Finite Group Databasebeta

← #7763434

Subgroups — #7763434

Order 512.

5064 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59147C214yesmaximal, complemented
2#59134C214yesmaximal, complemented
3#51230C214yesmaximal, complemented
4#50918C214yesmaximal, complemented
5#43975C218yesmaximal, complemented
6#42705C214yesmaximal, complemented
7#42061C218yesmaximal, complemented
8#41390C214yesmaximal, complemented
9#39811C214yesmaximal, complemented
10#39741C214yesmaximal, complemented
11#37536C211yesmaximal, characteristic
12#35959C214yesmaximal, complemented
13#35837C214yesmaximal, complemented
14#35289C211yesmaximal, characteristic, complemented
15#34878C211yesmaximal, characteristic, complemented
16C2×#2658C211yesmaximal, characteristic, complemented
17#34371C211yesmaximal, characteristic, complemented
18#34240C211yesmaximal, characteristic, complemented
19#34222C211yesmaximal, characteristic, complemented
20C2×#559C2214yes—
21C2×#556C2214yescomplemented
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2212yes—
25C22×#124C2211yescharacteristic
26C22×#124C2212yes—
27#2862C2212yescomplemented
28#2858C2212yescomplemented
29#2837C2218yescomplemented
30#2819C2214yes—
31#2798C2218yescomplemented
32#2773C2218yescomplemented
33#2754C2218yescomplemented
34#2754C2218yescomplemented
35#2748C2218yescomplemented
36#2743C2218yescomplemented
37#2741C2218yescomplemented
38#2740C2218yescomplemented
39#2730C2218yescomplemented
40#2730C2218yescomplemented
41#2716C2218yescomplemented
42#2716C2218yescomplemented
43#2712C2218yes—
44#2710C2218yes—
45#2705C2218yescomplemented
46#2705C2218yescomplemented
47#2663C2218yescomplemented
48#2658C2214yes—
49#2658C2214yes—
50#2658C2214yes—
51#2658C2212yes—
52#2658C2212yes—
53#2657C2212yes—
54#2651C2218yescomplemented
55#2649C2218yescomplemented
56#2640C2212yes—
57#2640C2214yescomplemented
58#2631C2212yes—
59#2631C2212yes—
60#2617C2214yes—
61#2612C2214yescomplemented
62#2607C2218yescomplemented
63#2606C2212yescomplemented
64#2605C2212yescomplemented
65#2592C2214yes—
66#2589C2218yescomplemented
67#2575C2218yescomplemented
68#2569C2212yes—
69#2568C2214yescomplemented
70#2564C2218yescomplemented
71#2563C2214yescomplemented
72#2557C2218yes—
73#2553C2218yescomplemented
74#2553C2218yescomplemented
75#2549C2212yes—
76#2548C2214yes—
77#2547C2214yescomplemented
78#2547C2214yescomplemented
79#2545C2214yescomplemented
80#2545C2214yescomplemented
81#2544C2214yes—
82#2544C2214yes—
83#2544C2214yes—
84#2521C2218yescomplemented
85#2521C2218yescomplemented
86#2517C2218yescomplemented
87#2516C2218yescomplemented
88#2504C2212yes—
89#2504C2212yes—
90#2498C2218yescomplemented
91#2492C2218yescomplemented
92#2481C2218yes—
93#2481C2218yes—
94#2472C2218yes—
95#2471C2218yescomplemented
96#2471C2218yescomplemented
97#2467C2218yescomplemented
98#2467C2218yescomplemented
99#2459C2218yes—
100#2448C2214yes—
101#2447C2214yes—
102#2446C2214yescomplemented
103#2446C2214yescomplemented
104#2439C2218yescomplemented
105#2438C2214yes—
106#2436C2214yes—
107#2436C2212yes—
108#2433C2212yes—
109#2418C2218yes—
110#2417C2218yes—
111#2412C2218yes—
112#2404C2214yes—
113#2402C2212yescomplemented
114#2399C2212yescomplemented
115#2395C2218yescomplemented
116C2×#399C2214yes—
117C2×#399C2214yes—
118#2381C2212yescomplemented
119#2381C2212yescomplemented
120#2372C2214yes—
121#2372C2214yescomplemented
122#2367C2214yes—
123#2367C2214yes—
124#2365C2214yescomplemented
125#2365C2214yescomplemented
126#2364C2214yes—
127#2358C2218yes—
128#2353C2214yescomplemented
129#2352C2218yes—
130#2345C2214yes—
131#2342C2214yes—
132Q8×C22⋊C4C2214yes—
133Q8×C22⋊C4C2212yes—
134#2339C2214yes—
135D4×C22⋊C4C2212yes—
136#2337C2214yes—
137#2331C2214yescomplemented
138#2331C2212yescomplemented
139#2328C2212yescomplemented
140#2327C2214yescomplemented
141#2319C2212yescomplemented
142#2313C2214yes—
143#2312C2212yes—
144#2311C2214yes—
145C4×#124C2214yes—
146C4×C22⋊Q8C2214yes—
147C4×#121C2214yes—
148#2295C2214yescomplemented
149#2283C2211yescharacteristic
150#2283C2211yescharacteristic
151#2275C2212yescomplemented
152#2273C2212yes—
153C4×#117C2211yescharacteristic
154C2×#376C2211yescharacteristic
155C22×#41C2312yes—
156C23×Q8C2311yescharacteristic
157C23×Q8C2312yes—
158C23×D4C2311yescharacteristic
159#559—416no—
160#556—416no—
161#532—28no—
162C2×C4⋊Q8—28no—
163C2×C4⋊Q8—48no—
164C2×C4⋊Q8C2312yes—
165C2×C4⋊Q8C2314yes—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2318yes—
171C2×C4⋊Q8C2314yes—
172C2×#127C2311yescharacteristic
173C2×#127C2314yes—
174C2×#126C2318yes—
175C2×#126C2318yes—
176C2×#124—28no—
177C2×#124—48no—
178C2×#124C2312yes—
179C2×#124C2312yes—
180C2×#124C2314yes—
181C2×#124C2312yes—
182C2×#124C2312yes—
183C2×#124C2312yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2318yes—
189C2×#124C2318yes—
190C2×#123C2318yes—
191C2×#123C2318yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2314yes—
194C2×#121C2312yes—
195C2×#121C2312yes—
196C2×#120C2318yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2314yes—
201C2×C4×D4C2312yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2318yes—
207C2×#117C2312yes—
208C2×#117C2318yes—
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2318yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2314yes—
215C22×C22⋊C4C2318yes—
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218#400C2318yes—
219#400C2318yes—
220#400C2314yes—
221#400C2318yes—
222#400C2318yes—
223#400C2314yes—
224#399C2318yes—
225#399C2318yes—
226#399C2314yes—
227#399C2318yes—
228#399C2318yes—
229#399C2318yes—
230#399C2314yes—
231#399C2314yes—
232#399C2318yes—
233#399C2318yes—
234#399C2314yes—
235#398C2314yes—
236#398C2314yes—
237#398C2318yes—
238#398C2314yes—
239#398C2314yes—
240#398C2318yes—
241#397C2314yes—
242#397C2318yes—
243#397C2318yes—
244#397C2318yes—
245#397C2314yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#396C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#395C2314yes—
256#395C2314yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#393C2318yes—
266#393C2318yes—
267#393C2318yes—
268#393C2314yes—
269#393C2314yes—
270#393C2318yes—
271#392C2314yes—
272#392C2314yes—
273#392C2318yes—
274#392C2314yes—
275#392C2314yes—
276#391C2318yes—
277#391C2314yes—
278#391C2314yes—
279#391C2314yes—
280#391C2318yes—
281#391C2314yes—
282#391C2314yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2314yes—
287#391C2318yes—
288#391C2314yes—
289#391C2314yes—
290#391C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2318yes—
298#390C2318yes—
299#389C2314yes—
300#389C2318yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2314yes—
327#387C2314yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2314yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2314yes—
339#387C2314yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2318yes—
357#385C2314yes—
358#383C2312yes—
359#383C2311yescharacteristic
360#383C2311yescharacteristic
361#382C2314yes—
362#382C2314yes—
363#382C2312yes—
364#382C2318yes—
365#382C2312yes—
366#381C2312yes—
367#381C2312yes—
368#381C2314yes—
369#381C2318yes—
370#380C2318yes—
371#380C2318yes—
372#380C2318yes—
373#380C2314yes—
374#380C2318yes—
375#380C2312yes—
376#380C2314yes—
377#380C2314yes—
378#380C2312yes—
379#380C2318yes—
380#379C2314yes—
381C4×C4⋊C4C2312yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2312yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2318yes—
386C4×C4⋊C4C2312yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C22⋊C4C2311yescharacteristic
392C4×C22⋊C4C2312yes—
393C4×C22⋊C4C2318yes—
394C4×C22⋊C4C2311yescharacteristic
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2318yes—
397C4×C22⋊C4C2312yes—
398C4×C22⋊C4C2314yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2318yes—
402C4×C22⋊C4C2318yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405#376C2311yescharacteristic
406#376C2312yes—
407#376C2312yes—
408#376C2312yes—
409#376C2312yes—
410#376C2312yes—
411#376C2312yes—
412#376C2311yescharacteristic
413C2×#95C2314yes—
414C2×#95C2312yes—
415C2×#95C2312yes—
416C43C2312yes—
417C25C2412yes—
418C2×#41—28no—
419C2×#41—48no—
420C22×Q8—24no—
421C22×Q8—28no—
422C22×Q8—44no—
423C22×Q8—44no—
424C22×Q8—44no—
425C22×Q8C2412yes—
426C22×Q8C2414yes—
427C22×Q8C2414yes—
428C22×Q8C2412yes—
429C22×Q8C2414yes—
430C22×Q8C2412yes—
431C22×D4—24no—
432C22×D4—44no—
433C22×D4C2412yes—
434C22×D4C2414yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2412yes—
438C22×D4C2412yes—
439C22×D4C2418yes—
440C22×D4C2418yes—
441C23×C4C2414yes—
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2414yes—
446C23×C4C2418yes—
447C23×C4C2414yes—
448C23×C4C2418yes—
449C23×C4C2411yescharacteristic
450C4⋊Q8—28no—
451C4⋊Q8—28no—
452C4⋊Q8—28no—
453C4⋊Q8—28no—
454C4⋊Q8—24no—
455C4⋊Q8—216no—
456C4⋊Q8—416no—
457C4⋊Q8—48no—
458#127—24no—
459#127—48no—
460#126—416no—
461#126—416no—
462#124—28no—
463#124—28no—
464#124—28no—
465#124—28no—
466#124—28no—
467#124—216no—
468#124—416no—
469#124—48no—
470#124—48no—
471#124—48no—
472#124—48no—
473#124—416no—
474#123—416no—
475#123—416no—
476C22⋊Q8—48no—
477C22⋊Q8—416no—
478#121—28no—
479#121—28no—
480#120—416no—
481C4×Q8—216no—
482C4×Q8—48no—
483C4×Q8—48no—
484C4×Q8—48no—
485C4×D4—28no—
486C4×D4—28no—
487C4×D4—216no—
488C4×D4—48no—
489C4×D4—416no—
490C4×D4—416no—
491#117—44no—
492#117—416no—
493C2×C4⋊C4—28no—
494C2×C4⋊C4—28no—
495C2×C4⋊C4—416no—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2414yes—
499C2×C4⋊C4C2414yes—
500C2×C4⋊C4C2414yes—
501C2×C4⋊C4C2414yes—
502C2×C4⋊C4C2414yes—
503C2×C4⋊C4C2414yes—
504C2×C4⋊C4C2414yes—
505C2×C4⋊C4C2412yes—
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2418yes—
509C2×C4⋊C4C2418yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C2418yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C2418yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C22⋊C4—28no—
523C2×C22⋊C4—28no—
524C2×C22⋊C4—416no—
525C2×C22⋊C4—48no—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C2414yes—
528C2×C22⋊C4C2418yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2414yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2414yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2418yes—
538C2×C22⋊C4C2414yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2418yes—
554C2×C42—28no—
555C2×C42#4118yes—
556C2×C42C2414yes—
557C2×C42C2414yes—
558C2×C42C2414yes—
559C2×C42C2412yes—
560C2×C42C2418yes—
561C2×C42C2418yes—
562C2×C42C2414yes—
563C2×C42C2418yes—
564C2×C42C2418yes—
565C2×C42C2412yes—
566C2×C42C2412yes—
567C2×C42C2414yes—
568C2×C42C2411yescharacteristic
569C2×C42C2411yescharacteristic
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572C2×C42C2412yes—
573#95C2412yes—
574#95C2412yes—
575#95C2412yes—
576#95C2414yes—
577#95C2414yes—
578#95C2412yes—
579#95C2414yes—
580#95C2418yes—
581#95C2412yes—
582#95C2414yes—
583#95C2414yes—
584#95C2414yes—
585#95C2412yes—
586#95C2412yes—
587#95C2412yes—
588#95C2414yes—
589#95C2418yes—
590#95C2414yes—
591#95C2414yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2412yes—
597#95C2412yes—
598#95C2418yes—
599#95C2418yes—
600#95C2414yes—
601#95C2418yes—
602#95C2418yes—
603#95C2414yes—
604#95C2412yes—
605#95C2412yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613C24—24no—
614C24—28no—
615C24—44no—
616C24—44no—
617C24C2514yes—
618C24C2514yes—
619C24C2511yescharacteristic
620#41—816no—
621C2×Q8—24no—
622C2×Q8—28no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—28no—
626C2×Q8—28no—
627C2×Q8—28no—
628C2×Q8—28no—
629C2×Q8—28no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—44no—
635C2×Q8—44no—
636C2×Q8—88no—
637C2×Q8—816no—
638C2×D4—28no—
639C2×D4—216no—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—48no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—48no—
652C2×D4—44no—
653C2×D4—48no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—88no—
657C22×C4—24no—
658C22×C4—24no—
659C22×C4—28no—
660C22×C4—24no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—28no—
664C22×C4—216no—
665C22×C4—42no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—48no—
671C22×C4—48no—
672C22×C4—48no—
673C22×C4—48no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4C2×#4114yes—
677C22×C4C2×#4114yes—
678C22×C4C2×#4114yes—
679C22×C4C2514yes—
680C22×C4C2514yes—
681C22×C4C2514yes—
682C22×C4C2518yes—
683C22×C4C2514yes—
684C22×C4C2514yes—
685C22×C4C2514yes—
686C22×C4C2514yes—
687C22×C4C2518yes—
688C22×C4C2511yescharacteristic
689C22×C4C2511yescharacteristic
690C22×C4C2511yescharacteristic
691C22×C4C2511yescharacteristic
692C22×C4C2511yescharacteristic
693C22×C4C2514yes—
694C22×C4C2511yescharacteristic
695C4⋊C4—28no—
696C4⋊C4—28no—
697C4⋊C4—28no—
698C4⋊C4—28no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—216no—
702C4⋊C4—216no—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—28no—
706C4⋊C4—28no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—48no—
715C4⋊C4—48no—
716C4⋊C4—48no—
717C4⋊C4—48no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C4⋊C4—44no—
721C22⋊C4—24no—
722C22⋊C4—28no—
723C22⋊C4—24no—
724C22⋊C4—28no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—216no—
732C22⋊C4—216no—
733C22⋊C4—216no—
734C22⋊C4—48no—
735C22⋊C4—48no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—48no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C42—28no—
750C42—24no—
751C42—28no—
752C42—28no—
753C42—44no—
754C42—42no—
755C42—42no—
756C42—44no—
757C42—48no—
758C42—48no—
759C42—48no—
760C42—48no—
761C42C2×#4114yes—
762C42C2×#4114yes—
763C42C2×#4114yes—
764C42C2×#4114yes—
765C42H(5,𝔽2)18yes—
766C23—22no—
767C23—22no—
768C23—24no—
769C23—24no—
770C23—28no—
771C23—28no—
772C23—24no—
773C23—24no—
774C23—28no—
775C23—24no—
776C23—28no—
777C23—24no—
778C23—48no—
779C23—84no—
780C23—84no—
781C23—816no—
782C23C22×#4112yes—
783C23#58514yes—
784C23C2611yescharacteristic
785Q8—48no—
786Q8—416no—
787Q8—88no—
788Q8—84no—
789Q8—88no—
790Q8—84no—
791D4—416no—
792D4—48no—
793D4—48no—
794D4—84no—
795D4—84no—
796D4—84no—
797D4—816no—
798D4—168no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—28no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—28no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—44no—
834C2×C4—416no—
835C2×C4—816no—
836C2×C4—88no—
837C2×C4—84no—
838C2×C4—88no—
839C2×C4—168no—
840C2×C4C22×#4112yes—
841C2×C4C22×#4112yes—
842C2×C4C22×#4112yes—
843C2×C4C22×#4112yes—
844C2×C4C22×#4112yes—
845C2×C4C22×#4112yes—
846C2×C4C2×H(5,𝔽2)18yes—
847C2×C4C2×H(5,𝔽2)14yes—
848C22—22no—
849C22—22no—
850C22—28no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—48no—
858C22—48no—
859C22—48no—
860C22—48no—
861C22—168no—
862C22#351014yes—
863C22C23×#4111yescharacteristic
864C22C22×H(5,𝔽2)12yes—
865C22C2×#58512yes—
866C222−1+612yes—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—28no—
873C4—44no—
874C4—48no—
875C4—44no—
876C4—44no—
877C4—48no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4#350814yes—
883C2—24no—
884C2—84no—
885C2—84no—
886C2C2×#350811yescharacteristic
887C2C2×#351011yescharacteristic
888C2#6286011yescharacteristic
889C2#6295414yes—
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. #59147C2semidirect
2. #59134C2semidirect
3. #51230C2semidirect
4. #50918C2semidirect
5. #43975C2semidirect
6. #42705C2semidirect
7. #42061C2semidirect
8. #41390C2semidirect
9. #39811C2semidirect
10. #39741C2semidirect
12. #35959C2semidirect
13. #35837C2semidirect
14. #35289C2semidirect
15. #34878C2semidirect
16. C2×#2658C2semidirect
17. #34371C2semidirect
18. #34240C2semidirect
19. #34222C2semidirect
21. C2×#556C22semidirect
27. #2862C22semidirect
28. #2858C22semidirect
29. #2837C22semidirect
31. #2798C22semidirect
32. #2773C22semidirect
33. #2754C22semidirect
34. #2754C22semidirect
35. #2748C22semidirect
36. #2743C22semidirect
37. #2741C22semidirect
38. #2740C22semidirect
39. #2730C22semidirect
40. #2730C22semidirect
41. #2716C22semidirect
42. #2716C22semidirect
45. #2705C22semidirect
46. #2705C22semidirect
47. #2663C22semidirect
54. #2651C22semidirect
55. #2649C22semidirect
57. #2640C22semidirect
61. #2612C22semidirect
62. #2607C22semidirect
63. #2606C22semidirect
64. #2605C22semidirect
66. #2589C22semidirect
67. #2575C22semidirect
69. #2568C22semidirect
70. #2564C22semidirect
71. #2563C22semidirect
73. #2553C22semidirect
74. #2553C22semidirect
77. #2547C22semidirect
78. #2547C22semidirect
79. #2545C22semidirect
80. #2545C22semidirect
84. #2521C22semidirect
85. #2521C22semidirect
86. #2517C22semidirect
87. #2516C22semidirect
90. #2498C22semidirect
91. #2492C22semidirect
95. #2471C22semidirect
96. #2471C22semidirect
97. #2467C22semidirect
98. #2467C22semidirect
102. #2446C22semidirect
103. #2446C22semidirect
104. #2439C22semidirect
113. #2402C22semidirect
114. #2399C22semidirect
115. #2395C22semidirect
118. #2381C22semidirect
119. #2381C22semidirect
121. #2372C22semidirect
124. #2365C22semidirect
125. #2365C22semidirect
128. #2353C22semidirect
137. #2331C22semidirect
138. #2331C22semidirect
139. #2328C22semidirect
140. #2327C22semidirect
141. #2319C22semidirect
148. #2295C22semidirect
151. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#591472
#591342
#512302
#509182
#439752
#427052
#420612
#413902
#398112
#397412
#375362
#359592
#358372
#352892
#348782
C2×#26582
#343712
#342402
#342222