Finite Group Databasebeta

← #6475294

Subgroups — #6475294

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 866 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#33151C212yesmaximal, complemented
4#32959C212yesmaximal, complemented
5#29968C211yesmaximal, characteristic, complemented
6#29966C211yesmaximal, characteristic, complemented
7#29952C211yesmaximal, characteristic, complemented
8#29950C211yesmaximal, characteristic, complemented
9#29239C214yesmaximal, complemented
10#29163C212yesmaximal, complemented
11#29162C212yesmaximal, complemented
12#27683C212yesmaximal, complemented
13#24841C214yesmaximal, complemented
14#24304C212yesmaximal, complemented
15#21944C212yesmaximal, complemented
16#21767C212yesmaximal
17#20626C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#478C2214yescomplemented
24C2×#423C2212yescomplemented
25C2×#407C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic, complemented
29#2857C2211yescharacteristic, complemented
30#2855—21no—
31#2855—21no—
32#2851C2212yes—
33#2851C2212yescomplemented
34#2848—21no—
35#2848—21no—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×#121—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121C2212yes—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48#2296C2212yescomplemented
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#388—21no—
52C2×#386—21no—
53#2285C2211yescharacteristic, complemented
54#2280C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4—21no—
58#2100C2212yescomplemented
59#2099C2212yescomplemented
60#2094C2212yescomplemented
61#2093C2212yescomplemented
62#2088C2214yescomplemented
63#2086C2214yescomplemented
64#2067C2214yescomplemented
65#2065C2214yescomplemented
66#2058C2212yescomplemented
67#2057C2212yescomplemented
68#2023C2212yescomplemented
69#2023C2212yescomplemented
70#1989C2214yescomplemented
71#1949C2214yescomplemented
72#1921C2214yescomplemented
73#1919C2214yescomplemented
74#1895C2214yes—
75#1895C2214yes—
76#1875C2214yes—
77#1875C2214yes—
78#1864C2214yescomplemented
79#1862C2214yescomplemented
80#1854C2214yescomplemented
81#1854C2214yescomplemented
82#1853C2212yes—
83#1853C2212yes—
84#1852C2212yes—
85#1852C2212yes—
86#1823C2212yes—
87#1823C2212yes—
88#1809C2214yescomplemented
89#1809C2214yescomplemented
90#1804C2214yescomplemented
91#1797C2211yescharacteristic
92#1797C2211yescharacteristic
93#1797C2212yes—
94#1797C2212yescomplemented
95#1797C2212yescomplemented
96#1786C2212yes—
97#1786C2212yes—
98#1728C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×M16C2314yes—
106#533—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×C4⋊Q8C2311yescharacteristic
109C2×#125C2312yes—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—24no—
119C2×#121Q818yescomplemented
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×C4×Q8—21no—
123C2×C4×Q8—21no—
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×#117C2312yes—
135C2×#117C2312yes—
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#478—48no—
160C2×#107C2314yes—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164#423—44no—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172#407—28no—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2314yes—
176#391—21no—
177#391—21no—
178#391—21no—
179#391—21no—
180#390—21no—
181#390—21no—
182#390C2312yes—
183#390C2312yes—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189#389—21no—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#387—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#386—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#384C2311yescharacteristic
215#384C2311yescharacteristic
216#382C2312yes—
217#381—22no—
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#380C2312yes—
232#379—22no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—22no—
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#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261C25—21no—
262C25C2×D411yescharacteristic
263C22×Q8—21no—
264C22×Q8—21no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—21no—
269C22×D4—22no—
270C22×D4—42no—
271C22×D4—42no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4C2×Q814yes—
275C22×D4C2412yes—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—42no—
283C23×C4—42no—
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×C4C2×Q814yes—
308C23×C4#4114yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C2×M16—28no—
313C2×M16—44no—
314C2×M16—44no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—42no—
318C4⋊Q8—42no—
319#125—28no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C22⋊Q8—44no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326#121—28no—
327#121—28no—
328#121—24no—
329#121—24no—
330#121C2×Q818yes—
331#121C2×Q818yes—
332C4×Q8—44no—
333C4×Q8—44no—
334C4×D4—28no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341C4×D4—48no—
342#117—44no—
343#117—44no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
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—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2×Q814yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
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—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—42no—
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—44no—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#107—44no—
428#107—44no—
429#106—44no—
430#106—44no—
431C4⋊C8—28no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434#102—44no—
435#102—44no—
436#102—44no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—28no—
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—24no—
460C24—22no—
461C24—41no—
462C24—41no—
463C24—41no—
464C24—41no—
465C24—42no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24C22⋊Q814yes—
472C24C22×D411yescharacteristic
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—24no—
486C2×D4—24no—
487C2×D4—48no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—432no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4C22×Q814yes—
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—48no—
531C22×C4—48no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
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—416no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—816no—
571C22×C4C22⋊Q814yes—
572C22×C4C22⋊Q814yes—
573C22×C4C22⋊Q814yes—
574C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×Q812yes—
587C22×C4C22×Q812yes—
588C22×C4C22×Q812yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2511yescharacteristic
593M16—88no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4C22×Q814yes—
625C22⋊C4—28no—
626C22⋊C4—28no—
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—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42H(5,𝔽2)14yes—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—28no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—24no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—48no—
686C23—48no—
687C23—48no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—84no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23C2×C22⋊Q812yes—
699C23C2×C22⋊Q812yes—
700C23C2×C22⋊Q812yes—
701C23C2×AGL(1,ℤ/8)12yes—
702C23#57512yes—
703C23C23×D411yescharacteristic
704Q8—84no—
705Q8—84no—
706D4—28no—
707D4—48no—
708D4—416no—
709D4—416no—
710D4—44no—
711C2×C4—28no—
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—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
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—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—48no—
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—42no—
777C2×C4—42no—
778C2×C4—88no—
779C2×C4—88no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4C2×C22⋊Q812yes—
783C2×C4C2×C22⋊Q812yes—
784C2×C4C2×C22⋊Q812yes—
785C2×C4#53412yes—
786C2×C4#53412yes—
787C2×C4C2×AGL(1,ℤ/8)12yes—
788C2×C4C2×AGL(1,ℤ/8)12yes—
789C2×C4#57512yes—
790C2×C4#57512yes—
791C2×C4C23×Q811yescharacteristic
792C2×C4C22×#4111yescharacteristic
793C2×C4C2×H(5,𝔽2)12yes—
794C2×C4#58512yes—
795C8—44no—
796C8—44no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—416no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—816no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22#307714yes—
827C22C22×C22⋊Q811yescharacteristic
828C22C2×#53411yescharacteristic
829C22#344911yescharacteristic
830C22C22×AGL(1,ℤ/8)11yescharacteristic
831C22C2×#57511yescharacteristic
832C22C2×#57511yescharacteristic
833C22C2×#57511yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—44no—
844C4—41no—
845C4—41no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4#350112yes—
853C4#350512yes—
854C2—24no—
855C2—42no—
856C2—42no—
857C2—84no—
858C2#3501011yescharacteristic
859C2C2×#307711yescharacteristic
860C2#6048411yescharacteristic
861C2#6074111yescharacteristic
862C2#6075011yescharacteristic
863C2#6095411yescharacteristic
864C2#6096511yescharacteristic
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. #33151C2semidirect
4. #32959C2semidirect
5. #29968C2semidirect
6. #29966C2semidirect
7. #29952C2semidirect
8. #29950C2semidirect
9. #29239C2semidirect
10. #29163C2semidirect
11. #29162C2semidirect
12. #27683C2semidirect
13. #24841C2semidirect
14. #24304C2semidirect
15. #21944C2semidirect
17. #20626C2semidirect
18. C2×#533C22semidirect
23. C2×#478C22semidirect
24. C2×#423C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
33. #2851C22semidirect
48. #2296C22semidirect
53. #2285C22semidirect
58. #2100C22semidirect
59. #2099C22semidirect
60. #2094C22semidirect
61. #2093C22semidirect
62. #2088C22semidirect
63. #2086C22semidirect
64. #2067C22semidirect
65. #2065C22semidirect
66. #2058C22semidirect
67. #2057C22semidirect
68. #2023C22semidirect
69. #2023C22semidirect
70. #1989C22semidirect
71. #1949C22semidirect
72. #1921C22semidirect
73. #1919C22semidirect
78. #1864C22semidirect
79. #1862C22semidirect
80. #1854C22semidirect
81. #1854C22semidirect
88. #1809C22semidirect
89. #1809C22semidirect
90. #1804C22semidirect
94. #1797C22semidirect
95. #1797C22semidirect
98. #1728C22semidirect
119. C2×#121Q8semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#331512
#329592
#299682
#299662
#299522
#299502
#292392
#291632
#291622
#276832
#248412
#243042
#219442
#217672
#206262