Finite Group Databasebeta

← #7698439

Subgroups — #7698439

Order 512.

6985 conjugacy classes of subgroups.

The subgroup lattice has 1450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59829C213yesmaximal, complemented
4#59115C213yesmaximal, complemented
5#59113C213yesmaximal, complemented
6#52152C213yesmaximal, complemented
7#45333C213yesmaximal, complemented
8#45287C213yesmaximal, complemented
9#45227C213yesmaximal, complemented
10#45051C213yesmaximal, complemented
11#44928C213yesmaximal, complemented
12#44875C213yesmaximal, complemented
13#39488C213yesmaximal, complemented
14#39377C213yesmaximal, complemented
15#38051C213yesmaximal, complemented
16#38041C213yesmaximal, complemented
17#37795C213yesmaximal, complemented
18#37794C213yesmaximal, complemented
19Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
20Q8×#123C211yesmaximal, characteristic, complemented
21#36433C211yesmaximal, characteristic, complemented
22#35996C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35801C211yesmaximal, characteristic, complemented
25#35771C211yesmaximal, characteristic, complemented
26#35748C211yesmaximal, characteristic, complemented
27#35711C211yesmaximal, characteristic, complemented
28#34312C211yesmaximal, characteristic, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31#34249C211yesmaximal, characteristic, complemented
32#3522—216no—
33#3518—216no—
34C2×#559C2213yes—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#556C2213yes—
38C2×#556C2213yes—
39C2×#556C2213yes—
40C2×#555C2213yes—
41C2×#554C2213yes—
42C2×#550C2211yescharacteristic
43C2×D4×Q8C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#548C2211yescharacteristic
46C2×#548C2211yescharacteristic
47C2×#548C2211yescharacteristic
48C2×#547C2213yes—
49C2×#547C2213yes—
50C2×#542C2213yes—
51C2×#542C2213yes—
52C2×#542C2213yes—
53C2×#542C2213yes—
54C2×#533C2213yes—
55C2×#532C2213yes—
56C2×#529C2213yes—
57C2×#529C2213yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#519C2211yescharacteristic
62C2×#519C2211yescharacteristic
63C2×#519C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C22×C4×Q8C2211yescharacteristic
66#2868C2213yes—
67#2855C2213yes—
68#2854C2213yes—
69#2727C2213yes—
70#2726C2213yes—
71#2725C2213yes—
72#2725C2213yes—
73#2724C2213yes—
74#2723C2216yes—
75#2720C2216yes—
76#2718C2213yes—
77#2718C2216yes—
78#2718C2216yes—
79#2718C2216yes—
80#2718C2213yes—
81#2717C2216yes—
82#2715C2216yes—
83#2710C2213yes—
84#2710C2213yes—
85#2701C2213yes—
86#2701C2213yes—
87#2698C2216yes—
88#2689C2213yes—
89#2689C2213yes—
90#2686C2216yes—
91#2682C2213yes—
92#2680C2216yes—
93#2674C2216yes—
94#2674C2216yes—
95#2674C2213yes—
96#2674C2211yescharacteristic
97#2672C2216yes—
98#2628C2213yes—
99#2628C2213yes—
100#2625C2213yes—
101#2624C2213yes—
102#2620C2213yes—
103#2620C2213yes—
104#2581C2213yes—
105#2580C2213yes—
106#2568C2213yes—
107#2567C2213yes—
108#2567C2213yes—
109#2553C2216yes—
110#2551C2213yes—
111#2551C2213yes—
112#2551C2213yes—
113#2551C2213yes—
114#2545C2213yes—
115#2544C2213yes—
116#2542C2213yes—
117#2538C2213yes—
118#2537C2213yes—
119#2521C2216yes—
120#2502C2213yes—
121#2502C2213yes—
122#2501C2216yes—
123#2500C2213yes—
124#2500C2213yes—
125#2496C2216yes—
126#2491C2216yes—
127#2488C2216yes—
128#2487C2213yes—
129#2486C2213yes—
130#2485C2213yes—
131#2485C2213yes—
132#2474C2216yes—
133#2470C2216yes—
134#2469C2216yes—
135#2466C2216yes—
136#2462C2216yes—
137#2461C2216yes—
138#2452C2213yes—
139#2452C2213yes—
140#2451C2213yes—
141#2451C2213yes—
142#2449C2216yes—
143#2448C2213yes—
144#2448C2213yes—
145#2447C2213yes—
146#2447C2213yes—
147#2446C2213yes—
148#2446C2213yes—
149#2445C2213yes—
150#2445C2213yes—
151#2440C2213yes—
152#2440C2216yes—
153#2440C2213yes—
154#2439C2213yes—
155#2439C2213yes—
156#2438C2216yes—
157#2432C2216yes—
158#2432C2216yes—
159#2430C2216yes—
160#2429C2216yes—
161#2429C2216yes—
162#2429C2213yes—
163#2428C2213yes—
164#2427C2213yes—
165#2426C2213yes—
166#2423C2213yes—
167#2423C2213yes—
168#2423C2213yes—
169#2422C2213yes—
170#2422C2213yes—
171#2422C2213yes—
172#2421C2213yes—
173#2420C2213yes—
174#2417C2213yes—
175#2416C2213yes—
176#2415C2213yes—
177#2414C2213yes—
178#2406C2216yes—
179#2396C2213yes—
180#2396C2213yes—
181#2395C2213yes—
182#2395C2213yes—
183#2392C2213yes—
184#2392C2213yes—
185#2367C2213yes—
186#2367C2213yes—
187#2363C2213yes—
188#2363C2213yes—
189#2360C2213yes—
190#2360C2213yes—
191#2359C2216yes—
192#2352C2213yes—
193#2352C2213yes—
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2213yes—
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2213yes—
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2213yes—
208#2349C2213yes—
209#2349C2213yes—
210D4×C4⋊C4C2213yes—
211D4×C4⋊C4C2213yes—
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215#2341C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218Q8×C22⋊C4C2211yescharacteristic
219Q8×C22⋊C4C2211yescharacteristic
220#2324C2213yes—
221#2324C2213yes—
222#2323C2213yes—
223#2323C2213yes—
224#2317C2213yes—
225#2317C2213yes—
226#2317C2213yes—
227#2316C2213yes—
228C4×C4⋊Q8C2213yes—
229C4×#124C2213yes—
230C4×#124C2213yes—
231C4×#123C2213yes—
232C4×#123C2213yes—
233#2296C2213yes—
234#2296C2213yes—
235#2296C2213yes—
236#2293C2213yes—
237#2293C2213yes—
238C2×#389C2213yes—
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2316yes—
243C23×Q8C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245#559—224no—
246Q82—28no—
247Q82—28no—
248#556—224no—
249#556—224no—
250#556—224no—
251#555—224no—
252#554—224no—
253#550—28no—
254D4×Q8—28no—
255#548—28no—
256#548—28no—
257#548—28no—
258#548D4116yescomplemented
259#547—224no—
260#547—224no—
261#542—224no—
262#542—224no—
263#542—224no—
264#542—224no—
265#533—224no—
266#532—224no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2313yes—
275C2×C4⋊Q8C2316yes—
276C2×C4⋊Q8C2316yes—
277C2×#127C2313yes—
278#529—224no—
279#529—224no—
280C2×#126C2313yes—
281C2×#126C2313yes—
282C2×#126C2313yes—
283C2×#126C2313yes—
284C2×#126C2316yes—
285C2×#126C2316yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#124C2313yes—
289C2×#124C2311yescharacteristic
290C2×#124C2313yes—
291C2×#124C2316yes—
292C2×#124C2316yes—
293C2×#124C2313yes—
294C2×#124C2313yes—
295C2×#124C2316yes—
296C2×#124C2313yes—
297C2×#123C2313yes—
298C2×#123C2313yes—
299C2×#123C2313yes—
300C2×#123C2313yes—
301C2×#123C2313yes—
302C2×#123C2316yes—
303C2×#123C2311yescharacteristic
304C2×#123C2316yes—
305C2×#123C2316yes—
306C2×#123C2316yes—
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2311yescharacteristic
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2316yes—
313C2×C22⋊Q8C2316yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2313yes—
316C2×C22⋊Q8C2316yes—
317C2×C22⋊Q8C2316yes—
318C2×C22⋊Q8C2316yes—
319C2×C22⋊Q8C2313yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325C2×#121C2313yes—
326C2×#121C2313yes—
327C2×#121C2316yes—
328C2×#121C2313yes—
329#520—28no—
330#520—28no—
331#520—28no—
332#519—28no—
333#519—28no—
334#519—28no—
335C4×#41—28no—
336C2×C4×Q8—28no—
337C2×C4×Q8C2313yes—
338C2×C4×Q8C2313yes—
339C2×C4×Q8C2313yes—
340C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2313yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2313yes—
356C2×C4×Q8C2316yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2316yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×#117C2313yes—
375C2×#117C2313yes—
376C2×#117C2313yes—
377C2×#117C2313yes—
378C2×#117C2313yes—
379C2×#117C2313yes—
380C2×#117C2313yes—
381C2×#117C2313yes—
382C2×#117C2313yes—
383C2×#117C2313yes—
384C2×#117C2316yes—
385C22×C4⋊C4C2313yes—
386C22×C4⋊C4C2313yes—
387C22×C4⋊C4C2313yes—
388C22×C4⋊C4C2313yes—
389C22×C4⋊C4C2316yes—
390C22×C42C2313yes—
391C22×C42C2313yes—
392#400C2313yes—
393#400C2316yes—
394#400C2313yes—
395#400C2313yes—
396#400C2313yes—
397#400C2316yes—
398#399C2316yes—
399#399C2316yes—
400#399C2313yes—
401#399C2311yescharacteristic
402#399C2313yes—
403#399C2313yes—
404#399C2316yes—
405#398C2316yes—
406#398C2313yes—
407#398C2313yes—
408#398C2313yes—
409#398C2313yes—
410#398C2313yes—
411#398C2313yes—
412#398C2313yes—
413#398C2313yes—
414#398C2316yes—
415#398C2316yes—
416#397C2316yes—
417#397C2316yes—
418#397C2316yes—
419#397C2313yes—
420#397C2313yes—
421#397C2311yescharacteristic
422#397C2313yes—
423#397C2313yes—
424#397C2313yes—
425#397C2313yes—
426#397C2313yes—
427#397C2316yes—
428#396C2313yes—
429#396C2316yes—
430#396C2316yes—
431#396C2316yes—
432#396C2311yescharacteristic
433#396C2313yes—
434#396C2313yes—
435#396C2313yes—
436#396C2313yes—
437#396C2313yes—
438#396C2313yes—
439#395C2316yes—
440#395C2316yes—
441#395C2316yes—
442#395C2316yes—
443#395C2313yes—
444#395C2316yes—
445#395C2316yes—
446#395C2311yescharacteristic
447#394C2313yes—
448#394C2316yes—
449#394C2316yes—
450#394C2316yes—
451#394C2313yes—
452#394C2316yes—
453#394C2311yescharacteristic
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2313yes—
460#394C2313yes—
461#394C2316yes—
462#394C2316yes—
463#394C2316yes—
464#393C2313yes—
465#393C2316yes—
466#393C2316yes—
467#393C2311yescharacteristic
468#392C2313yes—
469#392C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2313yes—
474#391C2316yes—
475#391C2316yes—
476#391C2313yes—
477#391C2313yes—
478#391C2313yes—
479#391C2313yes—
480#391C2313yes—
481#391C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2313yes—
486#390C2313yes—
487#390C2313yes—
488#390C2313yes—
489#390C2313yes—
490#390C2313yes—
491#390C2313yes—
492#390C2313yes—
493#390C2313yes—
494#390C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2313yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2316yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2313yes—
516#389C2316yes—
517#389C2316yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#389C2313yes—
531#389C2313yes—
532#389C2316yes—
533#389C2311yescharacteristic
534#389C2313yes—
535#388C2316yes—
536#388C2316yes—
537#388C2316yes—
538#388C2316yes—
539#388C2313yes—
540#388C2316yes—
541#388C2313yes—
542#388C2313yes—
543#388C2316yes—
544#388C2316yes—
545#388C2313yes—
546#388C2313yes—
547#388C2316yes—
548#388C2316yes—
549#388C2311yescharacteristic
550#388C2311yescharacteristic
551#388C2313yes—
552#388C2313yes—
553#388C2316yes—
554#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#387C2316yes—
558#387C2316yes—
559#387C2316yes—
560#387C2316yes—
561#387C2316yes—
562#387C2316yes—
563#387C2313yes—
564#387C2316yes—
565#387C2311yescharacteristic
566#387C2313yes—
567#387C2313yes—
568#386C2316yes—
569#386C2316yes—
570#386C2316yes—
571#386C2316yes—
572#386C2316yes—
573#386C2313yes—
574#386C2313yes—
575#385C2313yes—
576#385C2316yes—
577#385C2313yes—
578#385C2316yes—
579#385C2316yes—
580#385C2316yes—
581#385C2316yes—
582#385C2316yes—
583#385C2316yes—
584#385C2316yes—
585#385C2313yes—
586#385C2313yes—
587#385C2313yes—
588#385C2313yes—
589#385C2316yes—
590#385C2311yescharacteristic
591#385C2313yes—
592#385C2316yes—
593#385C2313yes—
594#385C2313yes—
595#384C2313yes—
596#384C2316yes—
597#384C2313yes—
598#384C2313yes—
599#384C2313yes—
600#384C2313yes—
601#384C2316yes—
602#384C2313yes—
603#384C2313yes—
604#382C2313yes—
605#382C2313yes—
606#382C2313yes—
607#382C2316yes—
608#382C2313yes—
609#381C2313yes—
610#381C2316yes—
611#381C2313yes—
612#380C2316yes—
613#380C2316yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2313yes—
618#380C2313yes—
619#380C2313yes—
620#380C2313yes—
621#380C2313yes—
622#380C2316yes—
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⋊C4C2316yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2316yes—
637C4×C4⋊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—
646C4×C22⋊C4C2316yes—
647C4×C22⋊C4C2316yes—
648C4×C22⋊C4C2316yes—
649C4×C22⋊C4C2316yes—
650C2×#95C2316yes—
651C43C2313yes—
652C2×#41—24no—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—224no—
658C2×#41—86no—
659C2×#41—86no—
660C2×#41C2×D418yes—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—24no—
664C22×Q8—24no—
665C22×Q8—24no—
666C22×Q8C2×D418yes—
667C22×Q8C2413yes—
668C22×Q8C2411yescharacteristic
669C22×Q8C2411yescharacteristic
670C22×Q8C2413yes—
671C22×Q8C2416yes—
672C22×Q8C2416yes—
673C22×Q8C2411yescharacteristic
674C22×D4C2413yes—
675C22×D4C2411yescharacteristic
676C22×D4C2413yes—
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2416yes—
682C22×D4C2413yes—
683C23×C4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2411yescharacteristic
687C23×C4C2413yes—
688C23×C4C2413yes—
689C23×C4C2416yes—
690C23×C4C2416yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2416yes—
694C4⋊Q8—212no—
695C4⋊Q8—212no—
696C4⋊Q8—212no—
697C4⋊Q8—212no—
698C4⋊Q8—212no—
699C4⋊Q8—24no—
700C4⋊Q8—212no—
701C4⋊Q8—212no—
702C4⋊Q8—86no—
703C4⋊Q8—86no—
704#127—212no—
705#126—212no—
706#126—212no—
707#126—212no—
708#126—212no—
709#126—224no—
710#126—224no—
711#125—212no—
712#125—212no—
713#124—212no—
714#124—212no—
715#124—224no—
716#124—24no—
717#124—212no—
718#124—224no—
719#124—224no—
720#124—212no—
721#124C2×D4124yes—
722#123—212no—
723#123—212no—
724#123—212no—
725#123—24no—
726#123—212no—
727#123—212no—
728#123—224no—
729#123—224no—
730#123—86no—
731#123—86no—
732C22⋊Q8—212no—
733C22⋊Q8—212no—
734C22⋊Q8—212no—
735C22⋊Q8—212no—
736C22⋊Q8—224no—
737C22⋊Q8—212no—
738C22⋊Q8—24no—
739C22⋊Q8—212no—
740C22⋊Q8—224no—
741C22⋊Q8—224no—
742C22⋊Q8—86no—
743C22⋊Q8—86no—
744C22⋊Q8C2×D4124yes—
745#121—212no—
746#121—212no—
747#121—212no—
748#121—212no—
749#121—212no—
750#121—212no—
751#121—212no—
752#121—86no—
753#121C2×D4124yes—
754C4×Q8—24no—
755C4×Q8—212no—
756C4×Q8—24no—
757C4×Q8—212no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—212no—
761C4×Q8—24no—
762C4×Q8—212no—
763C4×Q8—24no—
764C4×Q8—24no—
765C4×Q8—24no—
766C4×Q8—24no—
767C4×Q8—212no—
768C4×Q8—224no—
769C4×Q8—212no—
770C4×Q8—212no—
771C4×Q8—212no—
772C4×Q8—212no—
773C4×Q8—212no—
774C4×Q8C2×D418yes—
775C4×Q8#4118yescomplemented
776C4×D4—212no—
777C4×D4—212no—
778C4×D4—212no—
779C4×D4—212no—
780C4×D4—212no—
781C4×D4—212no—
782C4×D4—212no—
783C4×D4—212no—
784C4×D4—212no—
785C4×D4—212no—
786C4×D4—224no—
787C4×D4—212no—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4C2×D4124yes—
791#117—212no—
792#117—212no—
793#117—212no—
794#117—212no—
795#117—212no—
796#117—212no—
797#117—224no—
798#117—212no—
799#117—212no—
800#117—212no—
801#117—212no—
802C2×C4⋊C4—212no—
803C2×C4⋊C4—212no—
804C2×C4⋊C4—212no—
805C2×C4⋊C4—212no—
806C2×C4⋊C4—86no—
807C2×C4⋊C4C2413yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2413yes—
810C2×C4⋊C4C2413yes—
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2416yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2413yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2416yes—
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2416yes—
849C2×C4⋊C4C2416yes—
850C2×C4⋊C4C2416yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2416yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2416yes—
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2413yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2413yes—
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2416yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2416yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2416yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2416yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2411yescharacteristic
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2416yes—
907C2×C22⋊C4C2413yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2416yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2416yes—
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2413yes—
919C2×C42—212no—
920C2×C42—212no—
921C2×C42C2413yes—
922C2×C42C2413yes—
923C2×C42C2416yes—
924C2×C42C2416yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2416yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2413yes—
939C2×C42C2413yes—
940C2×C42C2413yes—
941C2×C42C2413yes—
942C2×C42C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2416yes—
946#95C2416yes—
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2413yes—
950#95C2411yescharacteristic
951#95C2413yes—
952#95C2411yescharacteristic
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2416yes—
960#95C2416yes—
961#95C2413yes—
962#95C2413yes—
963#95C2416yes—
964#95C2413yes—
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2416yes—
971#95C2411yescharacteristic
972#95C2413yes—
973#95C2413yes—
974#95C2411yescharacteristic
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2416yes—
985#95C2413yes—
986#95C2416yes—
987#95C2416yes—
988C24C2511yescharacteristic
989C24C2513yes—
990C24C2511yescharacteristic
991C24C2513yes—
992#41—232no—
993#41—416no—
994#41—848no—
995C2×Q8—232no—
996C2×Q8—22no—
997C2×Q8—22no—
998C2×Q8—26no—
999C2×Q8—212no—
1000C2×Q8—212no—
1001C2×Q8—26no—
1002C2×Q8—26no—
1003C2×Q8—26no—
1004C2×Q8—22no—
1005C2×Q8—22no—
1006C2×Q8—26no—
1007C2×Q8—41no—
1008C2×Q8—41no—
1009C2×Q8—46no—
1010C2×Q8—46no—
1011C2×Q8—46no—
1012C2×Q8—46no—
1013C2×Q8—416no—
1014C2×Q8C22×D4112yes—
1015C2×Q8C22×D414yes—
1016C2×Q8C2×#4114yes—
1017C2×Q82−1+414yes—
1018C2×D4—22no—
1019C2×D4—26no—
1020C2×D4—26no—
1021C2×D4—26no—
1022C2×D4—212no—
1023C2×D4—26no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—22no—
1029C2×D4—26no—
1030C2×D4—26no—
1031C2×D4—41no—
1032C2×D4—43no—
1033C2×D4—43no—
1034C2×D4—43no—
1035C2×D4—43no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—43no—
1039C2×D4—46no—
1040C2×D4—43no—
1041C2×D4—46no—
1042C2×D4—43no—
1043C2×D4C22×D4112yes—
1044C2×D4C22×D4112yes—
1045C22×C4—26no—
1046C22×C4—26no—
1047C22×C4—26no—
1048C22×C4—26no—
1049C22×C4—22no—
1050C22×C4—26no—
1051C22×C4—26no—
1052C22×C4—26no—
1053C22×C4—212no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—26no—
1058C22×C4—26no—
1059C22×C4—22no—
1060C22×C4—26no—
1061C22×C4—26no—
1062C22×C4—212no—
1063C22×C4—212no—
1064C22×C4—43no—
1065C22×C4—41no—
1066C22×C4—43no—
1067C22×C4—43no—
1068C22×C4—43no—
1069C22×C4—46no—
1070C22×C4—46no—
1071C22×C4—46no—
1072C22×C4—46no—
1073C22×C4—43no—
1074C22×C4—46no—
1075C22×C4—46no—
1076C22×C4C22×D4112yes—
1077C22×C4C22×D4112yes—
1078C22×C4C2513yes—
1079C22×C4C2513yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2513yes—
1082C22×C4C2513yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2511yescharacteristic
1085C22×C4C2513yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2513yes—
1090C22×C4C2513yes—
1091C22×C4C2513yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2513yes—
1094C22×C4C2513yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2513yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2513yes—
1105C4⋊C4—26no—
1106C4⋊C4—26no—
1107C4⋊C4—26no—
1108C4⋊C4—26no—
1109C4⋊C4—26no—
1110C4⋊C4—212no—
1111C4⋊C4—26no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—26no—
1115C4⋊C4—26no—
1116C4⋊C4—26no—
1117C4⋊C4—26no—
1118C4⋊C4—26no—
1119C4⋊C4—26no—
1120C4⋊C4—26no—
1121C4⋊C4—26no—
1122C4⋊C4—22no—
1123C4⋊C4—26no—
1124C4⋊C4—26no—
1125C4⋊C4—26no—
1126C4⋊C4—212no—
1127C4⋊C4—26no—
1128C4⋊C4—26no—
1129C4⋊C4—26no—
1130C4⋊C4—26no—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—22no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—22no—
1140C4⋊C4—26no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—43no—
1145C4⋊C4—43no—
1146C4⋊C4—46no—
1147C4⋊C4—46no—
1148C4⋊C4—43no—
1149C4⋊C4—41no—
1150C4⋊C4—43no—
1151C4⋊C4—46no—
1152C4⋊C4—43no—
1153C4⋊C4—43no—
1154C4⋊C4—43no—
1155C4⋊C4—43no—
1156C4⋊C4—46no—
1157C4⋊C4—43no—
1158C4⋊C4—46no—
1159C4⋊C4—46no—
1160C4⋊C4—43no—
1161C4⋊C4—43no—
1162C4⋊C4—43no—
1163C4⋊C4—43no—
1164C4⋊C4C22×D4112yes—
1165C4⋊C4C22×D4112yes—
1166C4⋊C4C2×#41112yes—
1167C4⋊C42−1+414yes—
1168C22⋊C4—26no—
1169C22⋊C4—22no—
1170C22⋊C4—26no—
1171C22⋊C4—26no—
1172C22⋊C4—212no—
1173C22⋊C4—212no—
1174C22⋊C4—22no—
1175C22⋊C4—26no—
1176C22⋊C4—26no—
1177C22⋊C4—26no—
1178C22⋊C4—26no—
1179C22⋊C4—22no—
1180C22⋊C4—26no—
1181C22⋊C4—26no—
1182C22⋊C4—22no—
1183C22⋊C4—26no—
1184C22⋊C4—212no—
1185C22⋊C4—26no—
1186C22⋊C4—26no—
1187C22⋊C4—26no—
1188C22⋊C4—22no—
1189C22⋊C4—26no—
1190C22⋊C4—26no—
1191C22⋊C4—22no—
1192C22⋊C4—26no—
1193C22⋊C4—212no—
1194C22⋊C4—26no—
1195C22⋊C4—22no—
1196C22⋊C4—26no—
1197C22⋊C4—22no—
1198C22⋊C4—26no—
1199C22⋊C4—22no—
1200C22⋊C4—43no—
1201C22⋊C4—46no—
1202C22⋊C4—43no—
1203C22⋊C4—41no—
1204C22⋊C4—43no—
1205C22⋊C4—43no—
1206C22⋊C4—46no—
1207C22⋊C4—43no—
1208C22⋊C4—43no—
1209C22⋊C4—46no—
1210C22⋊C4—46no—
1211C22⋊C4—43no—
1212C22⋊C4—43no—
1213C22⋊C4—43no—
1214C22⋊C4C22×D4124yes—
1215C22⋊C4C22×D414yes—
1216C22⋊C4C22×D4112yes—
1217C42—22no—
1218C42—26no—
1219C42—26no—
1220C42—26no—
1221C42—26no—
1222C42—26no—
1223C42—26no—
1224C42—26no—
1225C42—212no—
1226C42—212no—
1227C42—26no—
1228C42—26no—
1229C42—26no—
1230C42—212no—
1231C42—26no—
1232C42—26no—
1233C42—22no—
1234C42—43no—
1235C42—43no—
1236C42—43no—
1237C42C22×D4112yes—
1238C42C2×#41112yes—
1239C23—21no—
1240C23—23no—
1241C23—21no—
1242C23—23no—
1243C23—21no—
1244C23—23no—
1245C23—23no—
1246C23—23no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—23no—
1251C23—21no—
1252C23—23no—
1253C23—23no—
1254C23—21no—
1255C23—21no—
1256C23—23no—
1257C23—21no—
1258C23—23no—
1259C23—21no—
1260C23—23no—
1261C23—23no—
1262C23—21no—
1263C23—23no—
1264C23—21no—
1265C23C23×D416yes—
1266C23C23×D412yes—
1267C23C2611yescharacteristic
1268Q8—224no—
1269Q8—44no—
1270Q8—44no—
1271Q8—412no—
1272Q8—812no—
1273Q8—812no—
1274Q8#547116yes—
1275D4—224no—
1276D4—412no—
1277D4—44no—
1278D4—412no—
1279D4—412no—
1280D4—412no—
1281D4—86no—
1282D4—86no—
1283D4—812no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—23no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—23no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—224no—
1303C2×C4—224no—
1304C2×C4—21no—
1305C2×C4—23no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—23no—
1318C2×C4—21no—
1319C2×C4—23no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—23no—
1323C2×C4—21no—
1324C2×C4—23no—
1325C2×C4—21no—
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—23no—
1339C2×C4—23no—
1340C2×C4—23no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—21no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—23no—
1352C2×C4—23no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—412no—
1356C2×C4—44no—
1357C2×C4—412no—
1358C2×C4—412no—
1359C2×C4—412no—
1360C2×C4—812no—
1361C2×C4—812no—
1362C2×C4—86no—
1363C2×C4—812no—
1364C2×C4C23×D416yes—
1365C2×C4C23×D412yes—
1366C2×C4C23×D416yes—
1367C2×C4C23×D412yes—
1368C2×C4C23×D416yes—
1369C2×C4C22×#4116yes—
1370C2×C4C22×#4112yes—
1371C2×C4C22×#4116yes—
1372C2×C4C2×2−1+412yes—
1373C2×C4C2×2−1+412yes—
1374C2×C4C2×2−1+412yes—
1375C2×C4C2×2−1+416yes—
1376C22—22no—
1377C22—26no—
1378C22—22no—
1379C22—26no—
1380C22—22no—
1381C22—26no—
1382C22—41no—
1383C22—43no—
1384C22—41no—
1385C22—43no—
1386C22—43no—
1387C22—41no—
1388C22—41no—
1389C22—43no—
1390C22—41no—
1391C22—43no—
1392C22—43no—
1393C22—41no—
1394C22—41no—
1395C22—43no—
1396C22—43no—
1397C22—41no—
1398C22—41no—
1399C22—43no—
1400C22—41no—
1401C22—43no—
1402C22—41no—
1403C22—43no—
1404C22C24×D411yescharacteristic
1405C22C23×#4111yescharacteristic
1406C22C22×2−1+411yescharacteristic
1407C22C22×2−1+411yescharacteristic
1408C22H(7,𝔽2)11yescharacteristic
1409C22H(7,𝔽2)11yescharacteristic
1410C222−1+611yescharacteristic
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—22no—
1415C4—26no—
1416C4—26no—
1417C4—22no—
1418C4—22no—
1419C4—26no—
1420C4—41no—
1421C4—43no—
1422C4—41no—
1423C4—41no—
1424C4—41no—
1425C4—43no—
1426C4—43no—
1427C4—43no—
1428C4—43no—
1429C4—41no—
1430C4—43no—
1431C4—43no—
1432C4—43no—
1433C4—41no—
1434C4—43no—
1435C4—41no—
1436C4—43no—
1437C4C2×#547112yes—
1438C2—42no—
1439C2—46no—
1440C2—83no—
1441C2—81no—
1442C2C22×#54711yescharacteristic
1443C2#6285211yescharacteristic
1444C2#6285711yescharacteristic
1445C2#6294311yescharacteristic
1446C2D4×2−1+411yescharacteristic
1447C2#6299911yescharacteristic
1448C2#6306111yescharacteristic
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×#3518C2semidirect
2. C2×#3522C2semidirect
3. #59829C2semidirect
4. #59115C2semidirect
5. #59113C2semidirect
6. #52152C2semidirect
7. #45333C2semidirect
8. #45287C2semidirect
9. #45227C2semidirect
10. #45051C2semidirect
11. #44928C2semidirect
12. #44875C2semidirect
13. #39488C2semidirect
14. #39377C2semidirect
15. #38051C2semidirect
16. #38041C2semidirect
17. #37795C2semidirect
18. #37794C2semidirect
19. Q8×C4⋊Q8C2semidirect
20. Q8×#123C2semidirect
21. #36433C2semidirect
22. #35996C2semidirect
23. #35831C2semidirect
24. #35801C2semidirect
25. #35771C2semidirect
26. #35748C2semidirect
27. #35711C2semidirect
28. #34312C2semidirect
29. #34312C2semidirect
30. #34250C2semidirect
31. #34249C2semidirect
258. #548D4semidirect
775. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#35222
#598292
#591152
#591132
#521522
#453332
#452872
#452272
#450512
#449282
#448752
#394882
#393772
#380512
#380412
#377952
#377942
Q8×C4⋊Q82
Q8×#1232
#364332
#359962
#358312
#358012
#357712
#357482
#357112
#343122
#342502
#342492