Finite Group Databasebeta

← #6458950

Subgroups — #6458950

Order 512.

2240 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#121C211yesmaximal, characteristic
2C2×#2283C211yesmaximal, characteristic, complemented
3#27684C212yesmaximal, complemented
4#27651C212yesmaximal, complemented
5#27633C214yesmaximal, complemented
6#27616C212yesmaximal, complemented
7#27601C211yesmaximal, characteristic, complemented
8#27600C211yesmaximal, characteristic, complemented
9#27588C212yesmaximal, complemented
10#24005C211yesmaximal, characteristic
11#24002C211yesmaximal, characteristic
12#23764C214yesmaximal, complemented
13#21580C212yesmaximal, complemented
14#21578C212yesmaximal, complemented
15#21363C212yesmaximal, complemented
16#20739C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4—21no—
20C22×C4×D4C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#481C2212yes—
23C2×#480C2212yes—
24C2×#432C2212yes—
25C4×#121—21no—
26C4×#121—21no—
27C4×#121—21no—
28C4×#121—21no—
29C4×#121C2212yes—
30C4×#121C2212yes—
31C4×#121C2212yes—
32C4×#121C2212yes—
33C2×#390C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#388—21no—
36C2×#386—21no—
37#2283—21no—
38#2283—21no—
39#2283—21no—
40#2283—21no—
41#2283C2212yes—
42#2283C2212yes—
43#2283C2212yescomplemented
44#2283C2212yescomplemented
45C2×#383—21no—
46C2×#382C2211yescharacteristic, complemented
47C2×#382C2211yescharacteristic, complemented
48C2×#381—21no—
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic, complemented
54C2×C4×C4⋊C4C2211yescharacteristic, complemented
55C2×C4×C22⋊C4—21no—
56C2×C4×C22⋊C4—21no—
57C2×#376—21no—
58#2101C2214yescomplemented
59#2092C2214yescomplemented
60#2085C2214yescomplemented
61#2077C2214yescomplemented
62#2075C2214yescomplemented
63#2073C2214yescomplemented
64#2034C2214yes—
65#2033C2214yes—
66#1949C2214yescomplemented
67#1949C2214yescomplemented
68#1926C2214yescomplemented
69#1925C2214yescomplemented
70#1921C2214yescomplemented
71#1920C2214yescomplemented
72#1874C2212yes—
73#1874C2212yes—
74#1853C2212yes—
75#1853C2212yes—
76#1853C2212yescomplemented
77#1852C2212yes—
78#1852C2212yes—
79#1852C2212yescomplemented
80#1824C2212yescomplemented
81#1823C2212yes—
82#1823C2212yes—
83#1823C2212yescomplemented
84#1817C2212yes—
85#1804C2214yescomplemented
86#1804C2214yescomplemented
87#1797C2212yescomplemented
88#1797C2212yescomplemented
89#1786C2212yes—
90#1786C2212yes—
91#1779C2211yescharacteristic
92#1779C2211yescharacteristic
93#1776C2214yescomplemented
94#1776C2214yescomplemented
95#1762C2214yescomplemented
96#1762C2214yescomplemented
97#1749C2212yescomplemented
98#1749C2212yescomplemented
99C23×D4—21no—
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C2×#121—21no—
106C2×#121—21no—
107C2×#121—28no—
108C2×#121C2312yes—
109C2×#121C2312yes—
110C2×C4×D4—22no—
111C2×C4×D4—22no—
112C2×C4×D4—22no—
113C2×C4×D4—22no—
114C2×C4×D4—21no—
115C2×C4×D4—21no—
116C2×C4×D4—28no—
117C2×C4×D4—48no—
118C2×C4×D4C2312yes—
119C2×C4×D4C2312yes—
120C22×C4⋊C4—21no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4—21no—
131C22×C22⋊C4—21no—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—21no—
134C22×C22⋊C4—21no—
135C22×C42—28no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151#481—28no—
152#480—28no—
153#432—28no—
154C2×#107C2314yes—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×C22⋊C8C2312yes—
164C2×C22⋊C8C2312yes—
165C2×C22⋊C8C2312yes—
166C2×C22⋊C8C2312yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×#97C2314yes—
170#390—21no—
171#390—21no—
172#390C2312yes—
173#390C2312yes—
174#389—21no—
175#389—21no—
176#389C2312yes—
177#389C2312yes—
178#388—22no—
179#388—22no—
180#388—22no—
181#388—22no—
182#386—22no—
183#386—22no—
184#386—22no—
185#386—22no—
186#383—22no—
187#383—22no—
188#383—22no—
189#383—22no—
190#382—21no—
191#382—21no—
192#382—21no—
193#382—21no—
194#382C2312yes—
195#382C2312yes—
196#382C2312yes—
197#382C2312yes—
198#381—22no—
199#381—22no—
200#381—22no—
201#381—22no—
202#380—21no—
203#380—21no—
204#380—21no—
205#380—21no—
206#380—21no—
207#380—21no—
208#380C2312yes—
209#380C2312yes—
210#380C2312yes—
211#380C2312yes—
212#380C2312yes—
213#380C2312yes—
214C4×C4⋊C4—21no—
215C4×C4⋊C4—21no—
216C4×C4⋊C4—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4C2312yes—
221C4×C4⋊C4C2312yes—
222C4×C4⋊C4C2312yes—
223C4×C4⋊C4C2312yes—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C22⋊C4—22no—
227C4×C22⋊C4—22no—
228C4×C22⋊C4—22no—
229C4×C22⋊C4—22no—
230C4×C22⋊C4—22no—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234#376—22no—
235#376—22no—
236#376—22no—
237#376—22no—
238C2×#95—21no—
239C2×#95—21no—
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—28no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—24no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4C2412yes—
271C23×C4—24no—
272C23×C4—21no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
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×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C22×C8C2414yes—
311C22×C8C2414yes—
312#121—28no—
313#121—28no—
314#121—24no—
315#121—24no—
316#121—24no—
317#121#4118yes—
318C4×D4—28no—
319C4×D4—28no—
320C4×D4—48no—
321C4×D4—48no—
322C4×D4—48no—
323C4×D4—48no—
324C4×D4—44no—
325C4×D4—44no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
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—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4C2412yes—
344C2×C4⋊C4C2412yes—
345C2×C4⋊C4C2412yes—
346C2×C4⋊C4C2412yes—
347C2×C4⋊C4C2412yes—
348C2×C4⋊C4C2412yes—
349C2×C4⋊C4C2412yes—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
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—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42C2×D411yescharacteristic
392C2×C42C2×D411yescharacteristic
393C2×C42C2×D411yescharacteristic
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×C42#4118yes—
404C2×C42C2411yescharacteristic
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408#107—28no—
409#107—44no—
410#106—28no—
411#106—44no—
412C4⋊C8—28no—
413#102—28no—
414#102—28no—
415#102—44no—
416#102—44no—
417C22⋊C8—24no—
418C22⋊C8—24no—
419C22⋊C8—24no—
420C22⋊C8—24no—
421C22⋊C8—42no—
422C22⋊C8—42no—
423#97—28no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
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—24no—
451C24—22no—
452C24—41no—
453C24—41no—
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—24no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—24no—
468C2×D4—22no—
469C2×D4—24no—
470C2×D4—416no—
471C2×D4—42no—
472C2×D4—432no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4C2×#4114yes—
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—24no—
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—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
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—416no—
538C22×C4—416no—
539C22×C4—416no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
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×C4—42no—
563C22×C4—42no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—816no—
567C22×C4#12314yes—
568C22×C4#12314yes—
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4C2511yescharacteristic
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4C2×#4114yes—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊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—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42#12314yes—
639C42#12314yes—
640C42C2×#4114yes—
641C42C2×#4114yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—28no—
651C23—28no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—24no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—48no—
665C23—48no—
666C23—48no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23C2×#12312yes—
678C23#52512yes—
679C23C2×AGL(1,ℤ/8)12yes—
680C23C2×AGL(1,ℤ/8)12yes—
681C23C2×AGL(1,ℤ/8)12yes—
682C23#57512yes—
683C23#57512yes—
684C23C23×D411yescharacteristic
685D4—28no—
686D4—48no—
687D4—416no—
688D4—416no—
689D4—44no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
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—28no—
707C2×C4—28no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—24no—
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—48no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
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—88no—
757C2×C4—88no—
758C2×C4—84no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4C2×#12312yes—
765C2×C4C2×#12312yes—
766C2×C4C2×#12312yes—
767C2×C4C2×#12312yes—
768C2×C4C2×#12312yes—
769C2×C4#52512yes—
770C2×C4#57512yes—
771C2×C4C22×#4112yes—
772C2×C4C22×#4112yes—
773C2×C4#58512yes—
774C8—44no—
775C8—44no—
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—22no—
789C22—22no—
790C22—22no—
791C22—416no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—816no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22#309414yes—
805C22#311414yes—
806C22C22×#12311yescharacteristic
807C22C2×#52511yescharacteristic
808C22#344911yescharacteristic
809C22C22×AGL(1,ℤ/8)11yescharacteristic
810C22C2×#57511yescharacteristic
811C22C2×#57511yescharacteristic
812C22C2×#57511yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—44no—
824C4—41no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#347514yes—
832C2—24no—
833C2—24no—
834C2—42no—
835C2—84no—
836C2#3480911yescharacteristic
837C2C2×#309411yescharacteristic
838C2#6051111yescharacteristic
839C2C2×#311411yescharacteristic
840C2#6056311yescharacteristic
841C2#6095811yescharacteristic
842C2#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×#2283C2semidirect
3. #27684C2semidirect
4. #27651C2semidirect
5. #27633C2semidirect
6. #27616C2semidirect
7. #27601C2semidirect
8. #27600C2semidirect
9. #27588C2semidirect
12. #23764C2semidirect
13. #21580C2semidirect
14. #21578C2semidirect
15. #21363C2semidirect
16. #20739C2semidirect
17. #20715C2semidirect
43. #2283C22semidirect
44. #2283C22semidirect
46. C2×#382C22semidirect
47. C2×#382C22semidirect
53. C2×C4×C4⋊C4C22semidirect
54. C2×C4×C4⋊C4C22semidirect
58. #2101C22semidirect
59. #2092C22semidirect
60. #2085C22semidirect
61. #2077C22semidirect
62. #2075C22semidirect
63. #2073C22semidirect
66. #1949C22semidirect
67. #1949C22semidirect
68. #1926C22semidirect
69. #1925C22semidirect
70. #1921C22semidirect
71. #1920C22semidirect
76. #1853C22semidirect
79. #1852C22semidirect
80. #1824C22semidirect
83. #1823C22semidirect
85. #1804C22semidirect
86. #1804C22semidirect
87. #1797C22semidirect
88. #1797C22semidirect
93. #1776C22semidirect
94. #1776C22semidirect
95. #1762C22semidirect
96. #1762C22semidirect
97. #1749C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1212
C2×#22832
#276842
#276512
#276332
#276162
#276012
#276002
#275882
#240052
#240022
#237642
#215802
#215782
#213632
#207392
#207152