Finite Group Databasebeta

← #6495209

Subgroups — #6495209

Order 512.

1782 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#33196C211yesmaximal, characteristic, complemented
4#33195C211yesmaximal, characteristic, complemented
5#33163C211yesmaximal, characteristic, complemented
6#33162C211yesmaximal, characteristic, complemented
7#29926C212yesmaximal, complemented
8#29665C212yesmaximal
9#29349C212yesmaximal, complemented
10#29257C212yesmaximal, complemented
11#28372C212yesmaximal, complemented
12#28159C212yesmaximal, complemented
13#24652C212yesmaximal, complemented
14#24651C212yesmaximal
15#24157C212yesmaximal, complemented
16#24153C212yesmaximal
17#22148C212yesmaximal, complemented
18#22146C212yesmaximal, complemented
19#20808C211yesmaximal, characteristic, complemented
20C2×#533C2212yes—
21C2×#529C2211yescharacteristic
22C2×#475C2212yes—
23C2×#474C2212yes—
24C2×#462C2212yes—
25C2×#462C2212yes—
26C2×#462C2212yes—
27C2×#461C2212yes—
28C2×#461C2212yes—
29C2×#461C2212yes—
30C2×#431C2212yes—
31#2868C2211yescharacteristic
32#2868C2211yescharacteristic
33#2862C2212yes—
34#2859—21no—
35#2859—21no—
36#2857—21no—
37#2857—21no—
38#2857C2212yes—
39#2857C2212yes—
40C4×C4⋊Q8—21no—
41C4×C4⋊Q8—21no—
42C4×C4⋊Q8C2212yes—
43C4×C4⋊Q8C2212yes—
44C4×#125C2211yescharacteristic
45C4×#125C2211yescharacteristic
46C4×#126—21no—
47C4×#126—21no—
48C4×#124C2211yescharacteristic
49C4×#124C2211yescharacteristic
50C4×C22⋊Q8C2211yescharacteristic
51C4×C22⋊Q8C2211yescharacteristic
52C4×#123—21no—
53C4×#123—21no—
54C4×#121C2211yescharacteristic
55C4×#121C2211yescharacteristic
56#2298—21no—
57#2295C2211yescharacteristic
58#2293C2211yescharacteristic
59#2290—21no—
60#2285—21no—
61#2285—21no—
62#2283C2211yescharacteristic
63C42×Q8C2211yescharacteristic
64C42×D4—21no—
65C42×D4C2211yescharacteristic
66C4×#117—21no—
67C2×C43C2211yescharacteristic
68#2097C2214yes—
69#2074C2214yes—
70#2036C2214yes—
71#2035C2214yes—
72#2026C2214yes—
73#2015C2214yes—
74#2001C2214yes—
75#2000C2214yes—
76#1988C2212yes—
77#1988C2212yes—
78#1981C2212yes—
79#1981C2212yes—
80#1981C2212yes—
81#1981C2212yes—
82#1981C2212yes—
83#1981C2212yes—
84#1969C2214yes—
85#1968C2214yes—
86#1948C2212yes—
87#1948C2212yes—
88#1947C2212yes—
89#1947C2212yes—
90#1933C2214yes—
91#1933C2214yes—
92#1880C2214yes—
93#1878C2214yes—
94#1865C2214yes—
95#1863C2214yes—
96#1842C2211yescharacteristic
97#1842C2211yescharacteristic
98#1831C2212yes—
99#1803C2212yes—
100#1803C2212yes—
101#1802C2212yes—
102#1802C2212yes—
103#1797C2212yes—
104#1797C2212yes—
105C4×C4⋊C8C2212yes—
106C4×C4⋊C8C2212yes—
107C22×Q16C2314yes—
108C22×SD16C2314yes—
109#533—44no—
110#533—44no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115C2×C4⋊Q8C2312yes—
116C2×C4⋊Q8C2312yes—
117#529—24no—
118#529—24no—
119C2×#126—21no—
120C2×#125—22no—
121C2×#125C2311yescharacteristic
122C2×#124C2311yescharacteristic
123C2×#123—21no—
124C2×C22⋊Q8—22no—
125C2×C22⋊Q8C2311yescharacteristic
126C2×C22⋊Q8C2314yes—
127C2×#121C2311yescharacteristic
128C2×C4×Q8—22no—
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×Q8C2311yescharacteristic
132C2×C4×Q8C2314yes—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×C4×D4C2311yescharacteristic
139C2×#117—22no—
140C2×#117—21no—
141C2×#117—21no—
142C22×C42—21no—
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#475—44no—
151#474—44no—
152#462—28no—
153#462—44no—
154#462—44no—
155#461—28no—
156#461—44no—
157#461—44no—
158#431—44no—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2314yes—
176C2×C4×C8C2314yes—
177#391—22no—
178#391—22no—
179#391C2314yes—
180#391C2314yes—
181#391C2311yescharacteristic
182#391C2311yescharacteristic
183#390C2311yescharacteristic
184#390C2311yescharacteristic
185#389—22no—
186#389—22no—
187#389—22no—
188#389—22no—
189#389—22no—
190#389—22no—
191#389—22no—
192#389—22no—
193#389C2311yescharacteristic
194#389C2311yescharacteristic
195#389C2311yescharacteristic
196#389C2311yescharacteristic
197#388—21no—
198#388—21no—
199#388—21no—
200#388—21no—
201#388—21no—
202#388—21no—
203#388—21no—
204#388—21no—
205#387—21no—
206#387—21no—
207#387—21no—
208#387—21no—
209#387—21no—
210#387—21no—
211#387—21no—
212#387—21no—
213#386—21no—
214#386—21no—
215#385—21no—
216#385—21no—
217#384—21no—
218#384—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384—21no—
223#384C2312yes—
224#384C2312yes—
225#383—21no—
226#382—22no—
227#382—22no—
228#382C2311yescharacteristic
229#382C2311yescharacteristic
230#381—21no—
231#380—22no—
232#380—22no—
233#380—22no—
234#380—22no—
235#380C2311yescharacteristic
236#380C2311yescharacteristic
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—22no—
246C4×C4⋊C4—22no—
247C4×C4⋊C4—22no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C4⋊C4C2311yescharacteristic
254C4×C4⋊C4C2311yescharacteristic
255C4×C4⋊C4C2311yescharacteristic
256C4×C4⋊C4C2311yescharacteristic
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267C4×C22⋊C4—21no—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270#376—21no—
271#376—21no—
272C43—21no—
273C43D411yescharacteristic
274C43D411yescharacteristic
275C43D411yescharacteristic
276C43D411yescharacteristic
277C43C2311yescharacteristic
278C43C2311yescharacteristic
279C43C2311yescharacteristic
280C43C2311yescharacteristic
281#340C2314yes—
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#336C2314yes—
286#336C2314yes—
287C22×Q8—22no—
288C22×Q8C2414yes—
289C22×Q8C2411yescharacteristic
290C22×D4—21no—
291C22×D4C2411yescharacteristic
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2411yescharacteristic
302C2×Q16—28no—
303C2×Q16—44no—
304C2×Q16—44no—
305C2×SD16—28no—
306C2×SD16—44no—
307C2×SD16—44no—
308C22×C8C2414yes—
309C22×C8C2414yes—
310C4⋊Q8—24no—
311C4⋊Q8—24no—
312C4⋊Q8—24no—
313C4⋊Q8—24no—
314C4⋊Q8—24no—
315C4⋊Q8—24no—
316C4⋊Q8—24no—
317C4⋊Q8—24no—
318C4⋊Q8—44no—
319C4⋊Q8—44no—
320#126—28no—
321#125—22no—
322#125—22no—
323#125—48no—
324#124—22no—
325#124—22no—
326#123—28no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—44no—
330C22⋊Q8—44no—
331C22⋊Q8—48no—
332#121—22no—
333#121—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—48no—
342C4×Q8#4114yes—
343C4×D4—28no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4#4114yes—
352#117—28no—
353#117—48no—
354#117—44no—
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—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4C2411yescharacteristic
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2414yes—
381C2×C4⋊C4C2411yescharacteristic
382C2×C4⋊C4C2411yescharacteristic
383C2×C4⋊C4C2411yescharacteristic
384C2×C4⋊C4C2411yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—24no—
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×C42—24no—
400C2×C42—21no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—42no—
419C2×C42—44no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
439C2×C42C2×D411yescharacteristic
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2411yescharacteristic
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C2×C42C2411yescharacteristic
446C2×C42C2411yescharacteristic
447C2×C42C2411yescharacteristic
448#107—44no—
449#106—44no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452C4⋊C8—24no—
453C4⋊C8—24no—
454C4⋊C8—24no—
455C4⋊C8—24no—
456#103—28no—
457#103—28no—
458#103—44no—
459#103—44no—
460#103—44no—
461#103—44no—
462#103—44no—
463#102—44no—
464C22⋊C8—44no—
465C4×C8—44no—
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—
484#95—21no—
485#95—21no—
486#95—24no—
487#95—24no—
488#95—24no—
489#95—24no—
490C24—21no—
491C24C22×D411yescharacteristic
492C2×Q8—21no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—24no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8C2×#4112yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4C2×#4112yes—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
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—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4#13714yes—
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2511yescharacteristic
572Q16—88no—
573SD16—88no—
574C2×C8—24no—
575C2×C8—24no—
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—42no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4C2×#4112yes—
616C4⋊C4C2×#4112yes—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—42no—
623C22⋊C4—48no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C42—22no—
632C42—22no—
633C42—24no—
634C42—22no—
635C42—22no—
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—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—41no—
657C42—41no—
658C42—48no—
659C42—42no—
660C42—42no—
661C42—42no—
662C42—42no—
663C42—42no—
664C42—42no—
665C42—42no—
666C42—42no—
667C42#13514yes—
668C42#13714yes—
669C42C2×#4112yes—
670C42C2×#4112yes—
671C42H(5,𝔽2)12yes—
672C42H(5,𝔽2)12yes—
673C42H(5,𝔽2)12yes—
674C422−1+412yes—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23C2×#13712yes—
689C23C23×D411yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—41no—
693Q8—41no—
694Q8—44no—
695Q8—44no—
696Q8—44no—
697Q8—44no—
698Q8—88no—
699D4—22no—
700D4—22no—
701D4—48no—
702D4—41no—
703D4—41no—
704C2×C4—28no—
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—28no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—44no—
742C2×C4—48no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—44no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—44no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—44no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4#52512yes—
769C2×C4#52512yes—
770C2×C4#53512yes—
771C2×C4#53512yes—
772C2×C4#53712yes—
773C2×C4#53712yes—
774C2×C4C2×#13512yes—
775C2×C4C2×#13512yes—
776C2×C4C2×#13512yes—
777C2×C4C2×#13712yes—
778C2×C4C2×#13712yes—
779C2×C4C2×#13712yes—
780C2×C4C2×#13712yes—
781C2×C4C2×#13712yes—
782C2×C4#57512yes—
783C2×C4C22×#4111yescharacteristic
784C2×C4C22×#4111yescharacteristic
785C2×C4C2×H(5,𝔽2)11yescharacteristic
786C2×C4C2×H(5,𝔽2)11yescharacteristic
787C2×C4C2×H(5,𝔽2)11yescharacteristic
788C2×C4C2×2−1+411yescharacteristic
789C8—44no—
790C8—44no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22C2×#52511yescharacteristic
806C22C2×#53511yescharacteristic
807C22C2×#53711yescharacteristic
808C22C22×#13511yescharacteristic
809C22C22×#13711yescharacteristic
810C22C22×#13711yescharacteristic
811C22C2×#57511yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—41no—
819C4—41no—
820C4—42no—
821C4—41no—
822C4—42no—
823C4—41no—
824C4—42no—
825C4—81no—
826C4—84no—
827C4—81no—
828C4—84no—
829C4—81no—
830C4—81no—
831C4#310714yes—
832C4#321214yes—
833C4#324814yes—
834C4#350811yescharacteristic
835C4#350811yescharacteristic
836C4#351111yescharacteristic
837C4#351111yescharacteristic
838C2—42no—
839C2—82no—
840C2#3529211yescharacteristic
841C2C2×#310711yescharacteristic
842C2#6056211yescharacteristic
843C2C2×#321211yescharacteristic
844C2#6080011yescharacteristic
845C2C2×#324811yescharacteristic
846C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36645C2semidirect
3. #33196C2semidirect
4. #33195C2semidirect
5. #33163C2semidirect
6. #33162C2semidirect
7. #29926C2semidirect
9. #29349C2semidirect
10. #29257C2semidirect
11. #28372C2semidirect
12. #28159C2semidirect
13. #24652C2semidirect
15. #24157C2semidirect
17. #22148C2semidirect
18. #22146C2semidirect
19. #20808C2semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#331962
#331952
#331632
#331622
#299262
#296652
#293492
#292572
#283722
#281592
#246522
#246512
#241572
#241532
#221482
#221462
#208082