Finite Group Databasebeta

← #8093543

Subgroups — #8093543

Order 512.

4798 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53127C214yesmaximal, complemented
2#53126C214yesmaximal, complemented
3#53126C214yesmaximal, complemented
4#53120C214yesmaximal, complemented
5#53079C214yesmaximal, complemented
6#53037C214yesmaximal, complemented
7#52995C214yesmaximal, complemented
8#52992C214yesmaximal, complemented
9#52510C218yesmaximal, complemented
10#52412C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35621C211yesmaximal, characteristic, complemented
15#35619C211yesmaximal, characteristic, complemented
16#35617C211yesmaximal, characteristic, complemented
17#35574C211yesmaximal, characteristic, complemented
18#35574C211yesmaximal, characteristic, complemented
19#35541C211yesmaximal, characteristic, complemented
20#35533C211yesmaximal, characteristic
21#35531C211yesmaximal, characteristic, complemented
22#35515C211yesmaximal, characteristic, complemented
23#34638C211yesmaximal, characteristic, complemented
24#34637C211yesmaximal, characteristic, complemented
25C2×#2640C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C2×#535C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#532C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#518C2211yescharacteristic
38#2841C2218yescomplemented
39#2836C2218yescomplemented
40#2836C2218yescomplemented
41#2832C2218yescomplemented
42#2832C2218yescomplemented
43#2831C2218yescomplemented
44#2830C2218yescomplemented
45#2830C2218yescomplemented
46#2829C2218yescomplemented
47#2827C2218yescomplemented
48#2827C2218yescomplemented
49#2826C2218yescomplemented
50#2824C2218yescomplemented
51#2816C2218yescomplemented
52#2814C2218yescomplemented
53#2814C2218yescomplemented
54#2798C2218yescomplemented
55#2788C2218yescomplemented
56#2786C2218yescomplemented
57#2786C2218yescomplemented
58#2751C2218yescomplemented
59#2751C2218yescomplemented
60#2747C2218yescomplemented
61#2739C2218yescomplemented
62#2708C2218yescomplemented
63#2701C2218yescomplemented
64#2696C2218yescomplemented
65#2692C2218yescomplemented
66#2692C2218yescomplemented
67#2687C2218yescomplemented
68#2687C2218yescomplemented
69#2681C2218yescomplemented
70#2647C2212yescomplemented
71#2647C2212yescomplemented
72#2647C2212yescomplemented
73#2647C2212yescomplemented
74#2646C2214yes—
75#2646C2214yes—
76#2642C2212yescomplemented
77#2641C2212yescomplemented
78#2640C2214yes—
79#2640C2214yes—
80#2640C2214yes—
81#2640C2214yes—
82#2640C2212yescomplemented
83#2640C2212yescomplemented
84#2639C2214yes—
85#2639C2214yes—
86#2582C2214yescomplemented
87#2581C2214yescomplemented
88#2580C2214yes—
89#2579C2214yes—
90#2579C2214yes—
91#2548C2214yes—
92#2548C2212yes—
93#2547C2214yes—
94#2547C2212yescomplemented
95#2546C2212yescomplemented
96#2545C2212yes—
97#2545C2214yes—
98#2545C2212yescomplemented
99#2544C2214yes—
100#2544C2212yes—
101#2544C2212yescomplemented
102#2541C2212yes—
103#2538C2214yes—
104#2504C2212yes—
105#2503C2212yescomplemented
106#2502C2212yescomplemented
107#2501C2212yes—
108#2500C2212yes—
109#2500C2212yes—
110#2499C2212yescomplemented
111#2499C2212yescomplemented
112#2498C2218yes—
113#2454C2214yes—
114#2453C2214yescomplemented
115#2452C2214yes—
116#2452C2214yescomplemented
117#2452C2214yescomplemented
118#2451C2214yescomplemented
119#2451C2214yescomplemented
120#2451C2214yescomplemented
121#2448C2214yes—
122#2448C2214yescomplemented
123#2447C2214yes—
124#2447C2214yescomplemented
125#2446C2214yescomplemented
126#2446C2214yescomplemented
127#2445C2214yes—
128#2445C2214yes—
129#2440C2214yescomplemented
130#2440C2214yescomplemented
131#2439C2214yescomplemented
132#2439C2214yescomplemented
133#2438C2218yes—
134#2437C2218yes—
135#2427C2214yes—
136#2427C2214yes—
137#2426C2214yes—
138#2426C2214yes—
139#2425C2218yes—
140#2424C2218yes—
141#2423C2214yescomplemented
142#2422C2214yes—
143#2421C2214yescomplemented
144#2420C2214yes—
145#2419C2218yes—
146#2418C2218yes—
147#2417C2214yescomplemented
148#2416C2214yes—
149#2415C2214yescomplemented
150#2414C2214yes—
151#2412C2214yes—
152#2412C2218yes—
153#2412C2214yes—
154#2411C2214yes—
155#2411C2214yes—
156#2409C2214yes—
157#2409C2214yes—
158#2402C2214yescomplemented
159#2402C2214yescomplemented
160#2398C2214yescomplemented
161#2398C2214yescomplemented
162C2×#397C2214yes—
163C2×#393C2214yes—
164#2317C2211yescharacteristic
165#2317C2211yescharacteristic
166#2316C2211yescharacteristic
167#2316C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2310C2211yescharacteristic
171#2309C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#390C2211yescharacteristic
183C2×#390C2211yescharacteristic
184#2285C2211yescharacteristic
185#2285C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2312yes—
191C23×D4C2311yescharacteristic
192#536—44no—
193#536—44no—
194#535—44no—
195#535—44no—
196#533—44no—
197#532—44no—
198C2×C4⋊Q8—44no—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×#127C2311yescharacteristic
206C2×#127C2312yes—
207C2×#127C2312yes—
208C2×#125C2312yes—
209C2×#124—44no—
210C2×#124C2314yes—
211C2×#124C2314yes—
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2312yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2318yes—
221C2×#123C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2318yes—
234C2×#120C2314yes—
235C2×#120C2314yes—
236#520—44no—
237#520—44no—
238#519—44no—
239#518—44no—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2314yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2314yes—
269C22×C22⋊C4C2314yes—
270C22×C22⋊C4C2314yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274#400C2314yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#400C2314yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2318yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2314yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#397C2318yes—
323#397C2314yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#394C2314yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2314yes—
342#394C2318yes—
343#394C2314yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2314yes—
349#394C2318yes—
350#393C2318yes—
351#393C2318yes—
352#393C2318yes—
353#393C2318yes—
354#393C2314yes—
355#393C2318yes—
356#393C2318yes—
357#393C2314yes—
358#393C2314yes—
359#393C2318yes—
360#393C2314yes—
361#392C2318yes—
362#391C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2312yes—
366#391C2312yes—
367#391C2318yes—
368#391C2318yes—
369#391C2318yes—
370#391C2314yes—
371#391C2312yes—
372#391C2312yes—
373#391C2314yes—
374#391C2312yes—
375#391C2312yes—
376#391C2312yes—
377#391C2312yes—
378#391C2312yes—
379#391C2312yes—
380#390C2312yes—
381#390C2312yes—
382#390C2314yes—
383#390C2312yes—
384#390C2312yes—
385#390C2318yes—
386#390C2318yes—
387#390C2318yes—
388#390C2314yes—
389#390C2312yes—
390#390C2312yes—
391#390C2314yes—
392#390C2312yes—
393#390C2312yes—
394#390C2312yes—
395#390C2312yes—
396#390C2312yes—
397#390C2312yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2318yes—
406#389C2318yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#386C2314yes—
431#386C2314yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2312yes—
439#386C2312yes—
440#386C2312yes—
441#386C2312yes—
442#386C2314yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2314yes—
451#385C2314yes—
452#385C2312yes—
453#385C2312yes—
454#385C2312yes—
455#385C2312yes—
456#385C2314yes—
457#385C2314yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2311yescharacteristic
462#384C2311yescharacteristic
463#382C2312yes—
464#382C2312yes—
465#382C2312yes—
466#382C2311yescharacteristic
467#382C2311yescharacteristic
468#381C2318yes—
469#381C2314yes—
470#381C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2314yes—
475#380C2318yes—
476#380C2318yes—
477#380C2314yes—
478#380C2314yes—
479#380C2318yes—
480#380C2318yes—
481#379C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496#376C2312yes—
497#376C2312yes—
498#376C2312yes—
499#376C2312yes—
500C2×#95C2312yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C25C2412yes—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8—44no—
515C22×Q8—84no—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2414yes—
521C22×Q8C2418yes—
522C22×D4—24no—
523C22×D4—24no—
524C22×D4—24no—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2418yes—
534C22×D4C2414yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2411yescharacteristic
541C23×C4C2412yes—
542C23×C4C2411yescharacteristic
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C4⋊Q8—48no—
549C4⋊Q8—48no—
550C4⋊Q8—44no—
551C4⋊Q8—42no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554#127—42no—
555#127—44no—
556#127—44no—
557#125—44no—
558#124—48no—
559#124—48no—
560#124—42no—
561#124—42no—
562#124—44no—
563#124—44no—
564#124—44no—
565#124—44no—
566#123—48no—
567#123—48no—
568#123—88no—
569#123—88no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—48no—
574C22⋊Q8—88no—
575C22⋊Q8—88no—
576C22⋊Q8—88no—
577#121—44no—
578#121—44no—
579#121—48no—
580#121—48no—
581#121—88no—
582#120—48no—
583#120—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×D4—48no—
590C4×D4—48no—
591C4×D4—44no—
592C4×D4—44no—
593C4×D4—48no—
594C4×D4—48no—
595C4×D4—48no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—48no—
603#117—44no—
604#117—44no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C22⋊C4—48no—
650C2×C22⋊C4—44no—
651C2×C22⋊C4—44no—
652C2×C22⋊C4—84no—
653C2×C22⋊C4—84no—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C42—24no—
690C2×C42—24no—
691C2×C42—24no—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2418yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2412yes—
716#95C2412yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749C24—24no—
750C24—24no—
751C24—24no—
752C24—44no—
753C24—44no—
754C24C2514yes—
755C24C2512yes—
756C24C2512yes—
757C24C2511yescharacteristic
758#41—416no—
759#41—416no—
760C2×Q8—24no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—22no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—48no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—44no—
778C2×Q8—416no—
779C2×Q8—816no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—22no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—48no—
803C2×D4—44no—
804C2×D4—48no—
805C2×D4—48no—
806C2×D4—48no—
807C2×D4—48no—
808C2×D4—416no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4H(5,𝔽2)14yes—
840C22×C4H(5,𝔽2)14yes—
841C22×C42−1+414yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—48no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C22⋊C4—24no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—44no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C42—24no—
938C42—24no—
939C42—24no—
940C42—22no—
941C42—22no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—22no—
949C42—22no—
950C42—24no—
951C42—44no—
952C42—44no—
953C42—48no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—28no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—28no—
971C23—48no—
972C23—84no—
973C23—88no—
974C23—88no—
975C23—84no—
976C23C2×H(5,𝔽2)12yes—
977C23C2×H(5,𝔽2)12yes—
978C23C2×2−1+412yes—
979C23C2611yescharacteristic
980Q8—48no—
981Q8—48no—
982Q8—44no—
983Q8—44no—
984Q8—88no—
985Q8—816no—
986D4—48no—
987D4—48no—
988D4—48no—
989D4—48no—
990D4—44no—
991D4—44no—
992D4—88no—
993D4—164no—
994D4—168no—
995D4—164no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—44no—
1048C2×C4—44no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—48no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—84no—
1056C2×C4—164no—
1057C2×C4—164no—
1058C2×C4—168no—
1059C2×C4#562116yes—
1060C2×C4C2×H(5,𝔽2)12yes—
1061C2×C4C2×H(5,𝔽2)12yes—
1062C2×C4C2×H(5,𝔽2)12yes—
1063C2×C4C2×H(5,𝔽2)12yes—
1064C2×C4C2×2−1+412yes—
1065C2×C4C2×2−1+412yes—
1066C22—22no—
1067C22—24no—
1068C22—24no—
1069C22—22no—
1070C22—42no—
1071C22—42no—
1072C22—44no—
1073C22—48no—
1074C22—44no—
1075C22—44no—
1076C22—44no—
1077C22—44no—
1078C22—48no—
1079C22—42no—
1080C22—44no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—44no—
1085C22—168no—
1086C22C2×#56214yes—
1087C22C22×H(5,𝔽2)11yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C22×2−1+411yescharacteristic
1090C22H(7,𝔽2)12yes—
1091C222−1+612yes—
1092C4—42no—
1093C4—44no—
1094C4—44no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—44no—
1111C4C2×#56214yes—
1112C4C2×#56214yes—
1113C2—24no—
1114C2—82no—
1115C2—82no—
1116C2—84no—
1117C2C22×#56211yescharacteristic
1118C2#6287611yescharacteristic
1119C2#6287812yes—
1120C2#6287912yes—
1121C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35533C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53127C2semidirect
2. #53126C2semidirect
3. #53126C2semidirect
4. #53120C2semidirect
5. #53079C2semidirect
6. #53037C2semidirect
7. #52995C2semidirect
8. #52992C2semidirect
9. #52510C2semidirect
10. #52412C2semidirect
11. #35677C2semidirect
12. #35673C2semidirect
13. #35662C2semidirect
14. #35621C2semidirect
15. #35619C2semidirect
16. #35617C2semidirect
17. #35574C2semidirect
18. #35574C2semidirect
19. #35541C2semidirect
21. #35531C2semidirect
22. #35515C2semidirect
23. #34638C2semidirect
24. #34637C2semidirect
25. C2×#2640C2semidirect
38. #2841C22semidirect
39. #2836C22semidirect
40. #2836C22semidirect
41. #2832C22semidirect
42. #2832C22semidirect
43. #2831C22semidirect
44. #2830C22semidirect
45. #2830C22semidirect
46. #2829C22semidirect
47. #2827C22semidirect
48. #2827C22semidirect
49. #2826C22semidirect
50. #2824C22semidirect
51. #2816C22semidirect
52. #2814C22semidirect
53. #2814C22semidirect
54. #2798C22semidirect
55. #2788C22semidirect
56. #2786C22semidirect
57. #2786C22semidirect
58. #2751C22semidirect
59. #2751C22semidirect
60. #2747C22semidirect
61. #2739C22semidirect
62. #2708C22semidirect
63. #2701C22semidirect
64. #2696C22semidirect
65. #2692C22semidirect
66. #2692C22semidirect
67. #2687C22semidirect
68. #2687C22semidirect
69. #2681C22semidirect
70. #2647C22semidirect
71. #2647C22semidirect
72. #2647C22semidirect
73. #2647C22semidirect
76. #2642C22semidirect
77. #2641C22semidirect
82. #2640C22semidirect
83. #2640C22semidirect
86. #2582C22semidirect
87. #2581C22semidirect
94. #2547C22semidirect
95. #2546C22semidirect
98. #2545C22semidirect
101. #2544C22semidirect
105. #2503C22semidirect
106. #2502C22semidirect
110. #2499C22semidirect
111. #2499C22semidirect
114. #2453C22semidirect
116. #2452C22semidirect
117. #2452C22semidirect
118. #2451C22semidirect
119. #2451C22semidirect
120. #2451C22semidirect
122. #2448C22semidirect
124. #2447C22semidirect
125. #2446C22semidirect
126. #2446C22semidirect
129. #2440C22semidirect
130. #2440C22semidirect
131. #2439C22semidirect
132. #2439C22semidirect
141. #2423C22semidirect
143. #2421C22semidirect
147. #2417C22semidirect
149. #2415C22semidirect
158. #2402C22semidirect
159. #2402C22semidirect
160. #2398C22semidirect
161. #2398C22semidirect

Maximal subgroups

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

subgroupindex
#531272
#531262
#531202
#530792
#530372
#529952
#529922
#525102
#524122
#356772
#356732
#356622
#356212
#356192
#356172
#355742
#355412
#355332
#355312
#355152
#346382
#346372
C2×#26402