Finite Group Databasebeta

← #6477081

Subgroups — #6477081

Order 512.

2218 conjugacy classes of subgroups.

The subgroup lattice has 871 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#33149C211yesmaximal, characteristic, complemented
4#33147C211yesmaximal, characteristic, complemented
5#32956C211yesmaximal, characteristic, complemented
6#32953C211yesmaximal, characteristic, complemented
7#30171C214yesmaximal, complemented
8#29298C212yesmaximal, complemented
9#29104C212yesmaximal, complemented
10#27646C212yesmaximal, complemented
11#27604C212yesmaximal, complemented
12#24701C212yesmaximal, complemented
13#24700C212yesmaximal, complemented
14#24300C212yesmaximal, complemented
15#24009C212yesmaximal
16#22080C214yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic, complemented
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#482C2214yes—
24C2×#476C2212yescomplemented
25C2×#474C2212yescomplemented
26C2×#431C2212yescomplemented
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic, complemented
30#2857C2211yescharacteristic, complemented
31#2855—21no—
32#2855—21no—
33#2851C2212yes—
34#2851C2212yescomplemented
35#2848—21no—
36#2848—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×#121—21no—
42C4×#121—21no—
43C4×#121—21no—
44C4×#121—21no—
45C4×#121C2212yes—
46C4×#121C2212yes—
47C4×#121C2212yes—
48C4×#121C2212yes—
49#2296C2212yescomplemented
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388—21no—
53C2×#386—21no—
54#2285C2211yescharacteristic, complemented
55#2280C2212yes—
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2085C2214yescomplemented
60#2077C2214yescomplemented
61#2075C2214yescomplemented
62#2073C2214yescomplemented
63#2059C2214yescomplemented
64#2034C2214yes—
65#2033C2214yes—
66#2025C2214yescomplemented
67#1988C2212yescomplemented
68#1987C2212yescomplemented
69#1948C2212yescomplemented
70#1947C2212yescomplemented
71#1942C2214yescomplemented
72#1941C2214yescomplemented
73#1934C2214yescomplemented
74#1934C2214yescomplemented
75#1921C2214yescomplemented
76#1919C2214yescomplemented
77#1875C2214yes—
78#1864C2214yescomplemented
79#1862C2214yescomplemented
80#1854C2214yescomplemented
81#1853C2212yes—
82#1853C2212yes—
83#1852C2212yes—
84#1852C2212yes—
85#1825C2214yescomplemented
86#1824C2212yes—
87#1824C2212yes—
88#1817C2212yescomplemented
89#1802C2212yescomplemented
90#1802C2212yescomplemented
91#1797C2211yescharacteristic
92#1797C2211yescharacteristic
93#1797C2212yescomplemented
94#1786C2212yes—
95#1786C2212yes—
96#1779C2212yes—
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105#533—44no—
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#125C2312yes—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—28no—
118C2×#121C2312yes—
119C2×#121C2312yes—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×D4—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—22no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4—44no—
129C2×C4×D4—48no—
130C2×C4×D4C2312yes—
131C2×C4×D4C2312yes—
132C2×#117C2312yes—
133C2×#117C2312yes—
134C22×C4⋊C4—21no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C42—21no—
144C22×C42—44no—
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#482—216no—
158#476—44no—
159#474—44no—
160#431—44no—
161C2×#107C2314yes—
162C2×#107C2314yes—
163C2×#106C2314yes—
164C2×#106C2314yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2314yes—
174C2×C22⋊C8C2314yes—
175C2×C4×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—24no—
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—42no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4C2412yes—
276C23×C4—21no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
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×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C22×C8C2414yes—
313C22×C8C2414yes—
314C4⋊Q8—24no—
315C4⋊Q8—24no—
316#125—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323#121—28no—
324#121—28no—
325#121—24no—
326#121—24no—
327#121—24no—
328#121#4118yes—
329C4×Q8—44no—
330C4×Q8—44no—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—42no—
334C4×D4—42no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—48no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341#117—28no—
342#117—44no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
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—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—22no—
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—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—42no—
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—44no—
410C2×C42C2×D411yescharacteristic
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×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426#107—28no—
427#107—44no—
428#106—28no—
429#106—44no—
430C4⋊C8—24no—
431C4⋊C8—24no—
432#102—28no—
433#102—28no—
434#102—44no—
435#102—44no—
436C22⋊C8—28no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—44no—
440C4×C8—44no—
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—22no—
460C24—24no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—42no—
467C24—42no—
468C24—42no—
469C24—42no—
470C24—42no—
471C24—42no—
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—24no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—42no—
492C2×D4—44no—
493C2×D4—432no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4C2×#4114yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
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—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
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—416no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—42no—
565C22×C4—416no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—816no—
578C22×C4#13514yes—
579C22×C4AGL(1,ℤ/8)14yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C2×#4114yes—
592C22×C42−1+412yes—
593C22×C42−1+412yes—
594C22×C4C2511yescharacteristic
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—24no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—42no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—44no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—42no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4C2×#4114yes—
628C22⋊C4—28no—
629C22⋊C4—28no—
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—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—44no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42H(5,𝔽2)14yes—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—28no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—24no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—48no—
688C23—48no—
689C23—48no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23#52512yes—
702C23#53612yes—
703C23C2×#13512yes—
704C23C2×AGL(1,ℤ/8)12yes—
705C23#57512yes—
706C23C23×D411yescharacteristic
707Q8—84no—
708Q8—84no—
709D4—24no—
710D4—24no—
711D4—48no—
712D4—416no—
713D4—416no—
714D4—42no—
715D4—42no—
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—28no—
729C2×C4—28no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
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—44no—
758C2×C4—48no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
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—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—88no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4—88no—
787C2×C4#52512yes—
788C2×C4#53412yes—
789C2×C4#53412yes—
790C2×C4#53612yes—
791C2×C4C2×#13512yes—
792C2×C4C2×#13512yes—
793C2×C4C2×AGL(1,ℤ/8)12yes—
794C2×C4C2×AGL(1,ℤ/8)12yes—
795C2×C4#57512yes—
796C2×C4C22×#4112yes—
797C2×C4C2×H(5,𝔽2)12yes—
798C2×C4C2×2−1+411yescharacteristic
799C2×C4C2×2−1+411yescharacteristic
800C8—44no—
801C8—44no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—416no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—816no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22#323314yes—
832C22C2×#52511yescharacteristic
833C22C2×#53411yescharacteristic
834C22C2×#53611yescharacteristic
835C22C22×#13511yescharacteristic
836C22C22×AGL(1,ℤ/8)11yescharacteristic
837C22C2×#57511yescharacteristic
838C22C2×#57511yescharacteristic
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—44no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4#318814yes—
857C4#352012yes—
858C4#352012yes—
859C2—24no—
860C2—42no—
861C2—42no—
862C2—84no—
863C2#3508411yescharacteristic
864C2#6053611yescharacteristic
865C2#6055811yescharacteristic
866C2C2×#318811yescharacteristic
867C2#6075211yescharacteristic
868C2C2×#323311yescharacteristic
869C2#6086411yescharacteristic
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. #33149C2semidirect
4. #33147C2semidirect
5. #32956C2semidirect
6. #32953C2semidirect
7. #30171C2semidirect
8. #29298C2semidirect
9. #29104C2semidirect
10. #27646C2semidirect
11. #27604C2semidirect
12. #24701C2semidirect
13. #24700C2semidirect
14. #24300C2semidirect
16. #22080C2semidirect
17. #20714C2semidirect
18. C2×#533C22semidirect
24. C2×#476C22semidirect
25. C2×#474C22semidirect
26. C2×#431C22semidirect
29. #2857C22semidirect
30. #2857C22semidirect
34. #2851C22semidirect
49. #2296C22semidirect
54. #2285C22semidirect
59. #2085C22semidirect
60. #2077C22semidirect
61. #2075C22semidirect
62. #2073C22semidirect
63. #2059C22semidirect
66. #2025C22semidirect
67. #1988C22semidirect
68. #1987C22semidirect
69. #1948C22semidirect
70. #1947C22semidirect
71. #1942C22semidirect
72. #1941C22semidirect
73. #1934C22semidirect
74. #1934C22semidirect
75. #1921C22semidirect
76. #1919C22semidirect
78. #1864C22semidirect
79. #1862C22semidirect
80. #1854C22semidirect
85. #1825C22semidirect
88. #1817C22semidirect
89. #1802C22semidirect
90. #1802C22semidirect
93. #1797C22semidirect
98. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×#1212
#331492
#331472
#329562
#329532
#301712
#292982
#291042
#276462
#276042
#247012
#247002
#243002
#240092
#220802
#207142