Finite Group Databasebeta

← #8932641

Subgroups — #8932641

Order 512.

5846 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#47122C216yesmaximal, complemented
2#47088C216yesmaximal, complemented
3#47063C213yesmaximal, complemented
4#47037C213yesmaximal, complemented
5#47018C212yesmaximal, complemented
6#47004C213yesmaximal, complemented
7#47003C216yesmaximal, complemented
8#47001C216yesmaximal, complemented
9#47000C216yesmaximal, complemented
10#46996C211yesmaximal, characteristic, complemented
11#35659C213yesmaximal, complemented
12#35357C213yesmaximal, complemented
13#35353C216yesmaximal, complemented
14#35352C216yesmaximal, complemented
15#35349C213yesmaximal, complemented
16C22×2−1+4C2211yescharacteristic, complemented
17C2×#525C2216yescomplemented
18C22×C22⋊Q8C2213yescomplemented
19C2×#520C2213yescomplemented
20C2×#518C2213yes—
21#2841C2216yescomplemented
22#2840C2211yescharacteristic
23#2835C2213yescomplemented
24#2824C2213yescomplemented
25#2812C2211yescharacteristic
26#2801C2212yescomplemented
27#2787C2216yescomplemented
28#2787C2216yescomplemented
29#2784C2216yescomplemented
30#2784C2216yescomplemented
31#2771C2216yescomplemented
32#2764C2216yescomplemented
33#2764C2213yescomplemented
34#2763C2216yescomplemented
35#2763C2213yescomplemented
36#2762C2216yescomplemented
37#2762C2216yescomplemented
38#2762C2216yescomplemented
39#2761C2216yescomplemented
40#2760C2213yes—
41#2760C2213yes—
42#2760C2216yes—
43#2752C2213yescomplemented
44#2750C2216yescomplemented
45#2750C2216yescomplemented
46#2750C2216yescomplemented
47#2750C2216yescomplemented
48#2749C2216yescomplemented
49#2743C2216yescomplemented
50#2742C2213yescomplemented
51#2742C2216yescomplemented
52#2737C2216yescomplemented
53#2708C2216yescomplemented
54#2708C2216yescomplemented
55#2706C2216yescomplemented
56#2703C2216yescomplemented
57#2693C2213yescomplemented
58#2675C2211yescharacteristic, complemented
59#2609C2216yescomplemented
60#2609C2216yescomplemented
61#2600C2216yes—
62#2599C2216yescomplemented
63#2598C2216yes—
64#2598C2216yescomplemented
65#2598C2216yescomplemented
66#2580C2216yescomplemented
67#2579C2216yescomplemented
68#2579C2216yescomplemented
69#2535C2216yes—
70#2534C2216yescomplemented
71#2487C2216yescomplemented
72#2484C2213yescomplemented
73#2482C2213yescomplemented
74#2477C2216yescomplemented
75#2477C2216yescomplemented
76#2477C2216yescomplemented
77#2476C2216yescomplemented
78#2471C2216yescomplemented
79#2470C2216yescomplemented
80#2465C2216yescomplemented
81#2465C2216yescomplemented
82#2465C2216yescomplemented
83#2464C2216yes—
84#2463C2216yes—
85#2463C2213yescomplemented
86#2458C2216yescomplemented
87#2457C2216yes—
88#2456C2216yes—
89#2455C2213yescomplemented
90#2450C2216yescomplemented
91#2450C2216yescomplemented
92#2450C2216yescomplemented
93#2449C2216yescomplemented
94#2449C2216yescomplemented
95#2449C2216yescomplemented
96#2444C2216yescomplemented
97#2443C2216yescomplemented
98#2438C2216yescomplemented
99#2438C2216yescomplemented
100#2438C2216yescomplemented
101#2437C2213yes—
102#2437C2216yes—
103#2430C2216yescomplemented
104#2424C2216yescomplemented
105#2424C2216yescomplemented
106#2418C2216yescomplemented
107#2418C2216yescomplemented
108#2411C2216yescomplemented
109#2410C2216yes—
110#2409C2216yescomplemented
111#2409C2216yescomplemented
112#2409C2216yescomplemented
113#2409C2216yescomplemented
114#2407C2216yes—
115#2407C2216yescomplemented
116#2407C2216yescomplemented
117#2407C2216yescomplemented
118#2406C2216yescomplemented
119#2406C2213yescomplemented
120#2406C2213yescomplemented
121#2406C2213yescomplemented
122#2404C2216yes—
123#2404C2213yes—
124#2404C2213yes—
125#2404C2216yescomplemented
126#2404C2213yescomplemented
127#2403C2213yes—
128#2325C2216yescomplemented
129#2325C2216yescomplemented
130#2322C2216yescomplemented
131#2322C2216yescomplemented
132#2321C2216yes—
133#2318C2216yescomplemented
134#2318C2216yescomplemented
135#2315C2213yescomplemented
136#2315C2213yescomplemented
137#2313C2213yescomplemented
138#2311C2216yescomplemented
139#2310C2213yescomplemented
140#2308C2213yes—
141C4×#120C2216yescomplemented
142C2×#386C2213yes—
143C2×#385C2213yescomplemented
144C2×2−1+4—412no—
145C22×#41C2316yes—
146C22×#41C2311yescharacteristic
147C22×#41C2313yes—
148C22×#41C2313yes—
149C23×Q8C2313yes—
150C23×Q8C2312yes—
151C23×D4C2313yes—
152C24×C4C2313yes—
153#525—424no—
154C2×#123C2316yes—
155C2×#123C2316yes—
156C2×#123C2316yes—
157C2×#123C2316yes—
158C2×C22⋊Q8—412no—
159C2×C22⋊Q8C2316yes—
160C2×C22⋊Q8C2316yes—
161C2×C22⋊Q8C2316yes—
162C2×C22⋊Q8C2316yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C2316yes—
165C2×#121C2316yes—
166C2×#121C2316yes—
167C2×#121C2316yes—
168C2×#121C2316yes—
169C2×#120C2312yes—
170C2×#120C2316yes—
171C2×#120C2316yes—
172C2×#120C2316yes—
173#520—412no—
174#518—412no—
175C2×C4×Q8C2316yes—
176C2×C4×D4C2316yes—
177C2×C4×D4C2316yes—
178C2×C4×D4C2316yes—
179C2×C4×D4C2316yes—
180C2×C4×D4C2316yes—
181C2×C4×D4C2316yes—
182C2×C4×D4C2316yes—
183C2×C4×D4C2316yes—
184C2×C4×D4C2316yes—
185C2×#117C2316yes—
186C2×#117C2316yes—
187C2×#117C2316yes—
188C2×#117C2313yes—
189C22×C4⋊C4C2313yes—
190C22×C4⋊C4C2313yes—
191C22×C4⋊C4C2313yes—
192C22×C4⋊C4C2316yes—
193C22×C22⋊C4C2313yes—
194C22×C22⋊C4C2313yes—
195C22×C22⋊C4C2313yes—
196C22×C22⋊C4C2313yes—
197C22×C22⋊C4C2313yes—
198C22×C22⋊C4C2316yes—
199#401C2312yes—
200#401C2316yes—
201#400C2316yes—
202#400C2316yes—
203#400C2316yes—
204#400C2316yes—
205#400C2316yes—
206#400C2316yes—
207#400C2316yes—
208#400C2316yes—
209#400C2316yes—
210#400C2316yes—
211#399C2312yes—
212#399C2316yes—
213#399C2316yes—
214#399C2313yes—
215#399C2313yes—
216#398C2316yes—
217#398C2316yes—
218#398C2316yes—
219#398C2316yes—
220#398C2316yes—
221#398C2316yes—
222#397C2316yes—
223#397C2316yes—
224#397C2313yes—
225#397C2316yes—
226#397C2316yes—
227#397C2316yes—
228#397C2313yes—
229#396C2316yes—
230#396C2316yes—
231#396C2316yes—
232#396C2316yes—
233#396C2316yes—
234#396C2316yes—
235#396C2312yes—
236#396C2312yes—
237#395C2316yes—
238#395C2316yes—
239#395C2316yes—
240#395C2316yes—
241#395C2316yes—
242#395C2316yes—
243#394C2316yes—
244#394C2316yes—
245#394C2316yes—
246#394C2316yes—
247#394C2316yes—
248#394C2316yes—
249#394C2316yes—
250#394C2316yes—
251#394C2316yes—
252#394C2316yes—
253#393C2316yes—
254#393C2313yes—
255#393C2313yes—
256#393C2316yes—
257#393C2313yes—
258#393C2313yes—
259#393C2316yes—
260#393C2313yes—
261#393C2316yes—
262#393C2316yes—
263#393C2313yes—
264#392C2313yes—
265#392C2316yes—
266#392C2316yes—
267#392C2313yes—
268#392C2313yes—
269#392C2313yes—
270#392C2311yescharacteristic
271#392C2316yes—
272#392C2316yes—
273#392C2313yes—
274#391C2316yes—
275#391C2316yes—
276#391C2316yes—
277#391C2316yes—
278#391C2316yes—
279#391C2316yes—
280#390C2316yes—
281#390C2316yes—
282#390C2316yes—
283#390C2316yes—
284#389C2316yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#388C2316yes—
289#388C2316yes—
290#388C2316yes—
291#388C2316yes—
292#388C2316yes—
293#388C2316yes—
294#388C2316yes—
295#388C2316yes—
296#388C2316yes—
297#388C2316yes—
298#388C2316yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#387C2316yes—
305#387C2316yes—
306#387C2316yes—
307#387C2316yes—
308#387C2316yes—
309#387C2316yes—
310#387C2316yes—
311#387C2316yes—
312#387C2316yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C2316yes—
320#386C2316yes—
321#386C2316yes—
322#386C2316yes—
323#386C2316yes—
324#386C2316yes—
325#386C2316yes—
326#386C2316yes—
327#386C2316yes—
328#386C2316yes—
329#386C2316yes—
330#386C2316yes—
331#386C2316yes—
332#386C2316yes—
333#386C2316yes—
334#386C2316yes—
335#386C2316yes—
336#386C2316yes—
337#386C2316yes—
338#386C2316yes—
339#386C2316yes—
340#386C2316yes—
341#386C2316yes—
342#386C2316yes—
343#386C2316yes—
344#386C2316yes—
345#386C2316yes—
346#386C2316yes—
347#386C2316yes—
348#386C2316yes—
349#386C2316yes—
350#385C2313yes—
351#385C2316yes—
352#385C2316yes—
353#385C2313yes—
354#385C2316yes—
355#385C2316yes—
356#385C2316yes—
357#385C2316yes—
358#385C2313yes—
359#385C2313yes—
360#385C2316yes—
361#385C2316yes—
362#385C2316yes—
363#385C2316yes—
364#385C2316yes—
365#385C2316yes—
366#385C2316yes—
367#385C2316yes—
368#385C2316yes—
369#385C2316yes—
370#385C2316yes—
371#385C2316yes—
372#385C2316yes—
373#385C2316yes—
374#385C2316yes—
375#385C2316yes—
376#385C2316yes—
377#385C2316yes—
378#383C2316yes—
379#383C2316yes—
380#382C2316yes—
381#382C2316yes—
382#381C2313yes—
383#381C2313yes—
384#381C2316yes—
385#381C2313yes—
386#381C2313yes—
387#381C2313yes—
388#381C2313yes—
389#381C2316yes—
390#381C2316yes—
391#380C2316yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2316yes—
399#380C2316yes—
400#379C2311yescharacteristic
401#379C2313yes—
402#379C2316yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406C2×#95C2316yes—
407C2×#95C2316yes—
408C25C2413yes—
409C25C2411yescharacteristic
4102−1+4—464no—
411C2×#41—224no—
412C2×#41—46no—
413C2×#41—412no—
414C2×#41—412no—
415C2×#41—46no—
416C2×#41—46no—
417C2×#41—412no—
418C2×#41—412no—
419C22×Q8—212no—
420C22×Q8—412no—
421C22×Q8—412no—
422C22×Q8C2413yes—
423C22×Q8C2416yes—
424C22×Q8C2413yes—
425C22×Q8C2411yescharacteristic
426C22×D4—212no—
427C22×D4—46no—
428C22×D4—46no—
429C22×D4C2413yes—
430C22×D4C2416yes—
431C22×D4C2416yes—
432C22×D4C2416yes—
433C22×D4C2413yes—
434C22×D4C2416yes—
435C22×D4C2416yes—
436C22×D4C2416yes—
437C22×D4C2411yescharacteristic
438C23×C4—412no—
439C23×C4—46no—
440C23×C4C2413yes—
441C23×C4C2413yes—
442C23×C4C2413yes—
443C23×C4C2416yes—
444C23×C4C2413yes—
445C23×C4C2416yes—
446C23×C4C2413yes—
447C23×C4C2416yes—
448C23×C4C2413yes—
449C23×C4C2416yes—
450C23×C4C2416yes—
451C23×C4C2413yes—
452C23×C4C2413yes—
453C23×C4C2413yes—
454#123—412no—
455#123—412no—
456#123—412no—
457#123—412no—
458C22⋊Q8—412no—
459C22⋊Q8—412no—
460C22⋊Q8—412no—
461C22⋊Q8—412no—
462C22⋊Q8—412no—
463C22⋊Q8—412no—
464#121—412no—
465#121—412no—
466#121—412no—
467#121—412no—
468#120—28no—
469#120—412no—
470#120—412no—
471#120—412no—
472C4×Q8—412no—
473C4×D4—224no—
474C4×D4—224no—
475C4×D4—412no—
476C4×D4—412no—
477C4×D4—412no—
478C4×D4—412no—
479C4×D4—412no—
480C4×D4—412no—
481C4×D4—412no—
482#117—412no—
483#117—412no—
484#117—412no—
485#117—46no—
486C2×C4⋊C4—212no—
487C2×C4⋊C4—412no—
488C2×C4⋊C4—46no—
489C2×C4⋊C4—46no—
490C2×C4⋊C4C2416yes—
491C2×C4⋊C4C2416yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C22⋊C4—212no—
513C2×C22⋊C4—412no—
514C2×C22⋊C4—46no—
515C2×C22⋊C4—46no—
516C2×C22⋊C4—46no—
517C2×C22⋊C4—46no—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2413yes—
523C2×C22⋊C4C2413yes—
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C2413yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2413yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2413yes—
535C2×C22⋊C4C2413yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C2416yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C2416yes—
551C2×C22⋊C4C2416yes—
552C2×C22⋊C4C2416yes—
553C2×C42C2416yes—
554C2×C42C2416yes—
555C2×C42C2416yes—
556C2×C42C2416yes—
557C2×C42C2416yes—
558#95C2416yes—
559#95C2416yes—
560#95C2416yes—
561#95C2416yes—
562#95C2416yes—
563#95C2416yes—
564#95C2416yes—
565#95C2416yes—
566#95C2416yes—
567#95C2416yes—
568#95C2416yes—
569#95C2416yes—
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2413yes—
574#95C2413yes—
575#95C2416yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2416yes—
580#95C2413yes—
581#95C2411yescharacteristic
582#95C2416yes—
583#95C2416yes—
584#95C2416yes—
585#95C2416yes—
586#95C2413yes—
587#95C2413yes—
588#95C2416yes—
589#95C2416yes—
590#95C2413yes—
591#95C2413yes—
592#95C2412yes—
593#95C2416yes—
594#95C2416yes—
595C24—26no—
596C24—26no—
597C24—26no—
598C24—43no—
599C24—43no—
600C24—46no—
601C24—46no—
602C242−1+414yescomplemented
603C24C2512yes—
604C24C2513yes—
605C24C2513yes—
606C24C2513yes—
607#41—496no—
608#41—448no—
609#41—448no—
610#41—416no—
611C2×Q8—212no—
612C2×Q8—212no—
613C2×Q8—212no—
614C2×Q8—43no—
615C2×Q8—43no—
616C2×Q8—46no—
617C2×Q8—43no—
618C2×Q8—46no—
619C2×Q8—448no—
620C2×Q8—432no—
621C2×D4—212no—
622C2×D4—212no—
623C2×D4—212no—
624C2×D4—212no—
625C2×D4—212no—
626C2×D4—212no—
627C2×D4—212no—
628C2×D4—212no—
629C2×D4—212no—
630C2×D4—212no—
631C2×D4—212no—
632C2×D4—212no—
633C2×D4—46no—
634C2×D4—43no—
635C2×D4—46no—
636C2×D4—46no—
637C2×D4—46no—
638C2×D4—43no—
639C2×D4—43no—
640C2×D4—46no—
641C2×D4—46no—
642C2×D4—46no—
643C2×D4—46no—
644C2×D4—448no—
645C22×C4—26no—
646C22×C4—212no—
647C22×C4—26no—
648C22×C4—26no—
649C22×C4—26no—
650C22×C4—212no—
651C22×C4—26no—
652C22×C4—26no—
653C22×C4—212no—
654C22×C4—212no—
655C22×C4—212no—
656C22×C4—46no—
657C22×C4—43no—
658C22×C4—43no—
659C22×C4—46no—
660C22×C4—46no—
661C22×C4—46no—
662C22×C4—46no—
663C22×C4—46no—
664C22×C4—46no—
665C22×C4—46no—
666C22×C4—46no—
667C22×C4—46no—
668C22×C4—46no—
669C22×C4—46no—
670C22×C4—46no—
671C22×C4—43no—
672C22×C4—46no—
673C22×C4—43no—
674C22×C4—46no—
675C22×C4—46no—
676C22×C4—46no—
677C22×C4—46no—
678C22×C4—824no—
679C22×C4H(5,𝔽2)112yes—
680C22×C4C2516yes—
681C22×C4C2516yes—
682C22×C4C2516yes—
683C22×C4C2513yes—
684C22×C4C2516yes—
685C22×C4C2513yes—
686C22×C4C2513yes—
687C22×C4C2511yescharacteristic
688C22×C4C2516yes—
689C22×C4C2516yes—
690C22×C4C2516yes—
691C4⋊C4—212no—
692C4⋊C4—212no—
693C4⋊C4—212no—
694C4⋊C4—212no—
695C4⋊C4—43no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—46no—
700C4⋊C4—46no—
701C4⋊C4—43no—
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—
712C4⋊C4—46no—
713C22⋊C4—212no—
714C22⋊C4—212no—
715C22⋊C4—212no—
716C22⋊C4—26no—
717C22⋊C4—26no—
718C22⋊C4—212no—
719C22⋊C4—212no—
720C22⋊C4—212no—
721C22⋊C4—212no—
722C22⋊C4—212no—
723C22⋊C4—46no—
724C22⋊C4—46no—
725C22⋊C4—43no—
726C22⋊C4—46no—
727C22⋊C4—43no—
728C22⋊C4—46no—
729C22⋊C4—43no—
730C22⋊C4—43no—
731C22⋊C4—43no—
732C22⋊C4—43no—
733C22⋊C4—46no—
734C22⋊C4—46no—
735C22⋊C4—46no—
736C22⋊C4—46no—
737C22⋊C4—46no—
738C22⋊C4—46no—
739C22⋊C4—46no—
740C22⋊C4—46no—
741C22⋊C4—46no—
742C22⋊C4—46no—
743C22⋊C4—46no—
744C22⋊C4—46no—
745C22⋊C4—46no—
746C22⋊C4—46no—
747C22⋊C4—46no—
748C42—212no—
749C42—212no—
750C42—46no—
751C42—46no—
752C42—46no—
753C23—224no—
754C23—23no—
755C23—23no—
756C23—26no—
757C23—26no—
758C23—26no—
759C23—23no—
760C23—23no—
761C23—23no—
762C23—23no—
763C23—26no—
764C23—26no—
765C23—26no—
766C23—26no—
767C23—22no—
768C23—26no—
769C23—412no—
770C23—86no—
771C23—812no—
772C23—86no—
773C23—812no—
774C23—161no—
775C23—163no—
776C23C2×H(5,𝔽2)16yes—
777C23C2×2−1+416yes—
778C23#58516yes—
779C23C2611yescharacteristic
780Q8—412no—
781Q8—424no—
782Q8—44no—
783Q8—412no—
784D4—424no—
785D4—424no—
786D4—424no—
787D4—424no—
788D4—412no—
789D4—412no—
790D4—44no—
791D4—812no—
792D4—812no—
793C2×C4—224no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—26no—
799C2×C4—26no—
800C2×C4—23no—
801C2×C4—26no—
802C2×C4—26no—
803C2×C4—26no—
804C2×C4—26no—
805C2×C4—23no—
806C2×C4—26no—
807C2×C4—23no—
808C2×C4—23no—
809C2×C4—26no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—26no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—26no—
817C2×C4—26no—
818C2×C4—26no—
819C2×C4—26no—
820C2×C4—26no—
821C2×C4—412no—
822C2×C4—424no—
823C2×C4—412no—
824C2×C4—412no—
825C2×C4—412no—
826C2×C4—424no—
827C2×C4—812no—
828C2×C4—812no—
829C2×C4—86no—
830C2×C4—86no—
831C2×C4—163no—
832C2×C4—166no—
833C2×C4—163no—
834C2×C4C2×H(5,𝔽2)112yes—
835C22—26no—
836C22—26no—
837C22—212no—
838C22—26no—
839C22—26no—
840C22—26no—
841C22—212no—
842C22—43no—
843C22—43no—
844C22—46no—
845C22—46no—
846C22—43no—
847C22—46no—
848C22—46no—
849C22—43no—
850C22—42no—
851C22—46no—
852C22—46no—
853C22—824no—
854C22—164no—
855C22C22×H(5,𝔽2)13yes—
856C22C22×2−1+411yescharacteristic
857C22C2×#58513yes—
858C4—212no—
859C4—43no—
860C4—41no—
861C4—46no—
862C4—46no—
863C4—46no—
864C4—43no—
865C4—46no—
866C4—43no—
867C4—46no—
868C4—46no—
869C2—46no—
870C2—46no—
871C2—46no—
872C2—82no—
873C2#6281711yescharacteristic
874C2#6281913yes—
875C2#6282113yes—
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. #47122C2semidirect
2. #47088C2semidirect
3. #47063C2semidirect
4. #47037C2semidirect
5. #47018C2semidirect
6. #47004C2semidirect
7. #47003C2semidirect
8. #47001C2semidirect
9. #47000C2semidirect
10. #46996C2semidirect
11. #35659C2semidirect
12. #35357C2semidirect
13. #35353C2semidirect
14. #35352C2semidirect
15. #35349C2semidirect
16. C22×2−1+4C22semidirect
17. C2×#525C22semidirect
18. C22×C22⋊Q8C22semidirect
19. C2×#520C22semidirect
21. #2841C22semidirect
23. #2835C22semidirect
24. #2824C22semidirect
26. #2801C22semidirect
27. #2787C22semidirect
28. #2787C22semidirect
29. #2784C22semidirect
30. #2784C22semidirect
31. #2771C22semidirect
32. #2764C22semidirect
33. #2764C22semidirect
34. #2763C22semidirect
35. #2763C22semidirect
36. #2762C22semidirect
37. #2762C22semidirect
38. #2762C22semidirect
39. #2761C22semidirect
43. #2752C22semidirect
44. #2750C22semidirect
45. #2750C22semidirect
46. #2750C22semidirect
47. #2750C22semidirect
48. #2749C22semidirect
49. #2743C22semidirect
50. #2742C22semidirect
51. #2742C22semidirect
52. #2737C22semidirect
53. #2708C22semidirect
54. #2708C22semidirect
55. #2706C22semidirect
56. #2703C22semidirect
57. #2693C22semidirect
58. #2675C22semidirect
59. #2609C22semidirect
60. #2609C22semidirect
62. #2599C22semidirect
64. #2598C22semidirect
65. #2598C22semidirect
66. #2580C22semidirect
67. #2579C22semidirect
68. #2579C22semidirect
70. #2534C22semidirect
71. #2487C22semidirect
72. #2484C22semidirect
73. #2482C22semidirect
74. #2477C22semidirect
75. #2477C22semidirect
76. #2477C22semidirect
77. #2476C22semidirect
78. #2471C22semidirect
79. #2470C22semidirect
80. #2465C22semidirect
81. #2465C22semidirect
82. #2465C22semidirect
85. #2463C22semidirect
86. #2458C22semidirect
89. #2455C22semidirect
90. #2450C22semidirect
91. #2450C22semidirect
92. #2450C22semidirect
93. #2449C22semidirect
94. #2449C22semidirect
95. #2449C22semidirect
96. #2444C22semidirect
97. #2443C22semidirect
98. #2438C22semidirect
99. #2438C22semidirect
100. #2438C22semidirect
103. #2430C22semidirect
104. #2424C22semidirect
105. #2424C22semidirect
106. #2418C22semidirect
107. #2418C22semidirect
108. #2411C22semidirect
110. #2409C22semidirect
111. #2409C22semidirect
112. #2409C22semidirect
113. #2409C22semidirect
115. #2407C22semidirect
116. #2407C22semidirect
117. #2407C22semidirect
118. #2406C22semidirect
119. #2406C22semidirect
120. #2406C22semidirect
121. #2406C22semidirect
125. #2404C22semidirect
126. #2404C22semidirect
128. #2325C22semidirect
129. #2325C22semidirect
130. #2322C22semidirect
131. #2322C22semidirect
133. #2318C22semidirect
134. #2318C22semidirect
135. #2315C22semidirect
136. #2315C22semidirect
137. #2313C22semidirect
138. #2311C22semidirect
139. #2310C22semidirect
141. C4×#120C22semidirect
143. C2×#385C22semidirect
602. C242−1+4semidirect

Maximal subgroups

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

subgroupindex
#471222
#470882
#470632
#470372
#470182
#470042
#470032
#470012
#470002
#469962
#356592
#353572
#353532
#353522
#353492