Finite Group Databasebeta

← #6660952

Subgroups — #6660952

Order 512.

1938 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic
2C2×#2851C211yesmaximal, characteristic, complemented
3#32747C214yesmaximal, complemented
4#30362C214yesmaximal, complemented
5#29972C212yesmaximal, complemented
6#29956C212yesmaximal, complemented
7#29912C212yesmaximal, complemented
8#29640C212yesmaximal, complemented
9#29303C212yesmaximal, complemented
10#29110C212yesmaximal, complemented
11#27601C211yesmaximal, characteristic, complemented
12#27600C211yesmaximal, characteristic, complemented
13#24608C212yesmaximal, complemented
14#24607C212yesmaximal, complemented
15#24005C211yesmaximal, characteristic
16#24002C211yesmaximal, characteristic
17#20715C211yesmaximal, characteristic, complemented
18C22×#125C2211yescharacteristic, complemented
19C22×#123—21no—
20C22×#121C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#481C2212yes—
23C2×#480C2212yes—
24C2×#432C2212yescomplemented
25#2854—21no—
26#2854—21no—
27#2854—21no—
28#2854—21no—
29#2854C2212yes—
30#2854C2212yes—
31#2854C2212yes—
32#2854C2212yes—
33#2851—21no—
34#2851—21no—
35#2851—21no—
36#2851—21no—
37#2851C2212yes—
38#2851C2212yes—
39#2851C2212yescomplemented
40#2851C2212yescomplemented
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic, complemented
46C2×#389C2211yescharacteristic, complemented
47C2×#388—21no—
48C2×#388—21no—
49C2×#387—21no—
50C2×#387—21no—
51C2×#386—21no—
52C2×#385—21no—
53C2×#385—21no—
54C2×#382C2211yescharacteristic, complemented
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58#2101C2214yescomplemented
59#2092C2214yescomplemented
60#2088C2214yescomplemented
61#2087C2214yescomplemented
62#2085C2214yescomplemented
63#2077C2214yescomplemented
64#2075C2214yescomplemented
65#2073C2214yescomplemented
66#2067C2214yescomplemented
67#2065C2214yescomplemented
68#2059C2214yescomplemented
69#2059C2214yescomplemented
70#2034C2214yes—
71#2033C2214yes—
72#2025C2214yescomplemented
73#2025C2214yescomplemented
74#1944C2214yescomplemented
75#1943C2214yescomplemented
76#1936C2214yescomplemented
77#1936C2214yescomplemented
78#1874C2212yes—
79#1874C2212yes—
80#1853C2212yes—
81#1853C2212yes—
82#1853C2212yescomplemented
83#1852C2212yes—
84#1852C2212yes—
85#1852C2212yescomplemented
86#1824C2212yescomplemented
87#1823C2212yes—
88#1823C2212yes—
89#1823C2212yescomplemented
90#1817C2212yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1786C2212yes—
94#1786C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97#1749C2212yes—
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C2×#125—21no—
105C2×#125—21no—
106C2×#125—44no—
107C2×#125C2312yes—
108C2×#125C2312yes—
109C2×#123—22no—
110C2×#123—22no—
111C2×#123—22no—
112C2×#123—22no—
113C2×#123—48no—
114C2×#121—21no—
115C2×#121—21no—
116C2×#121—44no—
117C2×#121C2312yes—
118C2×#121C2312yes—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C42—44no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#481—44no—
154#480—44no—
155#432—44no—
156C2×#107C2314yes—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×#106C2314yes—
160C2×C4⋊C8C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×#97C2314yes—
172#390—21no—
173#390—21no—
174#390—21no—
175#390—21no—
176#390C2312yes—
177#390C2312yes—
178#390C2312yes—
179#390C2312yes—
180#389—21no—
181#389—21no—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#388—22no—
197#388—22no—
198#388—22no—
199#388—22no—
200#388—22no—
201#388—22no—
202#388—22no—
203#388—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#387—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#386—22no—
213#386—22no—
214#386—22no—
215#386—22no—
216#385—22no—
217#385—22no—
218#385—22no—
219#385—22no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#382—21no—
225#382—21no—
226#382C2312yes—
227#382C2312yes—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235#380C2312yes—
236#380C2312yes—
237#380C2312yes—
238#380C2312yes—
239#380C2312yes—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95—21no—
243C2×#95—21no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#336C2314yes—
258#336C2314yes—
259C25—21no—
260C25C2×D411yescharacteristic
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—21no—
264C22×D4—24no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4C2412yes—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
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×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22×C8C2414yes—
306C22×C8C2414yes—
307#125—44no—
308#125—44no—
309#125—44no—
310#125—44no—
311#123—48no—
312#123—48no—
313#123—48no—
314#123—48no—
315#121—24no—
316#121—24no—
317#121—42no—
318#121—42no—
319#121—44no—
320#121—44no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
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—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
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×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412#107—44no—
413#107—44no—
414#106—44no—
415#106—44no—
416C4⋊C8—44no—
417#102—44no—
418#102—44no—
419#102—44no—
420#102—44no—
421C22⋊C8—24no—
422C22⋊C8—24no—
423C22⋊C8—24no—
424C22⋊C8—24no—
425C22⋊C8—42no—
426C22⋊C8—42no—
427#97—44no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—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—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—41no—
452C24—41no—
453C24—42no—
454C24—42no—
455C24—42no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24AGL(1,ℤ/8)14yes—
461C24C22×D411yescharacteristic
462C24C22×D411yescharacteristic
463C24C22×D411yescharacteristic
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—88no—
478C2×D4—816no—
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—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—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—41no—
517C22×C4—41no—
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—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—416no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
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—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
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×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4H(5,𝔽2)14yes—
574C22×C42−1+414yes—
575C22×C4C2511yescharacteristic
576C2×C8—24no—
577C2×C8—24no—
578C2×C8—24no—
579C2×C8—24no—
580C2×C8—24no—
581C2×C8—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—42no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—41no—
639C42—41no—
640C42—41no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—28no—
653C23—28no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23#53412yes—
677C23#53612yes—
678C23C2×AGL(1,ℤ/8)12yes—
679C23C2×AGL(1,ℤ/8)12yes—
680C23C2×AGL(1,ℤ/8)12yes—
681C23#57512yes—
682C23#57512yes—
683C23C23×D411yescharacteristic
684D4—44no—
685D4—44no—
686D4—84no—
687D4—88no—
688D4—88no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
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—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4#53412yes—
766C2×C4#53612yes—
767C2×C4#57512yes—
768C2×C4C2×H(5,𝔽2)12yes—
769C2×C4C2×2−1+412yes—
770C2×C4#58512yes—
771C8—44no—
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—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22—168no—
801C22#319414yes—
802C22#323414yes—
803C22C2×#53411yescharacteristic
804C22C2×#53611yescharacteristic
805C22#344911yescharacteristic
806C22C22×AGL(1,ℤ/8)11yescharacteristic
807C22C2×#57511yescharacteristic
808C22C2×#57511yescharacteristic
809C22C2×#57511yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4#353514yes—
829C2—24no—
830C2—24no—
831C2—42no—
832C2—162no—
833C2#3744111yescharacteristic
834C2C2×#319411yescharacteristic
835C2#6075211yescharacteristic
836C2C2×#323411yescharacteristic
837C2#6086611yescharacteristic
838C2#6095811yescharacteristic
839C2#6096411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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×#2851C2semidirect
3. #32747C2semidirect
4. #30362C2semidirect
5. #29972C2semidirect
6. #29956C2semidirect
7. #29912C2semidirect
8. #29640C2semidirect
9. #29303C2semidirect
10. #29110C2semidirect
11. #27601C2semidirect
12. #27600C2semidirect
13. #24608C2semidirect
14. #24607C2semidirect
17. #20715C2semidirect
18. C22×#125C22semidirect
24. C2×#432C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
54. C2×#382C22semidirect
58. #2101C22semidirect
59. #2092C22semidirect
60. #2088C22semidirect
61. #2087C22semidirect
62. #2085C22semidirect
63. #2077C22semidirect
64. #2075C22semidirect
65. #2073C22semidirect
66. #2067C22semidirect
67. #2065C22semidirect
68. #2059C22semidirect
69. #2059C22semidirect
72. #2025C22semidirect
73. #2025C22semidirect
74. #1944C22semidirect
75. #1943C22semidirect
76. #1936C22semidirect
77. #1936C22semidirect
82. #1853C22semidirect
85. #1852C22semidirect
86. #1824C22semidirect
89. #1823C22semidirect
90. #1817C22semidirect
92. #1797C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#28512
#327472
#303622
#299722
#299562
#299122
#296402
#293032
#291102
#276012
#276002
#246082
#246072
#240052
#240022
#207152