Finite Group Databasebeta

← #6476788

Subgroups — #6476788

Order 512.

2308 conjugacy classes of subgroups.

The subgroup lattice has 886 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#30008C214yesmaximal, complemented
8#29240C212yesmaximal, complemented
9#28120C212yesmaximal, complemented
10#27625C212yesmaximal, complemented
11#24836C212yesmaximal, complemented
12#24751C212yesmaximal, complemented
13#24551C212yesmaximal, complemented
14#24379C212yesmaximal
15#24151C212yesmaximal, complemented
16#22180C214yesmaximal, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#483C2212yes—
24C2×#476C2212yescomplemented
25C2×#465C2214yes—
26C2×#461C2212yescomplemented
27C2×#450C2212yes—
28C22×C4⋊C8C2212yescomplemented
29C22×C22⋊C8C2212yes—
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic, complemented
33#2857C2211yescharacteristic, complemented
34#2855—21no—
35#2855C2212yescomplemented
36#2851—21no—
37#2851—21no—
38#2848—21no—
39#2848C2212yes—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yescomplemented
44C4×#121—21no—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121—21no—
48C4×#121C2212yes—
49C4×#121C2212yes—
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2296—21no—
53C2×#390C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#386—21no—
57#2285C2211yescharacteristic, complemented
58#2280—21no—
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62#2088C2214yescomplemented
63#2077C2214yescomplemented
64#2066C2214yescomplemented
65#2065C2214yescomplemented
66#2055C2214yescomplemented
67#2035C2214yescomplemented
68#2034C2214yes—
69#2000C2214yes—
70#1987C2212yescomplemented
71#1981C2212yescomplemented
72#1948C2212yescomplemented
73#1948C2212yescomplemented
74#1927C2214yescomplemented
75#1926C2214yescomplemented
76#1920C2214yescomplemented
77#1919C2214yescomplemented
78#1893C2214yes—
79#1892C2214yescomplemented
80#1880C2214yescomplemented
81#1877C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1865C2214yescomplemented
85#1864C2214yescomplemented
86#1853C2212yes—
87#1853C2212yes—
88#1823C2212yes—
89#1807C2214yescomplemented
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2212yes—
93#1797C2211yescharacteristic
94#1797C2211yescharacteristic
95#1797C2212yescomplemented
96#1797C2212yescomplemented
97#1786C2212yes—
98C2×#336C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C23×C8C2314yes—
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#483—44no—
160#476—44no—
161#465—216no—
162#461—44no—
163#450—44no—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×#106C2314yes—
167C2×C4⋊C8—44no—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—44no—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2314yes—
181#391—21no—
182#391—21no—
183#391C2312yes—
184#391C2312yes—
185#390—21no—
186#390—21no—
187#390C2312yes—
188#390C2312yes—
189#389—21no—
190#389—21no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389C2312yes—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#388—22no—
202#388—22no—
203#388—22no—
204#388—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#386—22no—
210#386—22no—
211#386—22no—
212#386—22no—
213#385—22no—
214#385—22no—
215#385—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#382—21no—
222#381—22no—
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#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#379—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2312yes—
262#336C2314yes—
263#336C2312yes—
264C25—21no—
265C25C2×D411yescharacteristic
266C22×Q8—21no—
267C22×Q8C2412yes—
268C22×D4—28no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—24no—
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—42no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4SD1618yescomplemented
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×C4C2×D411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C2×SD16—28no—
316C2×SD16—44no—
317C2×SD16—44no—
318C22×C8—28no—
319C22×C8—44no—
320C22×C8—44no—
321C22×C8C2414yes—
322C22×C8C2414yes—
323C4⋊Q8—24no—
324C4⋊Q8—24no—
325#125—44no—
326C22⋊Q8—28no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—44no—
332C22⋊Q8—44no—
333#121—28no—
334#121—28no—
335#121—24no—
336#121—24no—
337#121—24no—
338#121#4118yes—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—42no—
344C4×D4—42no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—48no—
348C4×D4—48no—
349C4×D4—48no—
350C4×D4—48no—
351#117—44no—
352#117—44no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C22⋊C4—28no—
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—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—44no—
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×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436#106—28no—
437#106—44no—
438#106—44no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—44no—
442#103—28no—
443#103—44no—
444#103—44no—
445#102—28no—
446#102—44no—
447#102—44no—
448C22⋊C8—24no—
449C22⋊C8—24no—
450C22⋊C8—44no—
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—
464#95—22no—
465#95—22no—
466#95—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—24no—
472C24—22no—
473C24—41no—
474C24—41no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24—42no—
479C24—42no—
480C24—42no—
481C24C2×SD1614yes—
482C24C22×D411yescharacteristic
483C24C22×D411yescharacteristic
484C24C22×D411yescharacteristic
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—22no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×D4—24no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—42no—
503C2×D4—432no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4C2×#4114yes—
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—21no—
520C22×C4—21no—
521C22×C4—24no—
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—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—416no—
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—41no—
566C22×C4—41no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—42no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—816no—
585C22×C4C2×SD1614yes—
586C22×C4C2×SD1614yes—
587C22×C4C2×SD1614yes—
588C22×C4C2×SD1614yes—
589C22×C4C2×SD1614yes—
590C22×C4C2×SD1614yes—
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×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C2×#4114yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C42−1+412yes—
605C22×C4C2511yescharacteristic
606SD16—88no—
607C2×C8—24no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—24no—
612C2×C8—24no—
613C2×C8—88no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—42no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4C2×#4114yes—
642C22⋊C4—28no—
643C22⋊C4—28no—
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—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—44no—
674C42—44no—
675C42—44no—
676C42—44no—
677C42H(5,𝔽2)14yes—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—28no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—28no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—24no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—48no—
701C23—48no—
702C23—48no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—84no—
710C23—84no—
711C23—84no—
712C23—84no—
713C23#52512yes—
714C23#53712yes—
715C23C22×SD1612yes—
716C23C22×SD1612yes—
717C23C22×SD1612yes—
718C23#57512yes—
719C23#57512yes—
720C23C23×D411yescharacteristic
721Q8—44no—
722Q8—44no—
723Q8—84no—
724D4—24no—
725D4—24no—
726D4—48no—
727D4—416no—
728D4—416no—
729D4—42no—
730D4—42no—
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—21no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—21no—
751C2×C4—24no—
752C2×C4—21no—
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—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—48no—
775C2×C4—44no—
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—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—88no—
799C2×C4—84no—
800C2×C4—84no—
801C2×C4—88no—
802C2×C4#52512yes—
803C2×C4#53412yes—
804C2×C4#53412yes—
805C2×C4#53712yes—
806C2×C4C22×SD1612yes—
807C2×C4C22×SD1612yes—
808C2×C4C22×SD1612yes—
809C2×C4C22×SD1612yes—
810C2×C4#57512yes—
811C2×C4C22×#4112yes—
812C2×C4C2×H(5,𝔽2)11yescharacteristic
813C2×C4C2×H(5,𝔽2)12yes—
814C2×C4C2×2−1+411yescharacteristic
815C8—44no—
816C8—44no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—416no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—816no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22#310114yes—
846C22#324614yes—
847C22C2×#52511yescharacteristic
848C22C2×#53411yescharacteristic
849C22C2×#53711yescharacteristic
850C22C23×SD1611yescharacteristic
851C22C2×#57511yescharacteristic
852C22C2×#57511yescharacteristic
853C22C2×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—44no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4#318714yes—
872C4#351912yes—
873C4#352012yes—
874C2—24no—
875C2—24no—
876C2—42no—
877C2—84no—
878C2#3507711yescharacteristic
879C2C2×#310111yescharacteristic
880C2#6054611yescharacteristic
881C2C2×#318711yescharacteristic
882C2#6075211yescharacteristic
883C2C2×#324611yescharacteristic
884C2#6091711yescharacteristic
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. #30008C2semidirect
8. #29240C2semidirect
9. #28120C2semidirect
10. #27625C2semidirect
11. #24836C2semidirect
12. #24751C2semidirect
13. #24551C2semidirect
15. #24151C2semidirect
16. #22180C2semidirect
17. C2×#1797C2semidirect
18. C2×#533C22semidirect
24. C2×#476C22semidirect
26. C2×#461C22semidirect
28. C22×C4⋊C8C22semidirect
32. #2857C22semidirect
33. #2857C22semidirect
35. #2855C22semidirect
43. C4×C22⋊Q8C22semidirect
57. #2285C22semidirect
62. #2088C22semidirect
63. #2077C22semidirect
64. #2066C22semidirect
65. #2065C22semidirect
66. #2055C22semidirect
67. #2035C22semidirect
70. #1987C22semidirect
71. #1981C22semidirect
72. #1948C22semidirect
73. #1948C22semidirect
74. #1927C22semidirect
75. #1926C22semidirect
76. #1920C22semidirect
77. #1919C22semidirect
79. #1892C22semidirect
80. #1880C22semidirect
81. #1877C22semidirect
84. #1865C22semidirect
85. #1864C22semidirect
89. #1807C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
95. #1797C22semidirect
96. #1797C22semidirect
98. C2×#336C22semidirect
296. 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
#300082
#292402
#281202
#276252
#248362
#247512
#245512
#243792
#241512
#221802
C2×#17972