Finite Group Databasebeta

← #6457041

Subgroups — #6457041

Order 512.

2622 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34175C211yesmaximal, characteristic
2C2×#2311C211yesmaximal, characteristic
3#27609C214yesmaximal, complemented
4#27606C214yesmaximal, complemented
5#27604C212yesmaximal, complemented
6#27602C212yesmaximal, complemented
7#27601C212yesmaximal, complemented
8#27601C212yesmaximal, complemented
9#23643C212yesmaximal, complemented
10#23640C212yesmaximal, complemented
11#20848C212yesmaximal, complemented
12#20844C211yesmaximal, characteristic, complemented
13C2×#1853C211yesmaximal, characteristic, complemented
14#20703C212yesmaximal, complemented
15#20702C211yesmaximal, characteristic, complemented
16#20699C211yesmaximal, characteristic, complemented
17#20581C211yesmaximal, characteristic
18C23×#41C2211yescharacteristic
19C2×#520C2211yescharacteristic
20C2×#520C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C2×#428C2212yescomplemented
24C22×#106C2212yescomplemented
25C2×#408C2212yes—
26C2×#408C2212yes—
27C2×#407C2211yescharacteristic
28C22×C22⋊C8C2211yescharacteristic
29#2341—21no—
30Q8×C22⋊C4—21no—
31#2339—22no—
32#2339—21no—
33D4×C22⋊C4—22no—
34D4×C22⋊C4—21no—
35#2311—22no—
36#2311—21no—
37#2311—21no—
38#2311C2211yescharacteristic
39#2311C2212yes—
40#2311C2211yescharacteristic
41#2311C2212yes—
42#2311C2212yes—
43#2311C2212yes—
44#2311C2214yes—
45C2×#391—21no—
46C2×#390—21no—
47C2×#386—22no—
48#2280C2211yescharacteristic
49#2280C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54#2077C2214yescomplemented
55#2077C2214yescomplemented
56#2077C2214yescomplemented
57#2077C2214yescomplemented
58#2077C2214yescomplemented
59#2077C2214yescomplemented
60#2076C2214yescomplemented
61#2075C2214yescomplemented
62#1854C2214yescomplemented
63#1854C2214yescomplemented
64#1853C2212yes—
65#1853C2212yes—
66#1853C2212yes—
67#1853C2214yescomplemented
68#1853C2212yescomplemented
69#1853C2214yescomplemented
70#1853C2214yescomplemented
71#1852C2212yes—
72#1852C2212yescomplemented
73#1825C2214yescomplemented
74#1825C2214yescomplemented
75#1825C2212yescomplemented
76#1825C2214yescomplemented
77#1825C2212yescomplemented
78#1824C2211yescharacteristic
79#1824C2212yes—
80#1824C2211yescharacteristic
81#1824C2214yescomplemented
82#1823C2211yescharacteristic
83#1823C2212yes—
84#1823C2211yescharacteristic
85#1823C2214yescomplemented
86#1780C2214yes—
87#1779C2212yes—
88#1779C2212yes—
89#1736C2212yescomplemented
90#1736C2212yescomplemented
91#1736C2212yescomplemented
92#1735C2212yescomplemented
93#1735C2212yescomplemented
94C2×#340C2212yescomplemented
95C22×#41—28no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—44no—
99C22×#41D411yescharacteristic
100C22×#41D412yes—
101C22×#41D411yescharacteristic
102C22×#41C2311yescharacteristic
103C22×#41C2312yes—
104C22×#41C2311yescharacteristic
105C23×Q8D411yescharacteristic
106C23×D4D412yes—
107C23×D4D411yescharacteristic
108C24×C4—21no—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C22×M16C2312yes—
112C23×C8C2312yes—
113#520—28no—
114#520—44no—
115C2×C4×Q8—21no—
116C2×C4×Q8—21no—
117C2×C4×D4—22no—
118C2×C4×D4—21no—
119C2×C4×D4—22no—
120C2×C4×D4—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—24no—
124C2×#117—24no—
125C2×#117C2312yes—
126C2×#117C2312yes—
127C2×#117C2312yes—
128C2×#117C2311yescharacteristic
129C2×#117C2311yescharacteristic
130C2×#117C2312yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—44no—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—22no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—22no—
148C22×C22⋊C4—22no—
149C22×C42—21no—
150#428—44no—
151C2×#107C2314yes—
152C2×#106—44no—
153C2×#106C2314yes—
154C2×#106C2314yes—
155C2×#106C2314yes—
156#408—28no—
157#408—44no—
158#407—24no—
159C2×C22⋊C8—24no—
160C2×C22⋊C8C2312yes—
161C2×C22⋊C8C2311yescharacteristic
162C2×C22⋊C8C2311yescharacteristic
163C2×C22⋊C8C2314yes—
164C2×C22⋊C8C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169#391—22no—
170#391—24no—
171#391—22no—
172#391—21no—
173#391—21no—
174#391—22no—
175#391—22no—
176#390—22no—
177#390—24no—
178#390—22no—
179#390—21no—
180#390—21no—
181#390—22no—
182#390—22no—
183#386—24no—
184#386—24no—
185#386—24no—
186#386—24no—
187#386—22no—
188#386—22no—
189#386—22no—
190#386—22no—
191#386—22no—
192#386—22no—
193#381—22no—
194#381—21no—
195#380—22no—
196#380—22no—
197#380—22no—
198#380—22no—
199#380—22no—
200#380—21no—
201#380—22no—
202#380—21no—
203#380C2312yes—
204#380C2314yes—
205#380C2314yes—
206#380C2312yes—
207#380C2312yes—
208#380C2312yes—
209#380C2314yes—
210#380C2314yes—
211#380C2311yescharacteristic
212#380C2312yes—
213#380C2311yescharacteristic
214#380C2311yescharacteristic
215#380C2311yescharacteristic
216#380C2312yes—
217#379—22no—
218#379—21no—
219C4×C22⋊C4—22no—
220C4×C22⋊C4—21no—
221C4×C22⋊C4—22no—
222C4×C22⋊C4—21no—
223C2×#95—22no—
224C2×#95—21no—
225C2×#95—22no—
226C2×#95—22no—
227#340C2312yes—
228#340C2314yes—
229#340C2314yes—
230#340C2312yes—
231#340C2314yes—
232#340C2314yes—
233#340C2312yes—
234#340C2312yes—
235#340C2312yes—
236#340C2314yes—
237#340C2312yes—
238#340C2314yes—
239#340C2312yes—
240#340C2312yes—
241#340C2314yes—
242#340C2314yes—
243C25C2×D412yes—
244C25C2×D411yescharacteristic
245C2×#41—24no—
246C2×#41—28no—
247C2×#41—24no—
248C2×#41—28no—
249C2×#41—24no—
250C2×#41—24no—
251C2×#41—22no—
252C2×#41—22no—
253C2×#41—28no—
254C2×#41—24no—
255C2×#41—24no—
256C2×#41—24no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—24no—
260C2×#41—24no—
261C2×#41—44no—
262C2×#41—44no—
263C2×#41—42no—
264C2×#41—42no—
265C2×#41—432no—
266C2×#41—432no—
267C2×#41#4118yes—
268C22×Q8—24no—
269C22×Q8—24no—
270C22×Q8—42no—
271C22×Q8C2×D411yescharacteristic
272C22×Q8C2×D412yes—
273C22×Q8C2×D411yescharacteristic
274C22×D4—28no—
275C22×D4—24no—
276C22×D4—28no—
277C22×D4—24no—
278C22×D4—42no—
279C22×D4—44no—
280C22×D4C2×D412yes—
281C22×D4C2×D411yescharacteristic
282C22×D4C2×D412yes—
283C22×D4C2×D412yes—
284C22×D4C2×D412yes—
285C22×D4C2×D412yes—
286C22×D4C2×D411yescharacteristic
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—28no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—44no—
302C23×C4—44no—
303C23×C4—82no—
304C23×C4—82no—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4#4114yes—
312C23×C4#4114yes—
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C2×M16—24no—
319C2×M16—24no—
320C2×M16—24no—
321C22×C8—24no—
322C22×C8—24no—
323C22×C8—24no—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2414yes—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×D4—48no—
330C4×D4—44no—
331C4×D4—48no—
332C4×D4—44no—
333#117—24no—
334#117—24no—
335#117—24no—
336#117—24no—
337#117—28no—
338#117—24no—
339#117—24no—
340#117—44no—
341#117—44no—
342#117—44no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2414yes—
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2411yescharacteristic
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2411yescharacteristic
375C2×C4⋊C4C2411yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—82no—
398C2×C22⋊C4—84no—
399C2×C22⋊C4—84no—
400C2×C22⋊C4—84no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—44no—
408#107—44no—
409#106—44no—
410#106—44no—
411#106—44no—
412C22⋊C8—22no—
413C22⋊C8—22no—
414C22⋊C8—24no—
415C22⋊C8—24no—
416C22⋊C8—24no—
417C22⋊C8—28no—
418C22⋊C8—28no—
419C22⋊C8—44no—
420C22⋊C8—44no—
421#95—21no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—21no—
431#95—22no—
432#95—22no—
433#95—21no—
434#95—21no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24#12314yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D411yescharacteristic
452C24C22×D411yescharacteristic
453C24C22×D411yescharacteristic
454#41—216no—
455#41—216no—
456#41—416no—
457#41—416no—
458#41—432no—
459#41—416no—
460#41—416no—
461#41—48no—
462#41—48no—
463C2×Q8—22no—
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—42no—
471C2×Q8—416no—
472C2×Q8#12314yes—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—416no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—432no—
494C2×D4#12318yes—
495C2×D4#12314yes—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—416no—
534C22×C4—416no—
535C22×C4—42no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—44no—
543C22×C4—42no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—82no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—82no—
557C22×C4—82no—
558C22×C4—81no—
559C22×C4—82no—
560C22×C4—81no—
561C22×C4—82no—
562C22×C4—816no—
563C22×C4#12314yes—
564C22×C4#12314yes—
565C22×C4#12314yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4118yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4112yes—
579C22×C4H(5,𝔽2)14yes—
580C22×C4C2511yescharacteristic
581M16—48no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—24no—
591C2×C8—48no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4—42no—
611C4⋊C4—44no—
612C4⋊C4—42no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—44no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—82no—
624C22⋊C4—81no—
625C22⋊C4—82no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—82no—
629C22⋊C4—82no—
630C22⋊C4—82no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—42no—
638C42—42no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—28no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—21no—
656C23—28no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—48no—
674C23—48no—
675C23—48no—
676C23—48no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23C2×#12312yes—
681C23C2×#12314yes—
682C23C2×#12312yes—
683C23C2×#12312yes—
684C23C2×#12312yes—
685C23#53412yes—
686C23#57712yes—
687C23#57712yes—
688C23C23×D411yescharacteristic
689Q8—28no—
690Q8—48no—
691Q8—44no—
692D4—216no—
693D4—28no—
694D4—48no—
695D4—48no—
696D4—48no—
697D4—48no—
698D4—44no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—28no—
711C2×C4—28no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—84no—
750C2×C4—88no—
751C2×C4—88no—
752C2×C4—88no—
753C2×C4—84no—
754C2×C4—162no—
755C2×C4—162no—
756C2×C4—164no—
757C2×C4—164no—
758C2×C4C2×#12312yes—
759C2×C4C2×#12314yes—
760C2×C4C2×#12312yes—
761C2×C4C2×#12312yes—
762C2×C4C2×#12312yes—
763C2×C4#53412yes—
764C2×C4#55118yes—
765C2×C4#55118yes—
766C2×C4C22×#4111yescharacteristic
767C2×C4C22×#4111yescharacteristic
768C2×C4C22×#4112yes—
769C2×C4C2×H(5,𝔽2)12yes—
770C8—42no—
771C8—42no—
772C8—44no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—24no—
788C22—24no—
789C22—22no—
790C22—24no—
791C22—416no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—816no—
808C22#248314yes—
809C22#309914yes—
810C22C22×#12311yescharacteristic
811C22C22×#12311yescharacteristic
812C22C2×#53411yescharacteristic
813C22C2×#57711yescharacteristic
814C22C2×#57711yescharacteristic
815C22#358511yescharacteristic
816C22#358611yescharacteristic
817C4—22no—
818C4—22no—
819C4—24no—
820C4—42no—
821C4—81no—
822C4—84no—
823C4—82no—
824C4—81no—
825C4—82no—
826C4—82no—
827C4—81no—
828C4—82no—
829C4—81no—
830C4#248314yes—
831C4C2×#55112yes—
832C4C2×#55112yes—
833C2—24no—
834C2—24no—
835C2—42no—
836C2—44no—
837C2—82no—
838C2C2×#248311yescharacteristic
839C2C2×#309911yescharacteristic
840C2#6052011yescharacteristic
841C2#6052211yescharacteristic
842C2#6052511yescharacteristic
843C2#6075711yescharacteristic
844C2#6075811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #27609C2semidirect
4. #27606C2semidirect
5. #27604C2semidirect
6. #27602C2semidirect
7. #27601C2semidirect
8. #27601C2semidirect
9. #23643C2semidirect
10. #23640C2semidirect
11. #20848C2semidirect
12. #20844C2semidirect
13. C2×#1853C2semidirect
14. #20703C2semidirect
15. #20702C2semidirect
16. #20699C2semidirect
23. C2×#428C22semidirect
24. C22×#106C22semidirect
54. #2077C22semidirect
55. #2077C22semidirect
56. #2077C22semidirect
57. #2077C22semidirect
58. #2077C22semidirect
59. #2077C22semidirect
60. #2076C22semidirect
61. #2075C22semidirect
62. #1854C22semidirect
63. #1854C22semidirect
67. #1853C22semidirect
68. #1853C22semidirect
69. #1853C22semidirect
70. #1853C22semidirect
72. #1852C22semidirect
73. #1825C22semidirect
74. #1825C22semidirect
75. #1825C22semidirect
76. #1825C22semidirect
77. #1825C22semidirect
81. #1824C22semidirect
85. #1823C22semidirect
89. #1736C22semidirect
90. #1736C22semidirect
91. #1736C22semidirect
92. #1735C22semidirect
93. #1735C22semidirect
94. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#341752
C2×#23112
#276092
#276062
#276042
#276022
#276012
#236432
#236402
#208482
#208442
C2×#18532
#207032
#207022
#206992
#205812