Finite Group Databasebeta

← #6469713

Subgroups — #6469713

Order 512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#29560C212yesmaximal, complemented
4#29559C212yesmaximal, complemented
5#29213C211yesmaximal, characteristic, complemented
6#29148C211yesmaximal, characteristic, complemented
7#28755C211yesmaximal, characteristic, complemented
8#28449C211yesmaximal, characteristic, complemented
9#27896C212yesmaximal, complemented
10#25604C212yesmaximal
11#24660C212yesmaximal, complemented
12#24659C212yesmaximal
13#23571C212yesmaximal, complemented
14#23568C212yesmaximal
15C4×#497C212yesmaximal, complemented
16C4×#491C212yesmaximal, complemented
17C4×#462C212yesmaximal, complemented
18C4×#461C212yesmaximal, complemented
19C4×#432C211yesmaximal, characteristic, complemented
20C2×#533C2212yes—
21C2×#529C2211yescharacteristic
22C2×#497C2212yes—
23C2×#491C2212yes—
24C2×#462C2212yes—
25C2×#461C2212yes—
26C2×C4×Q16C2214yes—
27C2×C4×SD16C2214yes—
28C2×#432C2212yes—
29#2868C2211yescharacteristic
30#2868C2211yescharacteristic
31#2862C2212yes—
32#2859—21no—
33#2859—21no—
34#2857—21no—
35#2857—21no—
36#2857C2212yes—
37#2857C2212yes—
38C4×C4⋊Q8—21no—
39C4×C4⋊Q8—21no—
40C4×C4⋊Q8C2212yes—
41C4×C4⋊Q8C2212yes—
42C4×#125C2211yescharacteristic
43C4×#125C2211yescharacteristic
44C4×#126—21no—
45C4×#126—21no—
46C4×#124C2211yescharacteristic
47C4×#124C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×#123—21no—
51C4×#123—21no—
52C4×#121C2211yescharacteristic
53C4×#121C2211yescharacteristic
54#2298—21no—
55#2295C2211yescharacteristic
56#2293C2211yescharacteristic
57#2290—21no—
58#2285—21no—
59#2285—21no—
60#2283C2211yescharacteristic
61C42×Q8C2211yescharacteristic
62C42×D4—21no—
63C42×D4C2211yescharacteristic
64C4×#117—21no—
65C2×C43C2211yescharacteristic
66#2058C2212yes—
67#2057C2212yes—
68#2043C2212yes—
69#2043C2212yes—
70#2036C2214yes—
71#2035C2214yes—
72#2024C2212yes—
73#2023C2212yes—
74#2016C2212yes—
75#2013C2212yes—
76#2001C2214yes—
77#2000C2214yes—
78#1992C2212yes—
79#1981C2212yes—
80#1981C2212yes—
81#1973C2214yes—
82#1971C2214yes—
83#1960C2212yes—
84#1960C2212yes—
85#1959C2212yes—
86#1948C2212yes—
87#1947C2212yes—
88#1935C2214yes—
89#1935C2214yes—
90#1928C2214yes—
91#1927C2214yes—
92#1878C2214yes—
93#1877C2214yes—
94#1847C2212yes—
95#1836C2212yes—
96#1803C2212yes—
97#1802C2212yes—
98#1767C2211yescharacteristic
99#1767C2211yescharacteristic
100C4×C4⋊C8C2212yes—
101C4×#103C2214yes—
102C4×#103C2214yes—
103#1749C2212yes—
104C4×C22⋊C8C2212yes—
105#1745C2212yes—
106C4×#97C2212yes—
107C22×Q16C2314yes—
108C22×SD16C2314yes—
109#533—48no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8C2312yes—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115C2×C4⋊Q8C2312yes—
116#529—24no—
117#529—24no—
118C2×#126—21no—
119C2×#125—22no—
120C2×#125C2311yescharacteristic
121C2×#124C2311yescharacteristic
122C2×#123—21no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8C2311yescharacteristic
125C2×C22⋊Q8C2314yes—
126C2×#121C2311yescharacteristic
127C2×C4×Q8—22no—
128C2×C4×Q8C2314yes—
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×Q8C2311yescharacteristic
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×#117—22no—
139C2×#117—21no—
140C2×#117—21no—
141C22×C42—21no—
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#497—28no—
150#491—28no—
151#462—28no—
152#461—28no—
153C4×Q16—48no—
154C4×SD16—48no—
155#432—28no—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8C2314yes—
169C2×#97C2312yes—
170C2×#97C2312yes—
171C2×#97C2314yes—
172C2×C4×C8C2314yes—
173#391—22no—
174#391—22no—
175#391C2314yes—
176#391C2314yes—
177#391C2311yescharacteristic
178#391C2311yescharacteristic
179#390C2311yescharacteristic
180#390C2311yescharacteristic
181#389—22no—
182#389—22no—
183#389—22no—
184#389—22no—
185#389—22no—
186#389—22no—
187#389—22no—
188#389—22no—
189#389C2311yescharacteristic
190#389C2311yescharacteristic
191#389C2311yescharacteristic
192#389C2311yescharacteristic
193#388—21no—
194#388—21no—
195#388—21no—
196#388—21no—
197#388—21no—
198#388—21no—
199#388—21no—
200#388—21no—
201#387—21no—
202#387—21no—
203#387—21no—
204#387—21no—
205#387—21no—
206#387—21no—
207#387—21no—
208#387—21no—
209#386—21no—
210#386—21no—
211#385—21no—
212#385—21no—
213#384—21no—
214#384—21no—
215#384—21no—
216#384—21no—
217#384—21no—
218#384—21no—
219#384C2312yes—
220#384C2312yes—
221#383—21no—
222#382—22no—
223#382—22no—
224#382C2311yescharacteristic
225#382C2311yescharacteristic
226#381—21no—
227#380—22no—
228#380—22no—
229#380—22no—
230#380—22no—
231#380C2311yescharacteristic
232#380C2311yescharacteristic
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—21no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—22no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4C2311yescharacteristic
248C4×C4⋊C4C2311yescharacteristic
249C4×C4⋊C4C2311yescharacteristic
250C4×C4⋊C4C2311yescharacteristic
251C4×C4⋊C4C2311yescharacteristic
252C4×C4⋊C4C2311yescharacteristic
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259C4×C22⋊C4—21no—
260C4×C22⋊C4—21no—
261C4×C22⋊C4—21no—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266#376—21no—
267#376—21no—
268C43—21no—
269C43D411yescharacteristic
270C43D411yescharacteristic
271C43D411yescharacteristic
272C43D411yescharacteristic
273C43C2311yescharacteristic
274C43C2311yescharacteristic
275C43C2311yescharacteristic
276C43C2311yescharacteristic
277#340C2314yes—
278#340C2314yes—
279#340C2314yes—
280#340C2314yes—
281#336C2312yes—
282#336C2314yes—
283#336C2312yes—
284C22×Q8—22no—
285C22×Q8C2414yes—
286C22×Q8C2411yescharacteristic
287C22×D4—21no—
288C22×D4C2411yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—21no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2411yescharacteristic
299C2×Q16—28no—
300C2×Q16—28no—
301C2×Q16—44no—
302C2×SD16—28no—
303C2×SD16—28no—
304C2×SD16—44no—
305C22×C8C2414yes—
306C22×C8C2414yes—
307C4⋊Q8—24no—
308C4⋊Q8—24no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8—44no—
312C4⋊Q8—44no—
313C4⋊Q8—44no—
314C4⋊Q8—44no—
315#126—28no—
316#125—22no—
317#125—48no—
318#125#4114yes—
319#124—22no—
320#124#4114yes—
321#123—28no—
322C22⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—44no—
325C22⋊Q8—44no—
326C22⋊Q8—48no—
327#121—22no—
328#121—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—24no—
332C4×Q8—28no—
333C4×Q8—28no—
334C4×Q8—24no—
335C4×Q8—48no—
336C4×D4—28no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—44no—
342C4×D4—44no—
343#117—28no—
344#117—44no—
345#117—48no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2411yescharacteristic
371C2×C4⋊C4C2414yes—
372C2×C4⋊C4C2411yescharacteristic
373C2×C4⋊C4C2411yescharacteristic
374C2×C4⋊C4C2411yescharacteristic
375C2×C4⋊C4C2411yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—24no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—44no—
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×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437#107—44no—
438#106—44no—
439C4⋊C8—24no—
440C4⋊C8#4118yes—
441#103—28no—
442#103—28no—
443#103—28no—
444#103—28no—
445#103—44no—
446#103—44no—
447#103—44no—
448#102—44no—
449C22⋊C8—28no—
450#97—28no—
451#97—24no—
452#97—24no—
453C4×C8—28no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—24no—
475#95—24no—
476#95—24no—
477#95—24no—
478C24—21no—
479C24C22×D411yescharacteristic
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—24no—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8C2×#4112yes—
493C2×D4—24no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—22no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4C2×#4112yes—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
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—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4#13714yes—
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×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2511yescharacteristic
554Q16—416no—
555SD16—416no—
556C2×C8—24no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8—24no—
561C2×C8C2×#4118yes—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—42no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—48no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—42no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—48no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—44no—
593C4⋊C4C2×#4112yes—
594C4⋊C4C2×#4112yes—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—48no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C42—24no—
610C42—22no—
611C42—22no—
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—41no—
632C42—41no—
633C42—41no—
634C42—41no—
635C42—42no—
636C42—42no—
637C42—48no—
638C42—42no—
639C42—42no—
640C42—42no—
641C42—42no—
642C42—42no—
643C42—42no—
644C42#13714yes—
645C42C2×#4112yes—
646C42C2×#4112yes—
647C42C2×#4114yes—
648C42H(5,𝔽2)14yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C2×#13712yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—42no—
666Q8—44no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670Q8—88no—
671D4—24no—
672D4—48no—
673D4—42no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
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—28no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
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—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—48no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4#52512yes—
739C2×C4#52512yes—
740C2×C4#53212yes—
741C2×C4#53212yes—
742C2×C4#53512yes—
743C2×C4#53512yes—
744C2×C4C2×#13712yes—
745C2×C4C2×#13712yes—
746C2×C4C2×#13712yes—
747C2×C4C2×#13712yes—
748C2×C4C2×#13712yes—
749C2×C4#57512yes—
750C2×C4#57512yes—
751C2×C4C22×#4111yescharacteristic
752C2×C4C22×#4112yes—
753C2×C4C22×#4111yescharacteristic
754C2×C4C2×H(5,𝔽2)12yes—
755C8—28no—
756C8—44no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×#52511yescharacteristic
772C22C2×#53211yescharacteristic
773C22C2×#53511yescharacteristic
774C22C22×#13711yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57511yescharacteristic
777C22C2×#57511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—42no—
789C4—42no—
790C4—41no—
791C4—42no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—84no—
797C4—84no—
798C4#317214yes—
799C4#321814yes—
800C4#348112yes—
801C4#348312yes—
802C2—42no—
803C2—82no—
804C2#3497711yescharacteristic
805C2#6056211yescharacteristic
806C2#6056211yescharacteristic
807C2C2×#317211yescharacteristic
808C2#6070111yescharacteristic
809C2C2×#321811yescharacteristic
810C2#6079011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36645C2semidirect
3. #29560C2semidirect
4. #29559C2semidirect
5. #29213C2semidirect
6. #29148C2semidirect
7. #28755C2semidirect
8. #28449C2semidirect
9. #27896C2semidirect
11. #24660C2semidirect
13. #23571C2semidirect
15. C4×#497C2semidirect
16. C4×#491C2semidirect
17. C4×#462C2semidirect
18. C4×#461C2semidirect
19. C4×#432C2semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#295602
#295592
#292132
#291482
#287552
#284492
#278962
#256042
#246602
#246592
#235712
#235682
C4×#4972
C4×#4912
C4×#4622
C4×#4612
C4×#4322