Finite Group Databasebeta

← #6476677

Subgroups — #6476677

Order 512.

2562 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#33110C212yesmaximal, complemented
4#32908C212yesmaximal, complemented
5#30107C214yesmaximal, complemented
6#29330C212yesmaximal, complemented
7#28303C212yesmaximal, complemented
8#27684C212yesmaximal, complemented
9#24654C214yesmaximal, complemented
10#24215C212yesmaximal, complemented
11#24006C211yesmaximal, characteristic, complemented
12#24005C211yesmaximal, characteristic, complemented
13#23919C211yesmaximal, characteristic, complemented
14#23918C211yesmaximal, characteristic
15#22041C212yesmaximal, complemented
16#22040C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic, complemented
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4—21no—
23C22×C4×D4C2211yescharacteristic, complemented
24C23×C42C2211yescharacteristic
25C2×#484C2212yescomplemented
26C2×#481C2212yes—
27C2×#463C2214yescomplemented
28C2×#448C2212yes—
29C2×#450C2212yescomplemented
30C2×#447C2212yes—
31C2×#447C2212yes—
32C2×#431C2212yescomplemented
33#2850—21no—
34#2850—21no—
35#2850—21no—
36#2850—21no—
37#2850C2212yes—
38#2850C2212yes—
39#2850C2212yescomplemented
40#2850C2212yescomplemented
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yescomplemented
48C4×#121C2212yescomplemented
49C2×#391C2211yescharacteristic, complemented
50C2×#390C2211yescharacteristic, complemented
51C2×#390C2211yescharacteristic, complemented
52C2×#389C2211yescharacteristic, complemented
53C2×#388—21no—
54C2×#388—21no—
55C2×#388—21no—
56C2×#386—21no—
57C2×#386—21no—
58C2×#386—21no—
59C2×#382C2211yescharacteristic, complemented
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic, complemented
62C2×C4×C22⋊C4—21no—
63#2101C2214yescomplemented
64#2092C2214yescomplemented
65#2042C2214yescomplemented
66#2036C2214yescomplemented
67#2034C2214yescomplemented
68#2012C2214yescomplemented
69#2000C2214yescomplemented
70#1999C2214yes—
71#1983C2214yescomplemented
72#1970C2214yescomplemented
73#1968C2214yescomplemented
74#1949C2214yescomplemented
75#1934C2214yescomplemented
76#1933C2214yescomplemented
77#1927C2214yescomplemented
78#1925C2214yescomplemented
79#1879C2214yescomplemented
80#1877C2214yescomplemented
81#1874C2212yes—
82#1874C2212yes—
83#1874C2212yes—
84#1874C2212yes—
85#1872C2212yescomplemented
86#1872C2212yescomplemented
87#1853C2212yescomplemented
88#1852C2212yescomplemented
89#1817C2212yescomplemented
90#1804C2214yescomplemented
91#1797C2212yescomplemented
92#1797C2212yescomplemented
93#1787C2212yescomplemented
94#1786C2212yescomplemented
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97C4×C22⋊C8C2212yescomplemented
98C4×C22⋊C8C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4—21no—
102C23×D4C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C24×C4—21no—
105C24×C4D411yescharacteristic
106C24×C4D411yescharacteristic
107C24×C4C2311yescharacteristic
108C22×SD16C2314yes—
109C22×D8C2314yes—
110C2×#124—21no—
111C2×#124—21no—
112C2×#124—44no—
113C2×#124C2312yes—
114C2×#124C2312yes—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—44no—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—28no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—44no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#121C2312yes—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—44no—
137C2×C4×D4—48no—
138C2×C4×D4C2312yes—
139C2×C4×D4C2312yes—
140C22×C4⋊C4—21no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C22⋊C4—21no—
155C22×C22⋊C4—21no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4—21no—
158C22×C42—21no—
159C22×C42—44no—
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#484—44no—
173#481—44no—
174#463—48no—
175#450—44no—
176#448—28no—
177#447—28no—
178#447—44no—
179#431—44no—
180C2×#107C2314yes—
181C2×#106C2314yes—
182C2×C4⋊C8C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#102C2314yes—
187C2×#102C2314yes—
188C2×#102C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C4×C8C2314yes—
198#391—21no—
199#391—21no—
200#391C2312yes—
201#391C2312yes—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390C2312yes—
207#390C2312yes—
208#390C2312yes—
209#390C2312yes—
210#389—21no—
211#389—21no—
212#389C2312yes—
213#389C2312yes—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#386—22no—
233#386—22no—
234#386—22no—
235#386—22no—
236#386—22no—
237#386—22no—
238#382—21no—
239#382—21no—
240#382C2312yes—
241#382C2312yes—
242#380—21no—
243#380—21no—
244#380C2312yes—
245#380C2312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4C2312yes—
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C2×#95—21no—
260C2×#95—21no—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#336C2314yes—
266#336C2314yes—
267C25—21no—
268C25—21no—
269C25C2×D411yescharacteristic
270C22×Q8—21no—
271C22×Q8—24no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8C2412yes—
275C22×D4—28no—
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—24no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—24no—
284C22×D4—24no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4—42no—
288C22×D4—44no—
289C22×D4—44no—
290C22×D4—44no—
291C22×D4—44no—
292C22×D4—44no—
293C22×D4C2412yes—
294C22×D4C2412yes—
295C23×C4—24no—
296C23×C4—21no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—21no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—44no—
313C23×C4—44no—
314C23×C4—44no—
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2×D411yescharacteristic
325C23×C4C2×D411yescharacteristic
326C23×C4C2×D411yescharacteristic
327C23×C4C2×D411yescharacteristic
328C23×C4C2×D411yescharacteristic
329C23×C4C2×D411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C2×SD16—28no—
334C2×SD16—44no—
335C2×SD16—44no—
336C2×D8—28no—
337C2×D8—44no—
338C2×D8—44no—
339C22×C8C2414yes—
340C22×C8C2414yes—
341#124—28no—
342#124—44no—
343#124—44no—
344#124—44no—
345C22⋊Q8—24no—
346C22⋊Q8—24no—
347C22⋊Q8—42no—
348C22⋊Q8—42no—
349C22⋊Q8—44no—
350C22⋊Q8—44no—
351#121—28no—
352#121—28no—
353#121—24no—
354#121—24no—
355#121—24no—
356#121—24no—
357#121—24no—
358#121—42no—
359#121—42no—
360#121—44no—
361#121—44no—
362#121#4118yes—
363C4×D4—28no—
364C4×D4—44no—
365C4×D4—44no—
366C4×D4—44no—
367C4×D4—48no—
368C4×D4—48no—
369C4×D4—48no—
370C4×D4—48no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—42no—
431C2×C42—42no—
432C2×C42—42no—
433C2×C42—42no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439C2×C42—44no—
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456#107—44no—
457#106—44no—
458C4⋊C8—28no—
459#103—28no—
460#103—44no—
461#103—44no—
462#102—28no—
463#102—44no—
464#102—44no—
465#102—44no—
466#102—44no—
467C22⋊C8—24no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—42no—
472C22⋊C8—42no—
473C4×C8—44no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—24no—
493C24—22no—
494C24—22no—
495C24—41no—
496C24—41no—
497C24—42no—
498C24—42no—
499C24—42no—
500C24—42no—
501C24—42no—
502C24—42no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24#13514yes—
511C24C22×D411yescharacteristic
512C24C22×D411yescharacteristic
513C24C22×D411yescharacteristic
514C2×Q8—24no—
515C2×Q8—22no—
516C2×Q8—24no—
517C2×Q8—22no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—88no—
522C2×D4—24no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—22no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—22no—
530C2×D4—24no—
531C2×D4—22no—
532C2×D4—416no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—44no—
537C2×D4—432no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—88no—
550C2×D4—816no—
551C2×D4C2×#4114yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—416no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—816no—
637C22×C4AGL(1,ℤ/8)14yes—
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C2×#4114yes—
650C22×C4H(5,𝔽2)14yes—
651C22×C4C2511yescharacteristic
652SD16—88no—
653D8—88no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—24no—
660C4⋊C4—24no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—42no—
669C4⋊C4—44no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4C2×#4114yes—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C42—22no—
700C42—22no—
701C42—22no—
702C42—22no—
703C42—22no—
704C42—22no—
705C42—22no—
706C42—22no—
707C42—22no—
708C42—41no—
709C42—41no—
710C42—41no—
711C42—41no—
712C42—41no—
713C42—41no—
714C42—44no—
715C42—44no—
716C42H(5,𝔽2)14yes—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—28no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—28no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—24no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—48no—
740C23—48no—
741C23—48no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23#52512yes—
767C23#53512yes—
768C23C2×#13512yes—
769C23C2×#13512yes—
770C23C2×#13512yes—
771C23C2×AGL(1,ℤ/8)12yes—
772C23#57512yes—
773C23C23×D411yescharacteristic
774Q8—44no—
775Q8—44no—
776Q8—84no—
777D4—28no—
778D4—48no—
779D4—416no—
780D4—416no—
781D4—44no—
782D4—44no—
783D4—44no—
784D4—84no—
785D4—88no—
786D4—88no—
787C2×C4—28no—
788C2×C4—28no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—28no—
804C2×C4—28no—
805C2×C4—21no—
806C2×C4—24no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—48no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—88no—
851C2×C4—88no—
852C2×C4—84no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4—84no—
856C2×C4—84no—
857C2×C4#52512yes—
858C2×C4#53412yes—
859C2×C4#53412yes—
860C2×C4#53512yes—
861C2×C4C2×AGL(1,ℤ/8)12yes—
862C2×C4C2×AGL(1,ℤ/8)12yes—
863C2×C4#57512yes—
864C2×C4C22×#4112yes—
865C2×C4C2×H(5,𝔽2)12yes—
866C2×C4C2×H(5,𝔽2)12yes—
867C8—44no—
868C8—44no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—22no—
883C22—22no—
884C22—416no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—816no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22—168no—
905C22#310514yes—
906C22#321114yes—
907C22C2×#52511yescharacteristic
908C22C2×#53411yescharacteristic
909C22C2×#53511yescharacteristic
910C22C22×#13511yescharacteristic
911C22C22×AGL(1,ℤ/8)11yescharacteristic
912C22C2×#57511yescharacteristic
913C22C2×#57511yescharacteristic
914C4—22no—
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—22no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—44no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4#351914yes—
932C2—24no—
933C2—24no—
934C2—42no—
935C2—84no—
936C2—162no—
937C2#3507611yescharacteristic
938C2C2×#310511yescharacteristic
939C2#6056311yescharacteristic
940C2#6073411yescharacteristic
941C2#6075011yescharacteristic
942C2C2×#321111yescharacteristic
943C2#6080311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23918C2
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. C2×#2850C2semidirect
2. C2×C4×#121C2semidirect
3. #33110C2semidirect
4. #32908C2semidirect
5. #30107C2semidirect
6. #29330C2semidirect
7. #28303C2semidirect
8. #27684C2semidirect
9. #24654C2semidirect
10. #24215C2semidirect
11. #24006C2semidirect
12. #24005C2semidirect
13. #23919C2semidirect
15. #22041C2semidirect
16. #22040C2semidirect
17. #20714C2semidirect
18. C22×#124C22semidirect
23. C22×C4×D4C22semidirect
25. C2×#484C22semidirect
27. C2×#463C22semidirect
29. C2×#450C22semidirect
32. C2×#431C22semidirect
39. #2850C22semidirect
40. #2850C22semidirect
47. C4×#121C22semidirect
48. C4×#121C22semidirect
49. C2×#391C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#389C22semidirect
59. C2×#382C22semidirect
61. C2×C4×C4⋊C4C22semidirect
63. #2101C22semidirect
64. #2092C22semidirect
65. #2042C22semidirect
66. #2036C22semidirect
67. #2034C22semidirect
68. #2012C22semidirect
69. #2000C22semidirect
71. #1983C22semidirect
72. #1970C22semidirect
73. #1968C22semidirect
74. #1949C22semidirect
75. #1934C22semidirect
76. #1933C22semidirect
77. #1927C22semidirect
78. #1925C22semidirect
79. #1879C22semidirect
80. #1877C22semidirect
85. #1872C22semidirect
86. #1872C22semidirect
87. #1853C22semidirect
88. #1852C22semidirect
89. #1817C22semidirect
90. #1804C22semidirect
91. #1797C22semidirect
92. #1797C22semidirect
93. #1787C22semidirect
94. #1786C22semidirect
97. C4×C22⋊C8C22semidirect
98. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×C4×#1212
#331102
#329082
#301072
#293302
#283032
#276842
#246542
#242152
#240062
#240052
#239192
#239182
#220412
#220402
#207142