Finite Group Databasebeta

← #6475542

Subgroups — #6475542

Order 512.

2242 conjugacy classes of subgroups.

The subgroup lattice has 882 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#33148C211yesmaximal, characteristic, complemented
4#33108C211yesmaximal, characteristic, complemented
5#32956C211yesmaximal, characteristic, complemented
6#32905C211yesmaximal, characteristic, complemented
7#29893C212yesmaximal, complemented
8#29596C212yesmaximal
9#29464C214yesmaximal, complemented
10#29410C214yesmaximal, complemented
11#27625C212yesmaximal, complemented
12#24701C212yesmaximal, complemented
13#24651C212yesmaximal, complemented
14#24151C212yesmaximal, complemented
15#22078C212yesmaximal, complemented
16#22043C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#483C2212yes—
24C2×#476C2212yescomplemented
25C2×#461C2212yescomplemented
26C2×#450C2212yes—
27C2×#431C2212yescomplemented
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2857C2211yescharacteristic, complemented
31#2857C2211yescharacteristic, complemented
32#2855—21no—
33#2855C2212yescomplemented
34#2851—21no—
35#2851—21no—
36#2848—21no—
37#2848C2212yes—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8C2212yes—
41C4×C22⋊Q8C2212yescomplemented
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121—21no—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49C4×#121C2212yes—
50#2296—21no—
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388—21no—
54C2×#386—21no—
55#2285C2211yescharacteristic, complemented
56#2280—21no—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2077C2214yescomplemented
61#2077C2214yescomplemented
62#2035C2214yescomplemented
63#2035C2214yescomplemented
64#2034C2214yes—
65#2034C2214yes—
66#2000C2214yes—
67#2000C2214yes—
68#1987C2212yescomplemented
69#1981C2212yescomplemented
70#1968C2214yescomplemented
71#1948C2212yescomplemented
72#1948C2212yescomplemented
73#1941C2214yescomplemented
74#1934C2214yescomplemented
75#1933C2214yescomplemented
76#1927C2214yescomplemented
77#1926C2214yescomplemented
78#1920C2214yescomplemented
79#1919C2214yescomplemented
80#1880C2214yescomplemented
81#1877C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1865C2214yescomplemented
85#1864C2214yescomplemented
86#1853C2212yes—
87#1853C2212yes—
88#1823C2212yes—
89#1817C2212yescomplemented
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2211yescharacteristic
93#1797C2211yescharacteristic
94#1797C2212yescomplemented
95#1786C2212yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106#533—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#125—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8C2312yes—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×#121—24no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121—24no—
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#483—28no—
160#476—44no—
161#461—44no—
162#450—28no—
163#431—44no—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×#106C2314yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2314yes—
178C2×C22⋊C8C2314yes—
179C2×C4×C8C2314yes—
180#391—21no—
181#391—21no—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390C2312yes—
187#390C2312yes—
188#389—21no—
189#389—21no—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389C2312yes—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
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#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#379—22no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2312yes—
261#336C2312yes—
262#336C2314yes—
263C25—21no—
264C25C2×D411yescharacteristic
265C22×Q8—21no—
266C22×Q8C2412yes—
267C22×D4—28no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4#4114yes—
277C22×D4C2412yes—
278C23×C4—21no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4SD1618yescomplemented
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×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×SD16—28no—
315C2×SD16—44no—
316C2×SD16—44no—
317C22×C8C2414yes—
318C22×C8C2414yes—
319C4⋊Q8—24no—
320C4⋊Q8—24no—
321#125—44no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—28no—
330#121—28no—
331#121—24no—
332#121—24no—
333#121—24no—
334#121—24no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—42no—
340C4×D4—42no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—48no—
344C4×D4—48no—
345C4×D4—48no—
346C4×D4—48no—
347#117—44no—
348#117—44no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
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—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4#4114yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—28no—
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—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—44no—
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×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#106—28no—
433#106—44no—
434#106—44no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437#103—28no—
438#103—44no—
439#103—44no—
440#102—28no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445C22⋊C8—44no—
446C22⋊C8—44no—
447C4×C8—44no—
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—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464C24—22no—
465C24—22no—
466C24—24no—
467C24—22no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24C2×SD1614yes—
479C24C22×D411yescharacteristic
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—48no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—48no—
501C2×D4—432no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4C2×#4114yes—
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—24no—
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—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
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—416no—
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—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—48no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—416no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—816no—
583C22×C4C2×SD1614yes—
584C22×C4C2×SD1614yes—
585C22×C4C2×SD1614yes—
586C22×C4C2×SD1614yes—
587C22×C4C2×SD1614yes—
588C22×C4C2×SD1614yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2511yescharacteristic
603SD16—88no—
604C2×C8—24no—
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4C2×#4114yes—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—44no—
670C42—44no—
671C42—44no—
672C42—44no—
673C42H(5,𝔽2)14yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—28no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—24no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—48no—
699C23—48no—
700C23—48no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—84no—
708C23—84no—
709C23—84no—
710C23—84no—
711C23#52512yes—
712C23C22×SD1612yes—
713C23C22×SD1612yes—
714C23C22×SD1612yes—
715C23#57512yes—
716C23C23×D411yescharacteristic
717Q8—44no—
718Q8—44no—
719Q8—84no—
720D4—24no—
721D4—24no—
722D4—48no—
723D4—416no—
724D4—416no—
725D4—42no—
726D4—42no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
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—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—24no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—88no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4—88no—
798C2×C4#52512yes—
799C2×C4#53412yes—
800C2×C4#53412yes—
801C2×C4C22×SD1612yes—
802C2×C4C22×SD1612yes—
803C2×C4C22×SD1612yes—
804C2×C4C22×SD1612yes—
805C2×C4#57512yes—
806C2×C4#57512yes—
807C2×C4C22×#4111yescharacteristic
808C2×C4C22×#4111yescharacteristic
809C2×C4C2×H(5,𝔽2)12yes—
810C2×C4#58512yes—
811C8—44no—
812C8—44no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—416no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—816no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22#310114yes—
843C22C2×#52511yescharacteristic
844C22C2×#53411yescharacteristic
845C22#344911yescharacteristic
846C22C23×SD1611yescharacteristic
847C22C2×#57511yescharacteristic
848C22C2×#57511yescharacteristic
849C22C2×#57511yescharacteristic
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—44no—
859C4—41no—
860C4—41no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4#318714yes—
868C4#350512yes—
869C4#350612yes—
870C2—24no—
871C2—42no—
872C2—42no—
873C2—84no—
874C2#3503111yescharacteristic
875C2C2×#310111yescharacteristic
876C2#6055911yescharacteristic
877C2C2×#318711yescharacteristic
878C2#6075211yescharacteristic
879C2#6094111yescharacteristic
880C2#6097011yescharacteristic
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. #33148C2semidirect
4. #33108C2semidirect
5. #32956C2semidirect
6. #32905C2semidirect
7. #29893C2semidirect
9. #29464C2semidirect
10. #29410C2semidirect
11. #27625C2semidirect
12. #24701C2semidirect
13. #24651C2semidirect
14. #24151C2semidirect
15. #22078C2semidirect
16. #22043C2semidirect
17. #20714C2semidirect
18. C2×#533C22semidirect
24. C2×#476C22semidirect
25. C2×#461C22semidirect
27. C2×#431C22semidirect
30. #2857C22semidirect
31. #2857C22semidirect
33. #2855C22semidirect
41. C4×C22⋊Q8C22semidirect
55. #2285C22semidirect
60. #2077C22semidirect
61. #2077C22semidirect
62. #2035C22semidirect
63. #2035C22semidirect
68. #1987C22semidirect
69. #1981C22semidirect
70. #1968C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1941C22semidirect
74. #1934C22semidirect
75. #1933C22semidirect
76. #1927C22semidirect
77. #1926C22semidirect
78. #1920C22semidirect
79. #1919C22semidirect
80. #1880C22semidirect
81. #1877C22semidirect
84. #1865C22semidirect
85. #1864C22semidirect
89. #1817C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
94. #1797C22semidirect
98. C4×C22⋊C8C22semidirect
295. C23×C4SD16semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#331482
#331082
#329562
#329052
#298932
#295962
#294642
#294102
#276252
#247012
#246512
#241512
#220782
#220432
#207142