Finite Group Databasebeta

← #6447019

Subgroups — #6447019

Order 512.

2140 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34935C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic, complemented
3#24980C214yesmaximal, complemented
4#24978C214yesmaximal, complemented
5#24972C212yesmaximal, complemented
6#24970C212yesmaximal, complemented
7#24968C212yesmaximal, complemented
8#24966C212yesmaximal, complemented
9#23642C212yesmaximal, complemented
10#23482C212yesmaximal, complemented
11#21190C211yesmaximal, characteristic, complemented
12#21170C211yesmaximal, characteristic, complemented
13#20910C212yesmaximal, complemented
14#20764C211yesmaximal, characteristic, complemented
15#20701C212yesmaximal, complemented
16#20648C211yesmaximal, characteristic, complemented
17C4×#417C211yesmaximal, characteristic, complemented
18C2×#525C2212yes—
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C2×#428C2212yes—
23C2×#423C2211yescharacteristic
24C2×#417C2211yescharacteristic
25C2×#417C2211yescharacteristic
26C2×#417C2212yes—
27C2×#407C2212yes—
28C2×#407C2212yes—
29C2×C4×M16C2211yescharacteristic
30#2538C2211yescharacteristic
31#2538C2211yescharacteristic
32#2537C2211yescharacteristic
33#2537C2211yescharacteristic
34#2536C2212yes—
35#2535C2212yes—
36#2534—22no—
37#2486—21no—
38#2408—21no—
39#2392—22no—
40#2354—22no—
41#2354—21no—
42#2354—21no—
43#2354C2212yes—
44#2354C2212yes—
45#2354C2214yes—
46C4×#121—21no—
47C4×#121—21no—
48C2×#390—21no—
49C2×#388—22no—
50#2285C2211yescharacteristic
51C2×#384C2211yescharacteristic
52#2280C2212yes—
53C2×#380C2212yes—
54C2×C4×C4⋊C4—21no—
55C2×C4×C4⋊C4C2211yescharacteristic
56#2077C2214yescomplemented
57#2077C2214yescomplemented
58#2076C2214yescomplemented
59#2075C2214yescomplemented
60#2036C2214yescomplemented
61#2035C2214yescomplemented
62#2034C2214yescomplemented
63#2033C2214yescomplemented
64#1955C2214yes—
65#1954C2212yes—
66#1954C2212yes—
67#1949C2214yescomplemented
68#1948C2212yescomplemented
69#1947C2212yescomplemented
70#1875C2214yescomplemented
71#1875C2214yescomplemented
72#1873C2214yescomplemented
73#1873C2214yescomplemented
74#1836C2214yescomplemented
75#1834C2212yescomplemented
76#1834C2212yescomplemented
77#1825C2214yescomplemented
78#1825C2214yescomplemented
79#1825C2214yescomplemented
80#1825C2214yescomplemented
81#1803C2212yescomplemented
82#1803C2212yescomplemented
83#1802C2212yescomplemented
84#1802C2212yescomplemented
85#1763C2212yescomplemented
86#1762C2212yescomplemented
87C4×#103C2212yescomplemented
88C4×#102C2212yescomplemented
89#1736C2212yes—
90#1736C2212yes—
91#1736C2211yescharacteristic
92#1736C2212yes—
93#1736C2212yes—
94#1736C2211yescharacteristic
95C22×#41C2311yescharacteristic
96C23×D4D411yescharacteristic
97C24×C4C2312yes—
98C22×M16C2311yescharacteristic
99C22×M16C2311yescharacteristic
100C22×M16C2312yes—
101#525—28no—
102#525—44no—
103C2×#123—22no—
104C2×C22⋊Q8C2312yes—
105C2×C22⋊Q8C2312yes—
106C2×#121—21no—
107C2×#121—21no—
108C2×#121C2312yes—
109C2×#121C2312yes—
110C2×#120—22no—
111C4×#41—24no—
112C4×#41—24no—
113C2×C4×Q8C2311yescharacteristic
114C2×C4×Q8C2311yescharacteristic
115C2×C4×D4—22no—
116C2×C4×D4—22no—
117C2×C4×D4—21no—
118C2×C4×D4—21no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4D412yes—
122C2×C4×D4D411yescharacteristic
123C2×C4×D4D411yescharacteristic
124C2×C4×D4C2311yescharacteristic
125C2×C4×D4C2311yescharacteristic
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2311yescharacteristic
128C2×C4×D4C2312yes—
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—21no—
132C2×#117—28no—
133C2×#117—44no—
134C2×#117C2312yes—
135C2×#117C2311yescharacteristic
136C2×#117C2314yes—
137C2×#117C2314yes—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—22no—
145C22×C22⋊C4—22no—
146C22×C22⋊C4D412yes—
147C22×C42—22no—
148C22×C42—21no—
149C22×C42—21no—
150C22×C42C2311yescharacteristic
151#428—44no—
152C2×#107C2314yes—
153C2×#106C2314yes—
154#423—24no—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2312yes—
157#417—24no—
158#417—24no—
159#417—44no—
160C2×#103C2312yes—
161C2×#103C2312yes—
162C2×#103C2314yes—
163C2×#102C2312yes—
164C2×#102C2312yes—
165C2×#102C2314yes—
166#407—44no—
167#407—44no—
168C2×C22⋊C8C2314yes—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171C2×C22⋊C8C2314yes—
172C4×M16—24no—
173C2×#97C2312yes—
174C2×C4×C8C2312yes—
175#398—22no—
176#397—22no—
177#396—22no—
178#396—22no—
179#394—22no—
180#394—22no—
181#394—22no—
182#392—22no—
183#390—22no—
184#390—22no—
185#390—24no—
186#390—21no—
187#390—21no—
188#389—21no—
189#389—21no—
190#388—24no—
191#388—24no—
192#388—24no—
193#388—24no—
194#388—22no—
195#388—22no—
196#386—22no—
197#386—22no—
198#384—21no—
199#384—21no—
200#384C2312yes—
201#384C2312yes—
202#384C2311yescharacteristic
203#384C2311yescharacteristic
204#382C2312yes—
205#381—22no—
206#380—22no—
207#380—22no—
208#380—21no—
209#380—21no—
210#380—21no—
211#380—21no—
212#380C2312yes—
213#380C2314yes—
214#380C2312yes—
215#380C2314yes—
216#380C2312yes—
217#380C2312yes—
218#379—22no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4—24no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230C2×#95—22no—
231C2×#95—21no—
232#340C2314yes—
233#340C2314yes—
234#340C2312yes—
235#340C2314yes—
236#340C2312yes—
237#340C2314yes—
238#340C2312yes—
239#340C2312yes—
240#340C2314yes—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244C25C2×D412yes—
245C2×#41—22no—
246C2×#41—22no—
247C2×#41—22no—
248C2×#41—22no—
249C2×#41—22no—
250C2×#41#4114yes—
251C22×Q8C2411yescharacteristic
252C22×D4—21no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4C2×D411yescharacteristic
259C22×D4C2×D411yescharacteristic
260C22×D4C2×D412yes—
261C22×D4C2411yescharacteristic
262C23×C4—21no—
263C23×C4—21no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4C2×D412yes—
275C23×C4C2×D412yes—
276C23×C4C2×D412yes—
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×M16—22no—
283C2×M16—22no—
284C2×M16—22no—
285C2×M16—22no—
286C2×M16—24no—
287C2×M16—22no—
288C2×M16—22no—
289C2×M16—24no—
290C2×M16—24no—
291C22×C8C2412yes—
292C22×C8C2412yes—
293C22×C8C2414yes—
294#123—48no—
295C22⋊Q8—24no—
296C22⋊Q8—24no—
297C22⋊Q8—42no—
298C22⋊Q8—42no—
299#121—24no—
300#121—24no—
301#121—42no—
302#121—42no—
303#121—44no—
304#121—44no—
305#120—48no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×D4—24no—
311C4×D4—24no—
312C4×D4—28no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—48no—
324C4×D4—48no—
325C4×D4—44no—
326C4×D4—44no—
327#117—22no—
328#117—22no—
329#117—24no—
330#117—24no—
331#117—28no—
332#117—28no—
333#117—44no—
334#117—44no—
335#117—48no—
336#117—48no—
337#117—44no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
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—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—82no—
361C2×C4⋊C4C2×D411yescharacteristic
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4C2×D412yes—
364C2×C4⋊C4#4114yes—
365C2×C4⋊C4C2414yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—48no—
390C2×C22⋊C4—84no—
391C2×C22⋊C4C2×D412yes—
392C2×C22⋊C4C2×D412yes—
393C2×C22⋊C4C2×D412yes—
394C2×C22⋊C4C2×D412yes—
395C2×C42—21no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—48no—
404C2×C42—44no—
405C2×C42—44no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42#4114yes—
409C2×C42#4114yes—
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412#107—44no—
413#106—44no—
414C4⋊C8—24no—
415C4⋊C8—24no—
416#103—24no—
417#103—24no—
418#103—44no—
419#102—24no—
420#102—24no—
421#102—44no—
422C22⋊C8—44no—
423C22⋊C8—44no—
424C22⋊C8—44no—
425C22⋊C8—44no—
426#97—24no—
427C4×C8—24no—
428#95—24no—
429#95—24no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438C24—24no—
439C24—21no—
440C24—24no—
441C24—24no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24C22×D412yes—
447C24C22×D412yes—
448C24C22×D411yescharacteristic
449#41—28no—
450#41—28no—
451#41—44no—
452#41—44no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×#4112yes—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—416no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—82no—
482C2×D4—82no—
483C2×D4C2×#4112yes—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
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—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—42no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4#12314yes—
540C22×C4#12314yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C2×#4112yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4H(5,𝔽2)12yes—
553C22×C4H(5,𝔽2)12yes—
554C22×C4C2511yescharacteristic
555M16—48no—
556M16—44no—
557M16—44no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—24no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—24no—
566C2×C8—24no—
567C4⋊C4—24no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—81no—
595C4⋊C4—81no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4C2×#4114yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—42no—
612C22⋊C4—44no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C42—48no—
620C42—48no—
621C42—44no—
622C42—42no—
623C42—42no—
624C42—42no—
625C42—44no—
626C42—44no—
627C42#12314yes—
628C42#12314yes—
629C42C2×#4112yes—
630C42C2×#4112yes—
631C42C2×#4112yes—
632C42C2×#4112yes—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—48no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—84no—
662C23—84no—
663C23—84no—
664C23—84no—
665C23C2×#12312yes—
666C23#54612yes—
667C23#54612yes—
668C23C23×D411yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—48no—
676D4—48no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—88no—
682D4—88no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—48no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—84no—
735C2×C4—88no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4C2×#12312yes—
739C2×C4C2×#12312yes—
740C2×C4C2×#12312yes—
741C2×C4C2×#12312yes—
742C2×C4C2×#12312yes—
743C2×C4#52914yes—
744C2×C4#54014yes—
745C2×C4#54612yes—
746C2×C4#54612yes—
747C2×C4#55314yes—
748C2×C4#55514yes—
749C2×C4#57512yes—
750C2×C4#57512yes—
751C2×C4C22×#4111yescharacteristic
752C2×C4C22×#4111yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C8—44no—
758C8—42no—
759C8—42no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22#242014yes—
789C22C22×#12311yescharacteristic
790C22C2×#54611yescharacteristic
791C22C2×#54611yescharacteristic
792C22C2×#57511yescharacteristic
793C22C2×#57511yescharacteristic
794C22#358511yescharacteristic
795C22#358611yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—81no—
804C4—81no—
805C4—84no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4#242014yes—
810C4#309314yes—
811C4C2×#52911yescharacteristic
812C4C2×#54011yescharacteristic
813C4C2×#55311yescharacteristic
814C4C2×#55511yescharacteristic
815C2—24no—
816C2—82no—
817C2—82no—
818C2—82no—
819C2C2×#242011yescharacteristic
820C2C2×#309311yescharacteristic
821C2#6051711yescharacteristic
822C2#6115911yescharacteristic
823C2#6116011yescharacteristic
824C2#6116511yescharacteristic
825C2#6116611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34935C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2354C2semidirect
3. #24980C2semidirect
4. #24978C2semidirect
5. #24972C2semidirect
6. #24970C2semidirect
7. #24968C2semidirect
8. #24966C2semidirect
9. #23642C2semidirect
10. #23482C2semidirect
11. #21190C2semidirect
12. #21170C2semidirect
13. #20910C2semidirect
14. #20764C2semidirect
15. #20701C2semidirect
16. #20648C2semidirect
17. C4×#417C2semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2076C22semidirect
59. #2075C22semidirect
60. #2036C22semidirect
61. #2035C22semidirect
62. #2034C22semidirect
63. #2033C22semidirect
67. #1949C22semidirect
68. #1948C22semidirect
69. #1947C22semidirect
70. #1875C22semidirect
71. #1875C22semidirect
72. #1873C22semidirect
73. #1873C22semidirect
74. #1836C22semidirect
75. #1834C22semidirect
76. #1834C22semidirect
77. #1825C22semidirect
78. #1825C22semidirect
79. #1825C22semidirect
80. #1825C22semidirect
81. #1803C22semidirect
82. #1803C22semidirect
83. #1802C22semidirect
84. #1802C22semidirect
85. #1763C22semidirect
86. #1762C22semidirect
87. C4×#103C22semidirect
88. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#349352
C2×#23542
#249802
#249782
#249722
#249702
#249682
#249662
#236422
#234822
#211902
#211702
#209102
#207642
#207012
#206482
C4×#4172