Finite Group Databasebeta

← #7690467

Subgroups — #7690467

Order 512.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#59213C213yesmaximal, complemented
4#59121C213yesmaximal, complemented
5#59117C213yesmaximal, complemented
6#59039C213yesmaximal, complemented
7#59031C213yesmaximal, complemented
8#45354C213yesmaximal, complemented
9#45255C213yesmaximal, complemented
10#45106C213yesmaximal, complemented
11#45100C213yesmaximal, complemented
12#38051C213yesmaximal, complemented
13#37870C213yesmaximal, complemented
14#37798C213yesmaximal, complemented
15#37764C213yesmaximal, complemented
16#36435C211yesmaximal, characteristic, complemented
17#36433C211yesmaximal, characteristic, complemented
18#36433C211yesmaximal, characteristic, complemented
19#36432C211yesmaximal, characteristic, complemented
20#36430C211yesmaximal, characteristic, complemented
21#36361C213yesmaximal, complemented
22#36139C213yesmaximal, complemented
23#36040C211yesmaximal, characteristic, complemented
24#35983C211yesmaximal, characteristic, complemented
25#35957C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#34735C213yesmaximal, complemented
28#34295C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32#3517—216no—
33#3480—216no—
34C2×#559C2213yes—
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#556C2213yes—
38C2×#553C2213yes—
39C2×#553C2213yes—
40C2×#553C2213yes—
41C2×#553C2213yes—
42C2×#550C2213yes—
43C2×#550C2211yescharacteristic
44C2×#550C2211yescharacteristic
45C2×#550C2211yescharacteristic
46C2×#548C2211yescharacteristic
47C2×#548C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#547C2213yes—
50C2×#540C2213yes—
51C2×#540C2213yes—
52C2×#532C2213yes—
53C2×#532C2213yes—
54C2×#529C2213yes—
55C2×#529C2213yes—
56C2×#529C2213yes—
57C2×#520C2211yescharacteristic
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×C4×#41C2213yes—
61C2×C4×#41C2211yescharacteristic
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C22×C4×Q8C2211yescharacteristic
66#2855C2213yes—
67#2854C2213yes—
68#2854C2213yes—
69#2851C2213yes—
70#2850C2213yes—
71#2724C2216yes—
72#2718C2216yes—
73#2717C2216yes—
74#2708C2216yes—
75#2708C2216yes—
76#2708C2216yes—
77#2701C2216yes—
78#2695C2216yes—
79#2695C2216yes—
80#2689C2216yes—
81#2686C2216yes—
82#2686C2216yes—
83#2686C2216yes—
84#2671C2216yes—
85#2660C2213yes—
86#2628C2213yes—
87#2625C2213yes—
88#2620C2213yes—
89#2584C2213yes—
90#2581C2213yes—
91#2580C2213yes—
92#2567C2213yes—
93#2565C2213yes—
94#2563C2213yes—
95#2552C2213yes—
96#2552C2213yes—
97#2550C2213yes—
98#2550C2213yes—
99#2544C2213yes—
100#2544C2213yes—
101#2537C2216yes—
102#2537C2213yes—
103#2535C2213yes—
104#2521C2216yes—
105#2503C2213yes—
106#2500C2213yes—
107#2500C2213yes—
108#2499C2213yes—
109#2496C2216yes—
110#2487C2213yes—
111#2486C2216yes—
112#2485C2213yes—
113#2485C2213yes—
114#2485C2213yes—
115#2479C2213yes—
116#2478C2213yes—
117#2475C2211yescharacteristic
118#2474C2213yes—
119#2470C2216yes—
120#2469C2216yes—
121#2469C2213yes—
122#2468C2216yes—
123#2468C2213yes—
124#2468C2216yes—
125#2462C2213yes—
126#2461C2213yes—
127#2455C2216yes—
128#2454C2213yes—
129#2454C2213yes—
130#2453C2213yes—
131#2451C2213yes—
132#2449C2213yes—
133#2447C2213yes—
134#2447C2213yes—
135#2447C2213yes—
136#2447C2213yes—
137#2445C2213yes—
138#2445C2213yes—
139#2445C2213yes—
140#2445C2213yes—
141#2443C2216yes—
142#2443C2213yes—
143#2443C2216yes—
144#2442C2213yes—
145#2442C2213yes—
146#2442C2213yes—
147#2440C2213yes—
148#2438C2213yes—
149#2430C2216yes—
150#2430C2213yes—
151#2428C2213yes—
152#2428C2213yes—
153#2427C2213yes—
154#2427C2213yes—
155#2425C2216yes—
156#2425C2213yes—
157#2422C2213yes—
158#2422C2213yes—
159#2422C2213yes—
160#2422C2216yes—
161#2420C2213yes—
162#2420C2213yes—
163#2420C2213yes—
164#2420C2213yes—
165#2420C2213yes—
166#2419C2213yes—
167#2419C2216yes—
168#2417C2213yes—
169#2416C2213yes—
170#2415C2213yes—
171#2414C2213yes—
172#2413C2213yes—
173#2407C2216yes—
174#2406C2216yes—
175#2406C2216yes—
176#2406C2213yes—
177#2399C2213yes—
178#2396C2213yes—
179#2395C2213yes—
180#2392C2213yes—
181#2367C2213yes—
182#2366C2213yes—
183#2363C2213yes—
184#2361C2216yes—
185#2361C2213yes—
186#2361C2213yes—
187#2360C2213yes—
188#2359C2216yes—
189#2352C2213yes—
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2349C2213yes—
201#2349C2213yes—
202#2349C2213yes—
203#2349C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208D4×C4⋊C4C2213yes—
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217#2339C2216yes—
218#2328C2213yes—
219#2326C2213yes—
220#2324C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231#2296C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234C2×#389C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2285C2213yes—
238#2276C2211yescharacteristic
239C2×C4×C4⋊C4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C22×#41C2316yes—
245C23×Q8C2311yescharacteristic
246#559—224no—
247#557—28no—
248#557—28no—
249#556—224no—
250#553—224no—
251#553—224no—
252#553—224no—
253#553—224no—
254#550—28no—
255#550—28no—
256#550—224no—
257#550D4116yescomplemented
258#548—28no—
259#548—28no—
260#548—28no—
261#547—224no—
262#540—224no—
263#540—224no—
264#532—224no—
265#532—224no—
266C2×C4⋊Q8C2313yes—
267C2×C4⋊Q8C2313yes—
268C2×#127C2313yes—
269C2×#127C2313yes—
270C2×#127C2313yes—
271#529—224no—
272#529—224no—
273#529—224no—
274C2×#126C2316yes—
275C2×#126C2313yes—
276C2×#126C2313yes—
277C2×#126C2316yes—
278C2×#125C2313yes—
279C2×#125C2311yescharacteristic
280C2×#125C2313yes—
281C2×#125C2313yes—
282C2×#125C2313yes—
283C2×#124C2313yes—
284C2×#124C2313yes—
285C2×#124C2313yes—
286C2×#124C2313yes—
287C2×#124C2316yes—
288C2×#123C2313yes—
289C2×#123C2316yes—
290C2×#123C2316yes—
291C2×#123C2313yes—
292C2×#123C2316yes—
293C2×#123C2316yes—
294C2×#123C2316yes—
295C2×#123C2313yes—
296C2×#123C2313yes—
297C2×#123C2313yes—
298C2×#123C2316yes—
299C2×C22⋊Q8C2313yes—
300C2×C22⋊Q8C2313yes—
301C2×C22⋊Q8C2313yes—
302C2×C22⋊Q8C2313yes—
303C2×C22⋊Q8C2313yes—
304C2×#121C2313yes—
305C2×#121C2313yes—
306C2×#121C2313yes—
307C2×#121C2316yes—
308C2×#121C2316yes—
309C2×#121C2313yes—
310C2×#121C2313yes—
311C2×#121C2313yes—
312C2×#121C2313yes—
313C2×#121C2313yes—
314C2×#121C2316yes—
315C2×#121C2316yes—
316C2×#121C2316yes—
317C2×#121C2313yes—
318C2×#121C2313yes—
319C2×#121C2313yes—
320#520—28no—
321#520—28no—
322#520—28no—
323C4×#41—28no—
324C4×#41—28no—
325C4×#41—28no—
326C4×#41—28no—
327C4×#41—224no—
328C2×C4×Q8—28no—
329C2×C4×Q8C2313yes—
330C2×C4×Q8C2313yes—
331C2×C4×Q8C2313yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2313yes—
342C2×C4×Q8C2313yes—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×D4C2313yes—
346C2×C4×D4C2313yes—
347C2×C4×D4C2313yes—
348C2×C4×D4C2316yes—
349C2×C4×D4C2313yes—
350C2×C4×D4C2313yes—
351C2×C4×D4C2313yes—
352C2×C4×D4C2313yes—
353C2×C4×D4C2313yes—
354C2×C4×D4C2313yes—
355C2×C4×D4C2313yes—
356C2×C4×D4C2313yes—
357C2×C4×D4C2313yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2316yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2316yes—
370C2×C4×D4C2316yes—
371C2×C4×D4C2313yes—
372C2×#117C2313yes—
373C2×#117C2313yes—
374C2×#117C2313yes—
375C2×#117C2313yes—
376C2×#117C2313yes—
377C2×#117C2313yes—
378C2×#117C2311yescharacteristic
379C2×#117C2313yes—
380C2×#117C2313yes—
381C2×#117C2313yes—
382C22×C4⋊C4C2313yes—
383C22×C4⋊C4C2313yes—
384C22×C4⋊C4C2313yes—
385C22×C4⋊C4C2313yes—
386C22×C4⋊C4C2313yes—
387C22×C4⋊C4C2313yes—
388C22×C4⋊C4C2316yes—
389C22×C42C2313yes—
390C22×C42C2313yes—
391C22×C42C2313yes—
392C22×C42C2313yes—
393C22×C42C2313yes—
394#400C2316yes—
395#400C2316yes—
396#400C2316yes—
397#400C2313yes—
398#400C2311yescharacteristic
399#399C2313yes—
400#399C2316yes—
401#399C2313yes—
402#398C2316yes—
403#398C2316yes—
404#398C2313yes—
405#398C2313yes—
406#398C2313yes—
407#398C2313yes—
408#398C2313yes—
409#398C2311yescharacteristic
410#398C2313yes—
411#398C2313yes—
412#398C2316yes—
413#398C2316yes—
414#397C2316yes—
415#397C2316yes—
416#397C2313yes—
417#397C2311yescharacteristic
418#397C2313yes—
419#397C2313yes—
420#397C2316yes—
421#397C2316yes—
422#397C2316yes—
423#397C2316yes—
424#397C2316yes—
425#397C2316yes—
426#396C2313yes—
427#396C2316yes—
428#396C2311yescharacteristic
429#396C2313yes—
430#396C2313yes—
431#395C2313yes—
432#395C2316yes—
433#395C2316yes—
434#395C2313yes—
435#395C2313yes—
436#395C2313yes—
437#395C2313yes—
438#394C2316yes—
439#394C2316yes—
440#394C2313yes—
441#394C2313yes—
442#394C2313yes—
443#394C2313yes—
444#394C2313yes—
445#394C2316yes—
446#394C2316yes—
447#394C2316yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2316yes—
454#393C2313yes—
455#393C2316yes—
456#392C2313yes—
457#392C2316yes—
458#391C2313yes—
459#391C2313yes—
460#391C2316yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2313yes—
465#391C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2316yes—
470#390C2313yes—
471#390C2313yes—
472#390C2313yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2316yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2316yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2313yes—
495#389C2313yes—
496#389C2313yes—
497#389C2316yes—
498#389C2316yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2311yescharacteristic
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2313yes—
512#388C2313yes—
513#388C2316yes—
514#388C2313yes—
515#388C2313yes—
516#388C2316yes—
517#388C2316yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2311yescharacteristic
523#388C2313yes—
524#388C2313yes—
525#388C2311yescharacteristic
526#387C2313yes—
527#387C2316yes—
528#387C2313yes—
529#387C2313yes—
530#387C2316yes—
531#387C2313yes—
532#387C2316yes—
533#387C2313yes—
534#387C2313yes—
535#387C2313yes—
536#387C2311yescharacteristic
537#387C2313yes—
538#387C2313yes—
539#387C2311yescharacteristic
540#387C2311yescharacteristic
541#386C2316yes—
542#386C2313yes—
543#386C2316yes—
544#386C2316yes—
545#386C2316yes—
546#386C2316yes—
547#386C2313yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2313yes—
553#386C2316yes—
554#386C2313yes—
555#386C2313yes—
556#386C2313yes—
557#386C2313yes—
558#386C2313yes—
559#386C2313yes—
560#385C2316yes—
561#385C2316yes—
562#385C2313yes—
563#385C2316yes—
564#385C2316yes—
565#385C2316yes—
566#385C2316yes—
567#385C2313yes—
568#385C2316yes—
569#385C2316yes—
570#385C2313yes—
571#385C2313yes—
572#385C2313yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2316yes—
577#385C2313yes—
578#385C2313yes—
579#385C2316yes—
580#385C2313yes—
581#385C2311yescharacteristic
582#385C2313yes—
583#385C2313yes—
584#385C2313yes—
585#385C2311yescharacteristic
586#384C2313yes—
587#384C2316yes—
588#384C2313yes—
589#384C2313yes—
590#384C2313yes—
591#382C2313yes—
592#382C2313yes—
593#382C2313yes—
594#382C2313yes—
595#382C2313yes—
596#382C2313yes—
597#381C2316yes—
598#381C2316yes—
599#381C2313yes—
600#381C2316yes—
601#381C2313yes—
602#381C2313yes—
603#380C2316yes—
604#380C2316yes—
605#380C2316yes—
606#380C2316yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2316yes—
616#380C2316yes—
617#380C2316yes—
618#380C2313yes—
619#380C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2316yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C4⋊C4C2311yescharacteristic
638C4×C22⋊C4C2316yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2316yes—
648#376C2313yes—
649C2×#95C2313yes—
650C2×#95C2316yes—
651C2×#95C2313yes—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—212no—
660C2×#41—224no—
661C2×#41—46no—
662C2×#41—46no—
663C2×#41—412no—
664C2×#41—86no—
665C2×#41C2×D418yes—
666C2×#41C2×D418yes—
667C22×Q8—24no—
668C22×Q8—24no—
669C22×Q8—24no—
670C22×Q8C2413yes—
671C22×Q8C2413yes—
672C22×Q8C2413yes—
673C22×Q8C2411yescharacteristic
674C22×D4C2413yes—
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2416yes—
682C22×D4C2413yes—
683C22×D4C2416yes—
684C22×D4C2416yes—
685C22×D4C2413yes—
686C23×C4C2413yes—
687C23×C4C2413yes—
688C23×C4C2411yescharacteristic
689C23×C4C2413yes—
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2416yes—
697C23×C4C2416yes—
698C23×C4C2413yes—
699C23×C4C2416yes—
700C23×C4C2413yes—
701C23×C4C2413yes—
702C23×C4C2413yes—
703C4⋊Q8—212no—
704C4⋊Q8—212no—
705#127—212no—
706#127—212no—
707#127C2×D4124yes—
708#126—212no—
709#126—212no—
710#126—224no—
711#126—224no—
712#125—24no—
713#125—212no—
714#125—212no—
715#125—212no—
716#125—212no—
717#124—212no—
718#124—212no—
719#124—224no—
720#124—212no—
721#124—212no—
722#123—212no—
723#123—224no—
724#123—224no—
725#123—224no—
726#123—212no—
727#123—224no—
728#123—46no—
729#123—412no—
730#123—46no—
731#123—46no—
732#123—86no—
733C22⋊Q8—212no—
734C22⋊Q8—212no—
735C22⋊Q8—212no—
736C22⋊Q8—212no—
737C22⋊Q8—46no—
738#121—212no—
739#121—224no—
740#121—212no—
741#121—212no—
742#121—224no—
743#121—212no—
744#121—224no—
745#121—224no—
746#121—212no—
747#121—212no—
748#121—212no—
749#121—212no—
750#121—46no—
751#121—412no—
752#121C2×D4124yes—
753#121C2×D4124yes—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—24no—
762C4×Q8—24no—
763C4×Q8—212no—
764C4×Q8—212no—
765C4×Q8—212no—
766C4×Q8—212no—
767C4×Q8—212no—
768C4×Q8C2×D418yes—
769C4×Q8#4118yescomplemented
770C4×D4—212no—
771C4×D4—212no—
772C4×D4—212no—
773C4×D4—212no—
774C4×D4—212no—
775C4×D4—212no—
776C4×D4—212no—
777C4×D4—212no—
778C4×D4—212no—
779C4×D4—224no—
780C4×D4—212no—
781C4×D4—212no—
782C4×D4—212no—
783C4×D4—212no—
784C4×D4—212no—
785C4×D4—212no—
786C4×D4—212no—
787C4×D4—212no—
788C4×D4—212no—
789C4×D4—224no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—212no—
794C4×D4—86no—
795C4×D4—86no—
796C4×D4C2×D4124yes—
797#117—212no—
798#117—212no—
799#117—212no—
800#117—212no—
801#117—24no—
802#117—212no—
803#117—212no—
804#117—212no—
805#117—212no—
806#117—212no—
807C2×C4⋊C4—212no—
808C2×C4⋊C4—212no—
809C2×C4⋊C4—212no—
810C2×C4⋊C4—212no—
811C2×C4⋊C4—46no—
812C2×C4⋊C4—46no—
813C2×C4⋊C4—86no—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2416yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2416yes—
841C2×C4⋊C4C2416yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2416yes—
852C2×C4⋊C4C2416yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2416yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2413yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2413yes—
873C2×C22⋊C4C2413yes—
874C2×C22⋊C4C2416yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2416yes—
878C2×C22⋊C4C2416yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2416yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2416yes—
890C2×C22⋊C4C2416yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2416yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2416yes—
901C2×C22⋊C4C2416yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2416yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2416yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C42—212no—
917C2×C42—212no—
918C2×C42—212no—
919C2×C42—212no—
920C2×C42—212no—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2413yes—
924C2×C42C2413yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2416yes—
941C2×C42C2413yes—
942C2×C42C2413yes—
943#95C2413yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2416yes—
953#95C2416yes—
954#95C2411yescharacteristic
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2411yescharacteristic
959#95C2413yes—
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2416yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2416yes—
975#95C2413yes—
976#95C2411yescharacteristic
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2413yes—
981#95C2416yes—
982#95C2413yes—
983#95C2416yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2416yes—
990#95C2416yes—
991#95C2416yes—
992C24C2513yes—
993C24C2513yes—
994C24C2513yes—
995C24C2511yescharacteristic
996#41—232no—
997#41—232no—
998#41—448no—
999#41—416no—
1000#41—848no—
1001C2×Q8—26no—
1002C2×Q8—26no—
1003C2×Q8—26no—
1004C2×Q8—26no—
1005C2×Q8—26no—
1006C2×Q8—26no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×Q8—43no—
1010C2×Q8—416no—
1011C2×Q8C22×D414yes—
1012C2×Q8C2×#4114yes—
1013C2×Q82−1+414yes—
1014C2×D4—26no—
1015C2×D4—26no—
1016C2×D4—26no—
1017C2×D4—26no—
1018C2×D4—26no—
1019C2×D4—26no—
1020C2×D4—212no—
1021C2×D4—26no—
1022C2×D4—212no—
1023C2×D4—26no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—26no—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—43no—
1033C2×D4—46no—
1034C2×D4—46no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—43no—
1040C2×D4—46no—
1041C2×D4—43no—
1042C2×D4—46no—
1043C2×D4—43no—
1044C2×D4—46no—
1045C2×D4—46no—
1046C2×D4C22×D4112yes—
1047C2×D4C22×D4112yes—
1048C2×D4C22×D4112yes—
1049C2×D4C22×D4124yes—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—26no—
1053C22×C4—26no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—22no—
1057C22×C4—26no—
1058C22×C4—26no—
1059C22×C4—26no—
1060C22×C4—26no—
1061C22×C4—26no—
1062C22×C4—26no—
1063C22×C4—212no—
1064C22×C4—26no—
1065C22×C4—26no—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—26no—
1069C22×C4—26no—
1070C22×C4—26no—
1071C22×C4—26no—
1072C22×C4—26no—
1073C22×C4—26no—
1074C22×C4—26no—
1075C22×C4—212no—
1076C22×C4—26no—
1077C22×C4—212no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4—43no—
1083C22×C4—43no—
1084C22×C4—43no—
1085C22×C4—43no—
1086C22×C4—46no—
1087C22×C4—46no—
1088C22×C4—43no—
1089C22×C4—43no—
1090C22×C4—46no—
1091C22×C4—46no—
1092C22×C4—43no—
1093C22×C4—43no—
1094C22×C4—43no—
1095C22×C4—43no—
1096C22×C4—43no—
1097C22×C4—46no—
1098C22×C4—46no—
1099C22×C4C22×D4112yes—
1100C22×C4C22×D4112yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C22×C4C2513yes—
1106C22×C4C2513yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2513yes—
1110C22×C4C2513yes—
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2513yes—
1114C22×C4C2513yes—
1115C22×C4C2513yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2513yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2513yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2513yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2513yes—
1128C4⋊C4—26no—
1129C4⋊C4—26no—
1130C4⋊C4—26no—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—212no—
1134C4⋊C4—22no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—26no—
1140C4⋊C4—26no—
1141C4⋊C4—26no—
1142C4⋊C4—26no—
1143C4⋊C4—26no—
1144C4⋊C4—22no—
1145C4⋊C4—22no—
1146C4⋊C4—212no—
1147C4⋊C4—212no—
1148C4⋊C4—22no—
1149C4⋊C4—26no—
1150C4⋊C4—26no—
1151C4⋊C4—26no—
1152C4⋊C4—26no—
1153C4⋊C4—22no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—22no—
1162C4⋊C4—22no—
1163C4⋊C4—43no—
1164C4⋊C4—43no—
1165C4⋊C4—43no—
1166C4⋊C4—43no—
1167C4⋊C4—43no—
1168C4⋊C4—43no—
1169C4⋊C4—46no—
1170C4⋊C4—46no—
1171C4⋊C4—43no—
1172C4⋊C4—46no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—46no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4C22×D4112yes—
1182C4⋊C4C22×D414yes—
1183C4⋊C4C2×#41112yes—
1184C22⋊C4—26no—
1185C22⋊C4—212no—
1186C22⋊C4—26no—
1187C22⋊C4—212no—
1188C22⋊C4—212no—
1189C22⋊C4—26no—
1190C22⋊C4—26no—
1191C22⋊C4—26no—
1192C22⋊C4—26no—
1193C22⋊C4—212no—
1194C22⋊C4—212no—
1195C22⋊C4—22no—
1196C22⋊C4—26no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—26no—
1205C22⋊C4—212no—
1206C22⋊C4—26no—
1207C22⋊C4—22no—
1208C22⋊C4—26no—
1209C22⋊C4—212no—
1210C22⋊C4—22no—
1211C22⋊C4—26no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4—46no—
1215C22⋊C4—46no—
1216C22⋊C4—46no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—46no—
1222C22⋊C4—43no—
1223C22⋊C4—43no—
1224C22⋊C4—43no—
1225C22⋊C4—46no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4C22×D4112yes—
1229C22⋊C4C22×D4112yes—
1230C42—22no—
1231C42—22no—
1232C42—26no—
1233C42—22no—
1234C42—26no—
1235C42—26no—
1236C42—26no—
1237C42—26no—
1238C42—26no—
1239C42—26no—
1240C42—26no—
1241C42—26no—
1242C42—26no—
1243C42—26no—
1244C42—22no—
1245C42—26no—
1246C42—26no—
1247C42—26no—
1248C42—26no—
1249C42—46no—
1250C42C22×D4112yes—
1251C42C2×#41112yes—
1252C23—21no—
1253C23—23no—
1254C23—23no—
1255C23—21no—
1256C23—21no—
1257C23—23no—
1258C23—23no—
1259C23—21no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23—23no—
1265C23—21no—
1266C23—23no—
1267C23—21no—
1268C23—23no—
1269C23—23no—
1270C23—23no—
1271C23—23no—
1272C23—23no—
1273C23—23no—
1274C23—23no—
1275C23—23no—
1276C23—23no—
1277C23C23×D416yes—
1278C23C23×D416yes—
1279C23#58512yes—
1280C23C2611yescharacteristic
1281Q8—412no—
1282Q8—412no—
1283Q8—412no—
1284Q8#547116yes—
1285D4—224no—
1286D4—224no—
1287D4—412no—
1288D4—424no—
1289D4—412no—
1290D4—412no—
1291D4—412no—
1292D4—412no—
1293D4—412no—
1294D4—812no—
1295D4—86no—
1296D4—812no—
1297C2×C4—28no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—23no—
1307C2×C4—23no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—21no—
1314C2×C4—224no—
1315C2×C4—224no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—23no—
1320C2×C4—21no—
1321C2×C4—23no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—23no—
1325C2×C4—23no—
1326C2×C4—23no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—23no—
1336C2×C4—21no—
1337C2×C4—23no—
1338C2×C4—21no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—23no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—21no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—23no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—23no—
1360C2×C4—21no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—21no—
1369C2×C4—23no—
1370C2×C4—412no—
1371C2×C4—412no—
1372C2×C4—412no—
1373C2×C4—412no—
1374C2×C4—412no—
1375C2×C4—412no—
1376C2×C4—86no—
1377C2×C4—812no—
1378C2×C4—86no—
1379C2×C4—812no—
1380C2×C4—86no—
1381C2×C4—86no—
1382C2×C4—86no—
1383C2×C4—812no—
1384C2×C4C23×D412yes—
1385C2×C4C23×D412yes—
1386C2×C4C23×D412yes—
1387C2×C4C23×D416yes—
1388C2×C4C23×D416yes—
1389C2×C4C22×#4112yes—
1390C2×C4C22×#4116yes—
1391C2×C4C22×#4116yes—
1392C2×C4C2×2−1+416yes—
1393C2×C4#58512yes—
1394C2×C4#58512yes—
1395C22—26no—
1396C22—26no—
1397C22—22no—
1398C22—22no—
1399C22—22no—
1400C22—26no—
1401C22—26no—
1402C22—26no—
1403C22—26no—
1404C22—41no—
1405C22—43no—
1406C22—43no—
1407C22—43no—
1408C22—43no—
1409C22—43no—
1410C22—43no—
1411C22—41no—
1412C22—41no—
1413C22—43no—
1414C22—43no—
1415C22—41no—
1416C22—43no—
1417C22—43no—
1418C22—43no—
1419C22—43no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22C24×D411yescharacteristic
1424C22C23×#4111yescharacteristic
1425C22C22×2−1+411yescharacteristic
1426C22C2×#58511yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22C2×#58511yescharacteristic
1429C22H(7,𝔽2)11yescharacteristic
1430C4—22no—
1431C4—26no—
1432C4—26no—
1433C4—22no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—22no—
1438C4—43no—
1439C4—41no—
1440C4—43no—
1441C4—41no—
1442C4—43no—
1443C4—43no—
1444C4—41no—
1445C4—41no—
1446C4—41no—
1447C4—43no—
1448C4—43no—
1449C4—43no—
1450C4—41no—
1451C4—43no—
1452C4—41no—
1453C4—43no—
1454C4—41no—
1455C4—43no—
1456C4C2×#547112yes—
1457C2—46no—
1458C2—46no—
1459C2—42no—
1460C2—83no—
1461C2C22×#54711yescharacteristic
1462C2#6279311yescharacteristic
1463C2#6281111yescharacteristic
1464C2#6295211yescharacteristic
1465C2#6298711yescharacteristic
1466C2#6300811yescharacteristic
1467C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3517C2semidirect
2. C2×#3480C2semidirect
3. #59213C2semidirect
4. #59121C2semidirect
5. #59117C2semidirect
6. #59039C2semidirect
7. #59031C2semidirect
8. #45354C2semidirect
9. #45255C2semidirect
10. #45106C2semidirect
11. #45100C2semidirect
12. #38051C2semidirect
13. #37870C2semidirect
14. #37798C2semidirect
15. #37764C2semidirect
16. #36435C2semidirect
17. #36433C2semidirect
18. #36433C2semidirect
19. #36432C2semidirect
20. #36430C2semidirect
21. #36361C2semidirect
22. #36139C2semidirect
23. #36040C2semidirect
24. #35983C2semidirect
25. #35957C2semidirect
26. #35831C2semidirect
27. #34735C2semidirect
28. #34295C2semidirect
29. #34294C2semidirect
30. #34250C2semidirect
31. C4⋊C4×#41C2semidirect
257. #550D4semidirect
769. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#34802
#592132
#591212
#591172
#590392
#590312
#453542
#452552
#451062
#451002
#380512
#378702
#377982
#377642
#364352
#364332
#364322
#364302
#363612
#361392
#360402
#359832
#359572
#358312
#347352
#342952
#342942
#342502
C4⋊C4×#412