×C4×D411yescharacteristic
896C2×C8C2×C4×D411yescharacteristic
897C2×C8C2×C4×D411yescharacteristic
898C2×C8C2×C4×D411yescharacteristic
899C2×C8C2×C4×D411yescharacteristic
900C2×C8C24×C411yescharacteristic
901C2×C8C22×#4111yescharacteristic
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—42no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42#44211yescharacteristic
941C42#44211yescharacteristic
942C42#44211yescharacteristic
943C42#44211yescharacteristic
944C42#44211yescharacteristic
945C42#44211yescharacteristic
946C42C2×C4×D411yescharacteristic
947C42C2×C4×D411yescharacteristic
948C42C2×C4×D411yescharacteristic
949C42C2×AGL(1,ℤ/8)11yescharacteristic
950C42C2×AGL(1,ℤ/8)11yescharacteristic
951C42C2×AGL(1,ℤ/8)11yescharacteristic
952C42C2×AGL(1,ℤ/8)11yescharacteristic
953C42C2×AGL(1,ℤ/8)11yescharacteristic
954C42C2×AGL(1,ℤ/8)11yescharacteristic
955C42C23×D411yescharacteristic
956C16—24no—
957C16—24no—
958C16—44no—
959C23—22no—
960C23—41no—
961C23—41no—
962C23—44no—
963C23—42no—
964C23—42no—
965C23—42no—
966C23—84no—
967C23—84no—
968C23—84no—
969C23—82no—
970C23—84no—
971C23—162no—
972C23—161no—
973C23—161no—
974C23—161no—
975C23—162no—
976C23—161no—
977C23—1616no—
978C23C2×#44211yescharacteristic
979C23C2×#44211yescharacteristic
980C23C2×#44211yescharacteristic
981Q8—42no—
982Q8—42no—
983Q8—82no—
984Q8—161no—
985D4—24no—
986D4—44no—
987D4—42no—
988D4—42no—
989D4—42no—
990D4—42no—
991D4—42no—
992D4—84no—
993D4—84no—
994D4—82no—
995D4—82no—
996D4—84no—
997D4—161no—
998D4—162no—
999D4—162no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—82no—
1027C2×C4—84no—
1028C2×C4—84no—
1029C2×C4—82no—
1030C2×C4—84no—
1031C2×C4—84no—
1032C2×C4—84no—
1033C2×C4—84no—
1034C2×C4—162no—
1035C2×C4—162no—
1036C2×C4—162no—
1037C2×C4—162no—
1038C2×C4—162no—
1039C2×C4—162no—
1040C2×C4—161no—
1041C2×C4—161no—
1042C2×C4C2×#44211yescharacteristic
1043C2×C4C2×#44211yescharacteristic
1044C2×C4C2×#44211yescharacteristic
1045C2×C4C2×#44211yescharacteristic
1046C2×C4C2×#44211yescharacteristic
1047C2×C4C2×#44211yescharacteristic
1048C2×C4C2×#44211yescharacteristic
1049C2×C4C2×#44211yescharacteristic
1050C2×C4C2×#44211yescharacteristic
1051C2×C4C22×C4×D411yescharacteristic
1052C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1053C2×C4C22×AGL(1,ℤ/8)11yescharacteristic
1054C8—21no—
1055C8—21no—
1056C8—21no—
1057C8—21no—
1058C8—21no—
1059C8—21no—
1060C8—21no—
1061C8—44no—
1062C8—44no—
1063C8—82no—
1064C8—82no—
1065C8—84no—
1066C8C2×#56812yes—
1067C22—21no—
1068C22—21no—
1069C22—21no—
1070C22—21no—
1071C22—21no—
1072C22—21no—
1073C22—21no—
1074C22—21no—
1075C22—44no—
1076C22—44no—
1077C22—82no—
1078C22—82no—
1079C22—82no—
1080C22—82no—
1081C22—82no—
1082C22—82no—
1083C22—82no—
1084C22—82no—
1085C22—168no—
1086C22—164no—
1087C22—168no—
1088C22—164no—
1089C22#3346912yes—
1090C22C22×#44211yescharacteristic
1091C4—21no—
1092C4—21no—
1093C4—21no—
1094C4—21no—
1095C4—21no—
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—21no—
1101C4—82no—
1102C4—82no—
1103C4—82no—
1104C4—82no—
1105C4—82no—
1106C4#3347112yes—
1107C4#6014111yescharacteristic
1108C4#6018211yescharacteristic
1109C2—22no—
1110C2—41no—
1111C2—41no—
1112C2—84no—
1113C2—162no—
1114C2—162no—
1115C2#634528711yescharacteristic
1116C2C2×#3346911yescharacteristic
1117C2C2×#3347111yescharacteristic
subgroupG/H
center, socleC22C22×#442
commutatorC2×C8C24×C4
Frattini, cosocleC4×C8C25
prime radical#7623096C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ #17323 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #6345776C2semidirect
3. #6345071C2semidirect
4. #484110C2semidirect
5. #484106C2semidirect
6. #484040C2semidirect
7. #484039C2semidirect
8. #483928C2semidirect
9. #483882C2semidirect
10. #483443C2semidirect
11. #481391C2semidirect
12. C2×#11663C2semidirect
13. #479971C2semidirect
34. #18073C22semidirect
35. #18072C22semidirect
37. #18065C22semidirect
39. #18063C22semidirect
45. #17974C22semidirect
54. #12089C22semidirect
55. #12087C22semidirect
56. #12080C22semidirect
57. #12078C22semidirect
58. #12078C22semidirect
59. #12077C22semidirect
60. #12067C22semidirect
61. #12065C22semidirect
62. #12029C22semidirect
63. #12028C22semidirect
64. #12020C22semidirect
65. #12020C22semidirect
66. #11679C22semidirect
67. #11678C22semidirect
68. #11666C22semidirect
73. #11656C22semidirect
75. #11416C22semidirect
76. #11414C22semidirect
77. #11413C22semidirect
189. #1594C23semidirect
190. #1593C23semidirect
200. #1580C23semidirect
201. #1579C23semidirect
232. #1368C23semidirect
233. #1368C23semidirect
234. #1334C23semidirect
239. #1333C23semidirect
240. #1313C23semidirect
241. #1313C23semidirect

Maximal subgroups

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

subgroupindex
#76230962
#63457762
#63450712
#4841102
#4841062
#4840402
#4840392
#4839282
#4838822
#4834432
#4813912
C2×#116632
#4799712