Finite Group Databasebeta

← #7663173

Subgroups — #7663173

Order 512.

6867 conjugacy classes of subgroups.

The subgroup lattice has 1491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic, complemented
2C2×#3516C211yesmaximal, characteristic, complemented
3#52168C213yesmaximal, complemented
4#42675C213yesmaximal, complemented
5#42674C213yesmaximal, complemented
6#42650C213yesmaximal, complemented
7#42645C213yesmaximal, complemented
8#42445C213yesmaximal, complemented
9#42441C213yesmaximal, complemented
10#39857C213yesmaximal, complemented
11#39856C213yesmaximal, complemented
12#39487C213yesmaximal, complemented
13#39165C213yesmaximal, complemented
14#38923C213yesmaximal, complemented
15#38922C213yesmaximal, complemented
16#37389C213yesmaximal, complemented
17#37378C213yesmaximal, complemented
18#37280C213yesmaximal, complemented
19#36577C211yesmaximal, characteristic, complemented
20#36444C211yesmaximal, characteristic, complemented
21#36444C211yesmaximal, characteristic, complemented
22#36434C211yesmaximal, characteristic, complemented
23#36431C211yesmaximal, characteristic, complemented
24#36430C211yesmaximal, characteristic, complemented
25#35845C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35786C211yesmaximal, characteristic, complemented
28#35771C211yesmaximal, characteristic, complemented
29#35737C211yesmaximal, characteristic, complemented
30#35700C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32#3524—216no—
33#3516—216no—
34C2×#559C2213yes—
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#556C2213yes—
38C2×#555C2213yes—
39C2×#554C2213yes—
40C2×#553C2213yes—
41C2×#553C2213yes—
42C2×#552C2213yes—
43C2×#552C2213yes—
44C2×#550C2211yescharacteristic
45C2×D4×Q8C2211yescharacteristic
46C2×D4×Q8C2211yescharacteristic
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2211yescharacteristic
51C2×#548C2211yescharacteristic
52C2×#548C2211yescharacteristic
53C2×#548C2211yescharacteristic
54C2×#542C2213yes—
55C2×#542C2213yes—
56C2×#541C2213yes—
57C2×#540C2213yes—
58C2×#529C2213yes—
59C2×#529C2213yes—
60C2×#529C2213yes—
61C2×#529C2213yes—
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×#519C2211yescharacteristic
65C2×#519C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C2×C4×#41C2211yescharacteristic
68C22×C4×Q8C2211yescharacteristic
69#2857C2213yes—
70#2857C2213yes—
71#2857C2213yes—
72#2851C2213yes—
73#2850C2213yes—
74#2850C2213yes—
75#2814C2216yes—
76#2813C2216yes—
77#2727C2216yes—
78#2726C2216yes—
79#2725C2213yes—
80#2725C2216yes—
81#2725C2216yes—
82#2725C2213yes—
83#2722C2216yes—
84#2722C2213yes—
85#2715C2216yes—
86#2715C2216yes—
87#2715C2216yes—
88#2712C2213yes—
89#2712C2216yes—
90#2707C2216yes—
91#2705C2213yes—
92#2705C2211yescharacteristic
93#2704C2216yes—
94#2704C2213yes—
95#2704C2213yes—
96#2702C2216yes—
97#2695C2216yes—
98#2695C2216yes—
99#2695C2216yes—
100#2695C2216yes—
101#2693C2213yes—
102#2691C2216yes—
103#2691C2213yes—
104#2691C2213yes—
105#2681C2213yes—
106#2681C2213yes—
107#2675C2213yes—
108#2672C2213yes—
109#2672C2216yes—
110#2672C2213yes—
111#2671C2216yes—
112#2639C2216yes—
113#2630C2216yes—
114#2630C2216yes—
115#2629C2213yes—
116#2628C2213yes—
117#2625C2216yes—
118#2624C2216yes—
119#2621C2213yes—
120#2621C2213yes—
121#2620C2213yes—
122#2620C2213yes—
123#2618C2216yes—
124#2582C2213yes—
125#2582C2213yes—
126#2581C2213yes—
127#2580C2213yes—
128#2568C2213yes—
129#2567C2213yes—
130#2566C2213yes—
131#2565C2213yes—
132#2547C2213yes—
133#2547C2213yes—
134#2547C2213yes—
135#2546C2213yes—
136#2545C2213yes—
137#2545C2213yes—
138#2544C2213yes—
139#2544C2213yes—
140#2538C2213yes—
141#2537C2213yes—
142#2537C2213yes—
143#2537C2213yes—
144#2536C2213yes—
145#2536C2213yes—
146#2535C2213yes—
147#2535C2213yes—
148#2498C2216yes—
149#2498C2216yes—
150#2485C2216yes—
151#2485C2216yes—
152#2454C2213yes—
153#2453C2213yes—
154#2453C2213yes—
155#2453C2213yes—
156#2453C2213yes—
157#2453C2213yes—
158#2452C2213yes—
159#2451C2213yes—
160#2442C2213yes—
161#2442C2213yes—
162#2441C2213yes—
163#2441C2213yes—
164#2441C2213yes—
165#2441C2213yes—
166#2439C2213yes—
167#2439C2213yes—
168#2429C2213yes—
169#2429C2213yes—
170#2429C2213yes—
171#2429C2213yes—
172#2428C2213yes—
173#2428C2213yes—
174#2427C2213yes—
175#2427C2213yes—
176#2427C2213yes—
177#2427C2213yes—
178#2427C2213yes—
179#2427C2213yes—
180#2427C2213yes—
181#2427C2213yes—
182#2426C2213yes—
183#2426C2213yes—
184#2417C2213yes—
185#2417C2213yes—
186#2417C2216yes—
187#2417C2213yes—
188#2417C2213yes—
189#2416C2216yes—
190#2416C2213yes—
191#2416C2213yes—
192#2415C2213yes—
193#2415C2213yes—
194#2415C2213yes—
195#2415C2213yes—
196#2415C2213yes—
197#2415C2213yes—
198#2415C2213yes—
199#2415C2213yes—
200#2414C2213yes—
201#2414C2213yes—
202#2396C2213yes—
203#2396C2213yes—
204#2392C2213yes—
205#2392C2213yes—
206#2392C2213yes—
207#2392C2213yes—
208#2351C2211yescharacteristic
209#2351C2211yescharacteristic
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214Q8×C4⋊C4C2211yescharacteristic
215Q8×C4⋊C4C2211yescharacteristic
216#2349C2213yes—
217#2349C2213yes—
218D4×C4⋊C4C2213yes—
219D4×C4⋊C4C2213yes—
220#2341C2211yescharacteristic
221#2341C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226Q8×C22⋊C4C2211yescharacteristic
227Q8×C22⋊C4C2211yescharacteristic
228#2325C2216yes—
229#2317C2213yes—
230#2316C2216yes—
231#2316C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236C4×#121C2213yes—
237C4×#121C2213yes—
238#2296C2213yes—
239C2×#389C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243C23×Q8C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245#559—224no—
246#557—28no—
247#557—28no—
248#556—224no—
249#555—224no—
250#554—224no—
251#553—224no—
252#553—224no—
253#552—224no—
254#552—224no—
255#550—28no—
256D4×Q8—28no—
257D4×Q8—44no—
258D4×Q8—44no—
259#548—28no—
260#548—28no—
261#548—28no—
262#548—28no—
263#548—44no—
264#548—44no—
265#542—224no—
266#542—224no—
267#541—224no—
268#540—224no—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×#127C2313yes—
275#529—224no—
276#529—224no—
277#529—224no—
278#529—224no—
279C2×#126C2313yes—
280C2×#126C2311yescharacteristic
281C2×#126C2316yes—
282C2×#126C2313yes—
283C2×#126C2313yes—
284C2×#126C2316yes—
285C2×#126C2316yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#125C2313yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
291C2×#125C2313yes—
292C2×#125C2316yes—
293C2×#124C2313yes—
294C2×#124C2313yes—
295C2×#124C2313yes—
296C2×#124C2313yes—
297C2×#124C2313yes—
298C2×#124C2316yes—
299C2×#124C2313yes—
300C2×#124C2313yes—
301C2×#124C2313yes—
302C2×#123C2316yes—
303C2×#123C2316yes—
304C2×#123C2316yes—
305C2×#123C2313yes—
306C2×#123C2311yescharacteristic
307C2×#123C2313yes—
308C2×#123C2313yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2316yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2313yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×C22⋊Q8C2313yes—
320C2×C22⋊Q8C2313yes—
321C2×C22⋊Q8C2313yes—
322C2×C22⋊Q8C2313yes—
323C2×C22⋊Q8C2313yes—
324C2×C22⋊Q8C2313yes—
325C2×C22⋊Q8C2313yes—
326C2×#121C2313yes—
327C2×#121C2316yes—
328C2×#121C2313yes—
329C2×#121C2313yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332C2×#121C2313yes—
333C2×#121C2313yes—
334C2×#121C2313yes—
335C2×#121C2316yes—
336C2×#121C2313yes—
337C2×#121C2313yes—
338C2×#121C2313yes—
339C2×#121C2313yes—
340C2×#121C2313yes—
341C2×#121C2313yes—
342#520—44no—
343#520D4116yescomplemented
344#519—28no—
345#519—28no—
346C4×#41—28no—
347C4×#41—44no—
348C2×C4×Q8—28no—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2313yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2313yes—
363C2×C4×Q8C2313yes—
364C2×C4×Q8C2313yes—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×D4C2313yes—
368C2×C4×D4C2316yes—
369C2×C4×D4C2316yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2313yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2313yes—
380C2×C4×D4C2313yes—
381C2×C4×D4C2313yes—
382C2×C4×D4C2313yes—
383C2×C4×D4C2313yes—
384C2×C4×D4C2313yes—
385C2×C4×D4C2313yes—
386C2×C4×D4C2313yes—
387C2×#117C2316yes—
388C2×#117C2316yes—
389C2×#117C2313yes—
390C2×#117C2313yes—
391C2×#117C2313yes—
392C2×#117C2313yes—
393C2×#117C2313yes—
394C2×#117C2313yes—
395C2×#117C2313yes—
396C2×#117C2313yes—
397C22×C4⋊C4C2313yes—
398C22×C4⋊C4C2316yes—
399C22×C4⋊C4C2313yes—
400C22×C4⋊C4C2313yes—
401C22×C42C2313yes—
402C22×C42C2313yes—
403C22×C42C2313yes—
404#400C2316yes—
405#400C2316yes—
406#400C2313yes—
407#400C2316yes—
408#400C2313yes—
409#399C2316yes—
410#399C2313yes—
411#399C2316yes—
412#399C2311yescharacteristic
413#398C2313yes—
414#398C2316yes—
415#398C2313yes—
416#398C2316yes—
417#398C2316yes—
418#398C2316yes—
419#398C2313yes—
420#398C2316yes—
421#398C2316yes—
422#398C2316yes—
423#398C2313yes—
424#398C2316yes—
425#398C2313yes—
426#398C2313yes—
427#398C2313yes—
428#398C2313yes—
429#397C2313yes—
430#397C2316yes—
431#397C2316yes—
432#397C2316yes—
433#397C2316yes—
434#397C2313yes—
435#397C2316yes—
436#397C2316yes—
437#397C2316yes—
438#397C2316yes—
439#397C2313yes—
440#397C2313yes—
441#396C2316yes—
442#396C2316yes—
443#396C2313yes—
444#396C2313yes—
445#396C2316yes—
446#396C2313yes—
447#396C2316yes—
448#396C2316yes—
449#396C2316yes—
450#396C2313yes—
451#396C2316yes—
452#396C2313yes—
453#396C2313yes—
454#396C2316yes—
455#396C2311yescharacteristic
456#396C2313yes—
457#396C2313yes—
458#396C2313yes—
459#396C2313yes—
460#396C2311yescharacteristic
461#395C2313yes—
462#395C2316yes—
463#395C2313yes—
464#394C2316yes—
465#394C2316yes—
466#394C2313yes—
467#394C2316yes—
468#394C2316yes—
469#394C2313yes—
470#394C2316yes—
471#394C2316yes—
472#394C2313yes—
473#394C2316yes—
474#394C2316yes—
475#394C2316yes—
476#394C2313yes—
477#394C2316yes—
478#394C2311yescharacteristic
479#394C2311yescharacteristic
480#394C2313yes—
481#394C2313yes—
482#394C2313yes—
483#394C2313yes—
484#394C2313yes—
485#394C2313yes—
486#393C2316yes—
487#393C2313yes—
488#393C2313yes—
489#392C2313yes—
490#392C2316yes—
491#392C2311yescharacteristic
492#392C2313yes—
493#392C2313yes—
494#391C2313yes—
495#391C2313yes—
496#391C2313yes—
497#391C2313yes—
498#391C2313yes—
499#391C2316yes—
500#391C2313yes—
501#391C2313yes—
502#391C2313yes—
503#391C2313yes—
504#391C2313yes—
505#391C2313yes—
506#391C2313yes—
507#391C2313yes—
508#391C2316yes—
509#391C2313yes—
510#390C2313yes—
511#390C2313yes—
512#390C2313yes—
513#390C2313yes—
514#390C2313yes—
515#390C2316yes—
516#390C2313yes—
517#390C2311yescharacteristic
518#390C2311yescharacteristic
519#389C2316yes—
520#389C2316yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2316yes—
525#389C2316yes—
526#389C2316yes—
527#389C2316yes—
528#389C2313yes—
529#389C2313yes—
530#389C2313yes—
531#389C2313yes—
532#389C2316yes—
533#389C2316yes—
534#389C2313yes—
535#389C2313yes—
536#389C2313yes—
537#389C2313yes—
538#389C2313yes—
539#389C2313yes—
540#389C2313yes—
541#389C2313yes—
542#389C2313yes—
543#389C2313yes—
544#389C2313yes—
545#389C2313yes—
546#389C2316yes—
547#389C2313yes—
548#389C2313yes—
549#389C2313yes—
550#389C2313yes—
551#389C2316yes—
552#389C2313yes—
553#389C2313yes—
554#389C2311yescharacteristic
555#388C2316yes—
556#388C2316yes—
557#388C2313yes—
558#388C2316yes—
559#388C2316yes—
560#388C2316yes—
561#388C2316yes—
562#388C2316yes—
563#388C2313yes—
564#388C2313yes—
565#388C2313yes—
566#388C2313yes—
567#388C2313yes—
568#388C2311yescharacteristic
569#388C2313yes—
570#387C2316yes—
571#387C2316yes—
572#387C2316yes—
573#387C2316yes—
574#387C2313yes—
575#387C2316yes—
576#387C2313yes—
577#387C2313yes—
578#387C2311yescharacteristic
579#386C2313yes—
580#386C2313yes—
581#386C2316yes—
582#386C2316yes—
583#386C2313yes—
584#386C2316yes—
585#386C2316yes—
586#386C2316yes—
587#386C2313yes—
588#386C2313yes—
589#386C2316yes—
590#386C2316yes—
591#386C2311yescharacteristic
592#386C2313yes—
593#386C2313yes—
594#385C2313yes—
595#385C2316yes—
596#385C2316yes—
597#385C2316yes—
598#385C2313yes—
599#385C2313yes—
600#385C2316yes—
601#385C2313yes—
602#385C2313yes—
603#385C2313yes—
604#385C2313yes—
605#385C2313yes—
606#384C2313yes—
607#384C2313yes—
608#384C2313yes—
609#384C2313yes—
610#382C2313yes—
611#382C2313yes—
612#382C2313yes—
613#382C2313yes—
614#380C2313yes—
615#380C2316yes—
616#380C2316yes—
617#380C2316yes—
618#380C2316yes—
619#380C2316yes—
620#380C2316yes—
621#380C2313yes—
622#380C2313yes—
623#380C2313yes—
624#380C2313yes—
625#380C2313yes—
626#380C2313yes—
627#380C2313yes—
628#380C2313yes—
629#380C2316yes—
630#380C2316yes—
631#380C2316yes—
632#380C2316yes—
633#380C2313yes—
634#380C2313yes—
635#380C2313yes—
636#380C2311yescharacteristic
637#380C2313yes—
638C4×C4⋊C4C2313yes—
639C4×C4⋊C4C2313yes—
640C4×C4⋊C4C2313yes—
641C4×C4⋊C4C2313yes—
642C4×C4⋊C4C2313yes—
643C4×C4⋊C4C2313yes—
644C4×C4⋊C4C2313yes—
645C4×C4⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2313yes—
649C4×C22⋊C4C2313yes—
650C4×C22⋊C4C2313yes—
651C4×C22⋊C4C2313yes—
652C4×C22⋊C4C2313yes—
653C4×C22⋊C4C2313yes—
654C2×#95C2316yes—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41C2×D418yes—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—24no—
664C22×Q8—24no—
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8—24no—
668C22×Q8—24no—
669C22×Q8—24no—
670C22×Q8C2413yes—
671C22×Q8C2413yes—
672C22×Q8C2413yes—
673C22×Q8C2413yes—
674C22×Q8C2413yes—
675C22×Q8C2411yescharacteristic
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2411yescharacteristic
679C22×D4C2411yescharacteristic
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2416yes—
686C22×D4C2413yes—
687C22×D4C2411yescharacteristic
688C22×D4C2413yes—
689C23×C4C2413yes—
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2411yescharacteristic
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2413yes—
698C23×C4C2413yes—
699C23×C4C2416yes—
700C23×C4C2413yes—
701C23×C4C2416yes—
702C4⋊Q8—212no—
703C4⋊Q8—212no—
704C4⋊Q8—212no—
705C4⋊Q8—46no—
706C4⋊Q8—46no—
707#127—212no—
708#126—24no—
709#126—212no—
710#126—224no—
711#126—212no—
712#126—224no—
713#126—212no—
714#126—224no—
715#125—212no—
716#125—212no—
717#125—212no—
718#125—212no—
719#125—212no—
720#125—224no—
721#125—212no—
722#124—212no—
723#124—212no—
724#124—212no—
725#124—212no—
726#124—212no—
727#124—224no—
728#124—212no—
729#124—46no—
730#124—46no—
731#123—224no—
732#123—224no—
733#123—24no—
734#123—212no—
735#123—212no—
736#123—224no—
737#123—212no—
738C22⋊Q8—212no—
739C22⋊Q8—212no—
740C22⋊Q8—212no—
741C22⋊Q8—224no—
742C22⋊Q8—212no—
743C22⋊Q8—212no—
744C22⋊Q8—212no—
745C22⋊Q8—212no—
746C22⋊Q8—212no—
747C22⋊Q8—46no—
748C22⋊Q8—46no—
749C22⋊Q8—46no—
750C22⋊Q8—46no—
751C22⋊Q8—46no—
752C22⋊Q8—46no—
753C22⋊Q8—46no—
754C22⋊Q8—46no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—224no—
760#121—212no—
761#121—212no—
762#121—212no—
763#121—212no—
764#121—46no—
765#121—46no—
766#121—46no—
767#121—46no—
768#121—412no—
769#121—46no—
770#121—46no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—212no—
780C4×Q8—212no—
781C4×Q8—212no—
782C4×Q8—212no—
783C4×Q8—212no—
784C4×Q8—212no—
785C4×Q8—212no—
786C4×Q8—212no—
787C4×Q8C2×D418yes—
788C4×Q8C2×D418yes—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—224no—
794C4×D4—224no—
795C4×D4—212no—
796C4×D4—212no—
797C4×D4—212no—
798C4×D4—212no—
799C4×D4—46no—
800C4×D4—46no—
801C4×D4—46no—
802C4×D4—46no—
803C4×D4—46no—
804C4×D4—46no—
805C4×D4—46no—
806C4×D4—46no—
807C4×D4C2×D4124yes—
808C4×D4C2×D4124yes—
809#117—224no—
810#117—224no—
811#117—212no—
812#117—212no—
813#117—212no—
814#117—212no—
815#117—212no—
816#117—46no—
817#117—46no—
818#117C2×D4124yes—
819C2×C4⋊C4—212no—
820C2×C4⋊C4—412no—
821C2×C4⋊C4—46no—
822C2×C4⋊C4C2×D4124yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2416yes—
829C2×C4⋊C4C2413yes—
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⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2416yes—
841C2×C4⋊C4C2416yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2416yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2416yes—
856C2×C4⋊C4C2416yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2416yes—
866C2×C4⋊C4C2416yes—
867C2×C4⋊C4C2416yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2413yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2416yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2413yes—
881C2×C4⋊C4C2413yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C22⋊C4C2411yescharacteristic
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2416yes—
890C2×C22⋊C4C2416yes—
891C2×C22⋊C4C2416yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2416yes—
900C2×C22⋊C4C2416yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2411yescharacteristic
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2416yes—
920C2×C22⋊C4C2416yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2416yes—
925C2×C22⋊C4C2413yes—
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2411yescharacteristic
928C2×C22⋊C4C2411yescharacteristic
929C2×C22⋊C4C2411yescharacteristic
930C2×C22⋊C4C2411yescharacteristic
931C2×C22⋊C4C2413yes—
932C2×C22⋊C4C2413yes—
933C2×C22⋊C4C2413yes—
934C2×C22⋊C4C2416yes—
935C2×C22⋊C4C2413yes—
936C2×C22⋊C4C2413yes—
937C2×C42—212no—
938C2×C42—212no—
939C2×C42—46no—
940C2×C42C2413yes—
941C2×C42C2416yes—
942C2×C42C2416yes—
943C2×C42C2413yes—
944C2×C42C2413yes—
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2413yes—
948C2×C42C2413yes—
949C2×C42C2413yes—
950C2×C42C2413yes—
951C2×C42C2413yes—
952C2×C42C2413yes—
953C2×C42C2411yescharacteristic
954C2×C42C2413yes—
955C2×C42C2411yescharacteristic
956C2×C42C2413yes—
957C2×C42C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2416yes—
961#95C2416yes—
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2411yescharacteristic
981#95C2411yescharacteristic
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2416yes—
993#95C2416yes—
994#95C2416yes—
995#95C2416yes—
996#95C2416yes—
997#95C2416yes—
998#95C2416yes—
999#95C2416yes—
1000C24C2511yescharacteristic
1001C24C2511yescharacteristic
1002C24C2513yes—
1003C24C2513yes—
1004C24C2511yescharacteristic
1005#41—232no—
1006#41—416no—
1007C2×Q8—26no—
1008C2×Q8—26no—
1009C2×Q8—26no—
1010C2×Q8—26no—
1011C2×Q8—26no—
1012C2×Q8—26no—
1013C2×Q8—26no—
1014C2×Q8—26no—
1015C2×Q8—26no—
1016C2×Q8—26no—
1017C2×Q8—26no—
1018C2×Q8—43no—
1019C2×Q8—43no—
1020C2×Q8—43no—
1021C2×Q8—43no—
1022C2×Q8—416no—
1023C2×Q8—416no—
1024C2×Q8—416no—
1025C2×Q8C22×D414yes—
1026C2×Q8H(5,𝔽2)14yes—
1027C2×Q82−1+414yes—
1028C2×D4—26no—
1029C2×D4—22no—
1030C2×D4—22no—
1031C2×D4—26no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—212no—
1035C2×D4—26no—
1036C2×D4—26no—
1037C2×D4—22no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—26no—
1043C2×D4—26no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C2×D4—41no—
1047C2×D4—41no—
1048C2×D4—41no—
1049C2×D4—43no—
1050C2×D4—41no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—43no—
1058C2×D4—46no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—46no—
1065C2×D4—43no—
1066C2×D4C22×D4112yes—
1067C22×C4—26no—
1068C22×C4—26no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—26no—
1072C22×C4—26no—
1073C22×C4—26no—
1074C22×C4—26no—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—26no—
1080C22×C4—26no—
1081C22×C4—26no—
1082C22×C4—26no—
1083C22×C4—26no—
1084C22×C4—26no—
1085C22×C4—26no—
1086C22×C4—26no—
1087C22×C4—46no—
1088C22×C4—46no—
1089C22×C4—41no—
1090C22×C4—43no—
1091C22×C4—43no—
1092C22×C4—43no—
1093C22×C4—43no—
1094C22×C4—43no—
1095C22×C4—43no—
1096C22×C4—43no—
1097C22×C4—43no—
1098C22×C4—43no—
1099C22×C4—43no—
1100C22×C4—43no—
1101C22×C4—46no—
1102C22×C4—46no—
1103C22×C4—46no—
1104C22×C4C22×D4112yes—
1105C22×C4C22×D4124yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2513yes—
1109C22×C4C2513yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2513yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2513yes—
1116C22×C4C2513yes—
1117C22×C4C2513yes—
1118C22×C4C2513yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2513yes—
1121C22×C4C2513yes—
1122C22×C4C2513yes—
1123C22×C4C2511yescharacteristic
1124C22×C4C2513yes—
1125C22×C4C2511yescharacteristic
1126C22×C4C2513yes—
1127C22×C4C2513yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2513yes—
1132C4⋊C4—26no—
1133C4⋊C4—212no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—26no—
1140C4⋊C4—26no—
1141C4⋊C4—26no—
1142C4⋊C4—26no—
1143C4⋊C4—212no—
1144C4⋊C4—212no—
1145C4⋊C4—22no—
1146C4⋊C4—26no—
1147C4⋊C4—26no—
1148C4⋊C4—26no—
1149C4⋊C4—26no—
1150C4⋊C4—212no—
1151C4⋊C4—26no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—26no—
1162C4⋊C4—22no—
1163C4⋊C4—43no—
1164C4⋊C4—46no—
1165C4⋊C4—46no—
1166C4⋊C4—43no—
1167C4⋊C4—41no—
1168C4⋊C4—43no—
1169C4⋊C4—41no—
1170C4⋊C4—46no—
1171C4⋊C4—43no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4—43no—
1179C4⋊C4—43no—
1180C4⋊C4—43no—
1181C4⋊C4—46no—
1182C4⋊C4—43no—
1183C4⋊C4—43no—
1184C4⋊C4—43no—
1185C4⋊C4—43no—
1186C4⋊C4—46no—
1187C4⋊C4—46no—
1188C4⋊C4C22×D4112yes—
1189C4⋊C4C22×D4112yes—
1190C4⋊C4C22×D4112yes—
1191C4⋊C4C22×D414yes—
1192C22⋊C4—26no—
1193C22⋊C4—26no—
1194C22⋊C4—212no—
1195C22⋊C4—212no—
1196C22⋊C4—26no—
1197C22⋊C4—212no—
1198C22⋊C4—26no—
1199C22⋊C4—26no—
1200C22⋊C4—26no—
1201C22⋊C4—22no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—22no—
1205C22⋊C4—212no—
1206C22⋊C4—22no—
1207C22⋊C4—26no—
1208C22⋊C4—22no—
1209C22⋊C4—22no—
1210C22⋊C4—22no—
1211C22⋊C4—26no—
1212C22⋊C4—212no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—22no—
1216C22⋊C4—26no—
1217C22⋊C4—43no—
1218C22⋊C4—41no—
1219C22⋊C4—43no—
1220C22⋊C4—46no—
1221C22⋊C4—43no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—43no—
1227C22⋊C4—43no—
1228C22⋊C4—46no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—43no—
1232C22⋊C4—43no—
1233C22⋊C4—43no—
1234C22⋊C4—43no—
1235C22⋊C4—43no—
1236C22⋊C4—43no—
1237C22⋊C4—46no—
1238C22⋊C4—43no—
1239C22⋊C4—43no—
1240C22⋊C4—43no—
1241C22⋊C4—46no—
1242C22⋊C4—46no—
1243C22⋊C4—43no—
1244C22⋊C4C22×D4112yes—
1245C22⋊C4C22×D4112yes—
1246C42—22no—
1247C42—26no—
1248C42—26no—
1249C42—26no—
1250C42—26no—
1251C42—26no—
1252C42—212no—
1253C42—212no—
1254C42—26no—
1255C42—26no—
1256C42—26no—
1257C42—26no—
1258C42—26no—
1259C42—26no—
1260C42—41no—
1261C42—43no—
1262C42C22×D4112yes—
1263C42C22×D4112yes—
1264C23—21no—
1265C23—21no—
1266C23—23no—
1267C23—21no—
1268C23—23no—
1269C23—23no—
1270C23—23no—
1271C23—21no—
1272C23—21no—
1273C23—23no—
1274C23—21no—
1275C23—23no—
1276C23—21no—
1277C23—23no—
1278C23—21no—
1279C23—21no—
1280C23—23no—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—23no—
1285C23—23no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—23no—
1291C23—21no—
1292C23—23no—
1293C23—23no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23C23×D416yes—
1298C23#58512yes—
1299C23C2611yescharacteristic
1300Q8—412no—
1301Q8—412no—
1302Q8—412no—
1303Q8—86no—
1304Q8—86no—
1305Q8#537116yes—
1306D4—224no—
1307D4—44no—
1308D4—44no—
1309D4—412no—
1310D4—44no—
1311D4—412no—
1312D4—86no—
1313D4—86no—
1314D4—86no—
1315D4—86no—
1316D4—812no—
1317D4—86no—
1318D4—86no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—23no—
1323C2×C4—23no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—23no—
1328C2×C4—21no—
1329C2×C4—23no—
1330C2×C4—21no—
1331C2×C4—224no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—21no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—23no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—21no—
1354C2×C4—23no—
1355C2×C4—21no—
1356C2×C4—23no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—23no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—21no—
1364C2×C4—23no—
1365C2×C4—21no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—23no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—23no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—23no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—23no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—23no—
1389C2×C4—424no—
1390C2×C4—44no—
1391C2×C4—412no—
1392C2×C4—412no—
1393C2×C4—412no—
1394C2×C4—412no—
1395C2×C4—86no—
1396C2×C4—86no—
1397C2×C4—86no—
1398C2×C4—86no—
1399C2×C4—86no—
1400C2×C4—166no—
1401C2×C4C23×D412yes—
1402C2×C4C23×D416yes—
1403C2×C4C23×D416yes—
1404C2×C4C23×D412yes—
1405C2×C4C23×D412yes—
1406C2×C4C23×D416yes—
1407C2×C4C2×H(5,𝔽2)16yes—
1408C2×C4C2×2−1+416yes—
1409C2×C4#58512yes—
1410C22—26no—
1411C22—22no—
1412C22—26no—
1413C22—22no—
1414C22—26no—
1415C22—22no—
1416C22—41no—
1417C22—43no—
1418C22—43no—
1419C22—41no—
1420C22—41no—
1421C22—43no—
1422C22—41no—
1423C22—43no—
1424C22—43no—
1425C22—41no—
1426C22—41no—
1427C22—43no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—43no—
1433C22—41no—
1434C22—41no—
1435C22—43no—
1436C22—41no—
1437C22—41no—
1438C22—43no—
1439C22—41no—
1440C22—41no—
1441C22—43no—
1442C22—41no—
1443C22—41no—
1444C22—43no—
1445C22C24×D411yescharacteristic
1446C22C22×H(5,𝔽2)11yescharacteristic
1447C22C22×2−1+411yescharacteristic
1448C22C2×#58511yescharacteristic
1449C22C2×#58511yescharacteristic
1450C222−1+611yescharacteristic
1451C222−1+611yescharacteristic
1452C4—26no—
1453C4—26no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—41no—
1459C4—43no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—43no—
1464C4—43no—
1465C4—43no—
1466C4—43no—
1467C4—43no—
1468C4—43no—
1469C4—41no—
1470C4—43no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—43no—
1475C4—43no—
1476C4—43no—
1477C4C2×#537112yes—
1478C2—46no—
1479C2—42no—
1480C2—83no—
1481C2—81no—
1482C2—81no—
1483C2C22×#53711yescharacteristic
1484C2#6294911yescharacteristic
1485C2#6295311yescharacteristic
1486C2#6298811yescharacteristic
1487C2#6300211yescharacteristic
1488C2#6302011yescharacteristic
1489C2#6304411yescharacteristic
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×#3524C2semidirect
2. C2×#3516C2semidirect
3. #52168C2semidirect
4. #42675C2semidirect
5. #42674C2semidirect
6. #42650C2semidirect
7. #42645C2semidirect
8. #42445C2semidirect
9. #42441C2semidirect
10. #39857C2semidirect
11. #39856C2semidirect
12. #39487C2semidirect
13. #39165C2semidirect
14. #38923C2semidirect
15. #38922C2semidirect
16. #37389C2semidirect
17. #37378C2semidirect
18. #37280C2semidirect
19. #36577C2semidirect
20. #36444C2semidirect
21. #36444C2semidirect
22. #36434C2semidirect
23. #36431C2semidirect
24. #36430C2semidirect
25. #35845C2semidirect
26. #35831C2semidirect
27. #35786C2semidirect
28. #35771C2semidirect
29. #35737C2semidirect
30. #35700C2semidirect
31. #34250C2semidirect
343. #520D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×#35162
#521682
#426752
#426742
#426502
#426452
#424452
#424412
#398572
#398562
#394872
#391652
#389232
#389222
#373892
#373782
#372802
#365772
#364442
#364342
#364312
#364302
#358452
#358312
#357862
#357712
#357372
#357002
#342502