Finite Group Databasebeta

← #6476340

Subgroups — #6476340

Order 512.

2166 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36624C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33096C212yesmaximal, complemented
4#33003C212yesmaximal, complemented
5#30176C212yesmaximal, complemented
6#30115C212yesmaximal, complemented
7#29413C214yesmaximal, complemented
8#29160C212yesmaximal, complemented
9#28574C212yesmaximal, complemented
10#27613C211yesmaximal, characteristic, complemented
11#27586C211yesmaximal, characteristic, complemented
12#24550C212yesmaximal, complemented
13#24381C212yesmaximal, complemented
14#24060C211yesmaximal, characteristic, complemented
15#23931C211yesmaximal, characteristic, complemented
16#22185C214yesmaximal, complemented
17C2×#1817C211yesmaximal, characteristic, complemented
18C2×#532C2211yescharacteristic
19C2×#525—21no—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#480C2212yes—
24C2×#465C2214yes—
25C2×#448C2212yes—
26C22×C22⋊C8C2212yes—
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2856C2211yescharacteristic
30#2856C2211yescharacteristic
31#2854—21no—
32#2854C2212yes—
33#2850—21no—
34#2850—21no—
35#2847—21no—
36#2847C2212yes—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8C2212yes—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yes—
44C4×C22⋊Q8C2212yes—
45C4×#121—21no—
46C4×#121—21no—
47C4×#121C2212yes—
48C4×#121C2212yes—
49#2297—21no—
50C2×#391C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#387—21no—
53C2×#385—21no—
54#2285C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2100C2212yescomplemented
60#2095C2212yescomplemented
61#2084C2212yescomplemented
62#2075C2214yes—
63#2072C2212yescomplemented
64#2057C2212yescomplemented
65#2041C2212yescomplemented
66#2035C2214yes—
67#2033C2214yes—
68#2024C2212yescomplemented
69#2014C2212yescomplemented
70#2000C2214yes—
71#1928C2214yescomplemented
72#1926C2214yescomplemented
73#1925C2214yescomplemented
74#1921C2214yescomplemented
75#1920C2214yescomplemented
76#1919C2214yescomplemented
77#1893C2214yes—
78#1892C2214yes—
79#1880C2214yescomplemented
80#1880C2214yescomplemented
81#1877C2214yescomplemented
82#1874C2212yes—
83#1874C2212yes—
84#1863C2214yescomplemented
85#1863C2214yescomplemented
86#1862C2214yescomplemented
87#1853C2212yes—
88#1852C2212yes—
89#1823C2212yes—
90#1817C2212yes—
91#1817C2211yescharacteristic
92#1817C2212yes—
93#1817C2211yescharacteristic
94#1817C2212yes—
95#1808C2214yes—
96#1787C2212yes—
97C2×#336C2212yes—
98C2×#336C2212yes—
99C22×#41—21no—
100C23×Q8C2311yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4C2311yescharacteristic
104C22×SD16C2314yes—
105C23×C8C2314yes—
106#532—44no—
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109C2×#124—21no—
110#525—48no—
111C2×#123—22no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—21no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×#121—21no—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121—21no—
123C2×#121—21no—
124C2×#121C2312yes—
125C2×#121C2312yes—
126C2×#121C2312yes—
127C2×#120—22no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—44no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—44no—
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#480—44no—
162#465—216no—
163#448—44no—
164C2×#107C2314yes—
165C2×#107C2314yes—
166C2×#106C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8—44no—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2314yes—
177#391—21no—
178#391—21no—
179#391—21no—
180#391—21no—
181#391C2312yes—
182#391C2312yes—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390C2312yes—
188#390C2312yes—
189#389—21no—
190#389—21no—
191#389—21no—
192#389—21no—
193#389C2312yes—
194#389C2312yes—
195#389C2312yes—
196#389C2312yes—
197#388—22no—
198#388—22no—
199#388—22no—
200#388—22no—
201#387—22no—
202#387—22no—
203#387—22no—
204#387—22no—
205#386—22no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#385—22no—
215#384C2311yescharacteristic
216#384C2311yescharacteristic
217#382—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#380C2312yes—
227#380C2312yes—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4C2312yes—
236C4×C4⋊C4C2312yes—
237C4×C4⋊C4C2312yes—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240C4×C22⋊C4—22no—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C2×#95—21no—
245C2×#95—21no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#336C2312yes—
256#336C2312yes—
257#336C2312yes—
258#336C2314yes—
259#336C2314yes—
260#336C2312yes—
261C25C2×D411yescharacteristic
262C2×#41—44no—
263C2×#41—44no—
264C2×#41—44no—
265C22×Q8—24no—
266C22×Q8—21no—
267C22×Q8—21no—
268C22×Q8—24no—
269C22×Q8—42no—
270C22×Q8C2412yes—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—21no—
275C22×D4—21no—
276C22×D4C2412yes—
277C23×C4—24no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—22no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C2×SD16—28no—
310C2×SD16—44no—
311C2×SD16—44no—
312C22×C8—28no—
313C22×C8—44no—
314C22×C8—44no—
315C22×C8C2414yes—
316C22×C8C2414yes—
317C4⋊Q8—42no—
318#127—42no—
319#124—44no—
320#123—48no—
321C22⋊Q8—28no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8#4118yescomplemented
329#121—28no—
330#121—24no—
331#121—24no—
332#121—44no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—44no—
337#121—44no—
338#120—48no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×Q8—44no—
343C4×D4—42no—
344C4×D4—42no—
345C4×D4—44no—
346C4×D4—48no—
347C4×D4—48no—
348#117—44no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
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—44no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—44no—
412C2×C42—44no—
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×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429#107—44no—
430#107—44no—
431#106—28no—
432#103—28no—
433#103—44no—
434#103—44no—
435#102—28no—
436#102—44no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440C22⋊C8—44no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—41no—
463C24—41no—
464C24AGL(1,ℤ/8)14yes—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468#41—816no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—416no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8C2×#4114yes—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—42no—
498C2×D4—42no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
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—22no—
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—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—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—416no—
559C22×C4—416no—
560C22×C4—416no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—44no—
574C22×C4#13514yes—
575C22×C4#13714yes—
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C2×#4114yes—
588C22×C4H(5,𝔽2)14yes—
589C22×C4C2511yescharacteristic
590SD16—88no—
591C2×C8—24no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—88no—
598C4⋊C4—24no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4C2×#4114yes—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—41no—
646C42—41no—
647C42—41no—
648C42—41no—
649C42—41no—
650C42—41no—
651C42—41no—
652C42—41no—
653C42—44no—
654C42—44no—
655C42—44no—
656C42—44no—
657C42—44no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—28no—
667C23—21no—
668C23—28no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23#52512yes—
687C23#53412yes—
688C23C2×#13512yes—
689C23C2×AGL(1,ℤ/8)12yes—
690C23C2×AGL(1,ℤ/8)12yes—
691C23C2×AGL(1,ℤ/8)12yes—
692C23C2×#13712yes—
693C23C23×D411yescharacteristic
694Q8—28no—
695Q8—48no—
696Q8—44no—
697Q8—84no—
698D4—44no—
699D4—44no—
700D4—84no—
701D4—84no—
702D4—88no—
703D4—88no—
704D4—88no—
705C2×C4—28no—
706C2×C4—21no—
707C2×C4—28no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
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—28no—
722C2×C4—28no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
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—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
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—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—88no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4#52512yes—
776C2×C4#53412yes—
777C2×C4C2×#13512yes—
778C2×C4C2×#13512yes—
779C2×C4C2×#13712yes—
780C2×C4C2×#13712yes—
781C2×C4#57512yes—
782C2×C4C22×#4112yes—
783C2×C4C2×H(5,𝔽2)12yes—
784C2×C4#58512yes—
785C8—44no—
786C8—44no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—416no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22#311214yes—
815C22#318814yes—
816C22C2×#52511yescharacteristic
817C22C2×#53411yescharacteristic
818C22#344911yescharacteristic
819C22C22×#13511yescharacteristic
820C22C22×AGL(1,ℤ/8)11yescharacteristic
821C22C22×#13711yescharacteristic
822C22C2×#57511yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—22no—
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—41no—
833C4—44no—
834C4—41no—
835C4—44no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4#351314yes—
842C2—24no—
843C2—24no—
844C2—42no—
845C2—162no—
846C2#3506311yescharacteristic
847C2#6053611yescharacteristic
848C2C2×#311211yescharacteristic
849C2C2×#318811yescharacteristic
850C2#6075111yescharacteristic
851C2#6094711yescharacteristic
852C2#6095811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36624C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Q8C2semidirect
3. #33096C2semidirect
4. #33003C2semidirect
5. #30176C2semidirect
6. #30115C2semidirect
7. #29413C2semidirect
8. #29160C2semidirect
9. #28574C2semidirect
10. #27613C2semidirect
11. #27586C2semidirect
12. #24550C2semidirect
13. #24381C2semidirect
14. #24060C2semidirect
15. #23931C2semidirect
16. #22185C2semidirect
17. C2×#1817C2semidirect
59. #2100C22semidirect
60. #2095C22semidirect
61. #2084C22semidirect
63. #2072C22semidirect
64. #2057C22semidirect
65. #2041C22semidirect
68. #2024C22semidirect
69. #2014C22semidirect
71. #1928C22semidirect
72. #1926C22semidirect
73. #1925C22semidirect
74. #1921C22semidirect
75. #1920C22semidirect
76. #1919C22semidirect
79. #1880C22semidirect
80. #1880C22semidirect
81. #1877C22semidirect
84. #1863C22semidirect
85. #1863C22semidirect
86. #1862C22semidirect
328. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#366242
C2×C4×C22⋊Q82
#330962
#330032
#301762
#301152
#294132
#291602
#285742
#276132
#275862
#245502
#243812
#240602
#239312
#221852
C2×#18172