Finite Group Databasebeta

← #6476337

Subgroups — #6476337

Order 512.

2458 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic, complemented
3#33096C212yesmaximal, complemented
4#33004C212yesmaximal, complemented
5#30173C212yesmaximal, complemented
6#30112C212yesmaximal, complemented
7#29412C214yesmaximal, complemented
8#29156C212yesmaximal, complemented
9#28572C212yesmaximal, complemented
10#27614C211yesmaximal, characteristic, complemented
11#27585C211yesmaximal, characteristic, complemented
12#24553C212yesmaximal, complemented
13#24378C212yesmaximal, complemented
14#24061C211yesmaximal, characteristic, complemented
15#23930C211yesmaximal, characteristic, complemented
16#22184C214yesmaximal, complemented
17C2×#1817C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×#121C2211yescharacteristic
21C22×C4×D4—21no—
22C22×C4×D4C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#481C2212yes—
25C2×#466C2214yes—
26C2×#447C2212yes—
27C22×C22⋊C8C2212yes—
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2856C2211yescharacteristic, complemented
31#2856C2211yescharacteristic, complemented
32#2854—21no—
33#2854C2212yes—
34#2850—21no—
35#2850—21no—
36#2847—21no—
37#2847C2212yes—
38C4×#121—21no—
39C4×#121—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yescomplemented
49C4×#121C2212yescomplemented
50#2297—21no—
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#386—21no—
55#2285C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2100C2212yescomplemented
60#2094C2212yescomplemented
61#2083C2212yescomplemented
62#2077C2214yescomplemented
63#2071C2212yescomplemented
64#2058C2212yescomplemented
65#2041C2212yescomplemented
66#2034C2214yescomplemented
67#2033C2214yes—
68#2023C2212yescomplemented
69#2011C2212yescomplemented
70#1999C2214yes—
71#1926C2214yescomplemented
72#1926C2214yescomplemented
73#1925C2214yescomplemented
74#1921C2214yescomplemented
75#1921C2214yescomplemented
76#1920C2214yescomplemented
77#1893C2214yes—
78#1893C2214yescomplemented
79#1879C2214yescomplemented
80#1879C2214yescomplemented
81#1879C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1864C2214yescomplemented
85#1864C2214yescomplemented
86#1864C2214yescomplemented
87#1853C2212yes—
88#1852C2212yes—
89#1824C2212yes—
90#1817C2212yes—
91#1817C2211yescharacteristic
92#1817C2211yescharacteristic
93#1817C2212yescomplemented
94#1817C2212yescomplemented
95#1807C2214yescomplemented
96#1786C2212yes—
97C2×#336C2212yescomplemented
98C2×#336C2212yescomplemented
99C22×#41—21no—
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×D8C2314yes—
107C23×C8C2314yes—
108#532—44no—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#124—21no—
112#525—48no—
113C2×#123—22no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—28no—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×#121C2312yes—
129C2×#120—22no—
130C2×C4×D4—22no—
131C2×C4×D4—22no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—22no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—44no—
140C2×C4×D4—48no—
141C2×C4×D4C2312yes—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×#117—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4—21no—
150C22×C22⋊C4—21no—
151C22×C22⋊C4—21no—
152C22×C22⋊C4—21no—
153C22×C22⋊C4—21no—
154C22×C42—21no—
155C22×C42—44no—
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42D411yescharacteristic
160C22×C42D411yescharacteristic
161C22×C42D411yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#481—44no—
169#466—216no—
170#447—44no—
171C2×#107C2314yes—
172C2×#106C2314yes—
173C2×#106C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8—44no—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2314yes—
184#391—21no—
185#391—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#384C2311yescharacteristic
223#384C2311yescharacteristic
224#382—21no—
225#380—21no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#336C2312yes—
257#336C2312yes—
258#336C2312yes—
259#336C2314yes—
260#336C2314yes—
261#336C2312yes—
262C25—21no—
263C25C2×D411yescharacteristic
264C2×#41—44no—
265C2×#41—44no—
266C2×#41—44no—
267C22×Q8—21no—
268C22×D4—28no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—24no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—24no—
279C22×D4—42no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4C2412yes—
283C22×D4C2412yes—
284C23×C4—24no—
285C23×C4—21no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4—44no—
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×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C2×D8—28no—
321C2×D8—44no—
322C2×D8—44no—
323C22×C8—28no—
324C22×C8—44no—
325C22×C8—44no—
326C22×C8C2414yes—
327C22×C8C2414yes—
328C4⋊Q8—42no—
329#127—42no—
330#124—44no—
331#123—48no—
332C22⋊Q8—44no—
333C22⋊Q8—44no—
334#121—28no—
335#121—28no—
336#121—24no—
337#121—24no—
338#121—24no—
339#121—28no—
340#121—24no—
341#121—24no—
342#121—44no—
343#121—44no—
344#121—44no—
345#121—44no—
346#121—44no—
347#121—44no—
348#121#4118yescomplemented
349#120—48no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—42no—
353C4×D4—42no—
354C4×D4—44no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—48no—
358C4×D4—48no—
359C4×D4—48no—
360C4×D4—48no—
361C4×D4—48no—
362C4×D4—48no—
363#117—44no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
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—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—44no—
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—28no—
445#106—44no—
446#106—44no—
447#102—28no—
448#102—28no—
449#102—44no—
450#102—44no—
451#102—44no—
452#102—44no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—44no—
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—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—24no—
473C24—22no—
474C24—22no—
475C24—41no—
476C24—41no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24—42no—
482C24—42no—
483C24AGL(1,ℤ/8)14yes—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487#41—816no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×D4—24no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—22no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—416no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—44no—
508C2×D4—432no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4C2×#4114yes—
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—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
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—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—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—816no—
603C22×C4#13514yes—
604C22×C4AGL(1,ℤ/8)14yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C2×#4114yes—
617C22×C4H(5,𝔽2)14yes—
618C22×C4C2511yescharacteristic
619D8—88no—
620C2×C8—24no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—24no—
624C2×C8—24no—
625C2×C8—24no—
626C2×C8—88no—
627C4⋊C4—24no—
628C4⋊C4—22no—
629C4⋊C4—24no—
630C4⋊C4—22no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—44no—
645C4⋊C4—42no—
646C4⋊C4C2×#4114yes—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—41no—
684C42—44no—
685C42—44no—
686C42—44no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—28no—
696C23—21no—
697C23—28no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—24no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—48no—
710C23—48no—
711C23—48no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#52512yes—
730C23#53412yes—
731C23C2×#13512yes—
732C23C2×AGL(1,ℤ/8)12yes—
733C23C2×AGL(1,ℤ/8)12yes—
734C23C2×AGL(1,ℤ/8)12yes—
735C23C2×AGL(1,ℤ/8)12yes—
736C23C23×D411yescharacteristic
737Q8—84no—
738D4—28no—
739D4—48no—
740D4—416no—
741D4—416no—
742D4—44no—
743D4—44no—
744D4—44no—
745D4—84no—
746D4—84no—
747D4—88no—
748D4—88no—
749D4—88no—
750C2×C4—28no—
751C2×C4—21no—
752C2×C4—28no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—21no—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—48no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—88no—
814C2×C4—88no—
815C2×C4—88no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4#52512yes—
819C2×C4#53412yes—
820C2×C4C2×#13512yes—
821C2×C4C2×#13512yes—
822C2×C4C2×AGL(1,ℤ/8)12yes—
823C2×C4C2×AGL(1,ℤ/8)12yes—
824C2×C4#57512yes—
825C2×C4C22×#4112yes—
826C2×C4C2×H(5,𝔽2)12yes—
827C2×C4#58512yes—
828C8—44no—
829C8—44no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—416no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—816no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22#310914yes—
866C22#318814yes—
867C22C2×#52511yescharacteristic
868C22C2×#53411yescharacteristic
869C22#344911yescharacteristic
870C22C22×#13511yescharacteristic
871C22C22×AGL(1,ℤ/8)11yescharacteristic
872C22C22×AGL(1,ℤ/8)11yescharacteristic
873C22C2×#57511yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—22no—
880C4—22no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—44no—
885C4—41no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4#351314yes—
892C2—24no—
893C2—24no—
894C2—42no—
895C2—84no—
896C2—162no—
897C2#3506311yescharacteristic
898C2#6053611yescharacteristic
899C2C2×#310911yescharacteristic
900C2C2×#318811yescharacteristic
901C2#6075011yescharacteristic
902C2#6094611yescharacteristic
903C2#6095811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #36624C2semidirect
2. C2×C4×#121C2semidirect
3. #33096C2semidirect
4. #33004C2semidirect
5. #30173C2semidirect
6. #30112C2semidirect
7. #29412C2semidirect
8. #29156C2semidirect
9. #28572C2semidirect
10. #27614C2semidirect
11. #27585C2semidirect
12. #24553C2semidirect
13. #24378C2semidirect
14. #24061C2semidirect
15. #23930C2semidirect
16. #22184C2semidirect
17. C2×#1817C2semidirect
28. #2857C22semidirect
29. #2857C22semidirect
30. #2856C22semidirect
31. #2856C22semidirect
48. C4×#121C22semidirect
49. C4×#121C22semidirect
59. #2100C22semidirect
60. #2094C22semidirect
61. #2083C22semidirect
62. #2077C22semidirect
63. #2071C22semidirect
64. #2058C22semidirect
65. #2041C22semidirect
66. #2034C22semidirect
68. #2023C22semidirect
69. #2011C22semidirect
71. #1926C22semidirect
72. #1926C22semidirect
73. #1925C22semidirect
74. #1921C22semidirect
75. #1921C22semidirect
76. #1920C22semidirect
78. #1893C22semidirect
79. #1879C22semidirect
80. #1879C22semidirect
81. #1879C22semidirect
84. #1864C22semidirect
85. #1864C22semidirect
86. #1864C22semidirect
93. #1817C22semidirect
94. #1817C22semidirect
95. #1807C22semidirect
97. C2×#336C22semidirect
98. C2×#336C22semidirect
348. #121#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×#1212
#330962
#330042
#301732
#301122
#294122
#291562
#285722
#276142
#275852
#245532
#243782
#240612
#239302
#221842
C2×#18172