Finite Group Databasebeta

← #8094473

Subgroups — #8094473

Order 512.

4760 conjugacy classes of subgroups.

The subgroup lattice has 1125 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53127C214yesmaximal, complemented
2#53030C214yesmaximal, complemented
3#53025C214yesmaximal, complemented
4#53010C214yesmaximal, complemented
5#52800C218yesmaximal, complemented
6#46072C214yesmaximal, complemented
7#46055C214yesmaximal, complemented
8#45682C214yesmaximal, complemented
9#45626C214yesmaximal, complemented
10#45475C218yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35633C211yesmaximal, characteristic, complemented
15#35620C211yesmaximal, characteristic, complemented
16#35618C211yesmaximal, characteristic, complemented
17#35339C211yesmaximal, characteristic, complemented
18#35334C211yesmaximal, characteristic, complemented
19#35312C211yesmaximal, characteristic, complemented
20#35308C211yesmaximal, characteristic, complemented
21#35224C211yesmaximal, characteristic, complemented
22#35223C211yesmaximal, characteristic
23#34813C211yesmaximal, characteristic, complemented
24C2×#2503C211yesmaximal, characteristic, complemented
25#34742C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2864C2214yescomplemented
39#2862C2212yescomplemented
40#2861C2212yescomplemented
41#2857C2212yescomplemented
42#2851C2214yescomplemented
43#2850C2212yescomplemented
44#2848C2214yes—
45#2847C2214yes—
46#2841C2218yes—
47#2841C2218yescomplemented
48#2839C2218yescomplemented
49#2839C2218yescomplemented
50#2836C2218yescomplemented
51#2832C2218yescomplemented
52#2831C2218yescomplemented
53#2831C2218yescomplemented
54#2827C2218yescomplemented
55#2816C2218yes—
56#2788C2218yescomplemented
57#2783C2218yescomplemented
58#2761C2218yes—
59#2755C2218yescomplemented
60#2755C2218yescomplemented
61#2751C2218yes—
62#2750C2218yes—
63#2750C2218yescomplemented
64#2744C2218yes—
65#2744C2218yescomplemented
66#2743C2218yes—
67#2743C2218yes—
68#2741C2218yescomplemented
69#2740C2218yes—
70#2739C2218yes—
71#2739C2218yescomplemented
72#2701C2218yes—
73#2700C2218yes—
74#2687C2218yes—
75#2686C2218yes—
76#2647C2214yescomplemented
77#2642C2212yescomplemented
78#2640C2212yescomplemented
79#2628C2214yescomplemented
80#2627C2214yes—
81#2621C2212yescomplemented
82#2620C2212yescomplemented
83#2618C2214yes—
84#2582C2214yescomplemented
85#2581C2214yescomplemented
86#2581C2214yescomplemented
87#2580C2214yescomplemented
88#2570C2214yescomplemented
89#2570C2214yescomplemented
90#2569C2218yes—
91#2568C2212yescomplemented
92#2566C2212yescomplemented
93#2565C2212yescomplemented
94#2564C2218yes—
95#2563C2212yescomplemented
96#2538C2214yes—
97#2536C2214yes—
98#2534C2214yes—
99#2504C2212yescomplemented
100#2503C2214yes—
101#2503C2214yes—
102#2503C2214yes—
103#2503C2214yes—
104#2503C2212yescomplemented
105#2500C2212yescomplemented
106#2499C2212yescomplemented
107#2498C2218yes—
108#2492C2212yes—
109#2492C2214yescomplemented
110#2491C2212yes—
111#2490C2212yes—
112#2489C2212yes—
113#2489C2214yescomplemented
114#2488C2214yes—
115#2488C2218yes—
116#2486C2214yes—
117#2472C2214yes—
118#2453C2214yescomplemented
119#2451C2214yescomplemented
120#2450C2218yes—
121#2448C2214yescomplemented
122#2446C2214yescomplemented
123#2444C2218yes—
124#2442C2214yes—
125#2442C2214yes—
126#2442C2214yescomplemented
127#2440C2214yes—
128#2440C2214yes—
129#2439C2214yescomplemented
130#2438C2218yes—
131#2429C2214yes—
132#2429C2214yes—
133#2429C2214yescomplemented
134#2427C2214yes—
135#2427C2214yescomplemented
136#2426C2214yes—
137#2425C2218yes—
138#2423C2212yes—
139#2423C2214yescomplemented
140#2422C2212yes—
141#2421C2212yes—
142#2421C2214yescomplemented
143#2421C2214yescomplemented
144#2420C2212yes—
145#2420C2214yescomplemented
146#2419C2214yes—
147#2418C2214yes—
148#2417C2214yes—
149#2417C2214yes—
150#2417C2214yes—
151#2416C2214yes—
152#2416C2214yes—
153#2415C2214yes—
154#2413C2214yes—
155#2411C2214yes—
156#2398C2214yes—
157#2395C2214yes—
158C2×#400C2214yes—
159#2378C2218yes—
160#2377C2218yes—
161#2317C2211yescharacteristic
162#2317C2211yescharacteristic
163#2317C2211yescharacteristic
164#2316C2211yescharacteristic
165#2316C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2310C2211yescharacteristic
171C4×#124C2214yes—
172C4×#123C2214yes—
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179#2285C2211yescharacteristic
180C2×#382C2211yescharacteristic
181C2×#382C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184C2×#381C2214yes—
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#544—44no—
193#537—44no—
194#536—44no—
195#536—44no—
196#533—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208#525—44no—
209#525—44no—
210C2×#123C2312yes—
211C2×#123C2312yes—
212C2×#123C2314yes—
213C2×#123C2314yes—
214C2×#123C2314yes—
215C2×C22⋊Q8—44no—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×#121C2318yes—
229C2×#121C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#120C2312yes—
235C2×#120C2312yes—
236#520—44no—
237#519—44no—
238C4×#41—44no—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C22×C4⋊C4—44no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2312yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#394C2314yes—
328#394C2314yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2314yes—
335#394C2314yes—
336#393C2318yes—
337#393C2318yes—
338#393C2318yes—
339#393C2314yes—
340#393C2314yes—
341#391C2311yescharacteristic
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2311yescharacteristic
349#391C2318yes—
350#391C2314yes—
351#391C2318yes—
352#391C2318yes—
353#391C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2311yescharacteristic
357#391C2312yes—
358#391C2312yes—
359#391C2311yescharacteristic
360#391C2312yes—
361#391C2314yes—
362#390C2311yescharacteristic
363#390C2312yes—
364#390C2311yescharacteristic
365#390C2312yes—
366#390C2312yes—
367#390C2311yescharacteristic
368#390C2314yes—
369#390C2318yes—
370#390C2311yescharacteristic
371#390C2312yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2314yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2318yes—
420#386C2318yes—
421#386C2318yes—
422#386C2314yes—
423#386C2318yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2314yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2312yes—
441#384C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2314yes—
449#382C2318yes—
450#382C2312yes—
451#382C2312yes—
452#382C2312yes—
453#382C2314yes—
454#381C2318yes—
455#381C2314yes—
456#381C2318yes—
457#381C2312yes—
458#381C2312yes—
459#381C2318yes—
460#381C2314yes—
461#381C2318yes—
462#381C2318yes—
463#380C2318yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#379C2312yes—
480#379C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497#376C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2411yescharacteristic
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×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2414yes—
519C22×Q8C2414yes—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—44no—
531C23×C4—48no—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2418yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552#125—44no—
553#125—44no—
554#125—44no—
555#124—44no—
556#124—44no—
557#124—48no—
558#123—48no—
559#123—44no—
560#123—44no—
561#123—48no—
562#123—48no—
563C22⋊Q8—416no—
564C22⋊Q8—48no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—48no—
571C22⋊Q8—44no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575#121—44no—
576#121—44no—
577#121—44no—
578#121—44no—
579#121—416no—
580#121—48no—
581#120—44no—
582#120—44no—
583C4×Q8—48no—
584C4×Q8—44no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—44no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—48no—
591C4×D4—48no—
592C4×D4—48no—
593C4×D4—48no—
594#117—24no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—44no—
601#117—48no—
602#117—44no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—44no—
609C2×C4⋊C4—44no—
610C2×C4⋊C4—44no—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C22⋊C4—44no—
653C2×C22⋊C4—44no—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
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—44no—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709#95C2412yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
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#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24—22no—
749C24—24no—
750C24—22no—
751C24—22no—
752C24—42no—
753C24C2512yes—
754C24C2512yes—
755C24C2512yes—
756C24C2511yescharacteristic
757#41—416no—
758#41—416no—
759C2×Q8—24no—
760C2×Q8—22no—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—44no—
772C2×Q8—44no—
773C2×Q8—44no—
774C2×Q8—44no—
775C2×Q8—48no—
776C2×Q8—416no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—48no—
797C22×C4—24no—
798C22×C4—22no—
799C22×C4—24no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—216no—
809C22×C4—24no—
810C22×C4—24no—
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—44no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—48no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—44no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—42no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—416no—
836C22×C4—816no—
837C22×C4H(5,𝔽2)14yes—
838C22×C4H(5,𝔽2)14yes—
839C22×C42−1+414yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2514yes—
848C22×C4C2514yes—
849C22×C4C2514yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
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—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C42—22no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—22no—
947C42—22no—
948C42—24no—
949C42—44no—
950C42—44no—
951C42—44no—
952C42—48no—
953C42—44no—
954C23—22no—
955C23—22no—
956C23—28no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—48no—
974C23—48no—
975C23—44no—
976C23—44no—
977C23C2×H(5,𝔽2)12yes—
978C23C2×H(5,𝔽2)12yes—
979C23C2×2−1+412yes—
980C23#58514yes—
981C23C2611yescharacteristic
982Q8—48no—
983Q8—48no—
984Q8—44no—
985Q8—44no—
986Q8—88no—
987Q8—164no—
988D4—48no—
989D4—48no—
990D4—44no—
991D4—44no—
992D4—88no—
993D4—88no—
994D4—164no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—44no—
1046C2×C4—48no—
1047C2×C4—48no—
1048C2×C4—48no—
1049C2×C4—48no—
1050C2×C4—48no—
1051C2×C4—84no—
1052C2×C4—84no—
1053C2×C4—84no—
1054C2×C4—84no—
1055C2×C4—816no—
1056C2×C4—84no—
1057C2×C4—88no—
1058C2×C4—164no—
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—22no—
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—24no—
1072C22—24no—
1073C22—416no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22—44no—
1086C22—42no—
1087C22—42no—
1088C22C2×#56214yes—
1089C22C22×H(5,𝔽2)11yescharacteristic
1090C22C22×H(5,𝔽2)11yescharacteristic
1091C22C22×2−1+411yescharacteristic
1092C22C2×#58512yes—
1093C222−1+612yes—
1094C4—44no—
1095C4—44no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—44no—
1102C4—42no—
1103C4—42no—
1104C4—44no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—44no—
1113C4C2×#56214yes—
1114C4C2×#56214yes—
1115C2—24no—
1116C2—44no—
1117C2—82no—
1118C2—82no—
1119C2C22×#56211yescharacteristic
1120C2#6282411yescharacteristic
1121C2#6288711yescharacteristic
1122C2#6292712yes—
1123C2#6292812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
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. #53030C2semidirect
3. #53025C2semidirect
4. #53010C2semidirect
5. #52800C2semidirect
6. #46072C2semidirect
7. #46055C2semidirect
8. #45682C2semidirect
9. #45626C2semidirect
10. #45475C2semidirect
11. #35673C2semidirect
12. #35662C2semidirect
13. #35661C2semidirect
14. #35633C2semidirect
15. #35620C2semidirect
16. #35618C2semidirect
17. #35339C2semidirect
18. #35334C2semidirect
19. #35312C2semidirect
20. #35308C2semidirect
21. #35224C2semidirect
23. #34813C2semidirect
24. C2×#2503C2semidirect
25. #34742C2semidirect
38. #2864C22semidirect
39. #2862C22semidirect
40. #2861C22semidirect
41. #2857C22semidirect
42. #2851C22semidirect
43. #2850C22semidirect
47. #2841C22semidirect
48. #2839C22semidirect
49. #2839C22semidirect
50. #2836C22semidirect
51. #2832C22semidirect
52. #2831C22semidirect
53. #2831C22semidirect
54. #2827C22semidirect
56. #2788C22semidirect
57. #2783C22semidirect
59. #2755C22semidirect
60. #2755C22semidirect
63. #2750C22semidirect
65. #2744C22semidirect
68. #2741C22semidirect
71. #2739C22semidirect
76. #2647C22semidirect
77. #2642C22semidirect
78. #2640C22semidirect
79. #2628C22semidirect
81. #2621C22semidirect
82. #2620C22semidirect
84. #2582C22semidirect
85. #2581C22semidirect
86. #2581C22semidirect
87. #2580C22semidirect
88. #2570C22semidirect
89. #2570C22semidirect
91. #2568C22semidirect
92. #2566C22semidirect
93. #2565C22semidirect
95. #2563C22semidirect
99. #2504C22semidirect
104. #2503C22semidirect
105. #2500C22semidirect
106. #2499C22semidirect
109. #2492C22semidirect
113. #2489C22semidirect
118. #2453C22semidirect
119. #2451C22semidirect
121. #2448C22semidirect
122. #2446C22semidirect
126. #2442C22semidirect
129. #2439C22semidirect
133. #2429C22semidirect
135. #2427C22semidirect
139. #2423C22semidirect
142. #2421C22semidirect
143. #2421C22semidirect
145. #2420C22semidirect

Maximal subgroups

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

subgroupindex
#531272
#530302
#530252
#530102
#528002
#460722
#460552
#456822
#456262
#454752
#356732
#356622
#356612
#356332
#356202
#356182
#353392
#353342
#353122
#353082
#352242
#352232
#348132
C2×#25032
#347422