Finite Group Databasebeta

← #6482932

Subgroups — #6482932

Order 512.

1712 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2#34012C211yesmaximal, characteristic
3#33101C214yesmaximal, complemented
4#29897C214yesmaximal
5#27892C211yesmaximal, characteristic, complemented
6#27892C211yesmaximal, characteristic, complemented
7#27889C211yesmaximal, characteristic, complemented
8#27889C211yesmaximal, characteristic, complemented
9#27878C211yesmaximal, characteristic, complemented
10#27877C211yesmaximal, characteristic, complemented
11#27876C211yesmaximal, characteristic, complemented
12#27875C211yesmaximal, characteristic, complemented
13#27635C214yesmaximal, complemented
14#27634C214yesmaximal, complemented
15#21984C211yesmaximal, characteristic, complemented
16#21984C211yesmaximal, characteristic, complemented
17#21864C211yesmaximal, characteristic, complemented
18#21864C211yesmaximal, characteristic, complemented
19#20714C211yesmaximal, characteristic
20C2×#533C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#431C2211yescharacteristic
23C2×#431C2211yescharacteristic
24#2857C2211yescharacteristic
25#2857C2211yescharacteristic
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2855—21no—
29#2855C2212yes—
30#2851—21no—
31#2851—21no—
32#2848—21no—
33#2848C2212yes—
34C4×C22⋊Q8—21no—
35C4×C22⋊Q8—21no—
36C4×C22⋊Q8C2212yes—
37C4×C22⋊Q8C2212yes—
38#2296—21no—
39#2285C2211yescharacteristic
40#2285C2211yescharacteristic
41#2285C2211yescharacteristic
42#2285C2211yescharacteristic
43#2285C2211yescharacteristic
44#2285C2211yescharacteristic
45#2285C2211yescharacteristic
46#2283—21no—
47#2283—21no—
48#2283—21no—
49#2283—21no—
50#2283C2212yes—
51#2283C2212yes—
52#2280—21no—
53#2280—21no—
54#2280—21no—
55#2280C2212yes—
56C4×#117—21no—
57C4×#117—21no—
58C4×#117C2212yes—
59#2077C2214yes—
60#2077C2214yes—
61#2076C2214yes—
62#2075C2214yes—
63#2036C2214yes—
64#2036C2214yes—
65#2035C2214yes—
66#2035C2214yes—
67#1990C2211yescharacteristic, complemented
68#1990C2211yescharacteristic, complemented
69#1990C2211yescharacteristic, complemented
70#1990C2211yescharacteristic, complemented
71#1956C2211yescharacteristic, complemented
72#1956C2211yescharacteristic, complemented
73#1956C2211yescharacteristic, complemented
74#1956C2211yescharacteristic, complemented
75#1949C2214yescomplemented
76#1949C2214yescomplemented
77#1928C2214yescomplemented
78#1928C2214yescomplemented
79#1927C2214yescomplemented
80#1927C2214yescomplemented
81#1921C2214yescomplemented
82#1920C2214yescomplemented
83#1919C2214yescomplemented
84#1918C2214yescomplemented
85#1873C2214yes—
86#1873C2214yes—
87#1854C2214yes—
88#1854C2214yes—
89#1845C2211yescharacteristic, complemented
90#1845C2211yescharacteristic, complemented
91#1844C2211yescharacteristic, complemented
92#1844C2211yescharacteristic, complemented
93#1834C2211yescharacteristic, complemented
94#1834C2211yescharacteristic, complemented
95#1834C2211yescharacteristic, complemented
96#1834C2211yescharacteristic, complemented
97#1817C2212yes—
98#1805C2214yescomplemented
99#1805C2214yescomplemented
100#1797C2212yes—
101#1797C2212yes—
102#1779C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110#533—24no—
111#533—24no—
112C2×C4⋊Q8C2311yescharacteristic
113C2×C4⋊Q8C2311yescharacteristic
114C2×#125—21no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C4×Q8—21no—
122C2×C4×Q8C2312yes—
123C2×#117—21no—
124C2×#117—21no—
125C2×#117—21no—
126C2×#117—21no—
127C2×#117—21no—
128C2×#117—21no—
129C2×#117C2312yes—
130C2×#117C2312yes—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42D411yescharacteristic
134C22×C42D411yescharacteristic
135C22×C42D411yescharacteristic
136C22×C42D411yescharacteristic
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145#431—24no—
146#431—24no—
147C2×#107C2314yes—
148C2×#107C2314yes—
149C2×#106C2314yes—
150C2×#106C2314yes—
151C2×C4⋊C8C2312yes—
152C2×C4⋊C8C2312yes—
153C2×#103C2314yes—
154C2×#103C2314yes—
155C2×#103C2314yes—
156C2×#103C2314yes—
157C2×C22⋊C8C2312yes—
158C2×C22⋊C8C2312yes—
159C2×C22⋊C8C2312yes—
160C2×C22⋊C8C2312yes—
161C2×C22⋊C8C2312yes—
162C2×C22⋊C8C2312yes—
163C2×C4×C8C2311yescharacteristic
164C2×C4×C8C2311yescharacteristic
165C2×C4×C8C2311yescharacteristic
166C2×C4×C8C2311yescharacteristic
167#391—21no—
168#391—21no—
169#391C2312yes—
170#391C2312yes—
171#389—21no—
172#389—21no—
173#389—21no—
174#389—21no—
175#389—21no—
176#389—21no—
177#389C2312yes—
178#389C2312yes—
179#387—22no—
180#387—22no—
181#387—22no—
182#387—22no—
183#385—22no—
184#385—22no—
185#385—22no—
186#385—22no—
187#385—22no—
188#385—22no—
189#384C2311yescharacteristic
190#384C2311yescharacteristic
191#384C2311yescharacteristic
192#384C2311yescharacteristic
193#384C2311yescharacteristic
194#384C2311yescharacteristic
195#383—22no—
196#383—22no—
197#382—21no—
198#382—21no—
199#382—21no—
200#382—21no—
201#382—21no—
202#382C2312yes—
203#382C2312yes—
204#381—22no—
205#381—22no—
206#381—22no—
207#381—22no—
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#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228#380C2312yes—
229#380C2312yes—
230#379—22no—
231#379—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256#376—22no—
257#376—22no—
258#376—22no—
259C43—22no—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#336C2312yes—
269#336C2312yes—
270#336C2312yes—
271#336C2312yes—
272C25C2×D411yescharacteristic
273C22×Q8—21no—
274C22×Q8C2412yes—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
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×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311#125—44no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—44no—
315C22⋊Q8—44no—
316C22⋊Q8—44no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C4×Q8—24no—
320C4×Q8—24no—
321C4×Q8—44no—
322#117—44no—
323#117—44no—
324#117—44no—
325#117—44no—
326#117—44no—
327#117—44no—
328#117—44no—
329#117—44no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42C2×D411yescharacteristic
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42C2×D411yescharacteristic
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42#4114yes—
407C2×C42#4114yes—
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412#107—44no—
413#107—44no—
414#106—44no—
415#106—44no—
416C4⋊C8—24no—
417C4⋊C8—24no—
418#103—44no—
419#103—44no—
420#103—44no—
421#103—44no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424C22⋊C8—42no—
425C22⋊C8—42no—
426C22⋊C8—42no—
427C22⋊C8—42no—
428C4×C8—22no—
429C4×C8—22no—
430C4×C8—22no—
431C4×C8—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
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—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24C22×D411yescharacteristic
462C24C22×D411yescharacteristic
463C24C22×D411yescharacteristic
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—42no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
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—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
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—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—416no—
531C22×C4—416no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4#12314yes—
535C22×C4#12314yes—
536C22×C4#13514yes—
537C22×C4#13714yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2511yescharacteristic
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—44no—
620C42—44no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—44no—
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—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23C2×#12312yes—
659C23C2×#13512yes—
660C23C2×#13712yes—
661C23C23×D411yescharacteristic
662Q8—44no—
663Q8—44no—
664Q8—84no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—28no—
676C2×C4—28no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4C2×#12312yes—
733C2×C4C2×#12312yes—
734C2×C4C2×#12312yes—
735C2×C4C2×#12312yes—
736C2×C4C2×#12312yes—
737C2×C4C2×#13512yes—
738C2×C4C2×#13512yes—
739C2×C4C2×#13712yes—
740C2×C4C2×#13712yes—
741C2×C4#57512yes—
742C2×C4#57512yes—
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4#58512yes—
746C2×C4#58512yes—
747C8—42no—
748C8—42no—
749C8—42no—
750C8—42no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—416no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22C22×#12311yescharacteristic
774C22#344911yescharacteristic
775C22#344911yescharacteristic
776C22C22×#13511yescharacteristic
777C22C22×#13711yescharacteristic
778C22C2×#57511yescharacteristic
779C22C2×#57511yescharacteristic
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#309114yes—
798C4#309514yes—
799C4#349312yes—
800C4#349312yes—
801C2—42no—
802C2—42no—
803C2—42no—
804C2#3515711yescharacteristic
805C2C2×#309111yescharacteristic
806C2C2×#309511yescharacteristic
807C2#6094411yescharacteristic
808C2#6094711yescharacteristic
809C2#6096611yescharacteristic
810C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
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
3. #33101C2semidirect
5. #27892C2semidirect
6. #27892C2semidirect
7. #27889C2semidirect
8. #27889C2semidirect
9. #27878C2semidirect
10. #27877C2semidirect
11. #27876C2semidirect
12. #27875C2semidirect
13. #27635C2semidirect
14. #27634C2semidirect
15. #21984C2semidirect
16. #21984C2semidirect
17. #21864C2semidirect
18. #21864C2semidirect
67. #1990C22semidirect
68. #1990C22semidirect
69. #1990C22semidirect
70. #1990C22semidirect
71. #1956C22semidirect
72. #1956C22semidirect
73. #1956C22semidirect
74. #1956C22semidirect
75. #1949C22semidirect
76. #1949C22semidirect
77. #1928C22semidirect
78. #1928C22semidirect
79. #1927C22semidirect
80. #1927C22semidirect
81. #1921C22semidirect
82. #1920C22semidirect
83. #1919C22semidirect
84. #1918C22semidirect
89. #1845C22semidirect
90. #1845C22semidirect
91. #1844C22semidirect
92. #1844C22semidirect
93. #1834C22semidirect
94. #1834C22semidirect
95. #1834C22semidirect
96. #1834C22semidirect
98. #1805C22semidirect
99. #1805C22semidirect

Maximal subgroups

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

subgroupindex
#366252
#340122
#331012
#298972
#278922
#278892
#278782
#278772
#278762
#278752
#276352
#276342
#219842
#218642
#207142