Finite Group Databasebeta

← #7661839

Subgroups — #7661839

Order 512.

6358 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic
2C2×#3502C211yesmaximal, characteristic, complemented
3#52166C213yesmaximal, complemented
4#42965C213yesmaximal, complemented
5#42915C213yesmaximal, complemented
6#42891C213yesmaximal, complemented
7#42875C213yesmaximal, complemented
8#42809C213yesmaximal, complemented
9#42804C213yesmaximal, complemented
10#39951C213yesmaximal, complemented
11#39891C213yesmaximal, complemented
12#39867C213yesmaximal, complemented
13#39855C213yesmaximal, complemented
14#39724C213yesmaximal, complemented
15#39172C213yesmaximal, complemented
16#37423C213yesmaximal, complemented
17#37279C213yesmaximal, complemented
18#37275C213yesmaximal, complemented
19#36578C211yesmaximal, characteristic, complemented
20#36482C211yesmaximal, characteristic, complemented
21#36474C211yesmaximal, characteristic, complemented
22#36467C211yesmaximal, characteristic, complemented
23#36456C211yesmaximal, characteristic, complemented
24#36431C211yesmaximal, characteristic, complemented
25#35937C211yesmaximal, characteristic, complemented
26#35854C211yesmaximal, characteristic, complemented
27#35801C211yesmaximal, characteristic, complemented
28#35786C211yesmaximal, characteristic, complemented
29#35723C211yesmaximal, characteristic, complemented
30#35711C211yesmaximal, characteristic, complemented
31#34262C211yesmaximal, characteristic, complemented
32#3518—216no—
33#3502—216no—
34C2×Q82C2213yes—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2213yes—
39C2×#557C2213yes—
40C2×#557C2213yes—
41C2×#557C2211yescharacteristic
42C2×#557C2211yescharacteristic
43C2×#556C2213yes—
44C2×#556C2213yes—
45C2×#556C2213yes—
46C2×#555C2213yes—
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#544C2213yes—
51C2×#544C2213yes—
52C2×#542C2213yes—
53C2×#542C2213yes—
54C2×#533C2213yes—
55C2×#533C2213yes—
56C2×#533C2213yes—
57C2×#529C2213yes—
58C2×#519C2211yescharacteristic
59C2×#519C2211yescharacteristic
60C2×#519C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62C22×C4×Q8C2211yescharacteristic
63#2862C2213yes—
64#2861C2213yes—
65#2857C2213yes—
66#2855C2213yes—
67#2854C2213yes—
68#2851C2213yes—
69#2821C2216yes—
70#2820C2216yes—
71#2721C2216yes—
72#2721C2213yes—
73#2719C2213yes—
74#2719C2216yes—
75#2716C2213yes—
76#2716C2216yes—
77#2716C2216yes—
78#2716C2216yes—
79#2716C2216yes—
80#2713C2213yes—
81#2700C2216yes—
82#2700C2216yes—
83#2700C2216yes—
84#2700C2211yescharacteristic
85#2698C2216yes—
86#2698C2213yes—
87#2694C2216yes—
88#2694C2213yes—
89#2690C2213yes—
90#2690C2216yes—
91#2690C2216yes—
92#2690C2216yes—
93#2689C2213yes—
94#2687C2213yes—
95#2687C2216yes—
96#2681C2216yes—
97#2681C2213yes—
98#2680C2213yes—
99#2677C2216yes—
100#2677C2216yes—
101#2677C2213yes—
102#2674C2213yes—
103#2674C2216yes—
104#2674C2213yes—
105#2672C2213yes—
106#2664C2216yes—
107#2660C2213yes—
108#2640C2216yes—
109#2640C2213yes—
110#2637C2216yes—
111#2634C2216yes—
112#2632C2216yes—
113#2629C2213yes—
114#2628C2213yes—
115#2625C2213yes—
116#2624C2213yes—
117#2621C2216yes—
118#2611C2216yes—
119#2604C2216yes—
120#2599C2216yes—
121#2592C2213yes—
122#2592C2213yes—
123#2584C2213yes—
124#2582C2213yes—
125#2581C2216yes—
126#2581C2213yes—
127#2580C2213yes—
128#2568C2216yes—
129#2568C2213yes—
130#2567C2213yes—
131#2566C2213yes—
132#2565C2213yes—
133#2563C2213yes—
134#2563C2213yes—
135#2562C2213yes—
136#2551C2213yes—
137#2551C2213yes—
138#2550C2213yes—
139#2550C2213yes—
140#2550C2213yes—
141#2550C2213yes—
142#2550C2213yes—
143#2550C2213yes—
144#2546C2213yes—
145#2546C2213yes—
146#2545C2216yes—
147#2538C2213yes—
148#2504C2213yes—
149#2503C2213yes—
150#2500C2213yes—
151#2499C2213yes—
152#2492C2213yes—
153#2491C2213yes—
154#2490C2213yes—
155#2490C2213yes—
156#2490C2213yes—
157#2489C2213yes—
158#2489C2213yes—
159#2489C2213yes—
160#2487C2213yes—
161#2486C2213yes—
162#2485C2213yes—
163#2485C2213yes—
164#2454C2213yes—
165#2453C2213yes—
166#2452C2213yes—
167#2452C2213yes—
168#2452C2213yes—
169#2451C2213yes—
170#2451C2213yes—
171#2451C2213yes—
172#2448C2213yes—
173#2448C2213yes—
174#2448C2213yes—
175#2448C2213yes—
176#2446C2213yes—
177#2446C2213yes—
178#2446C2213yes—
179#2446C2213yes—
180#2441C2213yes—
181#2441C2213yes—
182#2439C2213yes—
183#2439C2213yes—
184#2439C2213yes—
185#2439C2213yes—
186#2439C2213yes—
187#2439C2213yes—
188#2423C2213yes—
189#2423C2213yes—
190#2421C2213yes—
191#2421C2213yes—
192#2421C2213yes—
193#2421C2213yes—
194#2421C2213yes—
195#2421C2213yes—
196#2399C2213yes—
197#2398C2213yes—
198#2396C2213yes—
199#2396C2213yes—
200#2395C2213yes—
201#2395C2213yes—
202#2356C2213yes—
203#2355C2213yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208#2351C2211yescharacteristic
209#2351C2211yescharacteristic
210#2351C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212Q8×C4⋊C4C2211yescharacteristic
213Q8×C4⋊C4C2211yescharacteristic
214#2347C2213yes—
215#2346C2213yes—
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224Q8×C22⋊C4C2211yescharacteristic
225Q8×C22⋊C4C2211yescharacteristic
226#2327C2216yes—
227#2323C2216yes—
228#2320C2213yes—
229#2314C2213yes—
230C4×C4⋊Q8C2213yes—
231C4×#124C2213yes—
232C4×C22⋊Q8C2213yes—
233C4×C22⋊Q8C2213yes—
234C4×#123C2213yes—
235C4×#123C2213yes—
236#2298C2213yes—
237#2295C2213yes—
238#2276C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243Q82—28no—
244Q82—224no—
245Q82—28no—
246#557—28no—
247#557—224no—
248#557—224no—
249#557—28no—
250#557—224no—
251#557—28no—
252#556—224no—
253#556—224no—
254#556—224no—
255#555—224no—
256D4×Q8—28no—
257#548—28no—
258#548—28no—
259#544—224no—
260#544—224no—
261#542—224no—
262#542—224no—
263#533—224no—
264#533—224no—
265#533—224no—
266C2×C4⋊Q8C2313yes—
267C2×C4⋊Q8C2313yes—
268C2×C4⋊Q8C2316yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2313yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2316yes—
277C2×C4⋊Q8C2313yes—
278C2×C4⋊Q8C2313yes—
279C2×C4⋊Q8C2313yes—
280C2×C4⋊Q8C2313yes—
281C2×C4⋊Q8C2316yes—
282#529—224no—
283C2×#126C2316yes—
284C2×#126C2313yes—
285C2×#126C2313yes—
286C2×#126C2316yes—
287C2×#125C2313yes—
288C2×#125C2316yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
291C2×#125C2313yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#125C2313yes—
295C2×#125C2316yes—
296C2×#125C2313yes—
297C2×#125C2313yes—
298C2×#124C2316yes—
299C2×#124C2313yes—
300C2×#124C2311yescharacteristic
301C2×#124C2316yes—
302C2×#124C2313yes—
303C2×#124C2313yes—
304C2×#123C2313yes—
305C2×#123C2313yes—
306C2×#123C2313yes—
307C2×#123C2313yes—
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2316yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2316yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×C22⋊Q8C2316yes—
320C2×C22⋊Q8C2313yes—
321C2×C22⋊Q8C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325#519—28no—
326#519—28no—
327#519D4116yes—
328C4×#41—28no—
329C2×C4×Q8—28no—
330C2×C4×Q8C2313yes—
331C2×C4×Q8C2313yes—
332C2×C4×Q8C2313yes—
333C2×C4×Q8C2316yes—
334C2×C4×Q8C2316yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2316yes—
338C2×C4×Q8C2313yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2313yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2313yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×#117C2316yes—
364C2×#117C2313yes—
365C2×#117C2313yes—
366C2×#117C2313yes—
367C2×#117C2313yes—
368C2×#117C2313yes—
369C2×#117C2313yes—
370C2×#117C2313yes—
371C22×C4⋊C4C2313yes—
372C22×C42C2313yes—
373C22×C42C2313yes—
374#400C2316yes—
375#400C2316yes—
376#400C2316yes—
377#400C2313yes—
378#400C2313yes—
379#400C2316yes—
380#400C2316yes—
381#400C2316yes—
382#400C2313yes—
383#400C2313yes—
384#400C2313yes—
385#400C2313yes—
386#399C2313yes—
387#399C2316yes—
388#399C2313yes—
389#399C2316yes—
390#399C2316yes—
391#399C2313yes—
392#399C2313yes—
393#398C2313yes—
394#398C2316yes—
395#398C2313yes—
396#398C2316yes—
397#398C2313yes—
398#398C2316yes—
399#398C2316yes—
400#398C2316yes—
401#398C2313yes—
402#398C2313yes—
403#398C2316yes—
404#398C2316yes—
405#398C2313yes—
406#398C2313yes—
407#398C2313yes—
408#398C2313yes—
409#398C2313yes—
410#397C2316yes—
411#397C2316yes—
412#397C2316yes—
413#397C2316yes—
414#397C2313yes—
415#397C2316yes—
416#397C2316yes—
417#397C2316yes—
418#397C2313yes—
419#397C2316yes—
420#397C2313yes—
421#397C2311yescharacteristic
422#397C2313yes—
423#397C2313yes—
424#397C2313yes—
425#397C2311yescharacteristic
426#396C2313yes—
427#396C2316yes—
428#396C2316yes—
429#396C2316yes—
430#396C2316yes—
431#396C2313yes—
432#396C2316yes—
433#396C2311yescharacteristic
434#396C2313yes—
435#395C2316yes—
436#395C2316yes—
437#395C2313yes—
438#395C2316yes—
439#395C2316yes—
440#395C2313yes—
441#395C2313yes—
442#395C2313yes—
443#395C2316yes—
444#395C2313yes—
445#395C2311yescharacteristic
446#394C2316yes—
447#394C2313yes—
448#394C2313yes—
449#394C2316yes—
450#394C2313yes—
451#394C2311yescharacteristic
452#394C2313yes—
453#394C2313yes—
454#393C2313yes—
455#393C2316yes—
456#393C2316yes—
457#393C2316yes—
458#393C2316yes—
459#393C2316yes—
460#393C2316yes—
461#393C2313yes—
462#393C2313yes—
463#393C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2316yes—
469#391C2316yes—
470#391C2313yes—
471#391C2316yes—
472#391C2316yes—
473#391C2316yes—
474#391C2313yes—
475#391C2313yes—
476#391C2316yes—
477#391C2316yes—
478#391C2313yes—
479#391C2313yes—
480#391C2313yes—
481#391C2313yes—
482#391C2313yes—
483#391C2313yes—
484#391C2313yes—
485#391C2316yes—
486#391C2313yes—
487#391C2313yes—
488#391C2311yescharacteristic
489#390C2313yes—
490#390C2313yes—
491#390C2316yes—
492#390C2313yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2316yes—
510#389C2316yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2313yes—
517#389C2316yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#388C2313yes—
529#388C2316yes—
530#388C2313yes—
531#388C2316yes—
532#388C2316yes—
533#388C2316yes—
534#388C2316yes—
535#388C2316yes—
536#388C2313yes—
537#388C2316yes—
538#388C2316yes—
539#388C2316yes—
540#388C2313yes—
541#388C2313yes—
542#388C2313yes—
543#388C2316yes—
544#388C2316yes—
545#388C2313yes—
546#388C2313yes—
547#388C2316yes—
548#388C2313yes—
549#388C2313yes—
550#388C2311yescharacteristic
551#388C2311yescharacteristic
552#387C2316yes—
553#387C2316yes—
554#387C2316yes—
555#387C2316yes—
556#387C2313yes—
557#387C2313yes—
558#387C2316yes—
559#387C2313yes—
560#387C2316yes—
561#387C2316yes—
562#387C2316yes—
563#387C2316yes—
564#387C2316yes—
565#387C2313yes—
566#387C2313yes—
567#387C2316yes—
568#387C2316yes—
569#387C2316yes—
570#387C2313yes—
571#387C2313yes—
572#387C2313yes—
573#387C2313yes—
574#387C2313yes—
575#387C2313yes—
576#387C2311yescharacteristic
577#386C2316yes—
578#386C2311yescharacteristic
579#386C2313yes—
580#385C2313yes—
581#385C2316yes—
582#385C2313yes—
583#385C2316yes—
584#385C2313yes—
585#385C2313yes—
586#385C2313yes—
587#385C2313yes—
588#384C2313yes—
589#384C2313yes—
590#384C2313yes—
591#384C2313yes—
592#383C2316yes—
593#382C2316yes—
594#382C2313yes—
595#382C2313yes—
596#382C2316yes—
597#382C2313yes—
598#382C2313yes—
599#382C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#381C2316yes—
604#381C2313yes—
605#381C2311yescharacteristic
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2316yes—
616#380C2313yes—
617#380C2313yes—
618#380C2313yes—
619C4×C4⋊C4C2313yes—
620C4×C4⋊C4C2313yes—
621C4×C4⋊C4C2313yes—
622C4×C4⋊C4C2313yes—
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2316yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C22⋊C4C2313yes—
637C4×C22⋊C4C2313yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646#376C2313yes—
647#376C2316yes—
648C43C2313yes—
649C2×#41—24no—
650C2×#41—24no—
651C2×#41—24no—
652C22×Q8—24no—
653C22×Q8—24no—
654C22×Q8—24no—
655C22×Q8—24no—
656C22×Q8—24no—
657C22×Q8C2×D418yes—
658C22×Q8C2413yes—
659C22×Q8C2411yescharacteristic
660C22×Q8C2411yescharacteristic
661C22×Q8C2413yes—
662C22×Q8C2413yes—
663C22×Q8C2416yes—
664C22×Q8C2413yes—
665C22×Q8C2416yes—
666C22×Q8C2413yes—
667C22×Q8C2411yescharacteristic
668C22×D4C2413yes—
669C22×D4C2411yescharacteristic
670C22×D4C2413yes—
671C22×D4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2411yescharacteristic
676C23×C4C2413yes—
677C23×C4C2413yes—
678C23×C4C2413yes—
679C4⋊Q8—212no—
680C4⋊Q8—212no—
681C4⋊Q8—212no—
682C4⋊Q8—212no—
683C4⋊Q8—212no—
684C4⋊Q8—212no—
685C4⋊Q8—212no—
686C4⋊Q8—212no—
687C4⋊Q8—212no—
688C4⋊Q8—224no—
689C4⋊Q8—212no—
690C4⋊Q8—212no—
691C4⋊Q8—224no—
692C4⋊Q8—212no—
693C4⋊Q8—46no—
694C4⋊Q8—412no—
695#126—212no—
696#126—224no—
697#126—212no—
698#126—224no—
699#125—212no—
700#125—212no—
701#125—212no—
702#125—212no—
703#125—212no—
704#125—212no—
705#125—212no—
706#125—224no—
707#125—212no—
708#125—224no—
709#125—212no—
710#124—212no—
711#124—24no—
712#124—224no—
713#124—212no—
714#124—224no—
715#124—46no—
716#123—212no—
717#123—212no—
718#123—46no—
719#123—46no—
720C22⋊Q8—212no—
721C22⋊Q8—212no—
722C22⋊Q8—212no—
723C22⋊Q8—212no—
724C22⋊Q8—224no—
725C22⋊Q8—212no—
726C22⋊Q8—212no—
727C22⋊Q8—24no—
728C22⋊Q8—212no—
729C22⋊Q8—224no—
730C22⋊Q8—212no—
731C22⋊Q8—46no—
732C22⋊Q8—46no—
733C22⋊Q8—412no—
734#121—212no—
735#121—212no—
736#121—212no—
737C4×Q8—212no—
738C4×Q8—24no—
739C4×Q8—212no—
740C4×Q8—24no—
741C4×Q8—24no—
742C4×Q8—24no—
743C4×Q8—212no—
744C4×Q8—24no—
745C4×Q8—212no—
746C4×Q8—24no—
747C4×Q8—24no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—24no—
751C4×Q8—212no—
752C4×Q8—212no—
753C4×Q8—212no—
754C4×Q8—224no—
755C4×Q8—212no—
756C4×Q8—224no—
757C4×Q8—212no—
758C4×Q8—212no—
759C4×Q8—224no—
760C4×Q8—212no—
761C4×Q8C2×D418yes—
762C4×Q8C2×D4124yes—
763C4×Q8C2×D418yes—
764C4×Q8C2×D4124yes—
765C4×D4—212no—
766C4×D4—212no—
767C4×D4—212no—
768C4×D4—212no—
769C4×D4—212no—
770#117—212no—
771#117—212no—
772#117—212no—
773#117—212no—
774#117—212no—
775#117—224no—
776#117C2×D4124yes—
777#117C2×D4124yes—
778C2×C4⋊C4—212no—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2413yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2413yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2416yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2416yes—
804C2×C4⋊C4C2413yes—
805C2×C4⋊C4C2416yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2416yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2416yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2416yes—
830C2×C4⋊C4C2416yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2411yescharacteristic
845C2×C22⋊C4C2413yes—
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2413yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2416yes—
862C2×C22⋊C4C2416yes—
863C2×C22⋊C4C2413yes—
864C2×C22⋊C4C2413yes—
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2413yes—
868C2×C22⋊C4C2413yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2416yes—
879C2×C22⋊C4C2416yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2411yescharacteristic
882C2×C42—212no—
883C2×C42—212no—
884C2×C42C2416yes—
885C2×C42C2413yes—
886C2×C42C2413yes—
887C2×C42C2413yes—
888C2×C42C2413yes—
889C2×C42C2416yes—
890C2×C42C2413yes—
891C2×C42C2413yes—
892C2×C42C2413yes—
893C2×C42C2413yes—
894C2×C42C2413yes—
895C2×C42C2413yes—
896C2×C42C2413yes—
897C2×C42C2413yes—
898C2×C42C2413yes—
899C2×C42C2411yescharacteristic
900C2×C42C2413yes—
901C2×C42C2413yes—
902C2×C42C2416yes—
903C2×C42C2411yescharacteristic
904C2×C42C2413yes—
905C2×C42C2413yes—
906C2×C42C2416yes—
907C2×C42C2413yes—
908#95C2411yescharacteristic
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2416yes—
915#95C2416yes—
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2413yes—
933#95C2413yes—
934#95C2413yes—
935#95C2411yescharacteristic
936#95C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2416yes—
939#95C2411yescharacteristic
940#95C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2411yescharacteristic
943#95C2413yes—
944#95C2413yes—
945#95C2416yes—
946#95C2413yes—
947#95C2413yes—
948#95C2413yes—
949#95C2413yes—
950#95C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2416yes—
957#95C2416yes—
958#95C2416yes—
959#95C2416yes—
960#95C2416yes—
961#95C2416yes—
962#95C2416yes—
963#95C2416yes—
964#95C2416yes—
965#95C2416yes—
966C24C2511yescharacteristic
967C24C2513yes—
968C24C2511yescharacteristic
969#41—416no—
970C2×Q8—232no—
971C2×Q8—22no—
972C2×Q8—22no—
973C2×Q8—26no—
974C2×Q8—26no—
975C2×Q8—212no—
976C2×Q8—26no—
977C2×Q8—212no—
978C2×Q8—26no—
979C2×Q8—26no—
980C2×Q8—26no—
981C2×Q8—26no—
982C2×Q8—26no—
983C2×Q8—22no—
984C2×Q8—26no—
985C2×Q8—22no—
986C2×Q8—43no—
987C2×Q8—41no—
988C2×Q8—41no—
989C2×Q8—46no—
990C2×Q8—43no—
991C2×Q8—46no—
992C2×Q8—43no—
993C2×Q8—46no—
994C2×Q8—43no—
995C2×Q8—43no—
996C2×Q8—46no—
997C2×Q8—416no—
998C2×Q8C22×D4112yes—
999C2×Q8C22×D414yes—
1000C2×Q82−1+414yes—
1001C2×Q82−1+414yes—
1002C2×D4—22no—
1003C2×D4—26no—
1004C2×D4—26no—
1005C2×D4—26no—
1006C2×D4—26no—
1007C2×D4—26no—
1008C2×D4—22no—
1009C2×D4—41no—
1010C2×D4—43no—
1011C2×D4—43no—
1012C2×D4—43no—
1013C2×D4—43no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—22no—
1017C22×C4—26no—
1018C22×C4—26no—
1019C22×C4—26no—
1020C22×C4—26no—
1021C22×C4—26no—
1022C22×C4—26no—
1023C22×C4—26no—
1024C22×C4—26no—
1025C22×C4—26no—
1026C22×C4—22no—
1027C22×C4—26no—
1028C22×C4—43no—
1029C22×C4—41no—
1030C22×C4—43no—
1031C22×C4—43no—
1032C22×C4—43no—
1033C22×C4—43no—
1034C22×C4C22×D4112yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2511yescharacteristic
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2511yescharacteristic
1054C22×C4C2513yes—
1055C22×C4C2513yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2513yes—
1058C22×C4C2513yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2513yes—
1063C4⋊C4—212no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—26no—
1073C4⋊C4—26no—
1074C4⋊C4—26no—
1075C4⋊C4—26no—
1076C4⋊C4—26no—
1077C4⋊C4—26no—
1078C4⋊C4—26no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—26no—
1082C4⋊C4—26no—
1083C4⋊C4—22no—
1084C4⋊C4—212no—
1085C4⋊C4—26no—
1086C4⋊C4—26no—
1087C4⋊C4—212no—
1088C4⋊C4—26no—
1089C4⋊C4—212no—
1090C4⋊C4—26no—
1091C4⋊C4—26no—
1092C4⋊C4—212no—
1093C4⋊C4—26no—
1094C4⋊C4—26no—
1095C4⋊C4—26no—
1096C4⋊C4—26no—
1097C4⋊C4—26no—
1098C4⋊C4—26no—
1099C4⋊C4—26no—
1100C4⋊C4—22no—
1101C4⋊C4—26no—
1102C4⋊C4—26no—
1103C4⋊C4—26no—
1104C4⋊C4—26no—
1105C4⋊C4—26no—
1106C4⋊C4—41no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4—43no—
1110C4⋊C4—41no—
1111C4⋊C4—43no—
1112C4⋊C4—43no—
1113C4⋊C4—43no—
1114C4⋊C4—43no—
1115C4⋊C4—46no—
1116C4⋊C4—43no—
1117C4⋊C4—43no—
1118C4⋊C4—43no—
1119C4⋊C4—46no—
1120C4⋊C4—46no—
1121C4⋊C4—43no—
1122C4⋊C4—43no—
1123C4⋊C4C22×D4112yes—
1124C4⋊C4C22×D4112yes—
1125C4⋊C4C22×D4112yes—
1126C4⋊C4C22×D4112yes—
1127C22⋊C4—22no—
1128C22⋊C4—26no—
1129C22⋊C4—22no—
1130C22⋊C4—26no—
1131C22⋊C4—26no—
1132C22⋊C4—22no—
1133C22⋊C4—212no—
1134C22⋊C4—212no—
1135C22⋊C4—212no—
1136C22⋊C4—22no—
1137C22⋊C4—26no—
1138C22⋊C4—26no—
1139C22⋊C4—26no—
1140C22⋊C4—26no—
1141C22⋊C4—22no—
1142C22⋊C4—41no—
1143C22⋊C4—43no—
1144C22⋊C4—41no—
1145C22⋊C4—46no—
1146C22⋊C4—41no—
1147C22⋊C4—43no—
1148C22⋊C4—46no—
1149C22⋊C4—43no—
1150C22⋊C4—41no—
1151C22⋊C4—41no—
1152C22⋊C4—43no—
1153C22⋊C4—43no—
1154C22⋊C4—46no—
1155C22⋊C4—46no—
1156C22⋊C4—43no—
1157C22⋊C4—43no—
1158C22⋊C4—43no—
1159C22⋊C4—43no—
1160C22⋊C4—43no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C22⋊C4C22×D4112yes—
1165C22⋊C4C22×D414yes—
1166C42—22no—
1167C42—26no—
1168C42—26no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—212no—
1174C42—26no—
1175C42—212no—
1176C42—26no—
1177C42—26no—
1178C42—26no—
1179C42—26no—
1180C42—26no—
1181C42—26no—
1182C42—43no—
1183C42—41no—
1184C42—43no—
1185C42—46no—
1186C42—43no—
1187C42C22×D4112yes—
1188C42C22×D4124yes—
1189C42C22×D4112yes—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—23no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—23no—
1201C23—23no—
1202C23—23no—
1203C23—21no—
1204C23—23no—
1205C23—21no—
1206C23—23no—
1207C23—21no—
1208C23—23no—
1209C23—21no—
1210C23C23×D412yes—
1211C23C2611yescharacteristic
1212Q8—224no—
1213Q8—44no—
1214Q8—44no—
1215Q8—412no—
1216Q8—412no—
1217Q8—812no—
1218Q8—86no—
1219Q8—812no—
1220Q8—86no—
1221Q8#536116yes—
1222D4—44no—
1223D4—412no—
1224D4—86no—
1225D4—86no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—224no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—23no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—21no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—21no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—23no—
1271C2×C4—23no—
1272C2×C4—21no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—23no—
1278C2×C4—23no—
1279C2×C4—23no—
1280C2×C4—23no—
1281C2×C4—23no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—23no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—23no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—23no—
1300C2×C4—23no—
1301C2×C4—412no—
1302C2×C4—44no—
1303C2×C4—412no—
1304C2×C4—412no—
1305C2×C4—86no—
1306C2×C4—86no—
1307C2×C4C23×D416yes—
1308C2×C4C23×D416yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D412yes—
1311C2×C4C23×D416yes—
1312C2×C4C23×D416yes—
1313C2×C4C2×2−1+416yes—
1314C2×C4C2×2−1+416yes—
1315C2×C4#58512yes—
1316C2×C4#58512yes—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—43no—
1325C22—43no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—43no—
1330C22—41no—
1331C22—43no—
1332C22—41no—
1333C22—43no—
1334C22—41no—
1335C22—41no—
1336C22—43no—
1337C22—43no—
1338C22C24×D411yescharacteristic
1339C22C22×2−1+411yescharacteristic
1340C22C22×2−1+411yescharacteristic
1341C22C2×#58511yescharacteristic
1342C22C2×#58511yescharacteristic
1343C222−1+611yescharacteristic
1344C222−1+611yescharacteristic
1345C4—22no—
1346C4—26no—
1347C4—22no—
1348C4—22no—
1349C4—26no—
1350C4—22no—
1351C4—26no—
1352C4—41no—
1353C4—43no—
1354C4—43no—
1355C4—43no—
1356C4—43no—
1357C4—41no—
1358C4—41no—
1359C4—43no—
1360C4—41no—
1361C4—43no—
1362C4—43no—
1363C4—43no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—43no—
1368C4—41no—
1369C4—41no—
1370C4—43no—
1371C4—43no—
1372C4C2×#536112yes—
1373C2—42no—
1374C2—83no—
1375C2—81no—
1376C2C22×#53611yescharacteristic
1377C2#6295311yescharacteristic
1378C2#6295311yescharacteristic
1379C2#6300211yescharacteristic
1380C2#6300211yescharacteristic
1381C2#6303411yescharacteristic
1382C2#6305711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3518C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3502C2semidirect
3. #52166C2semidirect
4. #42965C2semidirect
5. #42915C2semidirect
6. #42891C2semidirect
7. #42875C2semidirect
8. #42809C2semidirect
9. #42804C2semidirect
10. #39951C2semidirect
11. #39891C2semidirect
12. #39867C2semidirect
13. #39855C2semidirect
14. #39724C2semidirect
15. #39172C2semidirect
16. #37423C2semidirect
17. #37279C2semidirect
18. #37275C2semidirect
19. #36578C2semidirect
20. #36482C2semidirect
21. #36474C2semidirect
22. #36467C2semidirect
23. #36456C2semidirect
24. #36431C2semidirect
25. #35937C2semidirect
26. #35854C2semidirect
27. #35801C2semidirect
28. #35786C2semidirect
29. #35723C2semidirect
30. #35711C2semidirect
31. #34262C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#35022
#521662
#429652
#429152
#428912
#428752
#428092
#428042
#399512
#398912
#398672
#398552
#397242
#391722
#374232
#372792
#372752
#365782
#364822
#364742
#364672
#364562
#364312
#359372
#358542
#358012
#357862
#357232
#357112
#342622