Finite Group Databasebeta

← #6476342

Subgroups — #6476342

Order 512.

2238 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33100C212yesmaximal, complemented
4#33009C212yesmaximal, complemented
5#30165C212yesmaximal, complemented
6#30106C212yesmaximal, complemented
7#29413C214yesmaximal, complemented
8#29162C212yesmaximal, complemented
9#28577C212yesmaximal, complemented
10#27614C211yesmaximal, characteristic, complemented
11#27585C211yesmaximal, characteristic, complemented
12#24556C212yesmaximal, complemented
13#24385C212yesmaximal
14#24064C211yesmaximal, characteristic, complemented
15#23933C211yesmaximal, characteristic, complemented
16#22191C214yesmaximal, complemented
17#20682C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#484C2212yes—
24C2×#468C2214yes—
25C2×#450C2212yes—
26C2×#407C2212yes—
27#2857C2211yescharacteristic, complemented
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2857C2211yescharacteristic, complemented
31#2855—21no—
32#2855C2212yes—
33#2851—21no—
34#2851—21no—
35#2848—21no—
36#2848C2212yes—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8C2212yescomplemented
40C4×C22⋊Q8C2212yescomplemented
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49#2296—21no—
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388—21no—
53C2×#386—21no—
54#2285C2211yescharacteristic
55#2280—21no—
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2100C2212yescomplemented
60#2094C2212yescomplemented
61#2083C2212yescomplemented
62#2075C2214yescomplemented
63#2071C2212yescomplemented
64#2057C2212yescomplemented
65#2043C2212yescomplemented
66#2035C2214yescomplemented
67#2033C2214yes—
68#2023C2212yescomplemented
69#2013C2212yescomplemented
70#2000C2214yes—
71#1928C2214yescomplemented
72#1927C2214yescomplemented
73#1926C2214yescomplemented
74#1921C2214yescomplemented
75#1919C2214yescomplemented
76#1918C2214yescomplemented
77#1895C2214yes—
78#1894C2214yescomplemented
79#1880C2214yescomplemented
80#1877C2214yescomplemented
81#1877C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1863C2214yescomplemented
85#1862C2214yescomplemented
86#1862C2214yescomplemented
87#1853C2212yes—
88#1852C2212yes—
89#1824C2212yes—
90#1817C2211yescharacteristic
91#1817C2212yes—
92#1817C2211yescharacteristic
93#1817C2212yescomplemented
94#1817C2212yescomplemented
95#1809C2214yescomplemented
96#1786C2212yes—
97#1728C2212yescomplemented
98#1728C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C22×M16C2314yes—
107#533—44no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2311yescharacteristic
110C2×#125—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×C22⋊Q8C2312yes—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—28no—
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×C4×Q8—21no—
123C2×C4×Q8C2312yes—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4—22no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—44no—
131C2×C4×D4—48no—
132C2×C4×D4C2312yes—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C42—21no—
146C22×C42—44no—
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159#484—44no—
160#468—216no—
161#450—44no—
162C2×#107C2314yes—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171#407—44no—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2314yes—
175#391—21no—
176#391—21no—
177#391C2312yes—
178#391C2312yes—
179#390—21no—
180#390—21no—
181#390C2312yes—
182#390C2312yes—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389—21no—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#388—22no—
196#388—22no—
197#388—22no—
198#388—22no—
199#387—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#384C2311yescharacteristic
214#384C2311yescharacteristic
215#382—21no—
216#381—22no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#380C2312yes—
231#379—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#336C2312yes—
256#336C2312yes—
257#336C2314yes—
258#336C2314yes—
259#336C2312yes—
260#336C2312yes—
261C25—21no—
262C25C2×D411yescharacteristic
263C22×Q8—21no—
264C22×Q8C2412yes—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—21no—
270C22×D4—24no—
271C22×D4—42no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4C2412yes—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C2×SD16—28no—
311C2×SD16—44no—
312C2×SD16—44no—
313C2×M16—28no—
314C2×M16—44no—
315C2×M16—44no—
316C22×C8C2414yes—
317C22×C8C2414yes—
318C4⋊Q8—42no—
319C4⋊Q8—42no—
320#125—44no—
321C22⋊Q8—28no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328#121—28no—
329#121—28no—
330#121—24no—
331#121—24no—
332#121—24no—
333#121#4118yes—
334C4×Q8—42no—
335C4×Q8—42no—
336C4×Q8—44no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—48no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—48no—
345#117—44no—
346#117—44no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
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—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C22⋊C4—28no—
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×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—44no—
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×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—28no—
430#107—44no—
431#106—44no—
432#103—28no—
433#103—44no—
434#103—44no—
435#102—28no—
436#102—44no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—44no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C2×Q8—24no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×D4—24no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—24no—
488C2×D4—416no—
489C2×D4—42no—
490C2×D4—44no—
491C2×D4—432no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4C2×#4114yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—416no—
556C22×C4—416no—
557C22×C4—416no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—816no—
573C22×C4AGL(1,ℤ/8)14yes—
574C22×C4#13714yes—
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×#4114yes—
587C22×C4H(5,𝔽2)14yes—
588C22×C4C2511yescharacteristic
589SD16—88no—
590M16—88no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—42no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4C2×#4114yes—
623C22⋊C4—28no—
624C22⋊C4—28no—
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—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—44no—
656C42—44no—
657C42—44no—
658C42—44no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—28no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—24no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—48no—
683C23—48no—
684C23—48no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23#52512yes—
697C23#53412yes—
698C23C2×AGL(1,ℤ/8)12yes—
699C23C2×#13712yes—
700C23#57512yes—
701C23C23×D411yescharacteristic
702Q8—44no—
703Q8—44no—
704Q8—84no—
705D4—28no—
706D4—48no—
707D4—416no—
708D4—416no—
709D4—44no—
710C2×C4—28no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—28no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—21no—
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—44no—
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—48no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
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—88no—
777C2×C4—88no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4#52512yes—
781C2×C4#53412yes—
782C2×C4C2×AGL(1,ℤ/8)12yes—
783C2×C4C2×AGL(1,ℤ/8)12yes—
784C2×C4C2×#13712yes—
785C2×C4C2×#13712yes—
786C2×C4#57512yes—
787C2×C4C22×#4112yes—
788C2×C4C2×H(5,𝔽2)12yes—
789C2×C4#58512yes—
790C8—44no—
791C8—44no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—416no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—816no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22#319614yes—
822C22C2×#52511yescharacteristic
823C22C2×#53411yescharacteristic
824C22#344911yescharacteristic
825C22C22×AGL(1,ℤ/8)11yescharacteristic
826C22C22×#13711yescharacteristic
827C22C2×#57511yescharacteristic
828C22C2×#57511yescharacteristic
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—22no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—44no—
840C4—41no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4#351314yes—
848C2—24no—
849C2—42no—
850C2—42no—
851C2—84no—
852C2#3506311yescharacteristic
853C2#6055811yescharacteristic
854C2#6056211yescharacteristic
855C2C2×#319611yescharacteristic
856C2#6075011yescharacteristic
857C2#6095411yescharacteristic
858C2#6096911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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
1. #36625C2semidirect
3. #33100C2semidirect
4. #33009C2semidirect
5. #30165C2semidirect
6. #30106C2semidirect
7. #29413C2semidirect
8. #29162C2semidirect
9. #28577C2semidirect
10. #27614C2semidirect
11. #27585C2semidirect
12. #24556C2semidirect
14. #24064C2semidirect
15. #23933C2semidirect
16. #22191C2semidirect
17. #20682C2semidirect
27. #2857C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
30. #2857C22semidirect
39. C4×C22⋊Q8C22semidirect
40. C4×C22⋊Q8C22semidirect
59. #2100C22semidirect
60. #2094C22semidirect
61. #2083C22semidirect
62. #2075C22semidirect
63. #2071C22semidirect
64. #2057C22semidirect
65. #2043C22semidirect
66. #2035C22semidirect
68. #2023C22semidirect
69. #2013C22semidirect
71. #1928C22semidirect
72. #1927C22semidirect
73. #1926C22semidirect
74. #1921C22semidirect
75. #1919C22semidirect
76. #1918C22semidirect
78. #1894C22semidirect
79. #1880C22semidirect
80. #1877C22semidirect
81. #1877C22semidirect
84. #1863C22semidirect
85. #1862C22semidirect
86. #1862C22semidirect
93. #1817C22semidirect
94. #1817C22semidirect
95. #1809C22semidirect
97. #1728C22semidirect
98. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#331002
#330092
#301652
#301062
#294132
#291622
#285772
#276142
#275852
#245562
#243852
#240642
#239332
#221912
#206822