Finite Group Databasebeta

← #8722286

Subgroups — #8722286

Order 512.

4234 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59432C213yesmaximal, complemented
2#59201C213yesmaximal, complemented
3#59197C213yesmaximal, complemented
4#58169C212yesmaximal, complemented
5#57666C216yesmaximal, complemented
6#55762C216yesmaximal, complemented
7#53119C213yesmaximal, complemented
8#52301C211yesmaximal, characteristic, complemented
9#46884C216yesmaximal, complemented
10#45212C213yesmaximal, complemented
11#44099C216yesmaximal, complemented
12#42599C213yesmaximal, complemented
13#41400C216yesmaximal, complemented
14#39910C213yesmaximal, complemented
15#39240C213yesmaximal, complemented
16#38938C213yesmaximal, complemented
17#35849C213yesmaximal, complemented
18#2860C2211yescharacteristic, complemented
19#2847C2211yescharacteristic, complemented
20#2847C2211yescharacteristic, complemented
21#2839C2216yescomplemented
22#2836C2216yescomplemented
23#2832C2216yescomplemented
24#2827C2216yes—
25#2821C2216yescomplemented
26#2804C2213yes—
27#2786C2216yes—
28#2784C2216yescomplemented
29#2782C2213yes—
30#2782C2213yes—
31#2781C2216yescomplemented
32#2770C2216yescomplemented
33#2764C2216yescomplemented
34#2762C2216yescomplemented
35#2759C2216yescomplemented
36#2758C2216yescomplemented
37#2758C2216yescomplemented
38#2757C2216yescomplemented
39#2756C2216yes—
40#2751C2216yescomplemented
41#2749C2216yes—
42#2747C2216yescomplemented
43#2743C2216yescomplemented
44#2741C2216yes—
45#2741C2216yescomplemented
46#2740C2216yes—
47#2737C2216yescomplemented
48#2736C2216yescomplemented
49#2729C2216yescomplemented
50#2716C2216yescomplemented
51#2716C2216yescomplemented
52#2710C2216yes—
53#2702C2216yes—
54#2697C2216yes—
55#2691C2216yes—
56#2686C2216yes—
57#2685C2216yescomplemented
58#2684C2213yes—
59#2684C2213yes—
60#2679C2211yescharacteristic
61#2668C2216yes—
62#2654C2216yescomplemented
63#2653C2216yescomplemented
64#2651C2216yescomplemented
65#2649C2216yescomplemented
66#2647C2213yescomplemented
67#2644C2211yescharacteristic, complemented
68#2639C2216yes—
69#2630C2216yes—
70#2596C2216yescomplemented
71#2584C2213yescomplemented
72#2580C2213yescomplemented
73#2578C2216yescomplemented
74#2577C2216yescomplemented
75#2573C2216yescomplemented
76#2572C2216yes—
77#2572C2216yes—
78#2572C2216yescomplemented
79#2569C2216yescomplemented
80#2563C2213yes—
81#2562C2213yes—
82#2560C2216yes—
83#2559C2216yes—
84#2546C2213yescomplemented
85#2537C2213yes—
86#2525C2216yescomplemented
87#2524C2216yescomplemented
88#2524C2216yescomplemented
89#2523C2216yescomplemented
90#2523C2216yescomplemented
91#2516C2216yescomplemented
92#2515C2216yescomplemented
93#2515C2216yescomplemented
94#2515C2216yescomplemented
95#2510C2216yes—
96#2498C2216yes—
97#2497C2213yescomplemented
98#2496C2213yescomplemented
99#2495C2213yescomplemented
100#2495C2213yescomplemented
101#2495C2213yescomplemented
102#2495C2213yescomplemented
103#2495C2213yescomplemented
104#2494C2213yescomplemented
105#2493C2216yescomplemented
106#2493C2216yescomplemented
107#2492C2216yescomplemented
108#2491C2216yes—
109#2491C2213yescomplemented
110#2490C2213yescomplemented
111#2487C2213yes—
112#2486C2213yes—
113#2485C2213yes—
114#2485C2213yes—
115#2476C2216yes—
116#2474C2216yes—
117#2472C2216yescomplemented
118#2447C2216yescomplemented
119#2444C2216yes—
120#2442C2213yescomplemented
121#2442C2213yescomplemented
122#2441C2213yescomplemented
123#2440C2213yescomplemented
124#2439C2213yescomplemented
125#2439C2213yescomplemented
126#2424C2216yes—
127#2420C2213yescomplemented
128#2420C2213yescomplemented
129#2416C2213yes—
130#2414C2213yes—
131#2412C2216yes—
132#2398C2213yes—
133#2398C2213yes—
134#2395C2216yescomplemented
135#2374C2216yes—
136#2363C2213yescomplemented
137#2361C2213yescomplemented
138#2355C2213yescomplemented
139#2352C2213yes—
140#2352C2213yes—
141#2352C2213yes—
142#2347C2213yescomplemented
143#2347C2213yescomplemented
144#2347C2216yescomplemented
145#2345C2213yescomplemented
146#2344C2213yescomplemented
147#2342C2216yescomplemented
148#2337C2216yescomplemented
149#2333C2216yes—
150#2331C2213yescomplemented
151#2318C2216yescomplemented
152C4×#125C2213yescomplemented
153C4×#124C2213yes—
154C4×#120C2213yes—
155C4×#120C2213yes—
156#2280C2213yescomplemented
157C2×#380C2213yescomplemented
158#2275C2211yescharacteristic, complemented
159C24×C4C2311yescharacteristic
160C24×C4C2311yescharacteristic
161C2×C4⋊Q8C2313yes—
162C2×C4⋊Q8C2316yes—
163C2×#126C2316yes—
164C2×#126C2312yes—
165C2×#125C2313yes—
166C2×#124C2316yes—
167C2×#124C2313yes—
168C2×#123C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×#121C2316yes—
171C2×#121C2313yes—
172C2×#121C2313yes—
173C2×#121C2316yes—
174C2×#120C2313yes—
175C2×#120C2313yes—
176C2×#120C2312yes—
177C2×#120C2312yes—
178C2×C4×Q8C2313yes—
179C2×C4×D4C2313yes—
180C2×C4×D4C2313yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2313yes—
183C2×C4×D4C2313yes—
184C2×#117C2316yes—
185C2×#117C2313yes—
186C2×#117C2313yes—
187C22×C4⋊C4C2313yes—
188C22×C4⋊C4C2313yes—
189C22×C22⋊C4C2316yes—
190#401C2316yes—
191#400C2316yes—
192#400C2316yes—
193#400C2316yes—
194#400C2316yes—
195#400C2316yes—
196#400C2316yes—
197#400C2316yes—
198#400C2316yes—
199#400C2316yes—
200#400C2313yes—
201#400C2316yes—
202#400C2316yes—
203#400C2316yes—
204#400C2316yes—
205#400C2313yes—
206#400C2313yes—
207#400C2313yes—
208#399C2316yes—
209#399C2316yes—
210#399C2316yes—
211#398C2316yes—
212#398C2316yes—
213#398C2316yes—
214#398C2316yes—
215#398C2316yes—
216#398C2316yes—
217#398C2316yes—
218#398C2316yes—
219#398C2316yes—
220#397C2316yes—
221#397C2316yes—
222#397C2316yes—
223#397C2316yes—
224#397C2316yes—
225#397C2316yes—
226#397C2316yes—
227#397C2316yes—
228#397C2316yes—
229#397C2316yes—
230#397C2313yes—
231#397C2316yes—
232#397C2316yes—
233#397C2313yes—
234#397C2316yes—
235#397C2316yes—
236#397C2313yes—
237#397C2313yes—
238#396C2316yes—
239#396C2316yes—
240#396C2316yes—
241#396C2312yes—
242#396C2316yes—
243#396C2316yes—
244#395C2316yes—
245#395C2316yes—
246#394C2313yes—
247#394C2316yes—
248#394C2313yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#394C2316yes—
254#394C2316yes—
255#394C2316yes—
256#394C2313yes—
257#394C2316yes—
258#394C2316yes—
259#394C2316yes—
260#394C2313yes—
261#393C2316yes—
262#393C2316yes—
263#393C2316yes—
264#393C2313yes—
265#393C2316yes—
266#393C2313yes—
267#393C2316yes—
268#393C2313yes—
269#393C2316yes—
270#393C2313yes—
271#392C2316yes—
272#391C2316yes—
273#391C2316yes—
274#391C2316yes—
275#391C2316yes—
276#391C2316yes—
277#391C2316yes—
278#391C2313yes—
279#390C2316yes—
280#390C2313yes—
281#390C2313yes—
282#390C2316yes—
283#390C2316yes—
284#390C2316yes—
285#390C2313yes—
286#389C2313yes—
287#389C2313yes—
288#389C2316yes—
289#389C2313yes—
290#389C2316yes—
291#389C2316yes—
292#389C2313yes—
293#389C2313yes—
294#389C2313yes—
295#389C2313yes—
296#389C2313yes—
297#389C2313yes—
298#389C2313yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2313yes—
309#388C2316yes—
310#388C2316yes—
311#388C2316yes—
312#388C2316yes—
313#388C2316yes—
314#388C2316yes—
315#388C2316yes—
316#388C2313yes—
317#388C2316yes—
318#388C2316yes—
319#388C2313yes—
320#388C2316yes—
321#388C2316yes—
322#388C2316yes—
323#388C2316yes—
324#388C2316yes—
325#388C2316yes—
326#388C2313yes—
327#387C2316yes—
328#387C2316yes—
329#387C2316yes—
330#387C2316yes—
331#387C2316yes—
332#387C2316yes—
333#387C2316yes—
334#387C2316yes—
335#387C2316yes—
336#387C2316yes—
337#387C2316yes—
338#387C2316yes—
339#387C2316yes—
340#387C2316yes—
341#387C2316yes—
342#387C2316yes—
343#387C2316yes—
344#387C2316yes—
345#387C2316yes—
346#387C2316yes—
347#387C2316yes—
348#386C2316yes—
349#386C2316yes—
350#386C2313yes—
351#386C2313yes—
352#386C2316yes—
353#386C2316yes—
354#386C2316yes—
355#386C2316yes—
356#386C2316yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2313yes—
362#386C2313yes—
363#386C2313yes—
364#386C2313yes—
365#385C2313yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C2316yes—
370#385C2313yes—
371#385C2316yes—
372#385C2313yes—
373#385C2316yes—
374#385C2316yes—
375#385C2313yes—
376#385C2313yes—
377#385C2313yes—
378#384C2313yes—
379#383C2316yes—
380#383C2316yes—
381#383C2316yes—
382#383C2316yes—
383#383C2316yes—
384#383C2316yes—
385#383C2316yes—
386#382C2313yes—
387#382C2316yes—
388#382C2313yes—
389#382C2313yes—
390#382C2313yes—
391#381C2316yes—
392#381C2316yes—
393#381C2316yes—
394#381C2316yes—
395#381C2316yes—
396#380C2313yes—
397#380C2313yes—
398#380C2313yes—
399#380C2313yes—
400#380C2313yes—
401#380C2313yes—
402#380C2313yes—
403#380C2313yes—
404#380C2316yes—
405#380C2316yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2313yes—
411#380C2313yes—
412#379C2313yes—
413#379C2316yes—
414#379C2313yes—
415C4×C4⋊C4C2316yes—
416C4×C4⋊C4C2313yes—
417C4×C4⋊C4C2316yes—
418C4×C4⋊C4C2313yes—
419C4×C4⋊C4C2316yes—
420C4×C4⋊C4C2313yes—
421C4×C4⋊C4C2316yes—
422C4×C4⋊C4C2313yes—
423C4×C4⋊C4C2313yes—
424C4×C4⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2316yes—
429C4×C22⋊C4C2316yes—
430C4×C22⋊C4C2316yes—
431C4×C22⋊C4C2316yes—
432C4×C22⋊C4C2316yes—
433C4×C22⋊C4C2313yes—
434C4×C22⋊C4C2313yes—
435C4×C22⋊C4C2313yes—
436C4×C22⋊C4C2313yes—
437C4×C22⋊C4C2313yes—
438C4×C22⋊C4C2313yes—
439#376C2311yescharacteristic
440#376C2311yescharacteristic
441C2×#95C2316yes—
442C2×#95C2312yes—
443C43C2311yescharacteristic
444C25C2411yescharacteristic
445C25C2411yescharacteristic
446C22×Q8C2413yes—
447C22×Q8C2416yes—
448C22×D4C2411yescharacteristic
449C22×D4C2413yes—
450C22×D4C2413yes—
451C22×D4C2413yes—
452C22×D4C2416yes—
453C22×D4C2416yes—
454C23×C4—46no—
455C23×C4—46no—
456C23×C4C2413yes—
457C23×C4C2413yes—
458C23×C4C2416yes—
459C23×C4C2416yes—
460C23×C4C2416yes—
461C23×C4C2413yes—
462C23×C4C2413yes—
463C4⋊Q8—46no—
464C4⋊Q8—86no—
465#126—82no—
466#126—86no—
467#125—46no—
468#124—412no—
469#124—46no—
470#123—412no—
471C22⋊Q8—86no—
472#121—412no—
473#121—46no—
474#121—46no—
475#121—86no—
476#120—46no—
477#120—46no—
478#120—82no—
479#120—82no—
480C4×Q8—46no—
481C4×D4—46no—
482C4×D4—46no—
483C4×D4—46no—
484C4×D4—46no—
485C4×D4—412no—
486#117—412no—
487#117—46no—
488#117—46no—
489C2×C4⋊C4—46no—
490C2×C4⋊C4—46no—
491C2×C4⋊C4C2413yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2413yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2413yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2413yes—
505C2×C4⋊C4C2413yes—
506C2×C4⋊C4C2413yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C22⋊C4—412no—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2413yes—
523C2×C22⋊C4C2413yes—
524C2×C22⋊C4C2413yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2413yes—
530C2×C22⋊C4C2413yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2416yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2413yes—
535C2×C22⋊C4C2413yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2413yes—
540C2×C22⋊C4C2413yes—
541C2×C22⋊C4C2413yes—
542C2×C22⋊C4C2413yes—
543C2×C22⋊C4C2413yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2413yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2413yes—
553C2×C22⋊C4C2413yes—
554C2×C22⋊C4C2416yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2413yes—
557C2×C42C2413yes—
558C2×C42C2413yes—
559C2×C42C2413yes—
560C2×C42C2416yes—
561C2×C42C2416yes—
562C2×C42C2416yes—
563C2×C42C2416yes—
564C2×C42C2416yes—
565C2×C42C2413yes—
566C2×C42C2416yes—
567C2×C42C2411yescharacteristic
568C2×C42C2416yes—
569#95C2411yescharacteristic
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2413yes—
576#95C2411yescharacteristic
577#95C2413yes—
578#95C2413yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2413yes—
583#95C2413yes—
584#95C2416yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2413yes—
590#95C2413yes—
591#95C2416yes—
592#95C2416yes—
593#95C2413yes—
594#95C2413yes—
595#95C2413yes—
596#95C2413yes—
597#95C2416yes—
598#95C2413yes—
599#95C2413yes—
600#95C2413yes—
601#95C2416yes—
602#95C2416yes—
603#95C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C2416yes—
607#95C2416yes—
608#95C2416yes—
609#95C2416yes—
610#95C2416yes—
611#95C2416yes—
612#95C2416yes—
613#95C2416yes—
614#95C2416yes—
615#95C2416yes—
616C24—26no—
617C24—43no—
618C24—43no—
619C24—41no—
620C24—41no—
621C24—43no—
622C24C2513yes—
623C24C2512yes—
624C24C2513yes—
625C2×Q8—43no—
626C2×Q8—43no—
627C2×Q8—43no—
628C2×Q8—46no—
629C2×Q8—46no—
630C2×Q8—46no—
631C2×D4—212no—
632C2×D4—26no—
633C2×D4—26no—
634C2×D4—26no—
635C2×D4—26no—
636C2×D4—43no—
637C2×D4—43no—
638C2×D4—43no—
639C2×D4—43no—
640C2×D4—43no—
641C2×D4—46no—
642C2×D4—46no—
643C2×D4—43no—
644C2×D4—46no—
645C2×D4—46no—
646C2×D4—46no—
647C22×C4—212no—
648C22×C4—26no—
649C22×C4—26no—
650C22×C4—26no—
651C22×C4—26no—
652C22×C4—26no—
653C22×C4—26no—
654C22×C4—46no—
655C22×C4—46no—
656C22×C4—43no—
657C22×C4—43no—
658C22×C4—43no—
659C22×C4—43no—
660C22×C4—43no—
661C22×C4—43no—
662C22×C4—46no—
663C22×C4—46no—
664C22×C4—46no—
665C22×C4—46no—
666C22×C4—46no—
667C22×C4—46no—
668C22×C4—88no—
669C22×C4—88no—
670C22×C4C2513yes—
671C22×C4C2513yes—
672C22×C4C2513yes—
673C22×C4C2516yes—
674C22×C4C2513yes—
675C22×C4C2513yes—
676C22×C4C2513yes—
677C22×C4C2516yes—
678C22×C4C2516yes—
679C22×C4C2516yes—
680C22×C4C2516yes—
681C22×C4C2513yes—
682C22×C4C2513yes—
683C22×C4C2511yescharacteristic
684C4⋊C4—26no—
685C4⋊C4—26no—
686C4⋊C4—26no—
687C4⋊C4—26no—
688C4⋊C4—26no—
689C4⋊C4—46no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C4⋊C4—46no—
693C4⋊C4—43no—
694C4⋊C4—43no—
695C4⋊C4—43no—
696C4⋊C4—46no—
697C4⋊C4—43no—
698C4⋊C4—43no—
699C4⋊C4—43no—
700C4⋊C4—46no—
701C4⋊C4—46no—
702C4⋊C4—46no—
703C4⋊C4—46no—
704C4⋊C4—46no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—46no—
710C4⋊C4—46no—
711C4⋊C4—46no—
712C22⋊C4—212no—
713C22⋊C4—212no—
714C22⋊C4—26no—
715C22⋊C4—26no—
716C22⋊C4—26no—
717C22⋊C4—46no—
718C22⋊C4—46no—
719C22⋊C4—46no—
720C22⋊C4—46no—
721C22⋊C4—43no—
722C22⋊C4—46no—
723C22⋊C4—43no—
724C22⋊C4—43no—
725C22⋊C4—43no—
726C22⋊C4—43no—
727C22⋊C4—43no—
728C22⋊C4—46no—
729C22⋊C4—43no—
730C22⋊C4—43no—
731C22⋊C4—43no—
732C22⋊C4—43no—
733C22⋊C4—43no—
734C22⋊C4—46no—
735C22⋊C4—46no—
736C22⋊C4—46no—
737C22⋊C4—46no—
738C22⋊C4—46no—
739C22⋊C4—46no—
740C22⋊C4—46no—
741C22⋊C4—43no—
742C22⋊C4—46no—
743C22⋊C4—46no—
744C22⋊C4—43no—
745C22⋊C4—46no—
746C22⋊C4—43no—
747C22⋊C4—46no—
748C22⋊C4—43no—
749C42—26no—
750C42—26no—
751C42—26no—
752C42—46no—
753C42—46no—
754C42—46no—
755C42—46no—
756C42—46no—
757C42—43no—
758C42—46no—
759C42—41no—
760C42—46no—
761C23—23no—
762C23—23no—
763C23—23no—
764C23—23no—
765C23—23no—
766C23—23no—
767C23—23no—
768C23—23no—
769C23—23no—
770C23—26no—
771C23—26no—
772C23—23no—
773C23—23no—
774C23—23no—
775C23—23no—
776C23—22no—
777C23—412no—
778C23—86no—
779C23—82no—
780C23—82no—
781C23—86no—
782C23—86no—
783C23#58516yes—
784C23C2611yescharacteristic
785Q8—86no—
786Q8—166no—
787D4—44no—
788D4—86no—
789D4—86no—
790D4—86no—
791D4—812no—
792D4—166no—
793C2×C4—23no—
794C2×C4—23no—
795C2×C4—23no—
796C2×C4—23no—
797C2×C4—23no—
798C2×C4—23no—
799C2×C4—23no—
800C2×C4—23no—
801C2×C4—26no—
802C2×C4—23no—
803C2×C4—23no—
804C2×C4—26no—
805C2×C4—23no—
806C2×C4—23no—
807C2×C4—26no—
808C2×C4—26no—
809C2×C4—26no—
810C2×C4—23no—
811C2×C4—26no—
812C2×C4—26no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—23no—
817C2×C4—23no—
818C2×C4—23no—
819C2×C4—23no—
820C2×C4—26no—
821C2×C4—23no—
822C2×C4—23no—
823C2×C4—26no—
824C2×C4—23no—
825C2×C4—23no—
826C2×C4—23no—
827C2×C4—26no—
828C2×C4—26no—
829C2×C4—23no—
830C2×C4—26no—
831C2×C4—23no—
832C2×C4—412no—
833C2×C4—412no—
834C2×C4—812no—
835C2×C4—86no—
836C2×C4—86no—
837C2×C4—166no—
838C2×C4—166no—
839C2×C4#58516yes—
840C22—26no—
841C22—26no—
842C22—26no—
843C22—43no—
844C22—43no—
845C22—43no—
846C22—43no—
847C22—43no—
848C22—42no—
849C22—46no—
850C22—43no—
851C22—43no—
852C22—43no—
853C22—46no—
854C22—43no—
855C22—43no—
856C22—43no—
857C22—88no—
858C22—88no—
859C22C2×#58513yes—
860C22C2×#58513yes—
861C22H(7,𝔽2)11yescharacteristic
862C4—43no—
863C4—43no—
864C4—43no—
865C4—46no—
866C4—46no—
867C4—43no—
868C4—43no—
869C4—46no—
870C4—46no—
871C4—43no—
872C4—46no—
873C4—43no—
874C4—43no—
875C4#356814yes—
876C2—46no—
877C2—82no—
878C2—83no—
879C2C2×#356811yescharacteristic
880C2#6291013yes—
881C2#6302713yes—
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. #59432C2semidirect
2. #59201C2semidirect
3. #59197C2semidirect
4. #58169C2semidirect
5. #57666C2semidirect
6. #55762C2semidirect
7. #53119C2semidirect
8. #52301C2semidirect
9. #46884C2semidirect
10. #45212C2semidirect
11. #44099C2semidirect
12. #42599C2semidirect
13. #41400C2semidirect
14. #39910C2semidirect
15. #39240C2semidirect
16. #38938C2semidirect
17. #35849C2semidirect
18. #2860C22semidirect
19. #2847C22semidirect
20. #2847C22semidirect
21. #2839C22semidirect
22. #2836C22semidirect
23. #2832C22semidirect
25. #2821C22semidirect
28. #2784C22semidirect
31. #2781C22semidirect
32. #2770C22semidirect
33. #2764C22semidirect
34. #2762C22semidirect
35. #2759C22semidirect
36. #2758C22semidirect
37. #2758C22semidirect
38. #2757C22semidirect
40. #2751C22semidirect
42. #2747C22semidirect
43. #2743C22semidirect
45. #2741C22semidirect
47. #2737C22semidirect
48. #2736C22semidirect
49. #2729C22semidirect
50. #2716C22semidirect
51. #2716C22semidirect
57. #2685C22semidirect
62. #2654C22semidirect
63. #2653C22semidirect
64. #2651C22semidirect
65. #2649C22semidirect
66. #2647C22semidirect
67. #2644C22semidirect
70. #2596C22semidirect
71. #2584C22semidirect
72. #2580C22semidirect
73. #2578C22semidirect
74. #2577C22semidirect
75. #2573C22semidirect
78. #2572C22semidirect
79. #2569C22semidirect
84. #2546C22semidirect
86. #2525C22semidirect
87. #2524C22semidirect
88. #2524C22semidirect
89. #2523C22semidirect
90. #2523C22semidirect
91. #2516C22semidirect
92. #2515C22semidirect
93. #2515C22semidirect
94. #2515C22semidirect
97. #2497C22semidirect
98. #2496C22semidirect
99. #2495C22semidirect
100. #2495C22semidirect
101. #2495C22semidirect
102. #2495C22semidirect
103. #2495C22semidirect
104. #2494C22semidirect
105. #2493C22semidirect
106. #2493C22semidirect
107. #2492C22semidirect
109. #2491C22semidirect
110. #2490C22semidirect
117. #2472C22semidirect
118. #2447C22semidirect
120. #2442C22semidirect
121. #2442C22semidirect
122. #2441C22semidirect
123. #2440C22semidirect
124. #2439C22semidirect
125. #2439C22semidirect
127. #2420C22semidirect
128. #2420C22semidirect
134. #2395C22semidirect
136. #2363C22semidirect
137. #2361C22semidirect
138. #2355C22semidirect
142. #2347C22semidirect
143. #2347C22semidirect
144. #2347C22semidirect
145. #2345C22semidirect
146. #2344C22semidirect
147. #2342C22semidirect
148. #2337C22semidirect
150. #2331C22semidirect
151. #2318C22semidirect
152. C4×#125C22semidirect
156. #2280C22semidirect
157. C2×#380C22semidirect
158. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#594322
#592012
#591972
#581692
#576662
#557622
#531192
#523012
#468842
#452122
#440992
#425992
#414002
#399102
#392402
#389382
#358492