Finite Group Databasebeta

← #6493622

Subgroups — #6493622

Order 512.

1966 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#33112C214yesmaximal, complemented
4#29924C214yesmaximal, complemented
5#27975C211yesmaximal, characteristic, complemented
6#27974C211yesmaximal, characteristic, complemented
7#27908C211yesmaximal, characteristic, complemented
8#27907C211yesmaximal, characteristic, complemented
9#27892C211yesmaximal, characteristic, complemented
10#27891C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#27889C211yesmaximal, characteristic, complemented
13#27590C214yesmaximal, complemented
14#24008C214yesmaximal, complemented
15#21984C211yesmaximal, characteristic, complemented
16#21984C211yesmaximal, characteristic, complemented
17#21805C211yesmaximal, characteristic, complemented
18#21805C211yesmaximal, characteristic, complemented
19#20714C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#525C2212yes—
22C23×C42C2211yescharacteristic
23C2×#485C2214yes—
24C2×#482C2214yes—
25C2×#431C2211yescharacteristic
26C2×#431C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2856C2211yescharacteristic
30#2856C2211yescharacteristic
31#2854—21no—
32#2854—21no—
33#2850C2212yes—
34#2850C2212yes—
35#2847—21no—
36#2847—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121—21no—
40C4×#121—21no—
41#2297C2212yes—
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2285C2211yescharacteristic
48#2285C2211yescharacteristic
49#2283—21no—
50#2283—21no—
51#2283—21no—
52#2283—21no—
53#2283C2212yes—
54#2283C2212yes—
55#2280—21no—
56#2280—21no—
57#2280C2212yes—
58C4×#117—21no—
59C4×#117—21no—
60C4×#117C2212yes—
61#2097C2214yescomplemented
62#2092C2214yescomplemented
63#2074C2214yescomplemented
64#2073C2214yescomplemented
65#2036C2214yes—
66#2035C2214yes—
67#2034C2214yes—
68#2033C2214yes—
69#1983C2214yescomplemented
70#1983C2214yescomplemented
71#1957C2211yescharacteristic, complemented
72#1957C2211yescharacteristic, complemented
73#1957C2211yescharacteristic, complemented
74#1957C2211yescharacteristic, complemented
75#1956C2211yescharacteristic, complemented
76#1956C2211yescharacteristic, complemented
77#1956C2211yescharacteristic, complemented
78#1956C2211yescharacteristic, complemented
79#1949C2214yescomplemented
80#1949C2214yescomplemented
81#1928C2214yescomplemented
82#1927C2214yescomplemented
83#1926C2214yescomplemented
84#1925C2214yescomplemented
85#1875C2214yes—
86#1873C2214yes—
87#1854C2214yes—
88#1854C2214yes—
89#1845C2211yescharacteristic, complemented
90#1845C2211yescharacteristic, complemented
91#1844C2211yescharacteristic, complemented
92#1844C2211yescharacteristic, complemented
93#1834C2211yescharacteristic, complemented
94#1834C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1817C2212yes—
98#1797C2212yes—
99#1797C2212yes—
100#1788C2214yes—
101#1788C2214yes—
102#1779C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C22×#41C2312yes—
108C24×C4D411yescharacteristic
109C24×C4D411yescharacteristic
110C24×C4C2311yescharacteristic
111#532—24no—
112#532—24no—
113C2×C4⋊Q8C2311yescharacteristic
114C2×#127C2311yescharacteristic
115C2×#124C2312yes—
116#525—48no—
117C2×#123—22no—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#120—22no—
129C2×C4×D4—22no—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×#117—21no—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—21no—
137C2×#117C2312yes—
138C2×#117C2312yes—
139C2×#117C2312yes—
140C22×C42—24no—
141C22×C42—24no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#485—48no—
155#482—48no—
156#431—24no—
157#431—24no—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390C2312yes—
189#390C2312yes—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#388—22no—
195#388—22no—
196#388—22no—
197#388—22no—
198#386—22no—
199#386—22no—
200#386—22no—
201#386—22no—
202#386—22no—
203#386—22no—
204#384C2311yescharacteristic
205#384C2311yescharacteristic
206#384C2311yescharacteristic
207#384C2311yescharacteristic
208#384C2311yescharacteristic
209#384C2311yescharacteristic
210#383—22no—
211#383—22no—
212#382—21no—
213#382—21no—
214#382—21no—
215#382—21no—
216#382C2312yes—
217#382C2312yes—
218#382C2312yes—
219#381—22no—
220#381—22no—
221#381—22no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380—21no—
235#380—21no—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240#379—22no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2312yes—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C4×C22⋊C4—22no—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263#376—22no—
264#376—22no—
265#376—22no—
266C43—22no—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275C25C2×D411yescharacteristic
276C2×#41—24no—
277C2×#41—24no—
278C2×#41—44no—
279C2×#41—44no—
280C22×Q8C2412yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2412yes—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C22×C8C2412yes—
317C22×C8C2412yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322#127—22no—
323#127—22no—
324#124—24no—
325#124—24no—
326#123—48no—
327C22⋊Q8—28no—
328C22⋊Q8—44no—
329#121—28no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#120—48no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—44no—
341C4×D4—44no—
342#117—28no—
343#117—44no—
344#117—44no—
345#117—44no—
346#117—44no—
347#117—44no—
348#117—44no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42#4114yes—
424C2×C42#4114yes—
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—44no—
430#107—44no—
431#106—44no—
432#106—44no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#102—44no—
440#102—44no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C22⋊C8—24no—
446C22⋊C8—24no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—41no—
476C24—41no—
477C24—41no—
478C24—41no—
479C24C22×D411yescharacteristic
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482#41—88no—
483#41—88no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—24no—
487C2×Q8—24no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—416no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4#12314yes—
573C22×C4#12314yes—
574C22×C4#13514yes—
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)14yes—
589C22×C4C2511yescharacteristic
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—44no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42#12314yes—
663C42#12314yes—
664C42C2×#4112yes—
665C42C2×#4112yes—
666C42C2×#4112yes—
667C42C2×#4112yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23C2×#12312yes—
701C23#53512yes—
702C23C2×#13512yes—
703C23C23×D411yescharacteristic
704Q8—44no—
705Q8—44no—
706D4—44no—
707D4—44no—
708D4—88no—
709D4—88no—
710D4—88no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—28no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—88no—
778C2×C4C2×#12312yes—
779C2×C4C2×#12312yes—
780C2×C4C2×#12312yes—
781C2×C4C2×#12312yes—
782C2×C4C2×#12312yes—
783C2×C4#53512yes—
784C2×C4C2×#13512yes—
785C2×C4C2×#13512yes—
786C2×C4#57512yes—
787C2×C4#57512yes—
788C2×C4#57512yes—
789C2×C4C22×#4111yescharacteristic
790C2×C4C22×#4111yescharacteristic
791C2×C4C2×H(5,𝔽2)12yes—
792C2×C4#58512yes—
793C8—42no—
794C8—42no—
795C8—42no—
796C8—42no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—416no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22C22×#12311yescharacteristic
827C22C2×#53511yescharacteristic
828C22#344911yescharacteristic
829C22C22×#13511yescharacteristic
830C22C2×#57511yescharacteristic
831C22C2×#57511yescharacteristic
832C22C2×#57511yescharacteristic
833C4—22no—
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4#309114yes—
850C4#309314yes—
851C4#349412yes—
852C4#349412yes—
853C2—42no—
854C2—42no—
855C2—42no—
856C2—162no—
857C2#3526211yescharacteristic
858C2C2×#309111yescharacteristic
859C2C2×#309311yescharacteristic
860C2#6078211yescharacteristic
861C2#6080111yescharacteristic
862C2#6094411yescharacteristic
863C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34012C2semidirect
3. #33112C2semidirect
4. #29924C2semidirect
5. #27975C2semidirect
6. #27974C2semidirect
7. #27908C2semidirect
8. #27907C2semidirect
9. #27892C2semidirect
10. #27891C2semidirect
11. #27890C2semidirect
12. #27889C2semidirect
13. #27590C2semidirect
14. #24008C2semidirect
15. #21984C2semidirect
16. #21984C2semidirect
17. #21805C2semidirect
18. #21805C2semidirect
19. #20714C2semidirect
61. #2097C22semidirect
62. #2092C22semidirect
63. #2074C22semidirect
64. #2073C22semidirect
69. #1983C22semidirect
70. #1983C22semidirect
71. #1957C22semidirect
72. #1957C22semidirect
73. #1957C22semidirect
74. #1957C22semidirect
75. #1956C22semidirect
76. #1956C22semidirect
77. #1956C22semidirect
78. #1956C22semidirect
79. #1949C22semidirect
80. #1949C22semidirect
81. #1928C22semidirect
82. #1927C22semidirect
83. #1926C22semidirect
84. #1925C22semidirect
89. #1845C22semidirect
90. #1845C22semidirect
91. #1844C22semidirect
92. #1844C22semidirect
93. #1834C22semidirect
94. #1834C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#366242
#340122
#331122
#299242
#279752
#279742
#279082
#279072
#278922
#278912
#278902
#278892
#275902
#240082
#219842
#218052
#207142