Finite Group Databasebeta

← #6464486

Subgroups — #6464486

Order 512.

2014 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C4×#532C211yesmaximal, characteristic, complemented
3#29476C214yesmaximal, complemented
4#29445C214yesmaximal, complemented
5#29192C211yesmaximal, characteristic, complemented
6#29177C211yesmaximal, characteristic, complemented
7#28654C211yesmaximal, characteristic, complemented
8#28615C211yesmaximal, characteristic, complemented
9#27891C211yesmaximal, characteristic, complemented
10#27875C211yesmaximal, characteristic, complemented
11#25671C211yesmaximal, characteristic, complemented
12#25599C211yesmaximal, characteristic
13#23708C214yesmaximal, complemented
14#21727C211yesmaximal, characteristic, complemented
15#21690C211yesmaximal, characteristic, complemented
16#21646C211yesmaximal, characteristic, complemented
17#21646C211yesmaximal, characteristic, complemented
18#21122C214yesmaximal, complemented
19C4×#432C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#529—21no—
22C2×C4×#41—21no—
23C2×#498C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#442C2214yes—
28C2×#432C2212yes—
29#2861—21no—
30#2860—21no—
31#2860C2212yes—
32#2859C2211yescharacteristic
33#2858C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2854—21no—
37#2854C2212yes—
38#2850—21no—
39C4×C4⋊Q8C2211yescharacteristic
40C4×C4⋊Q8C2211yescharacteristic
41C4×C4⋊Q8C2211yescharacteristic
42C4×#127C2211yescharacteristic
43C4×#127C2211yescharacteristic
44C4×#127C2211yescharacteristic
45C4×#124—21no—
46C4×#124—21no—
47C4×#124—21no—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121—21no—
51C4×#121C2212yes—
52C4×#121C2212yes—
53C4×#121C2212yes—
54#2297—21no—
55#2293—21no—
56#2293—21no—
57#2293C2212yes—
58#2293C2212yes—
59#2285C2211yescharacteristic
60C42×D4—21no—
61C42×D4C2212yes—
62C2×C43C2211yescharacteristic
63#2088C2214yes—
64#2077C2214yes—
65#2067C2214yes—
66#2065C2214yes—
67#2054C2214yes—
68#2034C2214yes—
69#2033C2214yes—
70#1999C2214yes—
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1972C2214yes—
76#1957C2211yescharacteristic
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1944C2214yes—
81#1936C2214yes—
82#1936C2214yes—
83#1926C2214yes—
84#1925C2214yes—
85#1920C2214yes—
86#1919C2214yes—
87#1879C2214yes—
88#1879C2214yes—
89#1864C2214yes—
90#1862C2214yes—
91#1845C2211yescharacteristic
92#1844C2211yescharacteristic
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1776C2214yes—
96#1767C2212yes—
97C4×C4⋊C8C2211yescharacteristic
98C4×C4⋊C8C2211yescharacteristic
99#1762C2214yes—
100#1762C2214yes—
101#1749C2212yes—
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104#1745C2212yes—
105C4×#97C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41—21no—
108C22×D8C2314yes—
109#532—24no—
110#532—24no—
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×#127C2311yescharacteristic
114C2×#127C2311yescharacteristic
115#529—48no—
116C2×#126—22no—
117C2×#125—21no—
118C2×#124—21no—
119C2×#124—21no—
120C2×#124—21no—
121C2×#123—22no—
122C2×C22⋊Q8—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C4×#41—48no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×#117—21no—
147C2×#117—22no—
148C2×#117—22no—
149C22×C42—22no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#498—24no—
158#493—24no—
159#486—24no—
160#486—24no—
161#442—216no—
162#432—28no—
163C2×#107C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×#97C2312yes—
179C2×#97C2312yes—
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184#391—21no—
185#391—21no—
186#391—21no—
187#391—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390—21no—
195#390—21no—
196#390—21no—
197#390—21no—
198#390C2312yes—
199#390C2312yes—
200#390C2312yes—
201#390C2312yes—
202#390C2312yes—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389C2312yes—
211#389C2312yes—
212#389C2312yes—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#386—22no—
229#386—22no—
230#386—22no—
231#386—22no—
232#384C2311yescharacteristic
233#384C2311yescharacteristic
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#382—21no—
237#382—21no—
238#380—21no—
239#380—21no—
240#380C2312yes—
241#380C2312yes—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C4⋊C4C2312yes—
249C4×C4⋊C4C2312yes—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257C4×C22⋊C4—22no—
258C43D411yescharacteristic
259C43D411yescharacteristic
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43C2311yescharacteristic
263C43C2311yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C2×#41—28no—
277C2×#41—44no—
278C2×#41—44no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4C2412yes—
288C22×D4C2412yes—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×D8—28no—
301C2×D8—28no—
302C2×D8—44no—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8#4114yes—
311#127—22no—
312#127—22no—
313#127—22no—
314#127#4114yes—
315#126—48no—
316#125—44no—
317#124—28no—
318#124—44no—
319#124—44no—
320#123—48no—
321C22⋊Q8—44no—
322#121—28no—
323#121—24no—
324#121—24no—
325#121—44no—
326#121—44no—
327#121—44no—
328C4×Q8—44no—
329C4×Q8—44no—
330C4×Q8—44no—
331C4×D4—28no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—28no—
335C4×D4—28no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—48no—
343C4×D4—48no—
344C4×D4—48no—
345C4×D4—44no—
346#117—48no—
347#117—48no—
348#117—44no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—48no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432#107—44no—
433#106—28no—
434#106—28no—
435C4⋊C8—24no—
436C4⋊C8—24no—
437#102—28no—
438#102—28no—
439#102—28no—
440#102—28no—
441#102—44no—
442#102—44no—
443C22⋊C8—24no—
444C22⋊C8—24no—
445#97—24no—
446#97—42no—
447#97—42no—
448#97#4118yescomplemented
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453#95—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#95—22no—
465C24—22no—
466C24—22no—
467C24C22×D411yescharacteristic
468#41—432no—
469C2×Q8—24no—
470C2×Q8—42no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×D4—28no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4C2×#4114yes—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—28no—
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—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—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C2511yescharacteristic
555D8—416no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8C2×#4114yes—
567C2×C8C2×#4114yes—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4C2×#4114yes—
592C22⋊C4—28no—
593C22⋊C4—28no—
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—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C42—21no—
629C42—21no—
630C42—22no—
631C42—22no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—41no—
636C42—41no—
637C42—41no—
638C42—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42AGL(1,ℤ/8)14yes—
643C42C2×#4112yes—
644C42C2×#4112yes—
645C42C2×#4114yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—24no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23C2×AGL(1,ℤ/8)12yes—
667C23C23×D411yescharacteristic
668Q8—48no—
669Q8—84no—
670D4—28no—
671D4—416no—
672D4—48no—
673D4—48no—
674D4—44no—
675D4—44no—
676D4—44no—
677D4—88no—
678D4—84no—
679D4—84no—
680C2×C4—21no—
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—28no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
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—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
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×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—88no—
736C2×C4—88no—
737C2×C4—88no—
738C2×C4#52512yes—
739C2×C4#52512yes—
740C2×C4#53212yes—
741C2×C4#53212yes—
742C2×C4C2×AGL(1,ℤ/8)12yes—
743C2×C4C2×AGL(1,ℤ/8)12yes—
744C2×C4C2×AGL(1,ℤ/8)12yes—
745C2×C4C2×AGL(1,ℤ/8)12yes—
746C2×C4C2×AGL(1,ℤ/8)12yes—
747C2×C4#57512yes—
748C2×C4#57512yes—
749C2×C4C22×#4111yescharacteristic
750C2×C4C22×#4112yes—
751C2×C4C22×#4111yescharacteristic
752C2×C4#58512yes—
753C8—24no—
754C8—24no—
755C8—42no—
756C8—42no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—44no—
765C22—44no—
766C22—44no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22C2×#52511yescharacteristic
779C22C2×#53211yescharacteristic
780C22#344911yescharacteristic
781C22C22×AGL(1,ℤ/8)11yescharacteristic
782C22C22×AGL(1,ℤ/8)11yescharacteristic
783C22C2×#57511yescharacteristic
784C22C2×#57511yescharacteristic
785C4—22no—
786C4—22no—
787C4—22no—
788C4—22no—
789C4—22no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—44no—
796C4—41no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#311414yes—
803C4#311514yes—
804C4#347512yes—
805C4#348012yes—
806C2—42no—
807C2—84no—
808C2—162no—
809C2#3491011yescharacteristic
810C2C2×#311411yescharacteristic
811C2C2×#311511yescharacteristic
812C2#6070011yescharacteristic
813C2#6070011yescharacteristic
814C2#6096811yescharacteristic
815C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25599C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36631C2semidirect
2. C4×#532C2semidirect
3. #29476C2semidirect
4. #29445C2semidirect
5. #29192C2semidirect
6. #29177C2semidirect
7. #28654C2semidirect
8. #28615C2semidirect
9. #27891C2semidirect
10. #27875C2semidirect
11. #25671C2semidirect
13. #23708C2semidirect
14. #21727C2semidirect
15. #21690C2semidirect
16. #21646C2semidirect
17. #21646C2semidirect
18. #21122C2semidirect
19. C4×#432C2semidirect
448. #97#41semidirect

Maximal subgroups

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

subgroupindex
#366312
C4×#5322
#294762
#294452
#291922
#291772
#286542
#286152
#278912
#278752
#256712
#255992
#237082
#217272
#216902
#216462
#211222
C4×#4322