Finite Group Databasebeta

← #7763436

Subgroups — #7763436

Order 512.

4636 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59874C214yesmaximal, complemented
2#59637C214yesmaximal, complemented
3#51092C214yesmaximal, complemented
4#50717C214yesmaximal, complemented
5#44023C218yesmaximal, complemented
6#42523C214yesmaximal, complemented
7#42405C218yesmaximal, complemented
8#40543C214yesmaximal, complemented
9#39810C214yesmaximal, complemented
10#39758C214yesmaximal, complemented
11#37536C211yesmaximal, characteristic
12#35970C214yesmaximal, complemented
13#35706C214yesmaximal, complemented
14#35289C211yesmaximal, characteristic, complemented
15#34878C211yesmaximal, characteristic, complemented
16C2×#2640C211yesmaximal, characteristic, complemented
17#34371C211yesmaximal, characteristic, complemented
18#34240C211yesmaximal, characteristic, complemented
19#34222C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23#2862C2212yescomplemented
24#2858C2212yescomplemented
25#2832C2218yescomplemented
26#2819C2214yes—
27#2798C2218yescomplemented
28#2798C2218yescomplemented
29#2798C2218yescomplemented
30#2797C2218yes—
31#2797C2218yescomplemented
32#2759C2218yescomplemented
33#2759C2218yescomplemented
34#2759C2218yescomplemented
35#2752C2218yes—
36#2752C2218yescomplemented
37#2746C2218yescomplemented
38#2741C2218yescomplemented
39#2737C2218yescomplemented
40#2717C2218yescomplemented
41#2712C2218yescomplemented
42#2710C2218yescomplemented
43#2657C2212yes—
44#2653C2218yescomplemented
45#2653C2218yescomplemented
46#2640C2212yes—
47#2640C2214yes—
48#2640C2214yes—
49#2640C2212yes—
50#2640C2214yes—
51#2640C2212yes—
52#2640C2214yescomplemented
53#2632C2218yescomplemented
54#2631C2212yes—
55#2631C2212yes—
56#2617C2214yes—
57#2612C2214yescomplemented
58#2606C2212yescomplemented
59#2605C2212yescomplemented
60#2602C2218yes—
61#2602C2218yescomplemented
62#2592C2214yescomplemented
63#2581C2214yescomplemented
64#2580C2214yes—
65#2578C2218yescomplemented
66#2572C2218yescomplemented
67#2569C2212yes—
68#2564C2218yes—
69#2563C2214yescomplemented
70#2557C2218yes—
71#2557C2218yescomplemented
72#2557C2218yescomplemented
73#2549C2212yes—
74#2548C2214yes—
75#2547C2214yescomplemented
76#2544C2214yes—
77#2531C2218yescomplemented
78#2527C2218yescomplemented
79#2527C2218yescomplemented
80#2527C2218yescomplemented
81#2523C2218yescomplemented
82#2523C2218yescomplemented
83#2523C2218yescomplemented
84#2514C2214yescomplemented
85#2514C2214yescomplemented
86#2513C2214yes—
87#2513C2214yes—
88#2510C2218yes—
89#2510C2218yes—
90#2510C2218yescomplemented
91#2504C2214yes—
92#2472C2218yes—
93#2459C2218yescomplemented
94#2458C2218yescomplemented
95#2458C2218yescomplemented
96#2448C2214yescomplemented
97#2447C2214yescomplemented
98#2445C2214yes—
99#2445C2214yes—
100#2438C2214yes—
101#2436C2212yes—
102#2436C2212yes—
103#2436C2212yes—
104#2433C2212yes—
105#2419C2218yescomplemented
106#2418C2218yes—
107#2412C2218yes—
108#2404C2214yes—
109#2402C2212yescomplemented
110#2399C2212yescomplemented
111#2398C2218yescomplemented
112C2×#397C2214yes—
113C2×#393C2214yes—
114#2381C2212yescomplemented
115#2381C2212yescomplemented
116#2372C2214yes—
117#2372C2214yescomplemented
118#2367C2214yes—
119#2367C2214yescomplemented
120#2366C2214yes—
121#2365C2214yescomplemented
122#2364C2214yes—
123#2358C2218yes—
124#2357C2214yes—
125#2356C2214yescomplemented
126#2353C2218yes—
127#2353C2214yescomplemented
128#2345C2214yes—
129#2342C2214yes—
130Q8×C22⋊C4C2214yes—
131Q8×C22⋊C4C2212yes—
132#2339C2214yes—
133D4×C22⋊C4C2212yes—
134#2337C2214yes—
135#2331C2214yescomplemented
136#2331C2212yescomplemented
137#2328C2212yescomplemented
138#2327C2214yescomplemented
139#2319C2212yescomplemented
140#2313C2214yes—
141#2312C2212yes—
142#2311C2214yes—
143C4×#124C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×#121C2214yes—
146#2295C2214yescomplemented
147C2×#391C2212yes—
148C2×#390C2212yes—
149#2283C2211yescharacteristic
150#2283C2211yescharacteristic
151#2275C2212yescomplemented
152#2273C2212yes—
153C4×#117C2211yescharacteristic
154C2×#376C2211yescharacteristic
155C22×#41C2312yes—
156C23×Q8C2311yescharacteristic
157C23×Q8C2312yes—
158C23×D4C2311yescharacteristic
159#532—28no—
160C2×C4⋊Q8—28no—
161C2×C4⋊Q8C2312yes—
162C2×C4⋊Q8C2312yes—
163C2×C4⋊Q8C2312yes—
164C2×C4⋊Q8C2311yescharacteristic
165C2×C4⋊Q8C2312yes—
166C2×#127C2311yescharacteristic
167C2×#127C2314yes—
168C2×#124—28no—
169C2×#124C2312yes—
170C2×#124C2312yes—
171C2×#124C2312yes—
172C2×#124C2312yes—
173C2×#124C2312yes—
174C2×#124C2314yes—
175C2×#124C2314yes—
176C2×#124C2314yes—
177C2×#124C2318yes—
178C2×#123C2318yes—
179C2×#123C2318yes—
180C2×C22⋊Q8C2314yes—
181C2×#121C2312yes—
182C2×#121C2312yes—
183C2×#120C2318yes—
184C2×C4×Q8C2314yes—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2318yes—
187C2×C4×D4C2312yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2318yes—
193C2×#117C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2314yes—
199C22×C22⋊C4C2318yes—
200C22×C42C2312yes—
201C22×C42C2311yescharacteristic
202#401C2318yes—
203#401C2318yes—
204#400C2318yes—
205#400C2314yes—
206#400C2318yes—
207#400C2314yes—
208#400C2318yes—
209#399C2318yes—
210#399C2318yes—
211#398C2314yes—
212#398C2314yes—
213#398C2314yes—
214#398C2314yes—
215#397C2318yes—
216#397C2318yes—
217#397C2318yes—
218#397C2318yes—
219#397C2318yes—
220#397C2318yes—
221#397C2318yes—
222#397C2314yes—
223#397C2314yes—
224#397C2318yes—
225#397C2318yes—
226#397C2318yes—
227#397C2318yes—
228#397C2318yes—
229#397C2318yes—
230#397C2318yes—
231#395C2318yes—
232#395C2314yes—
233#395C2314yes—
234#394C2318yes—
235#394C2318yes—
236#394C2318yes—
237#394C2318yes—
238#394C2318yes—
239#394C2318yes—
240#394C2318yes—
241#394C2318yes—
242#393C2318yes—
243#393C2318yes—
244#393C2314yes—
245#393C2314yes—
246#393C2318yes—
247#393C2318yes—
248#393C2314yes—
249#393C2314yes—
250#393C2318yes—
251#393C2314yes—
252#393C2314yes—
253#393C2318yes—
254#393C2318yes—
255#392C2314yes—
256#392C2318yes—
257#392C2314yes—
258#392C2314yes—
259#392C2314yes—
260#391C2318yes—
261#391C2318yes—
262#391C2314yes—
263#391C2314yes—
264#391C2318yes—
265#391C2318yes—
266#391C2318yes—
267#391C2314yes—
268#391C2318yes—
269#391C2314yes—
270#391C2314yes—
271#391C2314yes—
272#391C2314yes—
273#391C2314yes—
274#391C2314yes—
275#391C2318yes—
276#390C2314yes—
277#390C2314yes—
278#390C2318yes—
279#390C2314yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2318yes—
284#390C2314yes—
285#390C2318yes—
286#390C2318yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#388C2318yes—
294#388C2318yes—
295#388C2318yes—
296#388C2318yes—
297#388C2318yes—
298#388C2318yes—
299#388C2318yes—
300#388C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2314yes—
318#387C2314yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2314yes—
325#387C2314yes—
326#387C2318yes—
327#387C2318yes—
328#387C2314yes—
329#387C2314yes—
330#386C2318yes—
331#386C2318yes—
332#386C2318yes—
333#386C2318yes—
334#386C2318yes—
335#386C2318yes—
336#386C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2314yes—
346#385C2318yes—
347#385C2318yes—
348#385C2318yes—
349#385C2314yes—
350#383C2318yes—
351#383C2318yes—
352#383C2312yes—
353#383C2311yescharacteristic
354#383C2311yescharacteristic
355#383C2318yes—
356#382C2314yes—
357#382C2314yes—
358#382C2312yes—
359#382C2312yes—
360#381C2312yes—
361#381C2312yes—
362#381C2318yes—
363#381C2318yes—
364#381C2314yes—
365#380C2318yes—
366#380C2318yes—
367#380C2314yes—
368#380C2318yes—
369#380C2312yes—
370#380C2314yes—
371#380C2314yes—
372#380C2312yes—
373#379C2314yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2312yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2312yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2314yes—
384C4×C22⋊C4C2311yescharacteristic
385C4×C22⋊C4C2312yes—
386C4×C22⋊C4C2318yes—
387C4×C22⋊C4C2311yescharacteristic
388C4×C22⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2318yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2312yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2318yes—
399#376C2311yescharacteristic
400#376C2312yes—
401#376C2312yes—
402#376C2312yes—
403#376C2312yes—
404#376C2318yes—
405#376C2312yes—
406#376C2312yes—
407#376C2311yescharacteristic
408C2×#95C2318yes—
409C2×#95C2312yes—
410C2×#95C2312yes—
411C2×#95C2314yes—
412C43C2312yes—
413C25C2412yes—
414C2×#41—28no—
415C2×#41—48no—
416C22×Q8—24no—
417C22×Q8—28no—
418C22×Q8—44no—
419C22×Q8—84no—
420C22×Q8C2412yes—
421C22×Q8C2414yes—
422C22×Q8C2414yes—
423C22×Q8C2412yes—
424C22×Q8C2412yes—
425C22×Q8C2414yes—
426C22×D4—24no—
427C22×D4—44no—
428C22×D4C2412yes—
429C22×D4C2414yes—
430C22×D4C2412yes—
431C22×D4C2412yes—
432C22×D4C2412yes—
433C22×D4C2412yes—
434C22×D4C2418yes—
435C22×D4C2418yes—
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2414yes—
439C23×C4C2414yes—
440C23×C4C2412yes—
441C23×C4C2414yes—
442C23×C4C2418yes—
443C23×C4C2418yes—
444C23×C4C2411yescharacteristic
445C4⋊Q8—28no—
446C4⋊Q8—28no—
447C4⋊Q8—28no—
448C4⋊Q8—28no—
449C4⋊Q8—24no—
450#127—24no—
451#127—48no—
452#124—28no—
453#124—28no—
454#124—28no—
455#124—28no—
456#124—28no—
457#124—48no—
458#124—88no—
459#124—84no—
460#124—84no—
461#123—88no—
462#123—88no—
463C22⋊Q8—48no—
464#121—28no—
465#121—28no—
466#120—416no—
467C4×Q8—48no—
468C4×Q8—48no—
469C4×Q8—88no—
470C4×D4—28no—
471C4×D4—28no—
472C4×D4—48no—
473C4×D4—48no—
474C4×D4—416no—
475C4×D4—88no—
476#117—44no—
477C2×C4⋊C4—28no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4C2414yes—
480C2×C4⋊C4C2414yes—
481C2×C4⋊C4C2414yes—
482C2×C4⋊C4C2414yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2412yes—
485C2×C4⋊C4C2412yes—
486C2×C4⋊C4C2414yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2418yes—
489C2×C4⋊C4C2414yes—
490C2×C4⋊C4C2418yes—
491C2×C4⋊C4C2418yes—
492C2×C4⋊C4C2414yes—
493C2×C4⋊C4C2418yes—
494C2×C4⋊C4C2414yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2414yes—
497C2×C4⋊C4C2414yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—48no—
504C2×C22⋊C4—88no—
505C2×C22⋊C4C2412yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2412yes—
512C2×C22⋊C4C2414yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2414yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C22⋊C4C2418yes—
520C2×C22⋊C4C2418yes—
521C2×C22⋊C4C2418yes—
522C2×C22⋊C4C2418yes—
523C2×C22⋊C4C2418yes—
524C2×C22⋊C4C2418yes—
525C2×C22⋊C4C2418yes—
526C2×C22⋊C4C2418yes—
527C2×C22⋊C4C2418yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C42—44no—
534C2×C42#4118yes—
535C2×C42C2412yes—
536C2×C42C2414yes—
537C2×C42C2412yes—
538C2×C42C2414yes—
539C2×C42C2414yes—
540C2×C42C2418yes—
541C2×C42C2418yes—
542C2×C42C2414yes—
543C2×C42C2418yes—
544C2×C42C2418yes—
545C2×C42C2412yes—
546C2×C42C2412yes—
547C2×C42C2414yes—
548C2×C42C2411yescharacteristic
549C2×C42C2411yescharacteristic
550C2×C42C2411yescharacteristic
551C2×C42C2411yescharacteristic
552#95C2412yes—
553#95C2412yes—
554#95C2412yes—
555#95C2414yes—
556#95C2414yes—
557#95C2412yes—
558#95C2418yes—
559#95C2414yes—
560#95C2418yes—
561#95C2418yes—
562#95C2418yes—
563#95C2418yes—
564#95C2414yes—
565#95C2412yes—
566#95C2414yes—
567#95C2414yes—
568#95C2414yes—
569#95C2412yes—
570#95C2418yes—
571#95C2412yes—
572#95C2412yes—
573#95C2414yes—
574#95C2418yes—
575#95C2418yes—
576#95C2414yes—
577#95C2414yes—
578#95C2414yes—
579#95C2418yes—
580#95C2418yes—
581#95C2418yes—
582#95C2418yes—
583#95C2412yes—
584#95C2412yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2412yes—
589#95C2412yes—
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596C24—24no—
597C24—28no—
598C24—44no—
599C24—44no—
600C24C2514yes—
601C24C2514yes—
602C24C2511yescharacteristic
603#41—816no—
604C2×Q8—24no—
605C2×Q8—28no—
606C2×Q8—24no—
607C2×Q8—24no—
608C2×Q8—28no—
609C2×Q8—28no—
610C2×Q8—48no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—44no—
616C2×Q8—44no—
617C2×Q8—44no—
618C2×Q8—88no—
619C2×Q8—816no—
620C2×D4—28no—
621C2×D4—216no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—28no—
628C2×D4—28no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—44no—
632C2×D4—48no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—88no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—24no—
642C22×C4—28no—
643C22×C4—28no—
644C22×C4—28no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—48no—
649C22×C4—44no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4C2×#4114yes—
658C22×C4C2×#4114yes—
659C22×C4C2×#4114yes—
660C22×C4C2514yes—
661C22×C4C2514yes—
662C22×C4C2514yes—
663C22×C4C2514yes—
664C22×C4C2514yes—
665C22×C4C2518yes—
666C22×C4C2514yes—
667C22×C4C2514yes—
668C22×C4C2518yes—
669C22×C4C2514yes—
670C22×C4C2511yescharacteristic
671C22×C4C2511yescharacteristic
672C22×C4C2511yescharacteristic
673C22×C4C2511yescharacteristic
674C22×C4C2511yescharacteristic
675C22×C4C2511yescharacteristic
676C4⋊C4—28no—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—28no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—28no—
683C4⋊C4—44no—
684C4⋊C4—48no—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—48no—
690C4⋊C4—44no—
691C4⋊C4—48no—
692C4⋊C4—48no—
693C4⋊C4—44no—
694C4⋊C4—44no—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C22⋊C4—24no—
699C22⋊C4—28no—
700C22⋊C4—24no—
701C22⋊C4—28no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C22⋊C4—48no—
725C22⋊C4—48no—
726C42—24no—
727C42—24no—
728C42—28no—
729C42—28no—
730C42—44no—
731C42—44no—
732C42—48no—
733C42—48no—
734C42—48no—
735C42—44no—
736C42—48no—
737C42—42no—
738C42—42no—
739C42C2×#4114yes—
740C42C2×#4114yes—
741C42C2×#4114yes—
742C42C2×#4114yes—
743C23—22no—
744C23—22no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—28no—
749C23—24no—
750C23—28no—
751C23—28no—
752C23—24no—
753C23—28no—
754C23—24no—
755C23—48no—
756C23—84no—
757C23—84no—
758C23—816no—
759C23C22×#4112yes—
760C23#58514yes—
761C23C2611yescharacteristic
762Q8—416no—
763Q8—48no—
764Q8—84no—
765Q8—88no—
766Q8—84no—
767Q8—88no—
768D4—416no—
769D4—48no—
770D4—48no—
771D4—84no—
772D4—84no—
773D4—84no—
774D4—816no—
775D4—168no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—28no—
782C2×C4—28no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—28no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—44no—
812C2×C4—88no—
813C2×C4—88no—
814C2×C4—84no—
815C2×C4—88no—
816C2×C4—168no—
817C2×C4—168no—
818C2×C4C22×#4112yes—
819C2×C4C22×#4112yes—
820C2×C4C22×#4112yes—
821C2×C4C22×#4112yes—
822C2×C4C22×#4112yes—
823C2×C4C22×#4112yes—
824C2×C4#58514yes—
825C22—22no—
826C22—22no—
827C22—28no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—48no—
835C22—48no—
836C22—48no—
837C22—48no—
838C22—168no—
839C22#351014yes—
840C22C23×#4111yescharacteristic
841C22C2×#58512yes—
842C22C2×#58512yes—
843C22H(7,𝔽2)12yes—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—44no—
850C4—44no—
851C4—48no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—48no—
856C4—44no—
857C4—44no—
858C4—44no—
859C4#351014yes—
860C2—24no—
861C2—84no—
862C2—84no—
863C2C2×#351011yescharacteristic
864C2C2×#351011yescharacteristic
865C2#6285511yescharacteristic
866C2#6297014yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37536C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59874C2semidirect
2. #59637C2semidirect
3. #51092C2semidirect
4. #50717C2semidirect
5. #44023C2semidirect
6. #42523C2semidirect
7. #42405C2semidirect
8. #40543C2semidirect
9. #39810C2semidirect
10. #39758C2semidirect
12. #35970C2semidirect
13. #35706C2semidirect
14. #35289C2semidirect
15. #34878C2semidirect
16. C2×#2640C2semidirect
17. #34371C2semidirect
18. #34240C2semidirect
19. #34222C2semidirect
23. #2862C22semidirect
24. #2858C22semidirect
25. #2832C22semidirect
27. #2798C22semidirect
28. #2798C22semidirect
29. #2798C22semidirect
31. #2797C22semidirect
32. #2759C22semidirect
33. #2759C22semidirect
34. #2759C22semidirect
36. #2752C22semidirect
37. #2746C22semidirect
38. #2741C22semidirect
39. #2737C22semidirect
40. #2717C22semidirect
41. #2712C22semidirect
42. #2710C22semidirect
44. #2653C22semidirect
45. #2653C22semidirect
52. #2640C22semidirect
53. #2632C22semidirect
57. #2612C22semidirect
58. #2606C22semidirect
59. #2605C22semidirect
61. #2602C22semidirect
62. #2592C22semidirect
63. #2581C22semidirect
65. #2578C22semidirect
66. #2572C22semidirect
69. #2563C22semidirect
71. #2557C22semidirect
72. #2557C22semidirect
75. #2547C22semidirect
77. #2531C22semidirect
78. #2527C22semidirect
79. #2527C22semidirect
80. #2527C22semidirect
81. #2523C22semidirect
82. #2523C22semidirect
83. #2523C22semidirect
84. #2514C22semidirect
85. #2514C22semidirect
90. #2510C22semidirect
93. #2459C22semidirect
94. #2458C22semidirect
95. #2458C22semidirect
96. #2448C22semidirect
97. #2447C22semidirect
105. #2419C22semidirect
109. #2402C22semidirect
110. #2399C22semidirect
111. #2398C22semidirect
114. #2381C22semidirect
115. #2381C22semidirect
117. #2372C22semidirect
119. #2367C22semidirect
121. #2365C22semidirect
125. #2356C22semidirect
127. #2353C22semidirect
135. #2331C22semidirect
136. #2331C22semidirect
137. #2328C22semidirect
138. #2327C22semidirect
139. #2319C22semidirect
146. #2295C22semidirect
151. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#598742
#596372
#510922
#507172
#440232
#425232
#424052
#405432
#398102
#397582
#375362
#359702
#357062
#352892
#348782
C2×#26402
#343712
#342402
#342222