Finite Group Databasebeta

← #8509007

Subgroups — #8509007

Order 512.

5495 conjugacy classes of subgroups.

The subgroup lattice has 1021 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#57151C218yesmaximal, complemented
3#53655C218yesmaximal, complemented
4#53488C214yesmaximal, complemented
5#53190C214yesmaximal, complemented
6#52957C212yesmaximal, complemented
7#52103C211yesmaximal, characteristic, complemented
8#48143C214yesmaximal, complemented
9#46089C212yesmaximal, complemented
10#45493C212yesmaximal, complemented
11#45079C214yesmaximal, complemented
12#42992C212yesmaximal, complemented
13#42454C214yesmaximal, complemented
14#39381C212yesmaximal, complemented
15#38904C212yesmaximal, complemented
16#37648C214yesmaximal, complemented
17#37271C214yesmaximal, complemented
18#37134C212yesmaximal, complemented
19#36260C211yesmaximal, characteristic, complemented
20#35196C212yesmaximal, complemented
21C2×#547C2211yescharacteristic, complemented
22C2×#546C2214yescomplemented
23C2×D42C2211yescharacteristic
24C2×#542C2214yescomplemented
25C2×#537C2212yes—
26C2×#525C2214yescomplemented
27C22×#121C2212yescomplemented
28#2858C2211yescharacteristic, complemented
29#2856C2212yescomplemented
30#2855C2214yescomplemented
31#2850C2214yescomplemented
32#2848C2214yescomplemented
33#2847C2212yescomplemented
34#2842C2214yescomplemented
35#2836C2218yescomplemented
36#2828C2214yescomplemented
37#2824C2214yescomplemented
38#2813C2214yescomplemented
39#2813C2218yescomplemented
40#2807C2214yescomplemented
41#2804C2212yes—
42#2804C2212yescomplemented
43#2790C2218yescomplemented
44#2784C2214yescomplemented
45#2780C2218yescomplemented
46#2780C2218yescomplemented
47#2761C2218yescomplemented
48#2753C2218yescomplemented
49#2748C2214yes—
50#2733C2214yescomplemented
51#2732C2214yescomplemented
52#2727C2214yescomplemented
53#2723C2218yescomplemented
54#2714C2218yescomplemented
55#2710C2218yescomplemented
56#2706C2218yescomplemented
57#2706C2218yescomplemented
58#2701C2218yescomplemented
59#2701C2218yescomplemented
60#2699C2218yescomplemented
61#2692C2218yescomplemented
62#2688C2218yescomplemented
63#2685C2218yescomplemented
64#2683C2211yescharacteristic
65#2682C2218yescomplemented
66#2682C2214yescomplemented
67#2682C2212yescomplemented
68#2681C2218yescomplemented
69#2681C2218yescomplemented
70#2681C2214yescomplemented
71#2680C2212yescomplemented
72#2679C2211yescharacteristic
73#2678C2218yescomplemented
74#2678C2214yescomplemented
75#2676C2218yescomplemented
76#2676C2218yescomplemented
77#2675C2218yescomplemented
78#2675C2214yescomplemented
79#2673C2218yescomplemented
80#2671C2218yescomplemented
81#2670C2218yescomplemented
82#2669C2212yes—
83#2668C2218yes—
84#2663C2214yescomplemented
85#2649C2218yescomplemented
86#2649C2218yescomplemented
87#2635C2218yescomplemented
88#2627C2214yescomplemented
89#2622C2214yescomplemented
90#2620C2214yescomplemented
91#2616C2212yescomplemented
92#2615C2214yescomplemented
93#2591C2214yescomplemented
94#2580C2218yescomplemented
95#2571C2212yescomplemented
96#2571C2212yescomplemented
97#2563C2214yescomplemented
98#2554C2218yescomplemented
99#2553C2218yescomplemented
100#2547C2212yescomplemented
101#2542C2211yescharacteristic
102#2542C2212yescomplemented
103#2541C2211yescharacteristic, complemented
104#2540C2214yescomplemented
105#2540C2214yescomplemented
106#2539C2218yescomplemented
107#2539C2218yescomplemented
108#2538C2214yescomplemented
109#2537C2212yes—
110#2537C2214yescomplemented
111#2536C2214yescomplemented
112#2535C2214yes—
113#2516C2218yescomplemented
114#2504C2212yescomplemented
115#2503C2212yescomplemented
116#2501C2212yescomplemented
117#2497C2214yescomplemented
118#2487C2212yes—
119#2487C2212yescomplemented
120#2472C2218yescomplemented
121#2457C2218yescomplemented
122#2437C2218yescomplemented
123#2437C2218yescomplemented
124#2433C2212yes—
125#2429C2214yescomplemented
126#2428C2214yescomplemented
127#2426C2214yescomplemented
128#2426C2218yescomplemented
129#2424C2218yescomplemented
130#2423C2214yescomplemented
131#2422C2214yescomplemented
132#2421C2214yescomplemented
133#2420C2214yescomplemented
134#2417C2214yescomplemented
135#2416C2214yescomplemented
136#2410C2218yescomplemented
137#2410C2214yescomplemented
138#2408C2214yes—
139#2408C2218yescomplemented
140#2407C2214yescomplemented
141#2403C2214yes—
142#2392C2214yescomplemented
143#2388C2212yescomplemented
144#2375C2214yes—
145#2367C2214yescomplemented
146#2366C2212yes—
147D4×C4⋊C4C2214yescomplemented
148#2341C2212yescomplemented
149D4×C22⋊C4C2212yescomplemented
150#2324C2214yescomplemented
151#2314C2214yescomplemented
152#2308C2214yes—
153C4×C4⋊Q8C2212yescomplemented
154C4×#127C2211yescharacteristic
155C4×#120C2212yes—
156#2293C2212yescomplemented
157C2×#390C2212yes—
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2312yes—
161C23×D4C2312yes—
162C23×D4C2312yes—
163C23×D4C2314yes—
164C24×C4C2312yes—
165#547—44no—
166#546—416no—
167D42—44no—
168#542—416no—
169#537—48no—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×#127C2311yescharacteristic
173C2×#127C2311yescharacteristic
174C2×#127C2312yes—
175C2×#126C2318yes—
176C2×#124C2314yes—
177C2×#124C2318yes—
178C2×#124C2314yes—
179#525—416no—
180C2×#123C2314yes—
181C2×#123C2314yes—
182C2×#123C2314yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×#123C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×#121—48no—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2312yes—
201C2×#121C2318yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2318yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2318yes—
214C2×#120C2312yes—
215C2×#120C2314yes—
216C2×#120C2314yes—
217C2×#120C2318yes—
218C2×#120C2314yes—
219C2×#120C2314yes—
220C2×#120C2318yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×#117C2314yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C22⋊C4C2314yes—
238C22×C22⋊C4C2318yes—
239C22×C22⋊C4C2314yes—
240C22×C42C2312yes—
241#400C2318yes—
242#400C2314yes—
243#400C2318yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#399C2314yes—
248#399C2314yes—
249#399C2318yes—
250#399C2318yes—
251#399C2314yes—
252#399C2318yes—
253#399C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2314yes—
273#396C2314yes—
274#396C2318yes—
275#395C2314yes—
276#395C2312yes—
277#394C2318yes—
278#394C2318yes—
279#394C2312yes—
280#394C2318yes—
281#394C2318yes—
282#394C2314yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2314yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#393C2318yes—
297#393C2318yes—
298#393C2312yes—
299#393C2318yes—
300#392C2314yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2318yes—
305#392C2314yes—
306#392C2318yes—
307#392C2318yes—
308#392C2314yes—
309#392C2312yes—
310#392C2318yes—
311#392C2318yes—
312#392C2318yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#390C2314yes—
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#390C2318yes—
320#390C2312yes—
321#390C2314yes—
322#390C2318yes—
323#390C2312yes—
324#390C2318yes—
325#390C2312yes—
326#390C2318yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2312yes—
331#390C2318yes—
332#390C2318yes—
333#390C2318yes—
334#390C2312yes—
335#390C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2314yes—
341#389C2312yes—
342#389C2318yes—
343#389C2312yes—
344#389C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2314yes—
355#388C2318yes—
356#388C2314yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#386C2312yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2314yes—
374#386C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2314yes—
378#385C2314yes—
379#385C2318yes—
380#385C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2312yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#384C2311yescharacteristic
392#384C2312yes—
393#384C2314yes—
394#384C2312yes—
395#382C2318yes—
396#382C2314yes—
397#382C2314yes—
398#381C2318yes—
399#381C2318yes—
400#380C2312yes—
401#380C2312yes—
402#380C2314yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2318yes—
410#380C2318yes—
411#379C2318yes—
412#379C2312yes—
413#379C2318yes—
414#379C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2312yes—
427C43C2311yescharacteristic
428C25C2414yes—
429C25C2412yes—
430C2×#41—28no—
431C2×#41—48no—
432C2×#41—44no—
433C2×#41—48no—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2412yes—
437C22×D4—28no—
438C22×D4—28no—
439C22×D4—48no—
440C22×D4—44no—
441C22×D4—48no—
442C22×D4—82no—
443C22×D4—88no—
444C22×D4C2412yes—
445C22×D4C2414yes—
446C22×D4C2411yescharacteristic
447C22×D4C2414yes—
448C22×D4C2412yes—
449C22×D4C2411yescharacteristic
450C22×D4C2414yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2418yes—
454C22×D4C2412yes—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2418yes—
458C22×D4C2412yes—
459C22×D4C2418yes—
460C22×D4C2414yes—
461C22×D4C2418yes—
462C22×D4C2411yescharacteristic
463C23×C4—44no—
464C23×C4—48no—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2418yes—
474C23×C4C2414yes—
475C23×C4C2414yes—
476C4⋊Q8—28no—
477C4⋊Q8—42no—
478#127—24no—
479#127—42no—
480#127—82no—
481#126—416no—
482#124—216no—
483#124—416no—
484#124—84no—
485#123—48no—
486#123—48no—
487#123—416no—
488#123—416no—
489#123—48no—
490#123—88no—
491C22⋊Q8—48no—
492C22⋊Q8—48no—
493C22⋊Q8—48no—
494C22⋊Q8—416no—
495C22⋊Q8—48no—
496C22⋊Q8—48no—
497C22⋊Q8—48no—
498C22⋊Q8—44no—
499C22⋊Q8—84no—
500C22⋊Q8—84no—
501#121—216no—
502#121—416no—
503#121—48no—
504#121—48no—
505#121—416no—
506#121—416no—
507#121—48no—
508#121—48no—
509#121—44no—
510#121—48no—
511#121—48no—
512#121—44no—
513#121—44no—
514#121—84no—
515#121—88no—
516#121—88no—
517#121—88no—
518#120—28no—
519#120—48no—
520#120—48no—
521#120—416no—
522#120—48no—
523#120—84no—
524#120—88no—
525C4×Q8—48no—
526C4×Q8—84no—
527C4×D4—24no—
528C4×D4—28no—
529C4×D4—216no—
530C4×D4—28no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534C4×D4—42no—
535C4×D4—42no—
536C4×D4—88no—
537#117—216no—
538C2×C4⋊C4—44no—
539C2×C4⋊C4—44no—
540C2×C4⋊C4—44no—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2411yescharacteristic
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2412yes—
571C2×C22⋊C4—416no—
572C2×C22⋊C4—48no—
573C2×C22⋊C4—84no—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C42—82no—
616C2×C42C2414yes—
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2418yes—
620C2×C42C2412yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2412yes—
624C2×C42C2411yescharacteristic
625C2×C42C2412yes—
626#95C2412yes—
627#95C2414yes—
628#95C2414yes—
629#95C2412yes—
630#95C2414yes—
631#95C2412yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648C24—28no—
649C24—28no—
650C24—24no—
651C24—42no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—42no—
656C24—48no—
657C24—48no—
658C24C2514yes—
659C24C2514yes—
660C24C2512yes—
661C24C2512yes—
662C24C2512yes—
663#41—816no—
664#41—816no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—28no—
668C2×Q8—44no—
669C2×Q8—42no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—216no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—24no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—22no—
684C2×D4—24no—
685C2×D4—41no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—48no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—42no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—816no—
722C2×D4—816no—
723C2×D4—832no—
724C2×D4H(5,𝔽2)14yes—
725C2×D42−1+414yes—
726C22×C4—24no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—24no—
736C22×C4—28no—
737C22×C4—42no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—44no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—44no—
750C22×C4—48no—
751C22×C4—48no—
752C22×C4—48no—
753C22×C4—816no—
754C22×C4C2512yes—
755C22×C4C2514yes—
756C22×C4C2518yes—
757C22×C4C2518yes—
758C22×C4C2514yes—
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2511yescharacteristic
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—28no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—24no—
773C4⋊C4—22no—
774C4⋊C4—24no—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—41no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—42no—
782C4⋊C4—44no—
783C4⋊C4—41no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—48no—
788C4⋊C4—44no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—42no—
796C4⋊C4—42no—
797C4⋊C4—48no—
798C4⋊C4—42no—
799C22⋊C4—216no—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—28no—
803C22⋊C4—216no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—216no—
810C22⋊C4—28no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—42no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—42no—
818C22⋊C4—44no—
819C22⋊C4—44no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—42no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C42—28no—
841C42—22no—
842C42—22no—
843C42—41no—
844C42—44no—
845C42—42no—
846C42—48no—
847C42—48no—
848C42—42no—
849C42H(5,𝔽2)18yes—
850C23—24no—
851C23—24no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—24no—
857C23—24no—
858C23—28no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—22no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—28no—
871C23—22no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—416no—
876C23—48no—
877C23—84no—
878C23—88no—
879C23—88no—
880C23—88no—
881C23—816no—
882C23—84no—
883C23—88no—
884C23—168no—
885C23C2×H(5,𝔽2)14yes—
886C23C2×2−1+414yes—
887C23C2611yescharacteristic
888Q8—48no—
889Q8—88no—
890Q8—84no—
891D4—28no—
892D4—44no—
893D4—416no—
894D4—48no—
895D4—84no—
896D4—82no—
897D4—84no—
898D4—88no—
899D4—88no—
900D4—816no—
901D4—88no—
902D4—88no—
903D4—88no—
904D4—816no—
905D4—84no—
906D4—88no—
907D4—162no—
908D4—168no—
909D4—168no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—21no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—28no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—416no—
948C2×C4—48no—
949C2×C4—88no—
950C2×C4—88no—
951C2×C4—88no—
952C2×C4—84no—
953C2×C4—88no—
954C2×C4—164no—
955C2×C4—168no—
956C2×C4C2×H(5,𝔽2)14yes—
957C2×C4C2×H(5,𝔽2)14yes—
958C2×C4C2×H(5,𝔽2)14yes—
959C2×C4C2×H(5,𝔽2)12yes—
960C2×C4C2×2−1+412yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—42no—
967C22—42no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—42no—
973C22—44no—
974C22—42no—
975C22—44no—
976C22—44no—
977C22—48no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—42no—
983C22—44no—
984C22—44no—
985C22—44no—
986C22—44no—
987C22—48no—
988C22—816no—
989C22—1616no—
990C22C22×H(5,𝔽2)11yescharacteristic
991C22C22×H(5,𝔽2)12yes—
992C22C22×2−1+411yescharacteristic
993C22H(7,𝔽2)12yes—
994C22H(7,𝔽2)11yescharacteristic
995C4—24no—
996C4—22no—
997C4—24no—
998C4—42no—
999C4—44no—
1000C4—42no—
1001C4—44no—
1002C4—48no—
1003C4—41no—
1004C4—44no—
1005C4—44no—
1006C4—48no—
1007C4—42no—
1008C4—44no—
1009C4#354314yes—
1010C2—44no—
1011C2—44no—
1012C2—82no—
1013C2—84no—
1014C2—84no—
1015C2C2×#354311yescharacteristic
1016C2#6288012yes—
1017C2#6289411yescharacteristic
1018C2#6294412yes—
1019C2#6304511yescharacteristic
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. #59864C2semidirect
2. #57151C2semidirect
3. #53655C2semidirect
4. #53488C2semidirect
5. #53190C2semidirect
6. #52957C2semidirect
7. #52103C2semidirect
8. #48143C2semidirect
9. #46089C2semidirect
10. #45493C2semidirect
11. #45079C2semidirect
12. #42992C2semidirect
13. #42454C2semidirect
14. #39381C2semidirect
15. #38904C2semidirect
16. #37648C2semidirect
17. #37271C2semidirect
18. #37134C2semidirect
19. #36260C2semidirect
20. #35196C2semidirect
21. C2×#547C22semidirect
22. C2×#546C22semidirect
24. C2×#542C22semidirect
26. C2×#525C22semidirect
27. C22×#121C22semidirect
28. #2858C22semidirect
29. #2856C22semidirect
30. #2855C22semidirect
31. #2850C22semidirect
32. #2848C22semidirect
33. #2847C22semidirect
34. #2842C22semidirect
35. #2836C22semidirect
36. #2828C22semidirect
37. #2824C22semidirect
38. #2813C22semidirect
39. #2813C22semidirect
40. #2807C22semidirect
42. #2804C22semidirect
43. #2790C22semidirect
44. #2784C22semidirect
45. #2780C22semidirect
46. #2780C22semidirect
47. #2761C22semidirect
48. #2753C22semidirect
50. #2733C22semidirect
51. #2732C22semidirect
52. #2727C22semidirect
53. #2723C22semidirect
54. #2714C22semidirect
55. #2710C22semidirect
56. #2706C22semidirect
57. #2706C22semidirect
58. #2701C22semidirect
59. #2701C22semidirect
60. #2699C22semidirect
61. #2692C22semidirect
62. #2688C22semidirect
63. #2685C22semidirect
65. #2682C22semidirect
66. #2682C22semidirect
67. #2682C22semidirect
68. #2681C22semidirect
69. #2681C22semidirect
70. #2681C22semidirect
71. #2680C22semidirect
73. #2678C22semidirect
74. #2678C22semidirect
75. #2676C22semidirect
76. #2676C22semidirect
77. #2675C22semidirect
78. #2675C22semidirect
79. #2673C22semidirect
80. #2671C22semidirect
81. #2670C22semidirect
84. #2663C22semidirect
85. #2649C22semidirect
86. #2649C22semidirect
87. #2635C22semidirect
88. #2627C22semidirect
89. #2622C22semidirect
90. #2620C22semidirect
91. #2616C22semidirect
92. #2615C22semidirect
93. #2591C22semidirect
94. #2580C22semidirect
95. #2571C22semidirect
96. #2571C22semidirect
97. #2563C22semidirect
98. #2554C22semidirect
99. #2553C22semidirect
100. #2547C22semidirect
102. #2542C22semidirect
103. #2541C22semidirect
104. #2540C22semidirect
105. #2540C22semidirect
106. #2539C22semidirect
107. #2539C22semidirect
108. #2538C22semidirect
110. #2537C22semidirect
111. #2536C22semidirect
113. #2516C22semidirect
114. #2504C22semidirect
115. #2503C22semidirect
116. #2501C22semidirect
117. #2497C22semidirect
119. #2487C22semidirect
120. #2472C22semidirect
121. #2457C22semidirect
122. #2437C22semidirect
123. #2437C22semidirect
125. #2429C22semidirect
126. #2428C22semidirect
127. #2426C22semidirect
128. #2426C22semidirect
129. #2424C22semidirect
130. #2423C22semidirect
131. #2422C22semidirect
132. #2421C22semidirect
133. #2420C22semidirect
134. #2417C22semidirect
135. #2416C22semidirect
136. #2410C22semidirect
137. #2410C22semidirect
139. #2408C22semidirect
140. #2407C22semidirect
142. #2392C22semidirect
143. #2388C22semidirect
145. #2367C22semidirect
147. D4×C4⋊C4C22semidirect
148. #2341C22semidirect
149. D4×C22⋊C4C22semidirect
150. #2324C22semidirect
151. #2314C22semidirect
153. C4×C4⋊Q8C22semidirect
156. #2293C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598642
#571512
#536552
#534882
#531902
#529572
#521032
#481432
#460892
#454932
#450792
#429922
#424542
#393812
#389042
#376482
#372712
#371342
#362602
#351962