Finite Group Databasebeta

← #7692402

Subgroups — #7692402

Order 512.

7394 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#59313C213yesmaximal, complemented
4#59113C213yesmaximal, complemented
5#59112C213yesmaximal, complemented
6#59072C213yesmaximal, complemented
7#59031C213yesmaximal, complemented
8#45077C213yesmaximal, complemented
9#45016C213yesmaximal, complemented
10#44964C213yesmaximal, complemented
11#44921C213yesmaximal, complemented
12#38043C213yesmaximal, complemented
13#37863C213yesmaximal, complemented
14#37795C213yesmaximal, complemented
15#37766C213yesmaximal, complemented
16Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
17#36483C211yesmaximal, characteristic, complemented
18#36482C211yesmaximal, characteristic, complemented
19#36434C211yesmaximal, characteristic, complemented
20#36433C211yesmaximal, characteristic, complemented
21#36259C213yesmaximal, complemented
22#36139C213yesmaximal, complemented
23#35996C211yesmaximal, characteristic, complemented
24#35937C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#35816C211yesmaximal, characteristic, complemented
27#34735C213yesmaximal, complemented
28#34294C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34250C211yesmaximal, characteristic, complemented
31C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
32#3522—216no—
33#3482—216no—
34C2×#559C2213yes—
35C2×Q82C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#556C2213yes—
38C2×#554C2213yes—
39C2×#552C2213yes—
40C2×#552C2213yes—
41C2×#550C2211yescharacteristic
42C2×D4×Q8C2211yescharacteristic
43C2×#548C2211yescharacteristic
44C2×#548C2211yescharacteristic
45C2×#548C2211yescharacteristic
46C2×#548C2211yescharacteristic
47C2×#547C2213yes—
48C2×#547C2213yes—
49C2×#547C2213yes—
50C2×#547C2216yes—
51C2×#542C2213yes—
52C2×#542C2213yes—
53C2×#533C2213yes—
54C2×#532C2213yes—
55C2×#529C2213yes—
56C2×#529C2213yes—
57C2×#529C2213yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62C2×C4×#41C2213yes—
63C22×C4×Q8C2211yescharacteristic
64C22×C4×Q8C2211yescharacteristic
65C22×C4×Q8C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2857C2213yes—
68#2855C2213yes—
69#2854C2213yes—
70#2854C2213yes—
71#2850C2213yes—
72#2726C2216yes—
73#2725C2216yes—
74#2722C2216yes—
75#2720C2216yes—
76#2720C2216yes—
77#2718C2216yes—
78#2718C2216yes—
79#2715C2216yes—
80#2695C2216yes—
81#2689C2216yes—
82#2680C2216yes—
83#2680C2216yes—
84#2674C2216yes—
85#2672C2216yes—
86#2660C2213yes—
87#2629C2213yes—
88#2625C2213yes—
89#2620C2213yes—
90#2584C2213yes—
91#2582C2213yes—
92#2567C2213yes—
93#2566C2213yes—
94#2551C2213yes—
95#2551C2213yes—
96#2550C2213yes—
97#2550C2213yes—
98#2546C2213yes—
99#2545C2213yes—
100#2544C2213yes—
101#2538C2213yes—
102#2537C2213yes—
103#2536C2213yes—
104#2521C2216yes—
105#2503C2213yes—
106#2502C2213yes—
107#2501C2213yes—
108#2500C2213yes—
109#2486C2213yes—
110#2486C2213yes—
111#2486C2213yes—
112#2486C2216yes—
113#2485C2213yes—
114#2479C2213yes—
115#2478C2213yes—
116#2475C2213yes—
117#2474C2216yes—
118#2474C2213yes—
119#2470C2216yes—
120#2469C2213yes—
121#2468C2216yes—
122#2468C2213yes—
123#2462C2213yes—
124#2461C2213yes—
125#2455C2216yes—
126#2454C2213yes—
127#2452C2213yes—
128#2451C2213yes—
129#2451C2213yes—
130#2449C2216yes—
131#2449C2211yescharacteristic
132#2448C2213yes—
133#2448C2213yes—
134#2447C2213yes—
135#2447C2213yes—
136#2446C2213yes—
137#2446C2213yes—
138#2445C2213yes—
139#2445C2213yes—
140#2443C2213yes—
141#2442C2213yes—
142#2440C2216yes—
143#2440C2213yes—
144#2440C2213yes—
145#2440C2213yes—
146#2438C2216yes—
147#2438C2213yes—
148#2430C2213yes—
149#2429C2213yes—
150#2429C2216yes—
151#2428C2213yes—
152#2427C2213yes—
153#2426C2213yes—
154#2425C2216yes—
155#2425C2216yes—
156#2425C2213yes—
157#2423C2213yes—
158#2423C2213yes—
159#2422C2213yes—
160#2422C2213yes—
161#2422C2213yes—
162#2422C2216yes—
163#2421C2213yes—
164#2421C2213yes—
165#2420C2213yes—
166#2419C2213yes—
167#2417C2213yes—
168#2417C2213yes—
169#2416C2213yes—
170#2416C2213yes—
171#2415C2216yes—
172#2413C2216yes—
173#2413C2216yes—
174#2413C2213yes—
175#2406C2216yes—
176#2406C2216yes—
177#2406C2213yes—
178#2399C2213yes—
179#2396C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2367C2213yes—
183#2367C2213yes—
184#2361C2213yes—
185#2361C2213yes—
186#2360C2213yes—
187#2360C2213yes—
188#2359C2216yes—
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192Q8×C4⋊C4C2213yes—
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2213yes—
196Q8×C4⋊C4C2213yes—
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2213yes—
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203#2349C2213yes—
204#2349C2213yes—
205D4×C4⋊C4C2213yes—
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208D4×C4⋊C4C2213yes—
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217#2339C2216yes—
218#2326C2213yes—
219#2326C2213yes—
220#2323C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231#2296C2213yes—
232C2×#389C2213yes—
233C2×#389C2213yes—
234C2×#389C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237C2×#384C2213yes—
238#2276C2211yescharacteristic
239C2×C4×C4⋊C4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2313yes—
242C22×#41C2311yescharacteristic
243C22×#41C2316yes—
244C23×Q8C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246#559—224no—
247Q82—28no—
248#557—28no—
249#556—224no—
250#554—224no—
251#552—224no—
252#552—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#547—224no—
262#547—424no—
263#542—224no—
264#542—224no—
265#533—224no—
266#532—224no—
267C2×C4⋊Q8C2313yes—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2316yes—
273C2×#127C2313yes—
274#529—224no—
275#529—224no—
276#529—224no—
277C2×#126C2313yes—
278C2×#126C2313yes—
279C2×#126C2316yes—
280C2×#126C2316yes—
281C2×#125C2313yes—
282C2×#125C2313yes—
283C2×#125C2313yes—
284C2×#125C2316yes—
285C2×#124C2313yes—
286C2×#124C2313yes—
287C2×#124C2313yes—
288C2×#124C2316yes—
289C2×#124C2313yes—
290C2×#124C2313yes—
291C2×#123C2313yes—
292C2×#123C2316yes—
293C2×#123C2313yes—
294C2×#123C2313yes—
295C2×#123C2313yes—
296C2×#123C2316yes—
297C2×#123C2316yes—
298C2×#123C2316yes—
299C2×#123C2316yes—
300C2×#123C2316yes—
301C2×#123C2313yes—
302C2×#123C2316yes—
303C2×C22⋊Q8C2313yes—
304C2×C22⋊Q8C2313yes—
305C2×C22⋊Q8C2313yes—
306C2×C22⋊Q8C2316yes—
307C2×C22⋊Q8C2311yescharacteristic
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2316yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2316yes—
312C2×C22⋊Q8C2311yescharacteristic
313C2×C22⋊Q8C2316yes—
314C2×C22⋊Q8C2316yes—
315C2×C22⋊Q8C2313yes—
316C2×#121C2313yes—
317C2×#121C2313yes—
318C2×#121C2313yes—
319C2×#121C2313yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2316yes—
324C2×#121C2313yes—
325#520—28no—
326#520—28no—
327#520—28no—
328C4×#41—28no—
329C4×#41—224no—
330C2×C4×Q8—28no—
331C2×C4×Q8—28no—
332C2×C4×Q8—28no—
333C2×C4×Q8—28no—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2313yes—
347C2×C4×Q8C2313yes—
348C2×C4×Q8C2313yes—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2313yes—
353C2×C4×Q8C2313yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×D4C2313yes—
357C2×C4×D4C2313yes—
358C2×C4×D4C2313yes—
359C2×C4×D4C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2316yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2316yes—
374C2×C4×D4C2316yes—
375C2×C4×D4C2313yes—
376C2×#117C2313yes—
377C2×#117C2313yes—
378C2×#117C2313yes—
379C2×#117C2313yes—
380C2×#117C2316yes—
381C2×#117C2313yes—
382C2×#117C2313yes—
383C2×#117C2313yes—
384C22×C4⋊C4C2313yes—
385C22×C4⋊C4C2313yes—
386C22×C4⋊C4C2313yes—
387C22×C4⋊C4C2313yes—
388C22×C4⋊C4C2313yes—
389C22×C4⋊C4C2313yes—
390C22×C4⋊C4C2313yes—
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2316yes—
393C22×C4⋊C4C2313yes—
394C22×C4⋊C4C2316yes—
395C22×C42C2313yes—
396C22×C42C2313yes—
397C22×C42C2313yes—
398C22×C42C2313yes—
399C22×C42C2313yes—
400#400C2313yes—
401#400C2313yes—
402#400C2316yes—
403#400C2316yes—
404#399C2311yescharacteristic
405#399C2313yes—
406#399C2316yes—
407#399C2316yes—
408#398C2316yes—
409#398C2316yes—
410#398C2316yes—
411#398C2316yes—
412#398C2313yes—
413#398C2316yes—
414#398C2313yes—
415#398C2313yes—
416#398C2311yescharacteristic
417#398C2313yes—
418#398C2313yes—
419#398C2313yes—
420#398C2313yes—
421#398C2316yes—
422#398C2316yes—
423#398C2316yes—
424#397C2316yes—
425#397C2316yes—
426#397C2313yes—
427#397C2313yes—
428#397C2313yes—
429#397C2313yes—
430#397C2316yes—
431#397C2316yes—
432#397C2316yes—
433#396C2313yes—
434#396C2316yes—
435#396C2313yes—
436#396C2316yes—
437#396C2316yes—
438#396C2311yescharacteristic
439#396C2313yes—
440#396C2316yes—
441#396C2316yes—
442#395C2316yes—
443#395C2316yes—
444#395C2313yes—
445#395C2313yes—
446#395C2311yescharacteristic
447#395C2313yes—
448#395C2313yes—
449#395C2316yes—
450#395C2316yes—
451#394C2316yes—
452#394C2316yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2316yes—
459#394C2316yes—
460#394C2316yes—
461#394C2316yes—
462#393C2313yes—
463#392C2313yes—
464#391C2313yes—
465#391C2313yes—
466#391C2313yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2313yes—
472#391C2313yes—
473#391C2316yes—
474#391C2316yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#389C2313yes—
485#389C2316yes—
486#389C2313yes—
487#389C2316yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2316yes—
494#389C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2316yes—
501#389C2316yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2313yes—
508#389C2313yes—
509#389C2313yes—
510#389C2316yes—
511#389C2313yes—
512#389C2316yes—
513#389C2316yes—
514#389C2313yes—
515#389C2316yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2311yescharacteristic
520#388C2316yes—
521#388C2316yes—
522#388C2316yes—
523#388C2316yes—
524#388C2313yes—
525#388C2313yes—
526#388C2316yes—
527#388C2316yes—
528#388C2313yes—
529#388C2316yes—
530#388C2316yes—
531#388C2316yes—
532#388C2313yes—
533#388C2313yes—
534#388C2313yes—
535#388C2313yes—
536#388C2313yes—
537#388C2313yes—
538#388C2313yes—
539#388C2313yes—
540#388C2313yes—
541#387C2313yes—
542#387C2313yes—
543#387C2316yes—
544#387C2316yes—
545#387C2313yes—
546#387C2313yes—
547#387C2313yes—
548#387C2313yes—
549#387C2313yes—
550#387C2313yes—
551#387C2313yes—
552#387C2313yes—
553#387C2313yes—
554#387C2311yescharacteristic
555#386C2313yes—
556#386C2316yes—
557#386C2313yes—
558#386C2316yes—
559#386C2316yes—
560#386C2316yes—
561#386C2313yes—
562#386C2313yes—
563#386C2313yes—
564#386C2311yescharacteristic
565#386C2313yes—
566#386C2311yescharacteristic
567#386C2313yes—
568#385C2316yes—
569#385C2316yes—
570#385C2316yes—
571#385C2316yes—
572#385C2316yes—
573#385C2316yes—
574#385C2316yes—
575#385C2316yes—
576#385C2313yes—
577#385C2313yes—
578#385C2313yes—
579#385C2313yes—
580#385C2313yes—
581#385C2313yes—
582#385C2313yes—
583#385C2316yes—
584#385C2313yes—
585#385C2313yes—
586#385C2316yes—
587#385C2311yescharacteristic
588#385C2311yescharacteristic
589#385C2313yes—
590#385C2311yescharacteristic
591#384C2313yes—
592#384C2313yes—
593#384C2313yes—
594#384C2313yes—
595#384C2313yes—
596#384C2313yes—
597#384C2316yes—
598#384C2316yes—
599#384C2313yes—
600#382C2313yes—
601#382C2313yes—
602#382C2313yes—
603#381C2316yes—
604#381C2316yes—
605#381C2313yes—
606#381C2313yes—
607#381C2313yes—
608#380C2316yes—
609#380C2316yes—
610#380C2313yes—
611#380C2313yes—
612#380C2316yes—
613#380C2313yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2313yes—
618#380C2313yes—
619#380C2313yes—
620#380C2313yes—
621#380C2316yes—
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⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C4⋊C4C2313yes—
638C4×C4⋊C4C2313yes—
639C4×C22⋊C4C2316yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2316yes—
649#376C2313yes—
650C2×#95C2313yes—
651C2×#95C2316yes—
652C2×#95C2313yes—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—212no—
659C2×#41—224no—
660C2×#41—212no—
661C2×#41—46no—
662C2×#41—412no—
663C2×#41—412no—
664C2×#41C2×D418yes—
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8—24no—
668C22×Q8—24no—
669C22×Q8—24no—
670C22×Q8C2×D418yes—
671C22×Q8C2413yes—
672C22×Q8C2411yescharacteristic
673C22×Q8C2413yes—
674C22×Q8C2413yes—
675C22×Q8C2416yes—
676C22×Q8C2411yescharacteristic
677C22×D4C2413yes—
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2411yescharacteristic
685C22×D4C2416yes—
686C23×C4C2413yes—
687C23×C4C2413yes—
688C23×C4C2411yescharacteristic
689C23×C4C2413yes—
690C23×C4C2413yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2411yescharacteristic
695C23×C4C2411yescharacteristic
696C23×C4C2413yes—
697C23×C4C2411yescharacteristic
698C23×C4C2413yes—
699C23×C4C2413yes—
700C23×C4C2416yes—
701C23×C4C2416yes—
702C23×C4C2416yes—
703C4⋊Q8—212no—
704C4⋊Q8—212no—
705C4⋊Q8—212no—
706C4⋊Q8—212no—
707C4⋊Q8—212no—
708C4⋊Q8—412no—
709#127—212no—
710#126—212no—
711#126—212no—
712#126—224no—
713#126—224no—
714#125—212no—
715#125—212no—
716#125—224no—
717#125—212no—
718#124—212no—
719#124—212no—
720#124—212no—
721#124—224no—
722#124—212no—
723#124C2×D4124yes—
724#123—212no—
725#123—224no—
726#123—212no—
727#123—212no—
728#123—212no—
729#123—224no—
730#123—224no—
731#123—224no—
732#123—412no—
733#123—412no—
734#123—46no—
735#123—412no—
736C22⋊Q8—212no—
737C22⋊Q8—212no—
738C22⋊Q8—212no—
739C22⋊Q8—212no—
740C22⋊Q8—224no—
741C22⋊Q8—212no—
742C22⋊Q8—24no—
743C22⋊Q8—24no—
744C22⋊Q8—224no—
745C22⋊Q8—224no—
746C22⋊Q8—412no—
747C22⋊Q8—412no—
748C22⋊Q8C2×D4124yes—
749#121—212no—
750#121—212no—
751#121—212no—
752#121—212no—
753#121—212no—
754#121—212no—
755#121—212no—
756#121—412no—
757#121C2×D4124yes—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—212no—
761C4×Q8—212no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—212no—
765C4×Q8—212no—
766C4×Q8—24no—
767C4×Q8—24no—
768C4×Q8—24no—
769C4×Q8—24no—
770C4×Q8—24no—
771C4×Q8—212no—
772C4×Q8—212no—
773C4×Q8—212no—
774C4×Q8—212no—
775C4×Q8—212no—
776C4×Q8—212no—
777C4×Q8—212no—
778C4×Q8C2×D418yes—
779C4×Q8#4118yescomplemented
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—212no—
790C4×D4—212no—
791C4×D4—24no—
792C4×D4—212no—
793C4×D4—224no—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—212no—
797C4×D4—412no—
798C4×D4—412no—
799C4×D4C2×D4124yes—
800#117—212no—
801#117—212no—
802#117—212no—
803#117—212no—
804#117—212no—
805#117—224no—
806#117—212no—
807#117—212no—
808C2×C4⋊C4—212no—
809C2×C4⋊C4—212no—
810C2×C4⋊C4—212no—
811C2×C4⋊C4—212no—
812C2×C4⋊C4—212no—
813C2×C4⋊C4—212no—
814C2×C4⋊C4—212no—
815C2×C4⋊C4—24no—
816C2×C4⋊C4—412no—
817C2×C4⋊C4—46no—
818C2×C4⋊C4—412no—
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⋊C4C2416yes—
831C2×C4⋊C4C2416yes—
832C2×C4⋊C4C2416yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2416yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2416yes—
848C2×C4⋊C4C2416yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2413yes—
859C2×C4⋊C4C2413yes—
860C2×C4⋊C4C2416yes—
861C2×C4⋊C4C2416yes—
862C2×C4⋊C4C2416yes—
863C2×C4⋊C4C2416yes—
864C2×C4⋊C4C2416yes—
865C2×C4⋊C4C2413yes—
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2416yes—
870C2×C4⋊C4C2416yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2413yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2413yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2413yes—
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2413yes—
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2416yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2416yes—
893C2×C22⋊C4C2411yescharacteristic
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2413yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2416yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2413yes—
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2416yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2413yes—
910C2×C22⋊C4C2413yes—
911C2×C22⋊C4C2413yes—
912C2×C22⋊C4C2416yes—
913C2×C22⋊C4C2416yes—
914C2×C22⋊C4C2416yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2413yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2416yes—
921C2×C22⋊C4C2411yescharacteristic
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2416yes—
924C2×C42—212no—
925C2×C42—212no—
926C2×C42—212no—
927C2×C42—212no—
928C2×C42—212no—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2413yes—
940C2×C42C2413yes—
941C2×C42C2413yes—
942C2×C42C2411yescharacteristic
943C2×C42C2413yes—
944C2×C42C2413yes—
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2413yes—
948C2×C42C2416yes—
949C2×C42C2413yes—
950C2×C42C2413yes—
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2413yes—
958#95C2413yes—
959#95C2413yes—
960#95C2416yes—
961#95C2416yes—
962#95C2411yescharacteristic
963#95C2413yes—
964#95C2413yes—
965#95C2413yes—
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2416yes—
976#95C2416yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2411yescharacteristic
986#95C2411yescharacteristic
987#95C2411yescharacteristic
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2413yes—
995#95C2416yes—
996#95C2416yes—
997#95C2416yes—
998C24C2513yes—
999C24C2513yes—
1000C24C2511yescharacteristic
1001C24C2511yescharacteristic
1002#41—232no—
1003#41—448no—
1004#41—416no—
1005#41—848no—
1006C2×Q8—232no—
1007C2×Q8—22no—
1008C2×Q8—26no—
1009C2×Q8—26no—
1010C2×Q8—212no—
1011C2×Q8—26no—
1012C2×Q8—26no—
1013C2×Q8—26no—
1014C2×Q8—26no—
1015C2×Q8—22no—
1016C2×Q8—26no—
1017C2×Q8—41no—
1018C2×Q8—43no—
1019C2×Q8—46no—
1020C2×Q8—46no—
1021C2×Q8—416no—
1022C2×Q8C22×D4112yes—
1023C2×Q8C22×D414yes—
1024C2×Q8C2×#4114yes—
1025C2×Q82−1+414yes—
1026C2×D4—22no—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—22no—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—26no—
1037C2×D4—212no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—26no—
1043C2×D4—26no—
1044C2×D4—26no—
1045C2×D4—43no—
1046C2×D4—43no—
1047C2×D4—43no—
1048C2×D4—46no—
1049C2×D4—46no—
1050C2×D4C22×D4112yes—
1051C2×D4C22×D4112yes—
1052C2×D4H(5,𝔽2)14yes—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—22no—
1058C22×C4—26no—
1059C22×C4—26no—
1060C22×C4—22no—
1061C22×C4—22no—
1062C22×C4—26no—
1063C22×C4—26no—
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—212no—
1073C22×C4—22no—
1074C22×C4—26no—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—26no—
1080C22×C4—26no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—26no—
1085C22×C4—26no—
1086C22×C4—26no—
1087C22×C4—212no—
1088C22×C4—212no—
1089C22×C4—41no—
1090C22×C4—43no—
1091C22×C4—41no—
1092C22×C4—43no—
1093C22×C4—41no—
1094C22×C4—43no—
1095C22×C4—43no—
1096C22×C4—46no—
1097C22×C4—46no—
1098C22×C4—46no—
1099C22×C4—46no—
1100C22×C4—46no—
1101C22×C4—46no—
1102C22×C4C22×D4112yes—
1103C22×C4C22×D4112yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C22×C4C2513yes—
1107C22×C4C2513yes—
1108C22×C4C2513yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2513yes—
1114C22×C4C2513yes—
1115C22×C4C2513yes—
1116C22×C4C2513yes—
1117C22×C4C2513yes—
1118C22×C4C2513yes—
1119C22×C4C2513yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2513yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2513yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2513yes—
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2513yes—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—26no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—212no—
1139C4⋊C4—212no—
1140C4⋊C4—212no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—26no—
1145C4⋊C4—26no—
1146C4⋊C4—26no—
1147C4⋊C4—26no—
1148C4⋊C4—26no—
1149C4⋊C4—212no—
1150C4⋊C4—212no—
1151C4⋊C4—22no—
1152C4⋊C4—26no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—212no—
1159C4⋊C4—26no—
1160C4⋊C4—22no—
1161C4⋊C4—26no—
1162C4⋊C4—26no—
1163C4⋊C4—26no—
1164C4⋊C4—26no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—26no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—26no—
1172C4⋊C4—46no—
1173C4⋊C4—43no—
1174C4⋊C4—43no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—46no—
1178C4⋊C4—46no—
1179C4⋊C4—46no—
1180C4⋊C4—46no—
1181C4⋊C4—43no—
1182C4⋊C4—43no—
1183C4⋊C4—41no—
1184C4⋊C4—43no—
1185C4⋊C4—46no—
1186C4⋊C4—43no—
1187C4⋊C4—43no—
1188C4⋊C4—46no—
1189C4⋊C4C22×D4112yes—
1190C4⋊C4C22×D4112yes—
1191C4⋊C4C2×#41112yes—
1192C4⋊C42−1+414yes—
1193C22⋊C4—26no—
1194C22⋊C4—26no—
1195C22⋊C4—26no—
1196C22⋊C4—212no—
1197C22⋊C4—26no—
1198C22⋊C4—212no—
1199C22⋊C4—22no—
1200C22⋊C4—26no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—26no—
1204C22⋊C4—26no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—26no—
1208C22⋊C4—26no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—212no—
1212C22⋊C4—26no—
1213C22⋊C4—26no—
1214C22⋊C4—26no—
1215C22⋊C4—22no—
1216C22⋊C4—26no—
1217C22⋊C4—212no—
1218C22⋊C4—26no—
1219C22⋊C4—22no—
1220C22⋊C4—22no—
1221C22⋊C4—26no—
1222C22⋊C4—26no—
1223C22⋊C4—26no—
1224C22⋊C4—43no—
1225C22⋊C4—41no—
1226C22⋊C4—46no—
1227C22⋊C4—43no—
1228C22⋊C4—46no—
1229C22⋊C4—46no—
1230C22⋊C4—46no—
1231C22⋊C4—43no—
1232C22⋊C4—43no—
1233C22⋊C4C22×D414yes—
1234C22⋊C4C22×D4112yes—
1235C22⋊C4C22×D4124yes—
1236C42—22no—
1237C42—26no—
1238C42—26no—
1239C42—26no—
1240C42—26no—
1241C42—26no—
1242C42—26no—
1243C42—26no—
1244C42—26no—
1245C42—26no—
1246C42—26no—
1247C42—26no—
1248C42—26no—
1249C42—26no—
1250C42—26no—
1251C42—26no—
1252C42—26no—
1253C42—26no—
1254C42—26no—
1255C42—46no—
1256C42C22×D4112yes—
1257C42C2×#41112yes—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—21no—
1262C23—21no—
1263C23—23no—
1264C23—21no—
1265C23—23no—
1266C23—21no—
1267C23—23no—
1268C23—21no—
1269C23—23no—
1270C23—21no—
1271C23—23no—
1272C23—23no—
1273C23—21no—
1274C23—23no—
1275C23—23no—
1276C23—23no—
1277C23—23no—
1278C23—23no—
1279C23—23no—
1280C23—23no—
1281C23C23×D416yes—
1282C23C23×D412yes—
1283C23C2×H(5,𝔽2)12yes—
1284C23C2×H(5,𝔽2)12yes—
1285C23#58512yes—
1286C23C2611yescharacteristic
1287Q8—224no—
1288Q8—44no—
1289Q8—412no—
1290Q8—412no—
1291Q8—812no—
1292Q8#547116yescomplemented
1293D4—224no—
1294D4—28no—
1295D4—224no—
1296D4—412no—
1297D4—412no—
1298D4—412no—
1299D4—412no—
1300D4—412no—
1301D4—812no—
1302C2×C4—28no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—23no—
1308C2×C4—21no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—23no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—23no—
1319C2×C4—21no—
1320C2×C4—23no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—224no—
1324C2×C4—224no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—23no—
1328C2×C4—21no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—23no—
1340C2×C4—21no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—23no—
1349C2×C4—21no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—21no—
1353C2×C4—23no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—23no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—23no—
1365C2×C4—23no—
1366C2×C4—21no—
1367C2×C4—23no—
1368C2×C4—21no—
1369C2×C4—23no—
1370C2×C4—21no—
1371C2×C4—23no—
1372C2×C4—21no—
1373C2×C4—44no—
1374C2×C4—412no—
1375C2×C4—44no—
1376C2×C4—412no—
1377C2×C4—44no—
1378C2×C4—412no—
1379C2×C4—412no—
1380C2×C4—412no—
1381C2×C4—412no—
1382C2×C4—412no—
1383C2×C4—412no—
1384C2×C4—812no—
1385C2×C4—812no—
1386C2×C4—812no—
1387C2×C4C23×D416yes—
1388C2×C4C23×D412yes—
1389C2×C4C23×D412yes—
1390C2×C4C23×D416yes—
1391C2×C4C23×D416yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4116yes—
1394C2×C4C22×#4116yes—
1395C2×C4C2×H(5,𝔽2)12yes—
1396C2×C4C2×2−1+412yes—
1397C2×C4C2×2−1+412yes—
1398C2×C4C2×2−1+412yes—
1399C2×C4C2×2−1+416yes—
1400C22—22no—
1401C22—22no—
1402C22—22no—
1403C22—22no—
1404C22—22no—
1405C22—22no—
1406C22—22no—
1407C22—26no—
1408C22—22no—
1409C22—22no—
1410C22—26no—
1411C22—26no—
1412C22—43no—
1413C22—41no—
1414C22—43no—
1415C22—43no—
1416C22—41no—
1417C22—41no—
1418C22—43no—
1419C22—41no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22—43no—
1424C22—43no—
1425C22—43no—
1426C22—43no—
1427C22#348814yes—
1428C22C24×D411yescharacteristic
1429C22C23×#4111yescharacteristic
1430C22C22×H(5,𝔽2)11yescharacteristic
1431C22C22×2−1+411yescharacteristic
1432C22C22×2−1+411yescharacteristic
1433C22C2×#58511yescharacteristic
1434C222−1+611yescharacteristic
1435C4—26no—
1436C4—22no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—26no—
1443C4—22no—
1444C4—26no—
1445C4—43no—
1446C4—43no—
1447C4—41no—
1448C4—41no—
1449C4—43no—
1450C4—41no—
1451C4—43no—
1452C4—41no—
1453C4—43no—
1454C4—43no—
1455C4—43no—
1456C4—43no—
1457C4—43no—
1458C4—41no—
1459C4—41no—
1460C4—43no—
1461C4C2×#547112yes—
1462C2—24no—
1463C2—42no—
1464C2—46no—
1465C2—83no—
1466C2C22×#54711yescharacteristic
1467C2#6278811yescharacteristic
1468C2C2×#348811yescharacteristic
1469C2#6294911yescharacteristic
1470C2#6298511yescharacteristic
1471C2D4×2−1+411yescharacteristic
1472C2#6303711yescharacteristic
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×#3522C2semidirect
2. C2×#3482C2semidirect
3. #59313C2semidirect
4. #59113C2semidirect
5. #59112C2semidirect
6. #59072C2semidirect
7. #59031C2semidirect
8. #45077C2semidirect
9. #45016C2semidirect
10. #44964C2semidirect
11. #44921C2semidirect
12. #38043C2semidirect
13. #37863C2semidirect
14. #37795C2semidirect
15. #37766C2semidirect
16. Q8×C22⋊Q8C2semidirect
17. #36483C2semidirect
18. #36482C2semidirect
19. #36434C2semidirect
20. #36433C2semidirect
21. #36259C2semidirect
22. #36139C2semidirect
23. #35996C2semidirect
24. #35937C2semidirect
25. #35831C2semidirect
26. #35816C2semidirect
27. #34735C2semidirect
28. #34294C2semidirect
29. #34294C2semidirect
30. #34250C2semidirect
31. C2×Q8×C4⋊C4C2semidirect
258. #548D4semidirect
779. C4×Q8#41semidirect
1292. Q8#547semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×#34822
#593132
#591132
#591122
#590722
#590312
#450772
#450162
#449642
#449212
#380432
#378632
#377952
#377662
Q8×C22⋊Q82
#364832
#364822
#364342
#364332
#362592
#361392
#359962
#359372
#358312
#358162
#347352
#342942
#342502
C2×Q8×C4⋊C42