Finite Group Databasebeta

← #7676089

Subgroups — #7676089

Order 512.

4676 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59287C218yesmaximal, complemented
2#59284C218yesmaximal, complemented
3#44512C218yesmaximal, complemented
4#43977C218yesmaximal, complemented
5#39541C214yesmaximal, complemented
6#37935C214yesmaximal, complemented
7#37886C214yesmaximal, complemented
8#36199C214yesmaximal, complemented
9#35456C212yesmaximal
10#35368C212yesmaximal
11#35090C211yesmaximal, characteristic
12#35090C211yesmaximal, characteristic
13#34994C211yesmaximal, characteristic
14C2×#2484C212yesmaximal
15#34270C211yesmaximal, characteristic
16#34177C211yesmaximal, characteristic
17#34177C212yesmaximal
18C2×#2344C211yesmaximal, characteristic
19#34052C211yesmaximal, characteristic
20C2×#543C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2212yes—
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25#2855C2214yes—
26#2855C2214yes—
27#2851C2214yes—
28#2794C2218yescomplemented
29#2791C2218yescomplemented
30#2776C2218yescomplemented
31#2774C2218yescomplemented
32#2769C2218yescomplemented
33#2767C2218yescomplemented
34#2767C2218yescomplemented
35#2766C2218yescomplemented
36#2766C2218yescomplemented
37#2762C2218yescomplemented
38#2758C2218yescomplemented
39#2719C2218yescomplemented
40#2646C2214yes—
41#2627C2214yes—
42#2627C2214yes—
43#2612C2218yescomplemented
44#2606C2218yescomplemented
45#2590C2218yescomplemented
46#2585C2218yescomplemented
47#2570C2214yescomplemented
48#2569C2218yes—
49#2565C2214yescomplemented
50#2533C2218yescomplemented
51#2533C2218yescomplemented
52#2533C2218yescomplemented
53#2528C2218yescomplemented
54#2528C2218yescomplemented
55#2528C2218yescomplemented
56#2524C2218yescomplemented
57#2524C2218yescomplemented
58#2524C2218yescomplemented
59#2520C2218yescomplemented
60#2514C2214yescomplemented
61#2511C2214yescomplemented
62#2508C2214yescomplemented
63#2506C2214yescomplemented
64#2505C2218yes—
65#2505C2218yes—
66#2505C2218yes—
67#2493C2218yes—
68#2493C2218yes—
69#2493C2218yes—
70#2493C2218yes—
71#2493C2218yes—
72#2493C2218yes—
73#2484C2214yes—
74#2484C2214yes—
75#2484C2214yes—
76#2484C2218yes—
77#2484C2218yes—
78#2484C2214yes—
79#2473C2218yes—
80#2473C2218yes—
81#2473C2218yes—
82#2462C2218yescomplemented
83#2442C2218yes—
84#2438C2218yes—
85#2438C2218yes—
86#2438C2218yes—
87#2438C2218yes—
88C2×#400C2214yes—
89C2×#398C2214yes—
90#2371C2218yescomplemented
91#2370C2214yescomplemented
92#2368C2218yes—
93#2360C2218yes—
94#2356C2214yescomplemented
95#2344C2218yes—
96#2344C2218yes—
97#2343C2218yes—
98#2343C2218yes—
99#2343C2218yes—
100#2343C2218yes—
101#2343C2218yes—
102#2343C2218yes—
103#2329C2214yes—
104#2317C2214yes—
105#2317C2214yes—
106#2316C2214yes—
107#2315C2211yescharacteristic
108#2315C2212yes—
109#2315C2211yescharacteristic
110#2315C2212yes—
111#2315C2212yes—
112#2315C2211yescharacteristic
113#2315C2212yes—
114#2313C2214yes—
115#2313C2214yes—
116#2313C2214yes—
117C4×C22⋊Q8C2214yes—
118#2296C2214yes—
119#2296C2214yes—
120C2×#389C2212yes—
121C2×#387C2212yes—
122C2×#387C2212yes—
123C2×#387C2214yes—
124C2×#387C2214yes—
125C2×#385C2212yes—
126C2×#385C2212yes—
127#2285C2214yes—
128#2283C2214yes—
129#2283C2214yes—
130#2283C2214yes—
131C2×#381C2212yes—
132C2×#381C2212yes—
133C2×#381C2211yescharacteristic
134C2×#381C2211yescharacteristic
135C2×#381C2212yes—
136C2×#380C2211yescharacteristic
137#2273C2212yes—
138#2273C2212yes—
139C2×C4×C4⋊C4C2212yes—
140C2×C4×C22⋊C4C2211yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144#543—28no—
145C2×#125C2314yes—
146C2×#125C2318yes—
147C2×C22⋊Q8C2314yes—
148C2×C22⋊Q8C2318yes—
149C2×C4×Q8C2314yes—
150C2×#117—216no—
151C2×#117—28no—
152C2×#117—28no—
153C2×#117C2314yes—
154C2×#117C2314yes—
155C2×#117C2314yes—
156C2×#117C2318yes—
157C2×#117C2314yes—
158C2×#117C2314yes—
159C2×#117C2314yes—
160C22×C4⋊C4—28no—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2314yes—
166C22×C4⋊C4C2314yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2314yes—
172C22×C4⋊C4C2314yes—
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C42C2312yes—
183C22×C42C2312yes—
184C22×C42C2312yes—
185C22×C42C2312yes—
186C22×C42C2312yes—
187#401C2318yes—
188#401C2318yes—
189#400C2318yes—
190#400C2318yes—
191#400C2318yes—
192#400C2318yes—
193#400C2318yes—
194#400C2318yes—
195#400C2318yes—
196#400C2318yes—
197#400C2318yes—
198#400C2318yes—
199#400C2318yes—
200#400C2318yes—
201#400C2318yes—
202#400C2318yes—
203#400C2318yes—
204#400C2318yes—
205#400C2318yes—
206#400C2318yes—
207#398C2318yes—
208#398C2318yes—
209#398C2318yes—
210#398C2318yes—
211#398C2318yes—
212#398C2318yes—
213#398C2318yes—
214#398C2318yes—
215#398C2318yes—
216#398C2318yes—
217#398C2318yes—
218#398C2318yes—
219#398C2318yes—
220#398C2318yes—
221#395C2318yes—
222#395C2318yes—
223#391C2314yes—
224#391C2314yes—
225#391C2318yes—
226#391C2314yes—
227#391C2314yes—
228#391C2314yes—
229#389C2314yes—
230#389C2314yes—
231#389C2318yes—
232#389C2318yes—
233#389C2318yes—
234#389C2318yes—
235#389C2318yes—
236#389C2318yes—
237#389C2314yes—
238#389C2318yes—
239#389C2314yes—
240#389C2314yes—
241#389C2314yes—
242#389C2318yes—
243#389C2318yes—
244#389C2314yes—
245#387C2318yes—
246#387C2318yes—
247#387C2318yes—
248#387C2318yes—
249#387C2318yes—
250#387C2318yes—
251#387C2318yes—
252#387C2318yes—
253#387C2318yes—
254#387C2318yes—
255#387C2318yes—
256#387C2318yes—
257#387C2318yes—
258#387C2318yes—
259#387C2318yes—
260#387C2318yes—
261#387C2318yes—
262#387C2318yes—
263#387C2318yes—
264#387C2318yes—
265#387C2318yes—
266#387C2318yes—
267#387C2318yes—
268#387C2318yes—
269#387C2318yes—
270#387C2318yes—
271#387C2318yes—
272#387C2318yes—
273#387C2318yes—
274#387C2318yes—
275#387C2318yes—
276#387C2318yes—
277#387C2318yes—
278#387C2318yes—
279#387C2318yes—
280#387C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#387C2318yes—
287#387C2318yes—
288#385C2314yes—
289#385C2318yes—
290#385C2314yes—
291#385C2314yes—
292#385C2314yes—
293#385C2314yes—
294#385C2314yes—
295#385C2314yes—
296#385C2314yes—
297#385C2318yes—
298#385C2318yes—
299#385C2318yes—
300#385C2318yes—
301#385C2318yes—
302#385C2318yes—
303#385C2318yes—
304#385C2314yes—
305#385C2314yes—
306#385C2314yes—
307#385C2318yes—
308#385C2314yes—
309#384C2314yes—
310#384C2314yes—
311#383C2318yes—
312#383C2318yes—
313#383C2318yes—
314#383C2318yes—
315#383C2318yes—
316#382C2314yes—
317#382C2314yes—
318#382C2314yes—
319#382C2318yes—
320#382C2318yes—
321#382C2318yes—
322#382C2318yes—
323#381C2314yes—
324#381C2314yes—
325#381C2314yes—
326#381C2314yes—
327#381C2314yes—
328#381C2314yes—
329#381C2318yes—
330#381C2314yes—
331#381C2318yes—
332#381C2314yes—
333#381C2318yes—
334#381C2314yes—
335#381C2314yes—
336#380C2314yes—
337#380C2314yes—
338#380C2314yes—
339#380C2314yes—
340#380C2314yes—
341#380C2314yes—
342#380C2318yes—
343#380C2318yes—
344#380C2314yes—
345#380C2318yes—
346C4×C4⋊C4C2314yes—
347C4×C4⋊C4C2314yes—
348C4×C4⋊C4C2314yes—
349C4×C4⋊C4C2318yes—
350C4×C4⋊C4C2318yes—
351C4×C4⋊C4C2318yes—
352C4×C4⋊C4C2314yes—
353C4×C4⋊C4C2314yes—
354C4×C4⋊C4C2314yes—
355C4×C4⋊C4C2314yes—
356C4×C4⋊C4C2314yes—
357C4×C4⋊C4C2314yes—
358C4×C4⋊C4C2318yes—
359C4×C22⋊C4C2314yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2314yes—
362C4×C22⋊C4C2314yes—
363C4×C22⋊C4C2314yes—
364C4×C22⋊C4C2318yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C2318yes—
367C4×C22⋊C4C2318yes—
368#376C2318yes—
369#376C2318yes—
370#376C2318yes—
371C2×#95C2314yes—
372C2×#95C2312yes—
373C2×#95C2312yes—
374C2×#95C2312yes—
375C2×#95C2314yes—
376C2×#95C2314yes—
377C2×#95C2314yes—
378C2×#95C2314yes—
379C2×#95C2314yes—
380C2×#95C2314yes—
381C2×#95C2314yes—
382C2×#95C2312yes—
383C2×#95C2312yes—
384C2×#95C2312yes—
385C25C2411yescharacteristic
386C22×Q8C2414yes—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—44no—
394C23×C4#4118yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2414yes—
398C23×C4C2411yescharacteristic
399C23×C4C2414yes—
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2412yes—
406C23×C4C2412yes—
407C23×C4C2412yes—
408C23×C4C2414yes—
409C23×C4C2414yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2412yes—
415#125—48no—
416#125—416no—
417C22⋊Q8—216no—
418C22⋊Q8—232no—
419C4×Q8—48no—
420#117—216no—
421#117—216no—
422#117—216no—
423#117—216no—
424#117—216no—
425#117—216no—
426#117—232no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—216no—
430C2×C4⋊C4—216no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—28no—
434C2×C4⋊C4—28no—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—28no—
437C2×C4⋊C4—48no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4—48no—
440C2×C4⋊C4C2412yes—
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2414yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2414yes—
447C2×C4⋊C4C2414yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2414yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C4⋊C4C2414yes—
457C2×C4⋊C4C2414yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—28no—
477C2×C22⋊C4—28no—
478C2×C22⋊C4—28no—
479C2×C22⋊C4—28no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4#4118yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2414yes—
487C2×C22⋊C4C2414yes—
488C2×C22⋊C4C2414yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C42—28no—
495C2×C42—28no—
496C2×C42—28no—
497C2×C42—28no—
498C2×C42—44no—
499C2×C42C2414yes—
500C2×C42C2414yes—
501C2×C42C2414yes—
502C2×C42C2414yes—
503C2×C42C2414yes—
504C2×C42C2414yes—
505C2×C42C2414yes—
506C2×C42C2414yes—
507C2×C42C2414yes—
508C2×C42C2418yes—
509C2×C42C2418yes—
510C2×C42C2418yes—
511C2×C42C2418yes—
512C2×C42C2414yes—
513#95C2414yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2414yes—
521#95C2414yes—
522#95C2414yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547#95C2418yes—
548#95C2418yes—
549#95C2418yes—
550#95C2418yes—
551#95C2418yes—
552C24—42no—
553C24—42no—
554C24C2×#4114yes—
555C24C2×#4114yes—
556C242−1+414yes—
557C24C2511yescharacteristic
558C24C2512yes—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C22×C4—232no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—24no—
593C22×C4—28no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—416no—
613C22×C4—416no—
614C22×C4C2×#4118yes—
615C22×C4C2×#4118yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4118yes—
619C22×C4C2512yes—
620C22×C4C2512yes—
621C22×C4C2514yes—
622C22×C4C2518yes—
623C22×C4C2514yes—
624C22×C4C2514yes—
625C22×C4C2518yes—
626C22×C4C2512yes—
627C22×C4C2514yes—
628C22×C4C2514yes—
629C22×C4C2514yes—
630C22×C4C2514yes—
631C22×C4C2511yescharacteristic
632C22×C4C2511yescharacteristic
633C22×C4C2512yes—
634C22×C4C2514yes—
635C22×C4C2512yes—
636C4⋊C4—24no—
637C4⋊C4—28no—
638C4⋊C4—24no—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—24no—
642C4⋊C4—216no—
643C4⋊C4—28no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—216no—
648C4⋊C4—216no—
649C4⋊C4—28no—
650C4⋊C4—216no—
651C4⋊C4—28no—
652C4⋊C4—216no—
653C4⋊C4—44no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4C2×#41116yes—
682C42—28no—
683C42—28no—
684C42—28no—
685C42—28no—
686C42—28no—
687C42—28no—
688C42—28no—
689C42—28no—
690C42—28no—
691C42—44no—
692C42—48no—
693C42—48no—
694C42—48no—
695C42—48no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—24no—
700C23—44no—
701C23—48no—
702C23—44no—
703C23—48no—
704C23#552116yes—
705C23C22×#4112yes—
706C23C22×#4114yes—
707C23C22×#4112yes—
708C23C22×#4114yes—
709C23C2×2−1+412yes—
710C23C2×2−1+414yes—
711C23C2611yescharacteristic
712Q8—88no—
713C2×C4—28no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—216no—
727C2×C4—216no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—48no—
760C2×C4—416no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—416no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—88no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—88no—
774C2×C4C22×#4112yes—
775C2×C4C22×#4118yes—
776C2×C4C22×#4114yes—
777C2×C4C22×#4112yes—
778C2×C4#58514yes—
779C22—24no—
780C22—28no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—28no—
787C22—416no—
788C22C2×#55214yes—
789C22C2×#55218yes—
790C22C23×#4111yescharacteristic
791C22C23×#4111yescharacteristic
792C22C22×2−1+411yescharacteristic
793C22C2×#58512yes—
794C222−1+612yes—
795C4—28no—
796C4—24no—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—44no—
801C4—44no—
802C4—48no—
803C4—42no—
804C4—44no—
805C4—44no—
806C4—44no—
807C4—44no—
808C4—44no—
809C4—48no—
810C4—42no—
811C4—42no—
812C2—24no—
813C2—28no—
814C2C22×#55211yescharacteristic
815C2#6281411yescharacteristic
816C2#6286011yescharacteristic
817C2#6290412yes—
818C2#6299112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59287C2semidirect
2. #59284C2semidirect
3. #44512C2semidirect
4. #43977C2semidirect
5. #39541C2semidirect
6. #37935C2semidirect
7. #37886C2semidirect
8. #36199C2semidirect
28. #2794C22semidirect
29. #2791C22semidirect
30. #2776C22semidirect
31. #2774C22semidirect
32. #2769C22semidirect
33. #2767C22semidirect
34. #2767C22semidirect
35. #2766C22semidirect
36. #2766C22semidirect
37. #2762C22semidirect
38. #2758C22semidirect
39. #2719C22semidirect
43. #2612C22semidirect
44. #2606C22semidirect
45. #2590C22semidirect
46. #2585C22semidirect
47. #2570C22semidirect
49. #2565C22semidirect
50. #2533C22semidirect
51. #2533C22semidirect
52. #2533C22semidirect
53. #2528C22semidirect
54. #2528C22semidirect
55. #2528C22semidirect
56. #2524C22semidirect
57. #2524C22semidirect
58. #2524C22semidirect
59. #2520C22semidirect
60. #2514C22semidirect
61. #2511C22semidirect
62. #2508C22semidirect
63. #2506C22semidirect
82. #2462C22semidirect
90. #2371C22semidirect
91. #2370C22semidirect
94. #2356C22semidirect

Maximal subgroups

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

subgroupindex
#592872
#592842
#445122
#439772
#395412
#379352
#378862
#361992
#354562
#353682
#350902
#349942
C2×#24842
#342702
#341772
C2×#23442
#340522