Finite Group Databasebeta

← #8095553

Subgroups — #8095553

Order 512.

5780 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53151C214yesmaximal, complemented
2#53128C214yesmaximal, complemented
3#53060C214yesmaximal, complemented
4#52962C214yesmaximal, complemented
5#52741C214yesmaximal, complemented
6#52398C214yesmaximal, complemented
7#46335C218yesmaximal, complemented
8#45687C214yesmaximal, complemented
9#45663C214yesmaximal, complemented
10#45608C214yesmaximal, complemented
11#45518C214yesmaximal, complemented
12#35676C211yesmaximal, characteristic, complemented
13#35659C212yesmaximal, complemented
14#35626C211yesmaximal, characteristic, complemented
15#35514C212yesmaximal, complemented
16#35311C212yesmaximal, complemented
17#35252C212yesmaximal, complemented
18#35160C212yesmaximal, complemented
19C2×#2540C211yesmaximal, characteristic, complemented
20#34737C212yesmaximal, complemented
21C22×2−1+4C2211yescharacteristic
22C2×#535C2212yes—
23C22×#124C2211yescharacteristic
24C2×#525C2212yes—
25C2×#525C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×#121C2212yes—
28C2×#518C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2856C2214yescomplemented
32#2855C2214yescomplemented
33#2855C2214yescomplemented
34#2852C2218yes—
35#2850C2214yescomplemented
36#2841C2214yescomplemented
37#2838C2218yescomplemented
38#2830C2218yescomplemented
39#2829C2218yescomplemented
40#2828C2218yescomplemented
41#2827C2218yescomplemented
42#2826C2214yescomplemented
43#2825C2218yescomplemented
44#2824C2218yescomplemented
45#2824C2214yescomplemented
46#2815C2214yescomplemented
47#2815C2218yescomplemented
48#2797C2218yescomplemented
49#2797C2218yescomplemented
50#2796C2218yescomplemented
51#2784C2218yescomplemented
52#2780C2218yescomplemented
53#2760C2214yescomplemented
54#2752C2214yescomplemented
55#2749C2218yescomplemented
56#2749C2218yescomplemented
57#2746C2218yescomplemented
58#2742C2214yescomplemented
59#2737C2218yescomplemented
60#2737C2218yescomplemented
61#2714C2218yescomplemented
62#2714C2218yescomplemented
63#2699C2218yescomplemented
64#2691C2218yescomplemented
65#2691C2218yescomplemented
66#2688C2218yescomplemented
67#2688C2218yescomplemented
68#2688C2218yescomplemented
69#2675C2214yescomplemented
70#2643C2218yes—
71#2625C2214yescomplemented
72#2625C2214yescomplemented
73#2620C2214yescomplemented
74#2619C2214yescomplemented
75#2540C2214yes—
76#2540C2214yes—
77#2540C2214yes—
78#2540C2214yes—
79#2537C2214yescomplemented
80#2537C2214yescomplemented
81#2535C2214yescomplemented
82#2535C2214yescomplemented
83#2514C2214yescomplemented
84#2513C2214yescomplemented
85#2512C2214yescomplemented
86#2511C2214yescomplemented
87#2503C2214yescomplemented
88#2502C2214yescomplemented
89#2499C2214yescomplemented
90#2499C2214yescomplemented
91#2497C2214yescomplemented
92#2496C2214yescomplemented
93#2495C2214yescomplemented
94#2494C2214yescomplemented
95#2484C2218yes—
96#2483C2214yes—
97#2483C2214yes—
98#2483C2218yes—
99#2447C2214yescomplemented
100#2447C2214yescomplemented
101#2447C2214yescomplemented
102#2447C2214yescomplemented
103#2436C2214yescomplemented
104#2436C2214yescomplemented
105#2431C2214yescomplemented
106#2431C2214yescomplemented
107#2428C2214yescomplemented
108#2428C2214yescomplemented
109#2427C2214yescomplemented
110#2427C2214yescomplemented
111#2417C2212yescomplemented
112#2417C2212yescomplemented
113#2416C2212yescomplemented
114#2416C2214yescomplemented
115#2416C2214yescomplemented
116#2416C2212yescomplemented
117#2415C2212yescomplemented
118#2415C2212yescomplemented
119#2414C2212yescomplemented
120#2414C2214yescomplemented
121#2414C2214yescomplemented
122#2414C2212yescomplemented
123#2413C2214yes—
124#2412C2218yes—
125#2412C2214yes—
126#2411C2218yes—
127#2411C2214yes—
128#2410C2214yes—
129#2410C2218yes—
130#2410C2218yes—
131#2409C2214yescomplemented
132#2409C2214yescomplemented
133#2409C2214yescomplemented
134#2409C2214yescomplemented
135#2407C2214yescomplemented
136#2407C2214yescomplemented
137#2407C2214yescomplemented
138#2407C2214yescomplemented
139#2406C2218yes—
140#2404C2214yes—
141#2404C2218yes—
142#2404C2214yes—
143C2×#399C2212yes—
144#2392C2214yescomplemented
145#2392C2214yescomplemented
146C2×#392C2212yes—
147#2377C2218yescomplemented
148#2377C2218yescomplemented
149#2317C2212yes—
150#2317C2212yes—
151#2311C2212yes—
152#2311C2212yes—
153#2310C2212yes—
154#2310C2211yescharacteristic
155#2309C2211yescharacteristic
156C4×#121C2214yescomplemented
157C4×#121C2214yescomplemented
158#2297C2212yes—
159#2296C2212yes—
160C2×#390C2214yes—
161#2280C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C2×2−1+4—48no—
164C2×2−1+4—44no—
165C22×#41C2312yes—
166C22×#41C2314yes—
167C22×#41C2314yes—
168C23×Q8C2311yescharacteristic
169C23×Q8C2314yes—
170C23×D4C2311yescharacteristic
171C23×D4C2311yescharacteristic
172C23×D4C2314yes—
173C24×C4C2312yes—
174#535—48no—
175C2×#127C2314yes—
176C2×#126C2318yes—
177C2×#124—44no—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181#525—48no—
182#525—48no—
183C2×#123C2314yes—
184C2×#123C2314yes—
185C2×C22⋊Q8—48no—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×#121—48no—
195C2×#121C2314yes—
196C2×#121C2312yes—
197C2×#121C2318yes—
198C2×#121C2312yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#120C2314yes—
212C2×#120C2314yes—
213C2×#120C2318yes—
214#518—44no—
215C2×C4×D4—44no—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×#117—48no—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2312yes—
230C2×#117C2314yes—
231C2×#117C2314yes—
232C2×#117C2312yes—
233C2×#117C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2314yes—
242C22×C22⋊C4C2314yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2312yes—
246C22×C42C2311yescharacteristic
247C22×C42C2314yes—
248C22×C42C2312yes—
249#401C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#399C2314yes—
256#399C2318yes—
257#399C2314yes—
258#398C2314yes—
259#398C2318yes—
260#398C2318yes—
261#398C2314yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2314yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#396C2318yes—
278#396C2314yes—
279#396C2318yes—
280#396C2314yes—
281#396C2314yes—
282#396C2318yes—
283#396C2314yes—
284#395C2318yes—
285#395C2318yes—
286#394C2314yes—
287#394C2314yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2314yes—
297#394C2314yes—
298#394C2318yes—
299#394C2318yes—
300#394C2314yes—
301#394C2314yes—
302#393C2318yes—
303#393C2314yes—
304#393C2314yes—
305#393C2318yes—
306#393C2318yes—
307#392C2314yes—
308#392C2318yes—
309#392C2314yes—
310#392C2318yes—
311#392C2318yes—
312#392C2314yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#392C2314yes—
317#392C2314yes—
318#392C2314yes—
319#392C2318yes—
320#392C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2318yes—
337#390C2318yes—
338#390C2314yes—
339#390C2318yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2318yes—
344#390C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2314yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#386C2314yes—
392#386C2314yes—
393#385C2318yes—
394#385C2314yes—
395#385C2314yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#384C2314yes—
407#384C2314yes—
408#383C2318yes—
409#382C2314yes—
410#382C2314yes—
411#381C2314yes—
412#381C2318yes—
413#381C2314yes—
414#381C2318yes—
415#381C2318yes—
416#381C2318yes—
417#381C2314yes—
418#381C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2318yes—
424#380C2312yes—
425#380C2312yes—
426#380C2312yes—
427#380C2312yes—
428#380C2314yes—
429#380C2318yes—
430#380C2314yes—
431#379C2314yes—
432#379C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C2×#95C2312yes—
442C25C2412yes—
443C25C2412yes—
4442−1+4—464no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—48no—
449C2×#41—416no—
450C2×#41—48no—
451C2×#41—48no—
452C2×#41—48no—
453C22×Q8—28no—
454C22×Q8—24no—
455C22×Q8—48no—
456C22×Q8—48no—
457C22×Q8—48no—
458C22×Q8C2414yes—
459C22×Q8C2412yes—
460C22×Q8C2414yes—
461C22×D4—24no—
462C22×D4—28no—
463C22×D4—42no—
464C22×D4—48no—
465C22×D4—44no—
466C22×D4—48no—
467C22×D4—84no—
468C22×D4C2414yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2411yescharacteristic
472C22×D4C2412yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2418yes—
476C22×D4C2411yescharacteristic
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C22×D4C2418yes—
482C22×D4C2414yes—
483C23×C4—28no—
484C23×C4—28no—
485C23×C4—28no—
486C23×C4C2412yes—
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2414yes—
493C23×C4C2411yescharacteristic
494C23×C4C2414yes—
495C23×C4C2411yescharacteristic
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2418yes—
501C23×C4C2411yescharacteristic
502#127—48no—
503#126—88no—
504#124—48no—
505#124—48no—
506#124—48no—
507#123—48no—
508#123—48no—
509C22⋊Q8—48no—
510C22⋊Q8—48no—
511C22⋊Q8—48no—
512C22⋊Q8—48no—
513C22⋊Q8—44no—
514C22⋊Q8—44no—
515C22⋊Q8—44no—
516C22⋊Q8—44no—
517#121—48no—
518#121—416no—
519#121—48no—
520#121—48no—
521#121—48no—
522#121—48no—
523#121—44no—
524#121—44no—
525#121—44no—
526#121—44no—
527#121—48no—
528#121—48no—
529#121—48no—
530#121—416no—
531#121—88no—
532#121—88no—
533#120—48no—
534#120—48no—
535#120—416no—
536C4×D4—48no—
537C4×D4—48no—
538C4×D4—44no—
539C4×D4—44no—
540C4×D4—44no—
541C4×D4—44no—
542C4×D4—48no—
543C4×D4—48no—
544C4×D4—48no—
545C4×D4—48no—
546#117—28no—
547#117—28no—
548#117—28no—
549#117—48no—
550#117—48no—
551#117—44no—
552#117—44no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—44no—
555C2×C4⋊C4—44no—
556C2×C4⋊C4—42no—
557C2×C4⋊C4—48no—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C22⋊C4—48no—
586C2×C22⋊C4—48no—
587C2×C22⋊C4—44no—
588C2×C22⋊C4—48no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4—44no—
591C2×C22⋊C4—44no—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C42—24no—
635C2×C42—48no—
636C2×C42—82no—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2414yes—
674C24—24no—
675C24—24no—
676C24—24no—
677C24—24no—
678C24—24no—
679C24—28no—
680C24—42no—
681C24—42no—
682C24—42no—
683C24—44no—
684C24—42no—
685C24—42no—
686C24C2512yes—
687C24C2514yes—
688C24C2514yes—
689C24C2512yes—
690C24C2511yescharacteristic
691#41—464no—
692#41—464no—
693#41—432no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—24no—
697C2×Q8—24no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—48no—
701C2×Q8—44no—
702C2×Q8—464no—
703C2×Q8—416no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—41no—
719C2×D4—42no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—416no—
747C2×D4—416no—
748C2×D4—832no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—28no—
773C22×C4—41no—
774C22×C4—44no—
775C22×C4—41no—
776C22×C4—42no—
777C22×C4—44no—
778C22×C4—48no—
779C22×C4—48no—
780C22×C4—48no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—48no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—432no—
792C22×C4H(5,𝔽2)14yes—
793C22×C4H(5,𝔽2)18yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2518yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—41no—
820C4⋊C4—42no—
821C4⋊C4—41no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—28no—
839C22⋊C4—28no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—42no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C42—24no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—28no—
883C42—44no—
884C42—44no—
885C42—48no—
886C23—22no—
887C23—21no—
888C23—21no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—22no—
898C23—28no—
899C23—22no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—22no—
906C23—28no—
907C23—22no—
908C23—24no—
909C23—22no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—48no—
915C23—48no—
916C23—48no—
917C23—48no—
918C23—48no—
919C23—84no—
920C23—84no—
921C23—84no—
922C23—88no—
923C23—84no—
924C23—84no—
925C23—88no—
926C23C2×H(5,𝔽2)12yes—
927C23C2×H(5,𝔽2)14yes—
928C23#58514yes—
929C23C2611yescharacteristic
930Q8—416no—
931Q8—416no—
932Q8—48no—
933D4—44no—
934D4—48no—
935D4—44no—
936D4—416no—
937D4—416no—
938D4—416no—
939D4—48no—
940D4—88no—
941D4—88no—
942D4—816no—
943D4—88no—
944D4—88no—
945D4—816no—
946D4—168no—
947D4—168no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—28no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—44no—
989C2×C4—416no—
990C2×C4—432no—
991C2×C4—48no—
992C2×C4—48no—
993C2×C4—48no—
994C2×C4—48no—
995C2×C4—48no—
996C2×C4—48no—
997C2×C4—416no—
998C2×C4—88no—
999C2×C4—88no—
1000C2×C4—164no—
1001C2×C4—164no—
1002C2×C4#560116yes—
1003C2×C4C2×H(5,𝔽2)14yes—
1004C2×C4C2×H(5,𝔽2)14yes—
1005C2×C4C2×H(5,𝔽2)14yes—
1006C22—22no—
1007C22—22no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—44no—
1018C22—42no—
1019C22—44no—
1020C22—44no—
1021C22—42no—
1022C22—44no—
1023C22—42no—
1024C22—48no—
1025C22—44no—
1026C22—44no—
1027C22—42no—
1028C22—44no—
1029C22—42no—
1030C22—44no—
1031C22—42no—
1032C22—44no—
1033C22—44no—
1034C22—48no—
1035C22—42no—
1036C22—816no—
1037C22—168no—
1038C22C2×#56014yes—
1039C22C22×H(5,𝔽2)11yescharacteristic
1040C22C22×H(5,𝔽2)12yes—
1041C22C2×#58512yes—
1042C22H(7,𝔽2)11yescharacteristic
1043C222−1+611yescharacteristic
1044C4—41no—
1045C4—41no—
1046C4—44no—
1047C4—42no—
1048C4—44no—
1049C4—48no—
1050C4—44no—
1051C4—44no—
1052C4—42no—
1053C4—42no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4C2×#56018yes—
1059C2—24no—
1060C2—44no—
1061C2—84no—
1062C2—82no—
1063C2—84no—
1064C2C22×#56011yescharacteristic
1065C2#6282111yescharacteristic
1066C2#6287511yescharacteristic
1067C2#6292412yes—
1068C2#6295412yes—
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. #53151C2semidirect
2. #53128C2semidirect
3. #53060C2semidirect
4. #52962C2semidirect
5. #52741C2semidirect
6. #52398C2semidirect
7. #46335C2semidirect
8. #45687C2semidirect
9. #45663C2semidirect
10. #45608C2semidirect
11. #45518C2semidirect
12. #35676C2semidirect
13. #35659C2semidirect
14. #35626C2semidirect
15. #35514C2semidirect
16. #35311C2semidirect
17. #35252C2semidirect
18. #35160C2semidirect
19. C2×#2540C2semidirect
20. #34737C2semidirect
31. #2856C22semidirect
32. #2855C22semidirect
33. #2855C22semidirect
35. #2850C22semidirect
36. #2841C22semidirect
37. #2838C22semidirect
38. #2830C22semidirect
39. #2829C22semidirect
40. #2828C22semidirect
41. #2827C22semidirect
42. #2826C22semidirect
43. #2825C22semidirect
44. #2824C22semidirect
45. #2824C22semidirect
46. #2815C22semidirect
47. #2815C22semidirect
48. #2797C22semidirect
49. #2797C22semidirect
50. #2796C22semidirect
51. #2784C22semidirect
52. #2780C22semidirect
53. #2760C22semidirect
54. #2752C22semidirect
55. #2749C22semidirect
56. #2749C22semidirect
57. #2746C22semidirect
58. #2742C22semidirect
59. #2737C22semidirect
60. #2737C22semidirect
61. #2714C22semidirect
62. #2714C22semidirect
63. #2699C22semidirect
64. #2691C22semidirect
65. #2691C22semidirect
66. #2688C22semidirect
67. #2688C22semidirect
68. #2688C22semidirect
69. #2675C22semidirect
71. #2625C22semidirect
72. #2625C22semidirect
73. #2620C22semidirect
74. #2619C22semidirect
79. #2537C22semidirect
80. #2537C22semidirect
81. #2535C22semidirect
82. #2535C22semidirect
83. #2514C22semidirect
84. #2513C22semidirect
85. #2512C22semidirect
86. #2511C22semidirect
87. #2503C22semidirect
88. #2502C22semidirect
89. #2499C22semidirect
90. #2499C22semidirect
91. #2497C22semidirect
92. #2496C22semidirect
93. #2495C22semidirect
94. #2494C22semidirect
99. #2447C22semidirect
100. #2447C22semidirect
101. #2447C22semidirect
102. #2447C22semidirect
103. #2436C22semidirect
104. #2436C22semidirect
105. #2431C22semidirect
106. #2431C22semidirect
107. #2428C22semidirect
108. #2428C22semidirect
109. #2427C22semidirect
110. #2427C22semidirect
111. #2417C22semidirect
112. #2417C22semidirect
113. #2416C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2416C22semidirect
117. #2415C22semidirect
118. #2415C22semidirect
119. #2414C22semidirect
120. #2414C22semidirect
121. #2414C22semidirect
122. #2414C22semidirect
131. #2409C22semidirect
132. #2409C22semidirect
133. #2409C22semidirect
134. #2409C22semidirect
135. #2407C22semidirect
136. #2407C22semidirect
137. #2407C22semidirect
138. #2407C22semidirect
144. #2392C22semidirect
145. #2392C22semidirect
147. #2377C22semidirect
148. #2377C22semidirect
156. C4×#121C22semidirect
157. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#531512
#531282
#530602
#529622
#527412
#523982
#463352
#456872
#456632
#456082
#455182
#356762
#356592
#356262
#355142
#353112
#352522
#351602
C2×#25402
#347372