Finite Group Databasebeta

← #7689237

Subgroups — #7689237

Order 512.

6955 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3502C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#59658C213yesmaximal, complemented
4#59137C213yesmaximal, complemented
5#59085C213yesmaximal, complemented
6#59084C213yesmaximal, complemented
7#59082C213yesmaximal, complemented
8#45338C213yesmaximal, complemented
9#45313C213yesmaximal, complemented
10#45159C213yesmaximal, complemented
11#45098C213yesmaximal, complemented
12#39718C213yesmaximal, complemented
13#39164C213yesmaximal, complemented
14#37759C213yesmaximal, complemented
15#37756C213yesmaximal, complemented
16#36505C213yesmaximal, complemented
17#36467C211yesmaximal, characteristic, complemented
18#36456C211yesmaximal, characteristic, complemented
19#36435C211yesmaximal, characteristic, complemented
20#36434C211yesmaximal, characteristic, complemented
21#36431C211yesmaximal, characteristic, complemented
22#36142C213yesmaximal, complemented
23#36049C211yesmaximal, characteristic, complemented
24#36018C211yesmaximal, characteristic, complemented
25#35948C211yesmaximal, characteristic, complemented
26#35771C211yesmaximal, characteristic, complemented
27#34720C213yesmaximal, complemented
28#34336C211yesmaximal, characteristic, complemented
29#34293C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32#3502—216no—
33#3480—216no—
34C2×#559C2213yes—
35C2×Q82C2213yes—
36C2×Q82C2211yescharacteristic
37C2×#557C2213yes—
38C2×#557C2213yes—
39C2×#557C2211yescharacteristic
40C2×#557C2211yescharacteristic
41C2×#557C2213yes—
42C2×#557C2211yescharacteristic
43C2×#556C2213yes—
44C2×#553C2213yes—
45C2×#553C2213yes—
46C2×#550C2211yescharacteristic
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2211yescharacteristic
51C2×#548C2211yescharacteristic
52C2×#544C2213yes—
53C2×#544C2213yes—
54C2×#533C2213yes—
55C2×#533C2213yes—
56C2×#532C2213yes—
57C2×#529C2213yes—
58C2×#529C2213yes—
59C2×#519C2211yescharacteristic
60C2×#519C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2213yes—
64C22×C4×Q8C2211yescharacteristic
65C22×C4×Q8C2211yescharacteristic
66#2861C2213yes—
67#2857C2213yes—
68#2851C2213yes—
69#2851C2213yes—
70#2850C2213yes—
71#2731C2216yes—
72#2731C2216yes—
73#2731C2216yes—
74#2730C2216yes—
75#2725C2216yes—
76#2716C2216yes—
77#2716C2216yes—
78#2711C2216yes—
79#2707C2216yes—
80#2707C2216yes—
81#2702C2216yes—
82#2696C2216yes—
83#2676C2216yes—
84#2674C2216yes—
85#2641C2213yes—
86#2640C2213yes—
87#2620C2213yes—
88#2619C2213yes—
89#2592C2213yes—
90#2592C2213yes—
91#2581C2213yes—
92#2580C2213yes—
93#2566C2213yes—
94#2565C2213yes—
95#2563C2213yes—
96#2562C2213yes—
97#2562C2213yes—
98#2560C2216yes—
99#2558C2216yes—
100#2548C2213yes—
101#2548C2213yes—
102#2547C2213yes—
103#2545C2213yes—
104#2545C2213yes—
105#2538C2213yes—
106#2538C2213yes—
107#2536C2213yes—
108#2536C2213yes—
109#2519C2216yes—
110#2492C2213yes—
111#2492C2213yes—
112#2492C2213yes—
113#2491C2213yes—
114#2491C2213yes—
115#2491C2213yes—
116#2491C2216yes—
117#2491C2213yes—
118#2491C2213yes—
119#2490C2213yes—
120#2490C2213yes—
121#2490C2213yes—
122#2489C2213yes—
123#2477C2213yes—
124#2477C2211yescharacteristic
125#2475C2216yes—
126#2475C2213yes—
127#2475C2213yes—
128#2469C2216yes—
129#2469C2216yes—
130#2463C2213yes—
131#2463C2213yes—
132#2463C2216yes—
133#2461C2216yes—
134#2460C2216yes—
135#2460C2213yes—
136#2460C2216yes—
137#2460C2216yes—
138#2460C2213yes—
139#2458C2216yes—
140#2458C2216yes—
141#2454C2213yes—
142#2453C2213yes—
143#2452C2213yes—
144#2452C2213yes—
145#2452C2213yes—
146#2452C2213yes—
147#2452C2216yes—
148#2451C2213yes—
149#2446C2213yes—
150#2446C2216yes—
151#2442C2213yes—
152#2441C2213yes—
153#2440C2213yes—
154#2439C2213yes—
155#2439C2213yes—
156#2439C2213yes—
157#2439C2213yes—
158#2432C2216yes—
159#2432C2213yes—
160#2429C2213yes—
161#2429C2213yes—
162#2427C2213yes—
163#2426C2216yes—
164#2426C2213yes—
165#2426C2213yes—
166#2426C2213yes—
167#2426C2213yes—
168#2421C2213yes—
169#2417C2213yes—
170#2416C2213yes—
171#2415C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2414C2213yes—
175#2414C2213yes—
176#2407C2213yes—
177#2398C2213yes—
178#2398C2213yes—
179#2392C2213yes—
180#2392C2213yes—
181#2370C2213yes—
182#2370C2213yes—
183#2369C2213yes—
184#2367C2216yes—
185#2367C2216yes—
186#2367C2213yes—
187#2367C2213yes—
188#2365C2213yes—
189#2363C2213yes—
190#2362C2213yes—
191#2362C2213yes—
192#2362C2213yes—
193#2362C2216yes—
194#2361C2213yes—
195#2360C2213yes—
196#2355C2213yes—
197#2354C2213yes—
198#2352C2213yes—
199#2352C2213yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203#2351C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2331C2213yes—
217#2330C2213yes—
218#2327C2213yes—
219#2326C2213yes—
220#2324C2213yes—
221#2323C2213yes—
222C4×#125C2213yes—
223C4×#124C2213yes—
224C4×#124C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×C22⋊Q8C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233#2295C2213yes—
234#2290C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237#2276C2211yescharacteristic
238C42×Q8C2211yescharacteristic
239C42×D4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C23×Q8C2311yescharacteristic
244C23×Q8C2311yescharacteristic
245#559—224no—
246Q82—224no—
247Q82—28no—
248#557—224no—
249#557—224no—
250#557—28no—
251#557—28no—
252#557—224no—
253#557D4116yescomplemented
254#556—224no—
255#553—224no—
256#553—224no—
257#550—28no—
258D4×Q8—28no—
259#548—28no—
260#548—28no—
261#548—28no—
262#548—28no—
263#544—224no—
264#544—224no—
265#533—224no—
266#533—224no—
267#532—224no—
268C2×C4⋊Q8C2313yes—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2316yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2313yes—
277C2×C4⋊Q8C2316yes—
278C2×C4⋊Q8C2313yes—
279C2×#127C2313yes—
280#529—224no—
281#529—224no—
282C2×#126C2316yes—
283C2×#126C2316yes—
284C2×#125C2313yes—
285C2×#125C2313yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#125C2313yes—
289C2×#125C2313yes—
290C2×#125C2316yes—
291C2×#125C2316yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#124C2313yes—
295C2×#124C2313yes—
296C2×#124C2313yes—
297C2×#124C2313yes—
298C2×#124C2316yes—
299C2×#124C2316yes—
300C2×#124C2316yes—
301C2×#124C2313yes—
302C2×#123C2316yes—
303C2×#123C2316yes—
304C2×C22⋊Q8C2316yes—
305C2×C22⋊Q8C2313yes—
306C2×C22⋊Q8C2313yes—
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2311yescharacteristic
315C2×C22⋊Q8C2316yes—
316C2×C22⋊Q8C2313yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×#121C2313yes—
320C2×#121C2313yes—
321C2×#121C2313yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325C2×#121C2316yes—
326C2×#121C2313yes—
327#519—28no—
328#519—28no—
329C4×#41—224no—
330C4×#41—28no—
331C4×#41—28no—
332C2×C4×Q8—28no—
333C2×C4×Q8—28no—
334C2×C4×Q8C2313yes—
335C2×C4×Q8C2313yes—
336C2×C4×Q8C2313yes—
337C2×C4×Q8C2313yes—
338C2×C4×Q8C2313yes—
339C2×C4×Q8C2313yes—
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×Q8C2313yes—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2316yes—
353C2×C4×Q8C2316yes—
354C2×C4×Q8C2313yes—
355C2×C4×Q8C2313yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2313yes—
360C2×C4×D4C2313yes—
361C2×C4×D4C2313yes—
362C2×C4×D4C2313yes—
363C2×C4×D4C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2316yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×#117C2313yes—
377C2×#117C2313yes—
378C2×#117C2313yes—
379C2×#117C2313yes—
380C2×#117C2313yes—
381C2×#117C2313yes—
382C2×#117C2313yes—
383C2×#117C2311yescharacteristic
384C2×#117C2313yes—
385C22×C4⋊C4C2313yes—
386C22×C4⋊C4C2313yes—
387C22×C42C2313yes—
388C22×C42C2313yes—
389C22×C42C2313yes—
390C22×C42C2313yes—
391#400C2313yes—
392#400C2316yes—
393#400C2316yes—
394#400C2311yescharacteristic
395#400C2313yes—
396#400C2313yes—
397#399C2316yes—
398#398C2316yes—
399#398C2316yes—
400#398C2313yes—
401#398C2313yes—
402#398C2316yes—
403#397C2313yes—
404#397C2316yes—
405#397C2316yes—
406#397C2313yes—
407#397C2311yescharacteristic
408#397C2313yes—
409#397C2313yes—
410#397C2313yes—
411#396C2316yes—
412#396C2316yes—
413#396C2316yes—
414#396C2316yes—
415#396C2313yes—
416#396C2313yes—
417#396C2313yes—
418#396C2313yes—
419#396C2316yes—
420#396C2316yes—
421#396C2316yes—
422#396C2316yes—
423#395C2316yes—
424#394C2313yes—
425#394C2316yes—
426#394C2316yes—
427#394C2316yes—
428#394C2316yes—
429#394C2313yes—
430#394C2316yes—
431#394C2313yes—
432#394C2316yes—
433#394C2316yes—
434#394C2311yescharacteristic
435#394C2313yes—
436#394C2313yes—
437#394C2313yes—
438#394C2313yes—
439#394C2313yes—
440#394C2313yes—
441#394C2316yes—
442#393C2316yes—
443#393C2316yes—
444#393C2316yes—
445#393C2313yes—
446#393C2316yes—
447#393C2316yes—
448#393C2316yes—
449#393C2311yescharacteristic
450#393C2313yes—
451#393C2313yes—
452#392C2313yes—
453#392C2316yes—
454#392C2313yes—
455#391C2316yes—
456#391C2313yes—
457#391C2313yes—
458#391C2313yes—
459#391C2313yes—
460#391C2313yes—
461#391C2313yes—
462#391C2313yes—
463#391C2313yes—
464#391C2316yes—
465#391C2313yes—
466#391C2316yes—
467#391C2313yes—
468#391C2313yes—
469#391C2313yes—
470#391C2313yes—
471#391C2311yescharacteristic
472#390C2316yes—
473#390C2313yes—
474#390C2313yes—
475#390C2313yes—
476#390C2313yes—
477#390C2313yes—
478#390C2313yes—
479#390C2313yes—
480#390C2313yes—
481#390C2313yes—
482#390C2313yes—
483#390C2313yes—
484#390C2313yes—
485#390C2316yes—
486#390C2316yes—
487#390C2313yes—
488#390C2316yes—
489#390C2313yes—
490#390C2316yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2313yes—
498#389C2313yes—
499#389C2313yes—
500#389C2316yes—
501#389C2313yes—
502#389C2313yes—
503#389C2313yes—
504#389C2313yes—
505#389C2313yes—
506#389C2313yes—
507#389C2316yes—
508#389C2313yes—
509#389C2313yes—
510#389C2313yes—
511#389C2313yes—
512#388C2316yes—
513#388C2316yes—
514#388C2316yes—
515#388C2313yes—
516#388C2316yes—
517#388C2316yes—
518#388C2313yes—
519#388C2316yes—
520#388C2316yes—
521#388C2316yes—
522#388C2313yes—
523#388C2316yes—
524#388C2316yes—
525#388C2316yes—
526#388C2316yes—
527#388C2313yes—
528#388C2316yes—
529#388C2316yes—
530#388C2313yes—
531#388C2316yes—
532#388C2313yes—
533#388C2316yes—
534#388C2316yes—
535#388C2313yes—
536#388C2316yes—
537#388C2316yes—
538#388C2316yes—
539#388C2311yescharacteristic
540#388C2313yes—
541#388C2311yescharacteristic
542#387C2316yes—
543#387C2313yes—
544#387C2316yes—
545#387C2313yes—
546#387C2316yes—
547#387C2316yes—
548#387C2313yes—
549#387C2313yes—
550#387C2316yes—
551#387C2316yes—
552#387C2316yes—
553#387C2316yes—
554#387C2313yes—
555#387C2316yes—
556#387C2316yes—
557#387C2313yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2313yes—
563#387C2313yes—
564#387C2311yescharacteristic
565#387C2311yescharacteristic
566#386C2316yes—
567#386C2313yes—
568#386C2313yes—
569#386C2313yes—
570#386C2316yes—
571#386C2313yes—
572#386C2311yescharacteristic
573#386C2311yescharacteristic
574#385C2313yes—
575#385C2316yes—
576#385C2316yes—
577#385C2313yes—
578#385C2313yes—
579#385C2313yes—
580#385C2316yes—
581#385C2316yes—
582#385C2313yes—
583#385C2316yes—
584#385C2313yes—
585#385C2313yes—
586#385C2313yes—
587#385C2313yes—
588#385C2311yescharacteristic
589#384C2313yes—
590#384C2313yes—
591#382C2313yes—
592#382C2313yes—
593#382C2313yes—
594#382C2313yes—
595#382C2313yes—
596#380C2313yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2313yes—
602#380C2313yes—
603#380C2313yes—
604#380C2316yes—
605#380C2313yes—
606#380C2313yes—
607#380C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611C4×C4⋊C4C2316yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2316yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
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⋊C4C2316yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C22⋊C4C2313yes—
633C4×C22⋊C4C2313yes—
634C4×C22⋊C4C2313yes—
635C4×C22⋊C4C2313yes—
636C4×C22⋊C4C2313yes—
637C4×C22⋊C4C2313yes—
638C4×C22⋊C4C2313yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2316yes—
644C4×C22⋊C4C2316yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2316yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2311yescharacteristic
649#376C2313yes—
650#376C2313yes—
651C43C2313yes—
652C2×#41—212no—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—46no—
660C2×#41—46no—
661C22×Q8—24no—
662C22×Q8—24no—
663C22×Q8—24no—
664C22×Q8—24no—
665C22×Q8—24no—
666C22×Q8#4118yescomplemented
667C22×Q8C2413yes—
668C22×Q8C2411yescharacteristic
669C22×Q8C2413yes—
670C22×Q8C2413yes—
671C22×Q8C2413yes—
672C22×Q8C2416yes—
673C22×Q8C2413yes—
674C22×Q8C2411yescharacteristic
675C22×D4C2413yes—
676C22×D4C2413yes—
677C22×D4C2411yescharacteristic
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2416yes—
683C22×D4C2413yes—
684C23×C4C2413yes—
685C23×C4C2413yes—
686C23×C4C2413yes—
687C23×C4C2411yescharacteristic
688C23×C4C2413yes—
689C23×C4C2413yes—
690C23×C4C2411yescharacteristic
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C4⋊Q8—212no—
697C4⋊Q8—224no—
698C4⋊Q8—212no—
699C4⋊Q8—212no—
700C4⋊Q8—212no—
701C4⋊Q8—212no—
702C4⋊Q8—224no—
703C4⋊Q8—212no—
704C4⋊Q8—212no—
705C4⋊Q8—212no—
706C4⋊Q8C2×D4124yes—
707#127—212no—
708#126—224no—
709#126—224no—
710#125—212no—
711#125—212no—
712#125—224no—
713#125—224no—
714#125—212no—
715#125—212no—
716#125—212no—
717#125—212no—
718#125C2×D4124yes—
719#125C2×D4124yes—
720#124—224no—
721#124—212no—
722#124—212no—
723#124—212no—
724#124—212no—
725#124—412no—
726#124—46no—
727#124—412no—
728#123—224no—
729#123—224no—
730C22⋊Q8—212no—
731C22⋊Q8—212no—
732C22⋊Q8—212no—
733C22⋊Q8—212no—
734C22⋊Q8—212no—
735C22⋊Q8—212no—
736C22⋊Q8—212no—
737C22⋊Q8—24no—
738C22⋊Q8—212no—
739C22⋊Q8—224no—
740C22⋊Q8—212no—
741C22⋊Q8—46no—
742C22⋊Q8—46no—
743C22⋊Q8—412no—
744C22⋊Q8—46no—
745#121—212no—
746#121—212no—
747#121—212no—
748#121—212no—
749#121—212no—
750#121—212no—
751#121—224no—
752#121—46no—
753C4×Q8—24no—
754C4×Q8—24no—
755C4×Q8—212no—
756C4×Q8—24no—
757C4×Q8—24no—
758C4×Q8—24no—
759C4×Q8—24no—
760C4×Q8—24no—
761C4×Q8—24no—
762C4×Q8—212no—
763C4×Q8—212no—
764C4×Q8—212no—
765C4×Q8—212no—
766C4×Q8—224no—
767C4×Q8—224no—
768C4×Q8—212no—
769C4×Q8—212no—
770C4×Q8—212no—
771C4×Q8—212no—
772C4×Q8—212no—
773C4×Q8—212no—
774C4×Q8—212no—
775C4×Q8C2×D418yes—
776C4×Q8C2×D418yes—
777C4×Q8C2×D418yes—
778C4×Q8C2×D4124yes—
779C4×D4—212no—
780C4×D4—212no—
781C4×D4—212no—
782C4×D4—212no—
783C4×D4—212no—
784C4×D4—212no—
785C4×D4—212no—
786C4×D4—212no—
787C4×D4—224no—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—46no—
794C4×D4—46no—
795#117—24no—
796#117—212no—
797#117—212no—
798#117—212no—
799#117—212no—
800#117—212no—
801#117—212no—
802#117—212no—
803#117—212no—
804C2×C4⋊C4—212no—
805C2×C4⋊C4—212no—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2416yes—
808C2×C4⋊C4C2413yes—
809C2×C4⋊C4C2416yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2413yes—
812C2×C4⋊C4C2413yes—
813C2×C4⋊C4C2413yes—
814C2×C4⋊C4C2413yes—
815C2×C4⋊C4C2413yes—
816C2×C4⋊C4C2413yes—
817C2×C4⋊C4C2413yes—
818C2×C4⋊C4C2413yes—
819C2×C4⋊C4C2413yes—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2413yes—
829C2×C4⋊C4C2413yes—
830C2×C4⋊C4C2413yes—
831C2×C4⋊C4C2413yes—
832C2×C4⋊C4C2416yes—
833C2×C4⋊C4C2413yes—
834C2×C4⋊C4C2413yes—
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2416yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2416yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2413yes—
845C2×C4⋊C4C2413yes—
846C2×C4⋊C4C2416yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2416yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2416yes—
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2411yescharacteristic
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2411yescharacteristic
865C2×C22⋊C4C2413yes—
866C2×C22⋊C4C2413yes—
867C2×C22⋊C4C2416yes—
868C2×C22⋊C4C2416yes—
869C2×C22⋊C4C2413yes—
870C2×C22⋊C4C2413yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2416yes—
875C2×C22⋊C4C2416yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2413yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2416yes—
882C2×C22⋊C4C2416yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2413yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2416yes—
896C2×C22⋊C4C2416yes—
897C2×C22⋊C4C2416yes—
898C2×C22⋊C4C2416yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2416yes—
902C2×C22⋊C4C2416yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C42—212no—
908C2×C42—212no—
909C2×C42—212no—
910C2×C42—212no—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2413yes—
914C2×C42C2413yes—
915C2×C42C2413yes—
916C2×C42C2413yes—
917C2×C42C2413yes—
918C2×C42C2416yes—
919C2×C42C2416yes—
920C2×C42C2413yes—
921C2×C42C2413yes—
922C2×C42C2413yes—
923C2×C42C2413yes—
924C2×C42C2413yes—
925C2×C42C2413yes—
926C2×C42C2413yes—
927C2×C42C2413yes—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2416yes—
933C2×C42C2416yes—
934C2×C42C2411yescharacteristic
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938#95C2411yescharacteristic
939#95C2411yescharacteristic
940#95C2413yes—
941#95C2413yes—
942#95C2413yes—
943#95C2413yes—
944#95C2413yes—
945#95C2413yes—
946#95C2413yes—
947#95C2411yescharacteristic
948#95C2411yescharacteristic
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2411yescharacteristic
952#95C2411yescharacteristic
953#95C2411yescharacteristic
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2416yes—
958#95C2413yes—
959#95C2413yes—
960#95C2413yes—
961#95C2413yes—
962#95C2413yes—
963#95C2413yes—
964#95C2416yes—
965#95C2416yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2411yescharacteristic
973#95C2413yes—
974#95C2411yescharacteristic
975#95C2416yes—
976#95C2411yescharacteristic
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2416yes—
981#95C2413yes—
982#95C2416yes—
983#95C2416yes—
984#95C2413yes—
985#95C2416yes—
986#95C2416yes—
987C24C2513yes—
988C24C2513yes—
989C24C2511yescharacteristic
990C24C2511yescharacteristic
991#41—448no—
992#41—416no—
993#41—416no—
994C2×Q8—232no—
995C2×Q8—26no—
996C2×Q8—26no—
997C2×Q8—22no—
998C2×Q8—26no—
999C2×Q8—26no—
1000C2×Q8—212no—
1001C2×Q8—26no—
1002C2×Q8—26no—
1003C2×Q8—26no—
1004C2×Q8—22no—
1005C2×Q8—26no—
1006C2×Q8—41no—
1007C2×Q8—43no—
1008C2×Q8—43no—
1009C2×Q8—43no—
1010C2×Q8—43no—
1011C2×Q8—46no—
1012C2×Q8—46no—
1013C2×Q8—43no—
1014C2×Q8—416no—
1015C2×Q8C22×D4112yes—
1016C2×Q8C22×D414yes—
1017C2×Q8C2×#41112yes—
1018C2×Q8C2×#4114yes—
1019C2×Q82−1+414yes—
1020C2×D4—22no—
1021C2×D4—26no—
1022C2×D4—22no—
1023C2×D4—26no—
1024C2×D4—26no—
1025C2×D4—26no—
1026C2×D4—26no—
1027C2×D4—26no—
1028C2×D4—26no—
1029C2×D4—26no—
1030C2×D4—26no—
1031C2×D4—212no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—43no—
1037C2×D4—43no—
1038C2×D4—41no—
1039C2×D4—43no—
1040C2×D4—43no—
1041C2×D4—43no—
1042C2×D4—43no—
1043C2×D4—43no—
1044C2×D4—46no—
1045C2×D4—46no—
1046C2×D4—43no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—26no—
1050C22×C4—26no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—26no—
1054C22×C4—26no—
1055C22×C4—26no—
1056C22×C4—26no—
1057C22×C4—26no—
1058C22×C4—26no—
1059C22×C4—26no—
1060C22×C4—26no—
1061C22×C4—26no—
1062C22×C4—26no—
1063C22×C4—26no—
1064C22×C4—22no—
1065C22×C4—26no—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—26no—
1069C22×C4—26no—
1070C22×C4—26no—
1071C22×C4—41no—
1072C22×C4—43no—
1073C22×C4—43no—
1074C22×C4—43no—
1075C22×C4—43no—
1076C22×C4—43no—
1077C22×C4—43no—
1078C22×C4—43no—
1079C22×C4—43no—
1080C22×C4—43no—
1081C22×C4—43no—
1082C22×C4C2×#41112yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2513yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2513yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2513yes—
1091C22×C4C2513yes—
1092C22×C4C2513yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2513yes—
1095C22×C4C2511yescharacteristic
1096C22×C4C2513yes—
1097C22×C4C2513yes—
1098C22×C4C2513yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2513yes—
1103C22×C4C2513yes—
1104C22×C4C2513yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2513yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2513yes—
1110C4⋊C4—26no—
1111C4⋊C4—212no—
1112C4⋊C4—212no—
1113C4⋊C4—26no—
1114C4⋊C4—22no—
1115C4⋊C4—26no—
1116C4⋊C4—26no—
1117C4⋊C4—26no—
1118C4⋊C4—26no—
1119C4⋊C4—26no—
1120C4⋊C4—26no—
1121C4⋊C4—26no—
1122C4⋊C4—26no—
1123C4⋊C4—26no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—26no—
1127C4⋊C4—26no—
1128C4⋊C4—212no—
1129C4⋊C4—212no—
1130C4⋊C4—26no—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—26no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—26no—
1138C4⋊C4—26no—
1139C4⋊C4—26no—
1140C4⋊C4—212no—
1141C4⋊C4—26no—
1142C4⋊C4—26no—
1143C4⋊C4—26no—
1144C4⋊C4—26no—
1145C4⋊C4—22no—
1146C4⋊C4—41no—
1147C4⋊C4—43no—
1148C4⋊C4—46no—
1149C4⋊C4—43no—
1150C4⋊C4—43no—
1151C4⋊C4—43no—
1152C4⋊C4—43no—
1153C4⋊C4—46no—
1154C4⋊C4—43no—
1155C4⋊C4—43no—
1156C4⋊C4C22×D4112yes—
1157C4⋊C4C22×D4112yes—
1158C4⋊C4C22×D4112yes—
1159C4⋊C4C22×D414yes—
1160C4⋊C4C22×D4112yes—
1161C4⋊C4C22×D4112yes—
1162C4⋊C4C22×D4124yes—
1163C22⋊C4—22no—
1164C22⋊C4—22no—
1165C22⋊C4—26no—
1166C22⋊C4—26no—
1167C22⋊C4—22no—
1168C22⋊C4—26no—
1169C22⋊C4—22no—
1170C22⋊C4—26no—
1171C22⋊C4—26no—
1172C22⋊C4—22no—
1173C22⋊C4—22no—
1174C22⋊C4—22no—
1175C22⋊C4—26no—
1176C22⋊C4—26no—
1177C22⋊C4—212no—
1178C22⋊C4—212no—
1179C22⋊C4—26no—
1180C22⋊C4—26no—
1181C22⋊C4—212no—
1182C22⋊C4—212no—
1183C22⋊C4—26no—
1184C22⋊C4—26no—
1185C22⋊C4—26no—
1186C22⋊C4—212no—
1187C22⋊C4—212no—
1188C22⋊C4—22no—
1189C22⋊C4—26no—
1190C22⋊C4—22no—
1191C22⋊C4—26no—
1192C22⋊C4—41no—
1193C22⋊C4—43no—
1194C22⋊C4—43no—
1195C22⋊C4—43no—
1196C22⋊C4—43no—
1197C22⋊C4—43no—
1198C22⋊C4—43no—
1199C22⋊C4—43no—
1200C22⋊C4—46no—
1201C22⋊C4—43no—
1202C22⋊C4—46no—
1203C22⋊C4—43no—
1204C22⋊C4—43no—
1205C22⋊C4—46no—
1206C22⋊C4—43no—
1207C22⋊C4—43no—
1208C22⋊C4—46no—
1209C22⋊C4—46no—
1210C22⋊C4—46no—
1211C42—22no—
1212C42—22no—
1213C42—26no—
1214C42—26no—
1215C42—26no—
1216C42—26no—
1217C42—26no—
1218C42—26no—
1219C42—26no—
1220C42—26no—
1221C42—212no—
1222C42—212no—
1223C42—26no—
1224C42—26no—
1225C42—26no—
1226C42—26no—
1227C42—26no—
1228C42—26no—
1229C42—41no—
1230C42—43no—
1231C42—43no—
1232C42—46no—
1233C42—46no—
1234C42—43no—
1235C42C22×D4112yes—
1236C42C22×D4112yes—
1237C42C22×D4112yes—
1238C23—21no—
1239C23—21no—
1240C23—21no—
1241C23—21no—
1242C23—21no—
1243C23—21no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—23no—
1251C23—23no—
1252C23—23no—
1253C23—23no—
1254C23—23no—
1255C23—23no—
1256C23—23no—
1257C23—23no—
1258C23—23no—
1259C23—23no—
1260C23—23no—
1261C23—23no—
1262C23—23no—
1263C23—23no—
1264C23C22×#4112yes—
1265C23#58512yes—
1266C23C2611yescharacteristic
1267Q8—224no—
1268Q8—412no—
1269Q8—44no—
1270Q8—412no—
1271Q8—412no—
1272Q8—86no—
1273Q8—812no—
1274Q8#548116yes—
1275D4—412no—
1276D4—412no—
1277D4—412no—
1278D4—44no—
1279D4—412no—
1280D4—412no—
1281D4—412no—
1282D4—812no—
1283D4—86no—
1284C2×C4—28no—
1285C2×C4—21no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—23no—
1289C2×C4—21no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—21no—
1295C2×C4—23no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—23no—
1302C2×C4—21no—
1303C2×C4—224no—
1304C2×C4—23no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—23no—
1308C2×C4—21no—
1309C2×C4—23no—
1310C2×C4—21no—
1311C2×C4—23no—
1312C2×C4—23no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—23no—
1317C2×C4—23no—
1318C2×C4—23no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—23no—
1322C2×C4—21no—
1323C2×C4—23no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—23no—
1327C2×C4—21no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—21no—
1331C2×C4—23no—
1332C2×C4—23no—
1333C2×C4—23no—
1334C2×C4—23no—
1335C2×C4—23no—
1336C2×C4—21no—
1337C2×C4—23no—
1338C2×C4—21no—
1339C2×C4—23no—
1340C2×C4—21no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—23no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—23no—
1353C2×C4—23no—
1354C2×C4—23no—
1355C2×C4—44no—
1356C2×C4—412no—
1357C2×C4—412no—
1358C2×C4—412no—
1359C2×C4—412no—
1360C2×C4—412no—
1361C2×C4—86no—
1362C2×C4—86no—
1363C2×C4—86no—
1364C2×C4—86no—
1365C2×C4C23×D412yes—
1366C2×C4C23×D412yes—
1367C2×C4C23×D416yes—
1368C2×C4C23×D416yes—
1369C2×C4C23×D416yes—
1370C2×C4C23×D412yes—
1371C2×C4C23×D416yes—
1372C2×C4C22×#4116yes—
1373C2×C4C22×#4116yes—
1374C2×C4C2×2−1+416yes—
1375C2×C4#58512yes—
1376C2×C4#58512yes—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—22no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—41no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—43no—
1392C22—43no—
1393C22—43no—
1394C22—43no—
1395C22—43no—
1396C22—43no—
1397C22—43no—
1398C22—43no—
1399C22—43no—
1400C22—43no—
1401C22—43no—
1402C22—43no—
1403C22—43no—
1404C22—43no—
1405C22C24×D411yescharacteristic
1406C22C23×#4111yescharacteristic
1407C22C22×2−1+411yescharacteristic
1408C22C2×#58511yescharacteristic
1409C22C2×#58511yescharacteristic
1410C22C2×#58511yescharacteristic
1411C222−1+611yescharacteristic
1412C4—22no—
1413C4—22no—
1414C4—22no—
1415C4—26no—
1416C4—22no—
1417C4—22no—
1418C4—26no—
1419C4—26no—
1420C4—26no—
1421C4—43no—
1422C4—43no—
1423C4—41no—
1424C4—41no—
1425C4—41no—
1426C4—43no—
1427C4—43no—
1428C4—41no—
1429C4—43no—
1430C4—43no—
1431C4—43no—
1432C4—41no—
1433C4—43no—
1434C4—41no—
1435C4—41no—
1436C4—41no—
1437C4—43no—
1438C4C2×#548112yes—
1439C2—42no—
1440C2—42no—
1441C2—83no—
1442C2—83no—
1443C2C22×#54811yescharacteristic
1444C2#6279311yescharacteristic
1445C2#6281111yescharacteristic
1446C2#6295311yescharacteristic
1447C2#6300211yescharacteristic
1448C2#6300511yescharacteristic
1449C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3502C2semidirect
2. C2×#3480C2semidirect
3. #59658C2semidirect
4. #59137C2semidirect
5. #59085C2semidirect
6. #59084C2semidirect
7. #59082C2semidirect
8. #45338C2semidirect
9. #45313C2semidirect
10. #45159C2semidirect
11. #45098C2semidirect
12. #39718C2semidirect
13. #39164C2semidirect
14. #37759C2semidirect
15. #37756C2semidirect
16. #36505C2semidirect
17. #36467C2semidirect
18. #36456C2semidirect
19. #36435C2semidirect
20. #36434C2semidirect
21. #36431C2semidirect
22. #36142C2semidirect
23. #36049C2semidirect
24. #36018C2semidirect
25. #35948C2semidirect
26. #35771C2semidirect
27. #34720C2semidirect
28. #34336C2semidirect
29. #34293C2semidirect
30. #34291C2semidirect
31. C4×#548C2semidirect
253. #557D4semidirect
666. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35022
C2×#34802
#596582
#591372
#590852
#590842
#590822
#453382
#453132
#451592
#450982
#397182
#391642
#377592
#377562
#365052
#364672
#364562
#364352
#364342
#364312
#361422
#360492
#360182
#359482
#357712
#347202
#343362
#342932
#342912
C4×#5482