Finite Group Databasebeta

← #6436915

Subgroups — #6436915

Order 512.

1909 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36621C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#29944C212yesmaximal, complemented
4#29943C212yesmaximal, complemented
5#29928C212yesmaximal, complemented
6#29927C212yesmaximal, complemented
7#29909C211yesmaximal, characteristic, complemented
8#29908C211yesmaximal, characteristic, complemented
9#29907C211yesmaximal, characteristic, complemented
10#29906C211yesmaximal, characteristic, complemented
11#29894C212yesmaximal, complemented
12#29891C212yesmaximal
13#23757C212yesmaximal, complemented
14#23756C212yesmaximal, complemented
15#23755C212yesmaximal, complemented
16#23754C212yesmaximal, complemented
17#21388C212yesmaximal, complemented
18#21361C212yesmaximal, complemented
19#20714C211yesmaximal, characteristic, complemented
20C2×#529C2211yescharacteristic
21C22×#117—21no—
22C23×C42C2211yescharacteristic
23C2×#431C2212yes—
24#2855C2211yescharacteristic
25#2854C2211yescharacteristic
26#2853—21no—
27#2852—21no—
28#2852—21no—
29#2851C2211yescharacteristic
30#2851C2211yescharacteristic
31#2850C2211yescharacteristic
32#2850C2211yescharacteristic
33#2849—21no—
34#2848C2211yescharacteristic
35#2847C2211yescharacteristic
36C4×C22⋊Q8C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C4×#123—21no—
39C4×#121C2211yescharacteristic
40C4×#121C2211yescharacteristic
41C4×#120—21no—
42#2290—21no—
43#2290—21no—
44#2285—21no—
45#2285—21no—
46#2285—21no—
47#2285—21no—
48#2285C2212yes—
49#2285C2212yes—
50#2285C2212yes—
51#2285C2212yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54#2283C2211yescharacteristic
55C2×#382—21no—
56C2×#380—21no—
57C2×#380C2212yes—
58C2×C4×C4⋊C4—21no—
59C2×C4×C4⋊C4C2212yes—
60#2100C2212yescomplemented
61#2100C2212yescomplemented
62#2099C2212yescomplemented
63#2099C2212yescomplemented
64#2096C2212yescomplemented
65#2095C2212yescomplemented
66#2094C2212yescomplemented
67#2093C2212yescomplemented
68#2084C2212yescomplemented
69#2084C2212yescomplemented
70#2083C2212yescomplemented
71#2083C2212yescomplemented
72#2077C2214yes—
73#2077C2214yes—
74#2076C2214yes—
75#2075C2214yes—
76#2072C2212yescomplemented
77#2072C2212yescomplemented
78#2071C2212yescomplemented
79#2071C2212yescomplemented
80#2036C2214yes—
81#2035C2214yes—
82#2034C2214yes—
83#2033C2214yes—
84#1989C2214yescomplemented
85#1983C2214yescomplemented
86#1949C2214yescomplemented
87#1949C2214yescomplemented
88#1874C2212yes—
89#1874C2212yes—
90#1872C2212yes—
91#1872C2212yes—
92#1853C2212yes—
93#1853C2212yes—
94#1852C2212yes—
95#1852C2212yes—
96#1817C2211yescharacteristic
97#1817C2211yescharacteristic
98#1797C2212yes—
99#1797C2212yes—
100#1779C2212yes—
101C4×#107C2214yescomplemented
102C4×#106C2214yescomplemented
103C4×#103C2214yescomplemented
104C4×#102C2214yescomplemented
105C4×C22⋊C8C2212yes—
106C4×C22⋊C8C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110#529—28no—
111C2×#126—21no—
112C2×#125C2311yescharacteristic
113C2×#124C2311yescharacteristic
114C2×#123—21no—
115C2×#123—21no—
116C2×C22⋊Q8C2311yescharacteristic
117C2×C22⋊Q8C2311yescharacteristic
118C2×C22⋊Q8C2311yescharacteristic
119C2×#121C2311yescharacteristic
120C2×#121C2311yescharacteristic
121C2×#121C2311yescharacteristic
122C2×#120—21no—
123C2×C4×Q8C2311yescharacteristic
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4C2311yescharacteristic
128C2×#117—22no—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—21no—
133C2×#117—48no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4—22no—
141C22×C42—28no—
142C22×C42—22no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#431—28no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×C4×C8C2314yes—
170#391C2311yescharacteristic
171#391C2311yescharacteristic
172#390C2311yescharacteristic
173#390C2311yescharacteristic
174#389C2311yescharacteristic
175#389C2311yescharacteristic
176#389C2311yescharacteristic
177#389C2311yescharacteristic
178#388—21no—
179#388—21no—
180#388—21no—
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#387—21no—
187#387—21no—
188#387—21no—
189#387—21no—
190#387—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#386—21no—
195#386—21no—
196#386—21no—
197#386—21no—
198#386—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#385—21no—
205#385—21no—
206#385—21no—
207#385—21no—
208#385—21no—
209#385—21no—
210#385—21no—
211#385—21no—
212#385—21no—
213#385—21no—
214#384—21no—
215#384—21no—
216#384—21no—
217#384—21no—
218#384C2312yes—
219#384C2312yes—
220#384C2312yes—
221#384C2312yes—
222#383—21no—
223#382—22no—
224#382—22no—
225#382—22no—
226#382—22no—
227#382C2311yescharacteristic
228#382C2311yescharacteristic
229#381—21no—
230#381—21no—
231#380—22no—
232#380—22no—
233#380—22no—
234#380—22no—
235#380—22no—
236#380—22no—
237#380C2311yescharacteristic
238#380C2314yes—
239#380C2311yescharacteristic
240#380C2314yes—
241#380C2311yescharacteristic
242#380C2311yescharacteristic
243#380C2311yescharacteristic
244#380C2311yescharacteristic
245#379—21no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—22no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4C2314yes—
255C4×C4⋊C4C2314yes—
256C4×C4⋊C4C2311yescharacteristic
257C4×C4⋊C4C2311yescharacteristic
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263#376—21no—
264C2×#95—22no—
265C2×#95—22no—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C25C2×D411yescharacteristic
279C22×Q8C2411yescharacteristic
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2411yescharacteristic
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—21no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
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
314C22×C8C2414yes—
315C22×C8C2414yes—
316#126—44no—
317#125—24no—
318#124—24no—
319#123—44no—
320#123—44no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—42no—
324#121—24no—
325#121—42no—
326#121—42no—
327#120—44no—
328C4×Q8—24no—
329C4×D4—24no—
330C4×D4—44no—
331C4×D4—44no—
332C4×D4—44no—
333#117—48no—
334#117—48no—
335#117—48no—
336#117—48no—
337#117—44no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
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—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2414yes—
365C2×C4⋊C4C2414yes—
366C2×C4⋊C4C2411yescharacteristic
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2411yescharacteristic
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—48no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—48no—
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×C42#4118yes—
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—44no—
429#107—44no—
430#106—44no—
431#106—44no—
432C4⋊C8—28no—
433#103—44no—
434#103—44no—
435#102—44no—
436#102—44no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—44no—
440C22⋊C8—44no—
441C4×C8—28no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—41no—
473C24—41no—
474C24C22×D411yescharacteristic
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C22×C4—232no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
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—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—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
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—416no—
551C22×C4—416no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4#12314yes—
562C22×C4#12314yes—
563C22×C4#13514yes—
564C22×C4AGL(1,ℤ/8)14yes—
565C22×C4#13714yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
578C22×C4C2511yescharacteristic
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C2×C8—24no—
583C2×C8—24no—
584C2×C8—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—48no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—48no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—48no—
649C42—42no—
650C42—48no—
651C42—42no—
652C42—42no—
653C42#12314yes—
654C42#12314yes—
655C42C2×#4114yes—
656C42C2×#4114yes—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—28no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23C2×#12312yes—
688C23C2×#13512yes—
689C23C2×AGL(1,ℤ/8)12yes—
690C23C2×#13712yes—
691C23#57512yes—
692C23C23×D411yescharacteristic
693Q8—44no—
694D4—44no—
695D4—84no—
696D4—84no—
697D4—84no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—44no—
752C2×C4—41no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—88no—
766C2×C4—88no—
767C2×C4—84no—
768C2×C4C2×#12312yes—
769C2×C4C2×#12312yes—
770C2×C4C2×#12312yes—
771C2×C4C2×#12312yes—
772C2×C4C2×#12312yes—
773C2×C4C2×#13512yes—
774C2×C4C2×#13512yes—
775C2×C4C2×AGL(1,ℤ/8)12yes—
776C2×C4C2×AGL(1,ℤ/8)12yes—
777C2×C4C2×#13712yes—
778C2×C4C2×#13712yes—
779C2×C4C22×#4112yes—
780C2×C4#58512yes—
781C2×C4#58512yes—
782C8—44no—
783C8—44no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—416no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22#309114yes—
813C22C22×#12311yescharacteristic
814C22#344911yescharacteristic
815C22#344911yescharacteristic
816C22C22×#13511yescharacteristic
817C22C22×AGL(1,ℤ/8)11yescharacteristic
818C22C22×#13711yescharacteristic
819C22C2×#57511yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4—84no—
832C4—81no—
833C4—84no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4—81no—
839C4#309214yes—
840C4#345514yes—
841C2—24no—
842C2—42no—
843C2—42no—
844C2—161no—
845C2#3463511yescharacteristic
846C2C2×#309111yescharacteristic
847C2C2×#309211yescharacteristic
848C2#6094611yescharacteristic
849C2#6094711yescharacteristic
850C2#6094911yescharacteristic
851C2#6095011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#2847C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2285C2semidirect
3. #29944C2semidirect
4. #29943C2semidirect
5. #29928C2semidirect
6. #29927C2semidirect
7. #29909C2semidirect
8. #29908C2semidirect
9. #29907C2semidirect
10. #29906C2semidirect
11. #29894C2semidirect
13. #23757C2semidirect
14. #23756C2semidirect
15. #23755C2semidirect
16. #23754C2semidirect
17. #21388C2semidirect
18. #21361C2semidirect
19. #20714C2semidirect
60. #2100C22semidirect
61. #2100C22semidirect
62. #2099C22semidirect
63. #2099C22semidirect
64. #2096C22semidirect
65. #2095C22semidirect
66. #2094C22semidirect
67. #2093C22semidirect
68. #2084C22semidirect
69. #2084C22semidirect
70. #2083C22semidirect
71. #2083C22semidirect
76. #2072C22semidirect
77. #2072C22semidirect
78. #2071C22semidirect
79. #2071C22semidirect
84. #1989C22semidirect
85. #1983C22semidirect
86. #1949C22semidirect
87. #1949C22semidirect
101. C4×#107C22semidirect
102. C4×#106C22semidirect
103. C4×#103C22semidirect
104. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#366212
C2×#22852
#299442
#299432
#299282
#299272
#299092
#299082
#299072
#299062
#298942
#298912
#237572
#237562
#237552
#237542
#213882
#213612
#207142