Finite Group Databasebeta

← #6485373

Subgroups — #6485373

Order 512.

1868 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36639C211yesmaximal, characteristic, complemented
2#36631C211yesmaximal, characteristic, complemented
3#33278C211yesmaximal, characteristic, complemented
4#33277C211yesmaximal, characteristic, complemented
5#33241C211yesmaximal, characteristic, complemented
6#33239C211yesmaximal, characteristic, complemented
7#30320C214yesmaximal, complemented
8#29497C214yesmaximal, complemented
9#28750C211yesmaximal, characteristic, complemented
10#28718C211yesmaximal, characteristic, complemented
11#28688C211yesmaximal, characteristic, complemented
12#28443C211yesmaximal, characteristic, complemented
13#25674C211yesmaximal, characteristic, complemented
14#25671C211yesmaximal, characteristic, complemented
15#25599C211yesmaximal, characteristic
16#25598C211yesmaximal, characteristic, complemented
17#24654C214yesmaximal, complemented
18#22149C214yesmaximal, complemented
19C4×#431C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#529—21no—
23C2×#500C2211yescharacteristic
24C2×#498C2211yescharacteristic
25C2×#493C2211yescharacteristic
26C2×#492C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#486C2211yescharacteristic
29C2×#486C2211yescharacteristic
30C2×#486C2211yescharacteristic
31C2×#463C2214yes—
32C2×#431C2212yes—
33#2862C2211yescharacteristic
34#2862C2211yescharacteristic
35#2861—21no—
36#2861—21no—
37#2861—21no—
38#2860—21no—
39#2860C2212yes—
40#2859C2211yescharacteristic
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2856C2211yescharacteristic
46#2854—21no—
47#2854C2212yes—
48#2850—21no—
49#2850—21no—
50#2850—21no—
51#2850C2212yes—
52#2850C2212yes—
53C4×C4⋊Q8C2211yescharacteristic
54C4×#127C2211yescharacteristic
55C4×#124—21no—
56C4×#124—21no—
57C4×#124—21no—
58C4×#124C2212yes—
59C4×#124C2212yes—
60C4×#121—21no—
61C4×#121C2212yes—
62#2297—21no—
63#2297—21no—
64#2293—21no—
65#2293C2212yes—
66C2×C43C2211yescharacteristic
67#2085C2214yes—
68#2073C2214yes—
69#2042C2214yes—
70#2036C2214yes—
71#2034C2214yes—
72#2012C2214yes—
73#2000C2214yes—
74#1999C2214yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1990C2211yescharacteristic
79#1983C2214yes—
80#1970C2214yes—
81#1970C2214yes—
82#1968C2214yes—
83#1968C2214yes—
84#1957C2211yescharacteristic
85#1957C2211yescharacteristic
86#1956C2211yescharacteristic
87#1956C2211yescharacteristic
88#1949C2214yes—
89#1934C2214yes—
90#1934C2214yes—
91#1933C2214yes—
92#1933C2214yes—
93#1880C2214yes—
94#1879C2214yes—
95#1864C2214yes—
96#1863C2214yes—
97#1804C2214yes—
98C4×C4⋊C8C2211yescharacteristic
99C4×C4⋊C8C2211yescharacteristic
100C4×C4⋊C8C2212yes—
101C4×C22⋊C8C2211yescharacteristic
102C4×C22⋊C8C2211yescharacteristic
103C4×C22⋊C8C2212yes—
104#1744C2212yes—
105C42×C8C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C22×#41—21no—
108C22×SD16C2314yes—
109C22×D8C2314yes—
110#533—42no—
111#533—42no—
112#532—42no—
113#532—42no—
114C2×C4⋊Q8C2311yescharacteristic
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127C2311yescharacteristic
119C2×#127C2311yescharacteristic
120#529—48no—
121C2×#126—22no—
122C2×#125—21no—
123C2×#125—21no—
124C2×#124—21no—
125C2×#124—21no—
126C2×#124—21no—
127C2×#124—21no—
128C2×#124—21no—
129C2×#124C2312yes—
130C2×#124C2312yes—
131C2×#123—22no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8C2312yes—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121—21no—
138C2×#121C2312yes—
139C2×#121C2312yes—
140C2×C4×Q8—21no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×C4×D4—22no—
144C2×C4×D4—21no—
145C2×C4×D4—21no—
146C2×C4×D4—21no—
147C2×C4×D4C2312yes—
148C2×C4×D4C2312yes—
149C2×#117—21no—
150C2×#117—22no—
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#500—42no—
159#498—42no—
160#493—42no—
161#492—42no—
162#487—42no—
163#486—42no—
164#486—42no—
165#486—42no—
166#463—216no—
167#431—28no—
168C2×#107C2314yes—
169C2×#106C2314yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2314yes—
179C2×#102C2314yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2311yescharacteristic
186C2×C4×C8C2312yes—
187C2×C4×C8C2312yes—
188C2×C4×C8C2312yes—
189C2×C4×C8C2312yes—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391C2312yes—
199#391C2312yes—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390—21no—
208#390—21no—
209#390—21no—
210#390—21no—
211#390—21no—
212#390C2312yes—
213#390C2312yes—
214#390C2312yes—
215#390C2312yes—
216#390C2312yes—
217#390C2312yes—
218#389—21no—
219#389—21no—
220#389—21no—
221#389—21no—
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#389C2312yes—
226#388—22no—
227#388—22no—
228#388—22no—
229#388—22no—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#388—22no—
241#388—22no—
242#386—22no—
243#386—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#384C2311yescharacteristic
249#384C2311yescharacteristic
250#382—21no—
251#382—21no—
252#382—21no—
253#382C2312yes—
254#382C2312yes—
255#380—21no—
256#380C2312yes—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C2312yes—
259C4×C22⋊C4—22no—
260C4×C22⋊C4—22no—
261C4×C22⋊C4—22no—
262C4×C22⋊C4—22no—
263C4×C22⋊C4—22no—
264C4×C22⋊C4—22no—
265C43D411yescharacteristic
266C43D411yescharacteristic
267C43D411yescharacteristic
268C43D411yescharacteristic
269C43C2311yescharacteristic
270C43C2311yescharacteristic
271C43C2311yescharacteristic
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280#336C2312yes—
281C2×#41—44no—
282C2×#41—44no—
283C2×#41—44no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8C2412yes—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2412yes—
295C22×D4C2412yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2411yescharacteristic
305C2×SD16—28no—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×D8—28no—
309C2×D8—44no—
310C2×D8—44no—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323#127—22no—
324#127—22no—
325#127—22no—
326#127—22no—
327#126—48no—
328#125—44no—
329#125—44no—
330#124—28no—
331#124—44no—
332#124—44no—
333#124—44no—
334#124—44no—
335#124—44no—
336#124—44no—
337#123—48no—
338C22⋊Q8—42no—
339C22⋊Q8—42no—
340C22⋊Q8—44no—
341C22⋊Q8—44no—
342#121—44no—
343#121—42no—
344#121—42no—
345#121—44no—
346#121—44no—
347#121—44no—
348C4×Q8—42no—
349C4×Q8—42no—
350C4×Q8—44no—
351C4×Q8—44no—
352C4×D4—28no—
353C4×D4—42no—
354C4×D4—42no—
355C4×D4—44no—
356C4×D4—44no—
357C4×D4—44no—
358C4×D4—48no—
359#117—48no—
360#117—44no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
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×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—42no—
412C2×C42—42no—
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×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42C2×D411yescharacteristic
434C2×C42C2×D411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—44no—
442#106—44no—
443C4⋊C8—24no—
444C4⋊C8#4118yescomplemented
445#103—28no—
446#103—44no—
447#103—44no—
448#102—28no—
449#102—44no—
450#102—44no—
451#102—44no—
452#102—44no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C4×C8—24no—
456C4×C8—24no—
457C4×C8—22no—
458C4×C8—22no—
459C4×C8—22no—
460C4×C8—22no—
461C4×C8—42no—
462C4×C8—42no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477C24—22no—
478C24—22no—
479C24C22×D411yescharacteristic
480#41—816no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—24no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4#13514yes—
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C2511yescharacteristic
568SD16—88no—
569D8—88no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8C2×#4114yes—
581C2×C8C2×#4114yes—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—24no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C22⋊C4—44no—
606C22⋊C4—44no—
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—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—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—21no—
645C42—21no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—44no—
653C42—44no—
654C42#13514yes—
655C42AGL(1,ℤ/8)14yes—
656C42C2×#4114yes—
657C42H(5,𝔽2)12yes—
658C42H(5,𝔽2)12yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23C2×#13512yes—
680C23C23×D411yescharacteristic
681Q8—44no—
682Q8—44no—
683Q8—84no—
684Q8—84no—
685Q8—84no—
686D4—44no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—88no—
691D4—88no—
692D4—84no—
693D4—84no—
694D4—84no—
695D4—84no—
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—28no—
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—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
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—88no—
749C2×C4—88no—
750C2×C4#53212yes—
751C2×C4#53212yes—
752C2×C4#53512yes—
753C2×C4#53512yes—
754C2×C4C2×#13512yes—
755C2×C4C2×#13512yes—
756C2×C4C2×#13512yes—
757C2×C4C2×#13512yes—
758C2×C4C2×#13512yes—
759C2×C4C2×AGL(1,ℤ/8)12yes—
760C2×C4C2×AGL(1,ℤ/8)12yes—
761C2×C4C2×AGL(1,ℤ/8)12yes—
762C2×C4#57512yes—
763C2×C4C22×#4112yes—
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×H(5,𝔽2)11yescharacteristic
766C2×C4#58512yes—
767C8—24no—
768C8—24no—
769C8—42no—
770C8—42no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C2×#53211yescharacteristic
793C22C2×#53511yescharacteristic
794C22#344911yescharacteristic
795C22C22×#13511yescharacteristic
796C22C22×#13511yescharacteristic
797C22C22×AGL(1,ℤ/8)11yescharacteristic
798C22C2×#57511yescharacteristic
799C4—22no—
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4#320714yes—
817C4#321114yes—
818C4#351412yes—
819C4#351712yes—
820C2—42no—
821C2—162no—
822C2—162no—
823C2#3519111yescharacteristic
824C2#6067311yescharacteristic
825C2#6070011yescharacteristic
826C2C2×#321111yescharacteristic
827C2C2×#320711yescharacteristic
828C2#6094411yescharacteristic
829C2#6094611yescharacteristic
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. #36639C2semidirect
2. #36631C2semidirect
3. #33278C2semidirect
4. #33277C2semidirect
5. #33241C2semidirect
6. #33239C2semidirect
7. #30320C2semidirect
8. #29497C2semidirect
9. #28750C2semidirect
10. #28718C2semidirect
11. #28688C2semidirect
12. #28443C2semidirect
13. #25674C2semidirect
14. #25671C2semidirect
16. #25598C2semidirect
17. #24654C2semidirect
18. #22149C2semidirect
19. C4×#431C2semidirect
444. C4⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#366392
#366312
#332782
#332772
#332412
#332392
#303202
#294972
#287502
#287182
#286882
#284432
#256742
#256712
#255992
#255982
#246542
#221492
C4×#4312