Finite Group Databasebeta

← #6489113

Subgroups — #6489113

Order 512.

2128 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C2×C4×#124C211yesmaximal, characteristic, complemented
3#32906C211yesmaximal, characteristic, complemented
4#32905C211yesmaximal, characteristic, complemented
5#32903C211yesmaximal, characteristic, complemented
6#32902C211yesmaximal, characteristic
7#30044C214yesmaximal, complemented
8#29140C212yesmaximal, complemented
9#28439C212yesmaximal, complemented
10#28159C212yesmaximal, complemented
11#28158C212yesmaximal, complemented
12#27977C212yesmaximal, complemented
13#25724C212yesmaximal, complemented
14#23937C212yesmaximal, complemented
15#23936C212yesmaximal, complemented
16#22271C214yesmaximal, complemented
17#20777C211yesmaximal, characteristic, complemented
18C2×#529C2212yes—
19C22×#124C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C2×#495C2214yes—
23C2×#462C2212yescomplemented
24C2×#460C2212yescomplemented
25C2×#461C2212yes—
26C2×#459C2212yes—
27C2×#451C2212yes—
28C2×#448C2212yes—
29C2×#450C2212yes—
30C2×#447C2212yes—
31#2861C2212yescomplemented
32#2860—21no—
33#2860—21no—
34#2859C2211yescharacteristic, complemented
35#2858C2211yescharacteristic, complemented
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2854—21no—
39#2854—21no—
40#2850C2212yes—
41C4×C4⋊Q8C2211yescharacteristic, complemented
42C4×#127C2211yescharacteristic, complemented
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#124—21no—
47C4×#124C2212yes—
48C4×#124C2212yes—
49C4×#124C2212yes—
50C4×#124C2212yes—
51C4×#124C2212yescomplemented
52C4×#121—21no—
53C4×#121—21no—
54C2×#391C2211yescharacteristic
55#2293—21no—
56#2293—21no—
57C2×#390C2211yescharacteristic
58C2×#388—21no—
59C2×#388—21no—
60C2×#382C2211yescharacteristic
61C2×C4×C22⋊C4—21no—
62C2×C4×C22⋊C4—21no—
63C2×C43C2211yescharacteristic
64#2074C2214yescomplemented
65#2073C2214yescomplemented
66#2026C2214yescomplemented
67#2025C2214yes—
68#2015C2214yes—
69#2015C2214yescomplemented
70#2012C2214yes—
71#2012C2214yes—
72#1958C2214yes—
73#1958C2214yescomplemented
74#1880C2214yes—
75#1880C2214yescomplemented
76#1879C2214yes—
77#1879C2214yes—
78#1878C2214yescomplemented
79#1878C2214yescomplemented
80#1877C2214yes—
81#1877C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1872C2212yes—
85#1872C2212yes—
86#1839C2212yescomplemented
87#1835C2214yescomplemented
88#1831C2212yescomplemented
89#1817C2212yes—
90#1803C2212yescomplemented
91#1803C2212yescomplemented
92#1802C2212yes—
93#1802C2212yes—
94#1797C2211yescharacteristic
95#1797C2211yescharacteristic
96C4×C4⋊C8C2212yescomplemented
97C4×C22⋊C8C2212yes—
98#1744C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C24×C4—21no—
102C22×Q16C2314yes—
103C22×SD16C2314yes—
104C22×SD16C2314yes—
105C22×D8C2314yes—
106C2×C4⋊Q8C2311yescharacteristic
107C2×#127C2311yescharacteristic
108#529—44no—
109#529—44no—
110C2×#126—22no—
111C2×#125C2312yes—
112C2×#124—28no—
113C2×#124—21no—
114C2×#124—21no—
115C2×#124C2312yes—
116C2×#124C2312yes—
117C2×#124C2312yes—
118C2×#124C2312yes—
119C2×#123—22no—
120C2×C22⋊Q8C2312yes—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121C2312yes—
124C2×C4×Q8—21no—
125C2×C4×Q8—21no—
126C2×C4×Q8—44no—
127C2×C4×Q8C2312yes—
128C2×C4×Q8C2312yes—
129C2×C4×Q8C2312yes—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—44no—
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×#117—22no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C42—21no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#495—216no—
157#462—44no—
158#461—44no—
159#460—44no—
160#459—44no—
161#451—44no—
162#450—44no—
163#448—44no—
164#447—44no—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2312yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C4×C8C2314yes—
178#391—21no—
179#391—21no—
180#391C2312yes—
181#391C2312yes—
182#391C2312yes—
183#391C2312yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390—21no—
193#390—21no—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#388—22no—
207#388—22no—
208#388—22no—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#386—22no—
223#386—22no—
224#384C2311yescharacteristic
225#384C2311yescharacteristic
226#382—21no—
227#382—21no—
228#382C2312yes—
229#382C2312yes—
230#382C2312yes—
231#380—21no—
232#380—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C43D411yescharacteristic
250C43D411yescharacteristic
251C43D411yescharacteristic
252C43D411yescharacteristic
253C43C2311yescharacteristic
254C43C2311yescharacteristic
255C43C2311yescharacteristic
256C43C2311yescharacteristic
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#340C2314yes—
261#336C2312yes—
262#336C2312yes—
263#336C2314yes—
264#336C2314yes—
265#336C2314yes—
266C25—21no—
267C22×Q8—24no—
268C22×Q8—21no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—42no—
272C22×Q8C2412yes—
273C22×Q8C2412yes—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—42no—
282C22×D4C2412yes—
283C22×D4C2412yes—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×Q16—28no—
301C2×Q16—44no—
302C2×Q16—44no—
303C2×SD16—28no—
304C2×SD16—28no—
305C2×SD16—44no—
306C2×SD16—44no—
307C2×SD16—44no—
308C2×SD16—44no—
309C2×D8—28no—
310C2×D8—44no—
311C2×D8—44no—
312C22×C8C2414yes—
313C22×C8C2414yes—
314C4⋊Q8—24no—
315#127—24no—
316#126—48no—
317#125—42no—
318#125—42no—
319#124—28no—
320#124—28no—
321#124—24no—
322#124—24no—
323#124—24no—
324#124—28no—
325#124—42no—
326#124—42no—
327#124#4118yes—
328#123—48no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331#121—24no—
332#121—24no—
333#121—44no—
334#121—44no—
335C4×Q8—24no—
336C4×Q8—24no—
337C4×Q8—42no—
338C4×Q8—42no—
339C4×Q8—42no—
340C4×Q8—42no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—42no—
346C4×D4—42no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—48no—
354#117—48no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
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×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—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—42no—
411C2×C42—42no—
412C2×C42—42no—
413C2×C42—44no—
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×C42C2×D411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C4⋊C8—24no—
443C4⋊C8—24no—
444#103—44no—
445#103—44no—
446#103—44no—
447#103—44no—
448#102—44no—
449#102—44no—
450#102—44no—
451#102—44no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C4×C8—28no—
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—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469C24—24no—
470C24—22no—
471C24—22no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24—42no—
477C24—42no—
478C24C22×D411yescharacteristic
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8C2×#4114yes—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—24no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—24no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×#4114yes—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
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—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
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—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—816no—
562C22×C4#13514yes—
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D411yescharacteristic
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4H(5,𝔽2)12yes—
577C22×C4H(5,𝔽2)12yes—
578C22×C4C2511yescharacteristic
579Q16—88no—
580SD16—88no—
581SD16—88no—
582D8—88no—
583C2×C8—24no—
584C2×C8—24no—
585C2×C8—24no—
586C2×C8—24no—
587C2×C8—24no—
588C2×C8—24no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—42no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
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—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
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—22no—
645C42—22no—
646C42—22no—
647C42—21no—
648C42—21no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42—41no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42C2×#4114yes—
664C42H(5,𝔽2)14yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—24no—
670C23—48no—
671C23—48no—
672C23—48no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—84no—
687C23—84no—
688C23—84no—
689C23—84no—
690C23#53512yes—
691C23C2×#13512yes—
692C23#57512yes—
693C23C23×D411yescharacteristic
694Q8—24no—
695Q8—24no—
696Q8—48no—
697Q8—42no—
698Q8—42no—
699Q8—44no—
700Q8—44no—
701D4—24no—
702D4—24no—
703D4—48no—
704D4—42no—
705D4—42no—
706D4—44no—
707D4—44no—
708D4—84no—
709D4—88no—
710D4—84no—
711C2×C4—21no—
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—28no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—24no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—88no—
769C2×C4—88no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—88no—
773C2×C4#52512yes—
774C2×C4#52512yes—
775C2×C4#53512yes—
776C2×C4#53512yes—
777C2×C4#53512yes—
778C2×C4C2×#13512yes—
779C2×C4C2×#13512yes—
780C2×C4#57512yes—
781C2×C4#57512yes—
782C2×C4C22×#4112yes—
783C2×C4C2×H(5,𝔽2)11yescharacteristic
784C2×C4C2×H(5,𝔽2)11yescharacteristic
785C2×C4C2×H(5,𝔽2)12yes—
786C8—44no—
787C8—44no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—816no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#321214yes—
810C22C2×#52511yescharacteristic
811C22C2×#53511yescharacteristic
812C22C2×#53511yescharacteristic
813C22C22×#13511yescharacteristic
814C22C2×#57511yescharacteristic
815C22C2×#57511yescharacteristic
816C22C2×#57511yescharacteristic
817C4—22no—
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—22no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—44no—
830C4—82no—
831C4—82no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4#321114yes—
836C4#351912yes—
837C4#351912yes—
838C2—24no—
839C2—84no—
840C2—162no—
841C2#3523711yescharacteristic
842C2#6053611yescharacteristic
843C2#6054611yescharacteristic
844C2C2×#321111yescharacteristic
845C2C2×#321211yescharacteristic
846C2#6080511yescharacteristic
847C2#6080511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32902C2
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. C2×C4×#124C2semidirect
3. #32906C2semidirect
4. #32905C2semidirect
5. #32903C2semidirect
7. #30044C2semidirect
8. #29140C2semidirect
9. #28439C2semidirect
10. #28159C2semidirect
11. #28158C2semidirect
12. #27977C2semidirect
13. #25724C2semidirect
14. #23937C2semidirect
15. #23936C2semidirect
16. #22271C2semidirect
17. #20777C2semidirect
23. C2×#462C22semidirect
24. C2×#460C22semidirect
31. #2861C22semidirect
34. #2859C22semidirect
35. #2858C22semidirect
41. C4×C4⋊Q8C22semidirect
42. C4×#127C22semidirect
51. C4×#124C22semidirect
64. #2074C22semidirect
65. #2073C22semidirect
66. #2026C22semidirect
69. #2015C22semidirect
73. #1958C22semidirect
75. #1880C22semidirect
78. #1878C22semidirect
79. #1878C22semidirect
81. #1877C22semidirect
86. #1839C22semidirect
87. #1835C22semidirect
88. #1831C22semidirect
90. #1803C22semidirect
91. #1803C22semidirect
96. C4×C4⋊C8C22semidirect
98. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#366312
C2×C4×#1242
#329062
#329052
#329032
#329022
#300442
#291402
#284392
#281592
#281582
#279772
#257242
#239372
#239362
#222712
#207772