Finite Group Databasebeta

← #6482935

Subgroups — #6482935

Order 512.

1893 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36621C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#33100C212yesmaximal, complemented
4#33096C212yesmaximal, complemented
5#29894C212yesmaximal, complemented
6#29891C212yesmaximal
7#27895C212yesmaximal, complemented
8#27894C212yesmaximal, complemented
9#27881C212yesmaximal, complemented
10#27880C212yesmaximal, complemented
11#27629C212yesmaximal, complemented
12#27628C212yesmaximal, complemented
13#27625C212yesmaximal, complemented
14#27624C212yesmaximal, complemented
15#21987C211yesmaximal, characteristic, complemented
16#21987C211yesmaximal, characteristic, complemented
17#21867C211yesmaximal, characteristic, complemented
18#21867C211yesmaximal, characteristic, complemented
19#20715C211yesmaximal, characteristic, complemented
20C2×#529C2211yescharacteristic
21C22×#117—21no—
22C23×C42C2211yescharacteristic
23C2×#432C2211yescharacteristic
24C2×#432C2211yescharacteristic
25#2855C2211yescharacteristic
26#2854C2211yescharacteristic
27#2853—21no—
28#2852—21no—
29#2852—21no—
30#2851C2211yescharacteristic
31#2851C2211yescharacteristic
32#2850C2211yescharacteristic
33#2850C2211yescharacteristic
34#2849—21no—
35#2848C2211yescharacteristic
36#2847C2211yescharacteristic
37C4×C22⋊Q8C2211yescharacteristic
38C4×C22⋊Q8C2211yescharacteristic
39C4×#123—21no—
40C4×#121C2211yescharacteristic
41C4×#121C2211yescharacteristic
42C4×#120—21no—
43#2290—21no—
44#2290—21no—
45#2285—21no—
46#2285—21no—
47#2285—21no—
48#2285—21no—
49#2285C2212yes—
50#2285C2212yes—
51#2285C2212yes—
52#2285C2212yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55#2283C2211yescharacteristic
56C2×#382—21no—
57C2×#380—21no—
58C2×#380C2212yes—
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2212yes—
61#2077C2214yes—
62#2077C2214yes—
63#2076C2214yes—
64#2075C2214yes—
65#2036C2214yes—
66#2035C2214yes—
67#2034C2214yes—
68#2033C2214yes—
69#1992C2212yescomplemented
70#1992C2212yescomplemented
71#1959C2212yescomplemented
72#1959C2212yescomplemented
73#1948C2212yescomplemented
74#1948C2212yescomplemented
75#1947C2212yescomplemented
76#1947C2212yescomplemented
77#1928C2214yescomplemented
78#1927C2214yescomplemented
79#1926C2214yescomplemented
80#1925C2214yescomplemented
81#1921C2214yescomplemented
82#1920C2214yescomplemented
83#1919C2214yescomplemented
84#1918C2214yescomplemented
85#1874C2212yes—
86#1874C2212yes—
87#1872C2212yes—
88#1872C2212yes—
89#1853C2212yes—
90#1853C2212yes—
91#1852C2212yes—
92#1852C2212yes—
93#1847C2212yescomplemented
94#1847C2212yescomplemented
95#1836C2212yescomplemented
96#1836C2212yescomplemented
97#1817C2212yes—
98#1803C2212yescomplemented
99#1803C2212yescomplemented
100#1802C2212yescomplemented
101#1802C2212yescomplemented
102#1797C2212yes—
103#1797C2212yes—
104#1779C2212yes—
105#1749C2212yes—
106#1749C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110#529—24no—
111#529—24no—
112C2×#126—21no—
113C2×#125C2311yescharacteristic
114C2×#124C2311yescharacteristic
115C2×#123—21no—
116C2×#123—21no—
117C2×C22⋊Q8C2311yescharacteristic
118C2×C22⋊Q8C2311yescharacteristic
119C2×C22⋊Q8C2311yescharacteristic
120C2×#121C2311yescharacteristic
121C2×#121C2311yescharacteristic
122C2×#121C2311yescharacteristic
123C2×#120—21no—
124C2×C4×Q8C2311yescharacteristic
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4C2311yescharacteristic
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—21no—
134C2×#117—48no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4—22no—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42—22no—
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#432—24no—
158#432—24no—
159C2×#107C2314yes—
160C2×#107C2314yes—
161C2×#106C2314yes—
162C2×#106C2314yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2314yes—
172C2×C22⋊C8C2314yes—
173C2×#97C2312yes—
174C2×#97C2312yes—
175#391C2311yescharacteristic
176#391C2311yescharacteristic
177#390C2311yescharacteristic
178#390C2311yescharacteristic
179#389C2311yescharacteristic
180#389C2311yescharacteristic
181#389C2311yescharacteristic
182#389C2311yescharacteristic
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187#388—21no—
188#388—21no—
189#388—21no—
190#388—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#387—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#386—21no—
205#386—21no—
206#386—21no—
207#386—21no—
208#386—21no—
209#385—21no—
210#385—21no—
211#385—21no—
212#385—21no—
213#385—21no—
214#385—21no—
215#385—21no—
216#385—21no—
217#385—21no—
218#385—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384—21no—
223#384C2312yes—
224#384C2312yes—
225#384C2312yes—
226#384C2312yes—
227#383—21no—
228#382—22no—
229#382—22no—
230#382—22no—
231#382—22no—
232#382C2311yescharacteristic
233#382C2311yescharacteristic
234#381—21no—
235#381—21no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380—22no—
240#380—22no—
241#380—22no—
242#380C2311yescharacteristic
243#380C2314yes—
244#380C2311yescharacteristic
245#380C2314yes—
246#380C2311yescharacteristic
247#380C2311yescharacteristic
248#380C2311yescharacteristic
249#380C2311yescharacteristic
250#379—21no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4C2314yes—
260C4×C4⋊C4C2314yes—
261C4×C4⋊C4C2311yescharacteristic
262C4×C4⋊C4C2311yescharacteristic
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268#376—21no—
269C2×#95—22no—
270C2×#95—22no—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#340C2314yes—
279#336C2314yes—
280#336C2314yes—
281C25C2×D411yescharacteristic
282C22×Q8C2411yescharacteristic
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2411yescharacteristic
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—21no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
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×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C22×C8C2414yes—
319C22×C8C2414yes—
320#126—44no—
321#125—22no—
322#125—22no—
323#124—22no—
324#124—22no—
325#123—44no—
326#123—44no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—42no—
330C22⋊Q8—42no—
331#121—22no—
332#121—22no—
333#121—42no—
334#121—42no—
335#120—44no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343#117—48no—
344#117—48no—
345#117—48no—
346#117—48no—
347#117—44no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
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—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2414yes—
375C2×C4⋊C4C2414yes—
376C2×C4⋊C4C2411yescharacteristic
377C2×C4⋊C4C2411yescharacteristic
378C2×C4⋊C4C2411yescharacteristic
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2411yescharacteristic
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
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—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—48no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—48no—
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2×D411yescharacteristic
436C2×C42C2×D411yescharacteristic
437C2×C42C2×D411yescharacteristic
438C2×C42#4114yes—
439C2×C42#4114yes—
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444#107—44no—
445#107—44no—
446#106—44no—
447#106—44no—
448C4⋊C8—24no—
449C4⋊C8—24no—
450#103—44no—
451#103—44no—
452#102—44no—
453#102—44no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—44no—
457C22⋊C8—44no—
458#97—24no—
459#97—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—21no—
490C24—41no—
491C24—41no—
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C22×C4—232no—
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—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
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—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—416no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4#12314yes—
586C22×C4#12314yes—
587C22×C4AGL(1,ℤ/8)14yes—
588C22×C4#13714yes—
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2511yescharacteristic
603C2×C8—24no—
604C2×C8—24no—
605C2×C8—24no—
606C2×C8—24no—
607C2×C8—24no—
608C2×C8—24no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—42no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—48no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—48no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—48no—
677C42—42no—
678C42—48no—
679C42—42no—
680C42—42no—
681C42#12314yes—
682C42#12314yes—
683C42C2×#4112yes—
684C42C2×#4112yes—
685C42C2×#4112yes—
686C42C2×#4112yes—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—28no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C2×#12312yes—
718C23C2×AGL(1,ℤ/8)12yes—
719C23C2×#13712yes—
720C23#57512yes—
721C23#57512yes—
722C23C23×D411yescharacteristic
723Q8—42no—
724Q8—42no—
725D4—42no—
726D4—42no—
727D4—84no—
728D4—84no—
729D4—84no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—28no—
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—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—21no—
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—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—41no—
802C2×C4—88no—
803C2×C4—88no—
804C2×C4—84no—
805C2×C4C2×#12312yes—
806C2×C4C2×#12312yes—
807C2×C4C2×#12312yes—
808C2×C4C2×#12312yes—
809C2×C4C2×#12312yes—
810C2×C4C2×AGL(1,ℤ/8)12yes—
811C2×C4C2×AGL(1,ℤ/8)12yes—
812C2×C4C2×#13712yes—
813C2×C4C2×#13712yes—
814C2×C4C22×#4111yescharacteristic
815C2×C4C22×#4111yescharacteristic
816C2×C4#58512yes—
817C2×C4#58512yes—
818C8—44no—
819C8—44no—
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—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22#309314yes—
849C22C22×#12311yescharacteristic
850C22#344911yescharacteristic
851C22#344911yescharacteristic
852C22C22×AGL(1,ℤ/8)11yescharacteristic
853C22C22×#13711yescharacteristic
854C22C2×#57511yescharacteristic
855C22C2×#57511yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—84no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—84no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4#309214yes—
876C4#349312yes—
877C4#349312yes—
878C2—24no—
879C2—42no—
880C2—42no—
881C2—161no—
882C2#3515711yescharacteristic
883C2C2×#309211yescharacteristic
884C2C2×#309311yescharacteristic
885C2#6094911yescharacteristic
886C2#6095011yescharacteristic
887C2#6096211yescharacteristic
888C2#6096311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
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. C2×#2285C2semidirect
3. #33100C2semidirect
4. #33096C2semidirect
5. #29894C2semidirect
7. #27895C2semidirect
8. #27894C2semidirect
9. #27881C2semidirect
10. #27880C2semidirect
11. #27629C2semidirect
12. #27628C2semidirect
13. #27625C2semidirect
14. #27624C2semidirect
15. #21987C2semidirect
16. #21987C2semidirect
17. #21867C2semidirect
18. #21867C2semidirect
19. #20715C2semidirect
69. #1992C22semidirect
70. #1992C22semidirect
71. #1959C22semidirect
72. #1959C22semidirect
73. #1948C22semidirect
74. #1948C22semidirect
75. #1947C22semidirect
76. #1947C22semidirect
77. #1928C22semidirect
78. #1927C22semidirect
79. #1926C22semidirect
80. #1925C22semidirect
81. #1921C22semidirect
82. #1920C22semidirect
83. #1919C22semidirect
84. #1918C22semidirect
93. #1847C22semidirect
94. #1847C22semidirect
95. #1836C22semidirect
96. #1836C22semidirect
98. #1803C22semidirect
99. #1803C22semidirect
100. #1802C22semidirect
101. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#366212
C2×#22852
#331002
#330962
#298942
#298912
#278952
#278942
#278812
#278802
#276292
#276282
#276252
#276242
#219872
#218672
#207152