Finite Group Databasebeta

← #6493703

Subgroups — #6493703

Order 512.

1976 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#36624C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic, complemented
3#33154C212yesmaximal, complemented
4#33113C212yesmaximal, complemented
5#29941C212yesmaximal, complemented
6#29925C212yesmaximal, complemented
7#27859C214yesmaximal, complemented
8#27679C212yesmaximal, complemented
9#27646C212yesmaximal, complemented
10#27627C212yesmaximal, complemented
11#27626C212yesmaximal, complemented
12#24555C214yesmaximal, complemented
13#21961C211yesmaximal, characteristic, complemented
14#21959C211yesmaximal, characteristic, complemented
15#21884C211yesmaximal, characteristic, complemented
16#21884C211yesmaximal, characteristic, complemented
17C2×#1797C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C23×C42C2211yescharacteristic
21C2×#482C2214yes—
22C22×C4⋊C8C2211yescharacteristic
23C22×C4⋊C8C2211yescharacteristic
24C22×C22⋊C8C2212yes—
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2856C2211yescharacteristic
28#2856C2211yescharacteristic
29#2854—21no—
30#2854C2212yes—
31#2850—21no—
32#2850—21no—
33#2847—21no—
34#2847C2212yes—
35C4×#121—21no—
36C4×#121—21no—
37C4×#121C2212yes—
38C4×#121C2212yes—
39#2297—21no—
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2285C2211yescharacteristic
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283—21no—
51#2283C2212yes—
52#2283C2212yes—
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59#2101C2214yescomplemented
60#2092C2214yescomplemented
61#2085C2214yescomplemented
62#2077C2214yes—
63#2076C2214yes—
64#2073C2214yescomplemented
65#2034C2214yes—
66#2033C2214yes—
67#1988C2212yescomplemented
68#1988C2212yescomplemented
69#1982C2212yescomplemented
70#1982C2212yescomplemented
71#1948C2212yescomplemented
72#1948C2212yescomplemented
73#1948C2212yescomplemented
74#1948C2212yescomplemented
75#1947C2212yescomplemented
76#1947C2212yescomplemented
77#1947C2212yescomplemented
78#1947C2212yescomplemented
79#1926C2214yescomplemented
80#1925C2214yescomplemented
81#1921C2214yescomplemented
82#1920C2214yescomplemented
83#1893C2214yes—
84#1893C2214yes—
85#1875C2214yes—
86#1854C2214yes—
87#1825C2214yes—
88#1808C2214yes—
89#1807C2214yes—
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1802C2212yescomplemented
93#1802C2212yescomplemented
94#1797C2212yes—
95#1797C2212yes—
96#1797C2212yes—
97#1797C2212yes—
98C2×#336C2212yes—
99C22×#41—21no—
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C23×C8C2312yes—
104C23×C8C2312yes—
105#532—24no—
106#532—24no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#124—21no—
110#525—48no—
111C2×#123—22no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—21no—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×#121C2312yes—
122C2×#120—22no—
123C2×C4×D4—22no—
124C2×C4×D4—22no—
125C2×C4×D4—21no—
126C2×C4×D4C2312yes—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117—21no—
132C2×#117C2312yes—
133C2×#117C2312yes—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#482—48no—
149C2×#107C2314yes—
150C2×#107C2314yes—
151C2×#106C2314yes—
152C2×#106C2314yes—
153C2×C4⋊C8—24no—
154C2×C4⋊C8—24no—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×C22⋊C8—44no—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2314yes—
166#391—21no—
167#391—21no—
168#390—21no—
169#390—21no—
170#390—21no—
171#390—21no—
172#390C2312yes—
173#390C2312yes—
174#389—21no—
175#389—21no—
176#389C2312yes—
177#389C2312yes—
178#388—22no—
179#388—22no—
180#388—22no—
181#388—22no—
182#386—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#386—22no—
187#386—22no—
188#384C2311yescharacteristic
189#384C2311yescharacteristic
190#384C2311yescharacteristic
191#384C2311yescharacteristic
192#384C2311yescharacteristic
193#384C2311yescharacteristic
194#383—22no—
195#383—22no—
196#382—21no—
197#382—21no—
198#382—21no—
199#382—21no—
200#382—21no—
201#382C2312yes—
202#382C2312yes—
203#381—22no—
204#381—22no—
205#381—22no—
206#380—21no—
207#380—21no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380—21no—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380C2312yes—
218#380C2312yes—
219#380C2312yes—
220#380C2312yes—
221#380C2312yes—
222#380C2312yes—
223#380C2312yes—
224#379—22no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4C2312yes—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C4⋊C4C2312yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247#376—22no—
248#376—22no—
249#376—22no—
250C43—22no—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#336C2314yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C22×Q8—21no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2412yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—42no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—42no—
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
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×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C22×C8—24no—
304C22×C8—24no—
305C22×C8—42no—
306C22×C8—42no—
307C22×C8—42no—
308C22×C8—42no—
309C22×C8C2414yes—
310C22×C8C2414yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313#127—22no—
314#127—22no—
315#124—44no—
316#123—48no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319#121—24no—
320#121—24no—
321#121—24no—
322#121—24no—
323#121—42no—
324#121—42no—
325#121—44no—
326#121—44no—
327#121—44no—
328#121—44no—
329#121—44no—
330#120—48no—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—48no—
334C4×D4—48no—
335C4×D4—44no—
336#117—24no—
337#117—24no—
338#117—42no—
339#117—42no—
340#117—44no—
341#117—44no—
342#117—44no—
343#117—44no—
344#117—44no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
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×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
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×C42#4114yes—
420C2×C42#4114yes—
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425#107—44no—
426#107—44no—
427#106—44no—
428#106—44no—
429C4⋊C8—24no—
430C4⋊C8—24no—
431C4⋊C8—24no—
432C4⋊C8—24no—
433#102—44no—
434#102—44no—
435#102—44no—
436#102—44no—
437C22⋊C8—28no—
438C22⋊C8—44no—
439#95—22no—
440#95—22no—
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—22no—
461C24—22no—
462C24—22no—
463C24—41no—
464C24—41no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468#41—816no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
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—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
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—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—416no—
560C22×C4—416no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4#12314yes—
565C22×C4#12314yes—
566C22×C4#13514yes—
567C22×C4AGL(1,ℤ/8)14yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C42−1+412yes—
583C22×C4C2511yescharacteristic
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C2×C8—24no—
590C2×C8—84no—
591C2×C8—84no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
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—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—44no—
656C42—44no—
657C42—44no—
658C42—44no—
659C42#12314yes—
660C42#12314yes—
661C42C2×#4112yes—
662C42C2×#4112yes—
663C42C2×#4112yes—
664C42C2×#4112yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—28no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23C2×#12312yes—
696C23#53712yes—
697C23C2×#13512yes—
698C23C2×AGL(1,ℤ/8)12yes—
699C23#57512yes—
700C23C23×D411yescharacteristic
701Q8—84no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—84no—
707D4—88no—
708D4—88no—
709D4—88no—
710D4—84no—
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—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
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—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—44no—
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—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
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—42no—
779C2×C4—42no—
780C2×C4—88no—
781C2×C4#482116yescomplemented
782C2×C4C2×#12312yes—
783C2×C4C2×#12312yes—
784C2×C4C2×#12312yes—
785C2×C4C2×#12312yes—
786C2×C4C2×#12312yes—
787C2×C4#53712yes—
788C2×C4C2×#13512yes—
789C2×C4C2×#13512yes—
790C2×C4C2×AGL(1,ℤ/8)12yes—
791C2×C4C2×AGL(1,ℤ/8)12yes—
792C2×C4#57512yes—
793C2×C4C22×#4111yescharacteristic
794C2×C4C22×#4111yescharacteristic
795C2×C4C2×H(5,𝔽2)11yescharacteristic
796C2×C4C2×2−1+411yescharacteristic
797C2×C4#58511yescharacteristic
798C2×C4#58511yescharacteristic
799C8—44no—
800C8—44no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—416no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22C2×#48214yes—
830C22C22×#12311yescharacteristic
831C22C2×#53711yescharacteristic
832C22#344911yescharacteristic
833C22C22×#13511yescharacteristic
834C22C22×AGL(1,ℤ/8)11yescharacteristic
835C22C2×#57511yescharacteristic
836C22C2×#57511yescharacteristic
837C4—22no—
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4C2×#48214yes—
854C4C2×#48214yes—
855C4#349411yescharacteristic
856C4#349411yescharacteristic
857C4#349511yescharacteristic
858C4#349511yescharacteristic
859C2—24no—
860C2—42no—
861C2—42no—
862C2—162no—
863C2#3526311yescharacteristic
864C2C22×#48211yescharacteristic
865C2#6051111yescharacteristic
866C2#6090011yescharacteristic
867C2#6091611yescharacteristic
868C2#6094811yescharacteristic
869C2#6096211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
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
2. #34012C2semidirect
3. #33154C2semidirect
4. #33113C2semidirect
5. #29941C2semidirect
6. #29925C2semidirect
7. #27859C2semidirect
8. #27679C2semidirect
9. #27646C2semidirect
10. #27627C2semidirect
11. #27626C2semidirect
12. #24555C2semidirect
13. #21961C2semidirect
14. #21959C2semidirect
15. #21884C2semidirect
16. #21884C2semidirect
17. C2×#1797C2semidirect
59. #2101C22semidirect
60. #2092C22semidirect
61. #2085C22semidirect
64. #2073C22semidirect
67. #1988C22semidirect
68. #1988C22semidirect
69. #1982C22semidirect
70. #1982C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1948C22semidirect
74. #1948C22semidirect
75. #1947C22semidirect
76. #1947C22semidirect
77. #1947C22semidirect
78. #1947C22semidirect
79. #1926C22semidirect
80. #1925C22semidirect
81. #1921C22semidirect
82. #1920C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
92. #1802C22semidirect
93. #1802C22semidirect
781. C2×C4#482semidirect

Maximal subgroups

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

subgroupindex
#366242
#340122
#331542
#331132
#299412
#299252
#278592
#276792
#276462
#276272
#276262
#245552
#219612
#219592
#218842
C2×#17972