Finite Group Databasebeta

← #6798563

Subgroups — #6798563

Order 512.

1717 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36134C211yesmaximal, characteristic, complemented
3#33232C211yesmaximal, characteristic, complemented
4#31853C214yesmaximal, complemented
5#31852C214yesmaximal, complemented
6#29807C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29220C211yesmaximal, characteristic, complemented
9#28438C211yesmaximal, characteristic, complemented
10#27975C211yesmaximal, characteristic, complemented
11#27972C211yesmaximal, characteristic, complemented
12#25598C211yesmaximal, characteristic, complemented
13#25598C211yesmaximal, characteristic, complemented
14#25582C214yesmaximal, complemented
15#25331C214yesmaximal, complemented
16#21864C211yesmaximal, characteristic, complemented
17#21860C211yesmaximal, characteristic, complemented
18#21646C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#553C2212yes—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#492C2211yescharacteristic
25C2×#491C2214yes—
26C2×#486C2211yescharacteristic
27C2×#461C2214yes—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2868C2211yescharacteristic
31#2859C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2566C2212yes—
37#2552—21no—
38#2542C2212yes—
39#2538—21no—
40#2512—21no—
41#2512—21no—
42#2504C2212yes—
43#2500C2212yes—
44#2441—21no—
45#2441—21no—
46#2429C2212yes—
47#2429C2212yes—
48#2423—21no—
49#2423—21no—
50#2422—21no—
51#2422—21no—
52#2416—21no—
53#2416—21no—
54#2365C2212yes—
55#2361—21no—
56#2361—21no—
57#2354—21no—
58Q8×C4⋊C4—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2101C2214yes—
65#2074C2214yes—
66#2072C2214yes—
67#2055C2214yes—
68#2055C2214yes—
69#2013C2214yes—
70#2000C2214yes—
71#2000C2214yes—
72#2000C2214yes—
73#2000C2214yes—
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1989C2214yes—
78#1960C2214yes—
79#1957C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1955C2212yes—
87#1940C2212yes—
88#1936C2214yes—
89#1924C2212yes—
90#1924C2212yes—
91#1880C2214yes—
92#1880C2214yes—
93#1873C2214yes—
94#1873C2214yes—
95#1872C2214yes—
96#1872C2214yes—
97#1834C2211yescharacteristic
98#1834C2211yescharacteristic
99#1834C2211yescharacteristic
100#1805C2214yes—
101#1803C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1762C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×SD16C2314yes—
108C22×SD16C2314yes—
109#553—48no—
110#533—24no—
111#533—24no—
112#533—42no—
113#533—42no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2312yes—
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#126—22no—
121C2×#125—21no—
122C2×#125—21no—
123C2×#125C2312yes—
124C2×#123—22no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121C2312yes—
137C2×#121C2312yes—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8C2312yes—
142C2×C4×Q8C2312yes—
143C2×C4×D4—22no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4D411yescharacteristic
147C2×C4×D4D411yescharacteristic
148C2×C4×D4C2312yes—
149C2×C4×D4C2311yescharacteristic
150C2×#117—21no—
151C2×#117—21no—
152C2×#117C2312yes—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#492—42no—
159#492—42no—
160#491—48no—
161#486—24no—
162#461—48no—
163#431—42no—
164#431—42no—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×#97C2312yes—
181C2×#97C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186#399—22no—
187#399—22no—
188#398—22no—
189#398—22no—
190#397—22no—
191#397—22no—
192#396—22no—
193#396—22no—
194#396—22no—
195#396—22no—
196#394—22no—
197#394—22no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#390—22no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390C2312yes—
209#390C2312yes—
210#390C2312yes—
211#389—22no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—22no—
222#389—22no—
223#389C2312yes—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#387—22no—
229#387—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#384—22no—
235#384—21no—
236#384—21no—
237#384—21no—
238#384—21no—
239#384—21no—
240#384—21no—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#384C2312yes—
244#384C2311yescharacteristic
245#384C2311yescharacteristic
246#382C2312yes—
247#382C2312yes—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—21no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4D411yescharacteristic
259C4×C4⋊C4D411yescharacteristic
260C4×C4⋊C4C2312yes—
261C4×C4⋊C4C2311yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4D411yescharacteristic
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4C2311yescharacteristic
267C4×C22⋊C4C2311yescharacteristic
268C43C2311yescharacteristic
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8C2412yes—
280C22×Q8C2412yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2×D411yescharacteristic
286C22×D4C2412yes—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C2×SD16—44no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—28no—
311C4⋊Q8—44no—
312C4⋊Q8#4114yes—
313#127—22no—
314#127—22no—
315#126—48no—
316#125—28no—
317#125—44no—
318#125—44no—
319#123—48no—
320C22⋊Q8—24no—
321C22⋊Q8—24no—
322C22⋊Q8—42no—
323C22⋊Q8—42no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328#121—44no—
329#121—44no—
330#121—44no—
331#121—48no—
332#121—44no—
333#121—82no—
334#121—82no—
335C4×Q8—24no—
336C4×Q8—24no—
337C4×Q8—42no—
338C4×Q8—42no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—28no—
345C4×D4—42no—
346C4×D4—48no—
347C4×D4—82no—
348C4×D4—82no—
349#117—44no—
350#117—44no—
351#117—44no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—82no—
383C2×C4⋊C4—82no—
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C4⋊C8—24no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440#103—44no—
441#103—44no—
442#102—28no—
443#102—44no—
444C22⋊C8—42no—
445C22⋊C8—42no—
446C22⋊C8—42no—
447C22⋊C8—42no—
448#97—24no—
449#97—42no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470C24—22no—
471C24C22×D411yescharacteristic
472C24C22×D411yescharacteristic
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—24no—
481C2×Q8—24no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—22no—
489C2×D4—24no—
490C2×D4—41no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—82no—
502C2×D4—82no—
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—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—82no—
534C22×C4—82no—
535C22×C4#13714yes—
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
549SD16—88no—
550SD16—88no—
551C2×C8—22no—
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—
563C4⋊C4—22no—
564C4⋊C4—24no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—41no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—42no—
583C4⋊C4—42no—
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—
593C4⋊C4—42no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—82no—
599C4⋊C4—82no—
600C4⋊C4C2×#4114yes—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C22⋊C4—82no—
620C22⋊C4—82no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—22no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42C2×#4112yes—
639C42H(5,𝔽2)14yes—
640C42H(5,𝔽2)12yes—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C2×#13712yes—
662C23C23×D411yescharacteristic
663Q8—48no—
664Q8—44no—
665Q8—44no—
666Q8—44no—
667Q8—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—88no—
672D4—84no—
673D4—84no—
674D4—164no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—21no—
691C2×C4—21no—
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—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
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—164no—
732C2×C4—164no—
733C2×C4#53512yes—
734C2×C4#53512yes—
735C2×C4#54612yes—
736C2×C4#54612yes—
737C2×C4C2×#13712yes—
738C2×C4C2×#13712yes—
739C2×C4#57512yes—
740C2×C4#57712yes—
741C2×C4#57712yes—
742C2×C4C22×#4111yescharacteristic
743C2×C4C2×H(5,𝔽2)12yes—
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4#58512yes—
746C8—42no—
747C8—42no—
748C8—42no—
749C8—42no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×#53511yescharacteristic
772C22C2×#54611yescharacteristic
773C22#350011yescharacteristic
774C22C22×#13711yescharacteristic
775C22C2×#57511yescharacteristic
776C22C2×#57711yescharacteristic
777C22C2×#57711yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—44no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4#330714yes—
796C4#332014yes—
797C4#351712yes—
798C4#354612yes—
799C2—42no—
800C2—81no—
801C2—162no—
802C2#3895611yescharacteristic
803C2#6080411yescharacteristic
804C2#6081811yescharacteristic
805C2C2×#332011yescharacteristic
806C2C2×#330711yescharacteristic
807C2#6254011yescharacteristic
808C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36182C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36134C2semidirect
3. #33232C2semidirect
4. #31853C2semidirect
5. #31852C2semidirect
6. #29807C2semidirect
7. #29807C2semidirect
8. #29220C2semidirect
9. #28438C2semidirect
10. #27975C2semidirect
11. #27972C2semidirect
12. #25598C2semidirect
13. #25598C2semidirect
14. #25582C2semidirect
15. #25331C2semidirect
16. #21864C2semidirect
17. #21860C2semidirect
18. #21646C2semidirect
19. #21265C2semidirect

Maximal subgroups

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

subgroupindex
#361822
#361342
#332322
#318532
#318522
#298072
#292202
#284382
#279752
#279722
#255982
#255822
#253312
#218642
#218602
#216462
#212652