Finite Group Databasebeta

← #6476177

Subgroups — #6476177

Order 512.

2174 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33094C212yesmaximal, complemented
4#33005C212yesmaximal, complemented
5#30019C214yesmaximal, complemented
6#29482C214yesmaximal, complemented
7#29243C212yesmaximal, complemented
8#28123C212yesmaximal, complemented
9#27603C211yesmaximal, characteristic, complemented
10#24607C212yesmaximal, complemented
11#24509C212yesmaximal, complemented
12#24006C211yesmaximal, characteristic, complemented
13#24005C211yesmaximal, characteristic
14#23919C211yesmaximal, characteristic
15#22085C212yesmaximal, complemented
16#22049C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic, complemented
18C22×#123—21no—
19C22×C22⋊Q8C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic, complemented
22C23×C42C2211yescharacteristic
23C2×#484C2212yes—
24C2×#481C2212yes—
25C2×#448C2212yes—
26C2×#450C2212yes—
27C2×#432C2212yescomplemented
28#2854—21no—
29#2854—21no—
30#2854—21no—
31#2854—21no—
32#2854C2212yes—
33#2854C2212yes—
34#2854C2212yes—
35#2854C2212yes—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8C2212yes—
41C4×C22⋊Q8C2212yes—
42C4×C22⋊Q8C2212yescomplemented
43C4×C22⋊Q8C2212yescomplemented
44C2×#391C2211yescharacteristic, complemented
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic, complemented
50C2×#388—21no—
51C2×#388—21no—
52C2×#387—21no—
53C2×#386—21no—
54C2×#385—21no—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4—21no—
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4—21no—
60#2088C2214yescomplemented
61#2076C2214yescomplemented
62#2068C2214yescomplemented
63#2067C2214yescomplemented
64#2055C2214yescomplemented
65#2036C2214yescomplemented
66#2034C2214yes—
67#2000C2214yes—
68#1973C2214yescomplemented
69#1943C2214yescomplemented
70#1936C2214yescomplemented
71#1935C2214yescomplemented
72#1925C2214yescomplemented
73#1925C2214yescomplemented
74#1918C2214yescomplemented
75#1918C2214yescomplemented
76#1880C2214yescomplemented
77#1880C2214yescomplemented
78#1874C2212yes—
79#1874C2212yes—
80#1872C2212yes—
81#1872C2212yes—
82#1865C2214yescomplemented
83#1865C2214yescomplemented
84#1853C2212yes—
85#1852C2212yes—
86#1852C2212yescomplemented
87#1852C2212yescomplemented
88#1824C2212yes—
89#1824C2212yescomplemented
90#1817C2212yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1787C2212yescomplemented
94#1786C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97#1749C2212yes—
98#1749C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4D411yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4C2311yescharacteristic
105C22×SD16C2314yes—
106C2×#123—22no—
107C2×#123—22no—
108C2×#123—22no—
109C2×#123—22no—
110C2×#123—48no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8C2312yes—
115C2×C22⋊Q8C2312yes—
116C2×#121—21no—
117C2×#121—21no—
118C2×#121—44no—
119C2×#121C2312yes—
120C2×#121C2312yes—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—44no—
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2312yes—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C42—21no—
146C22×C42—21no—
147C22×C42—44no—
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#484—28no—
161#481—44no—
162#450—28no—
163#448—44no—
164#432—44no—
165C2×#107C2314yes—
166C2×#107C2314yes—
167C2×#106C2314yes—
168C2×C4⋊C8C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×#97C2314yes—
182#391—21no—
183#391—21no—
184#391C2312yes—
185#391C2312yes—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390C2312yes—
191#390C2312yes—
192#390C2312yes—
193#390C2312yes—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#389C2312yes—
205#389C2312yes—
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#387—22no—
215#387—22no—
216#387—22no—
217#387—22no—
218#386—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#385—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#380—21no—
227#380—21no—
228#380—21no—
229#380—21no—
230#380C2312yes—
231#380C2312yes—
232#380C2312yes—
233#380C2312yes—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C2×#95—21no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#340C2314yes—
259#340C2314yes—
260#336C2314yes—
261#336C2314yes—
262C25—21no—
263C25C2×D411yescharacteristic
264C22×Q8—24no—
265C22×Q8—21no—
266C22×Q8—24no—
267C22×Q8—42no—
268C22×Q8C2412yes—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—21no—
272C22×D4—24no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2412yes—
279C23×C4—24no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
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×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C2×SD16—28no—
314C2×SD16—44no—
315C2×SD16—44no—
316C22×C8C2414yes—
317C22×C8C2414yes—
318#123—48no—
319#123—48no—
320#123—48no—
321#123—48no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8#4118yes—
328#121—24no—
329#121—24no—
330#121—42no—
331#121—42no—
332#121—44no—
333#121—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8—44no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C22⋊C4—28no—
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—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—24no—
396C2×C42—24no—
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—28no—
430#107—44no—
431#106—44no—
432C4⋊C8—44no—
433#103—28no—
434#103—44no—
435#103—44no—
436#102—28no—
437#102—44no—
438#102—44no—
439C22⋊C8—24no—
440C22⋊C8—24no—
441C22⋊C8—24no—
442C22⋊C8—24no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445#97—44no—
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—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—41no—
468C24—41no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24#13714yes—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C24C22×D411yescharacteristic
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—416no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8C2×#4114yes—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—24no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—88no—
502C2×D4—816no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
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—22no—
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—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—416no—
564C22×C4—416no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—416no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4AGL(1,ℤ/8)14yes—
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C2×#4114yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4C2511yescharacteristic
600SD16—88no—
601C2×C8—24no—
602C2×C8—24no—
603C2×C8—24no—
604C2×C8—24no—
605C2×C8—24no—
606C2×C8—24no—
607C4⋊C4—24no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4C2×#4114yes—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—44no—
664C42—44no—
665C42—44no—
666C42—44no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—28no—
676C23—21no—
677C23—21no—
678C23—28no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23#52512yes—
703C23#53412yes—
704C23C2×AGL(1,ℤ/8)12yes—
705C23C2×#13712yes—
706C23C2×#13712yes—
707C23C2×#13712yes—
708C23#57512yes—
709C23C23×D411yescharacteristic
710Q8—28no—
711Q8—48no—
712Q8—44no—
713D4—44no—
714D4—44no—
715D4—84no—
716D4—88no—
717D4—88no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—28no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—24no—
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—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—48no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—48no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4#52512yes—
793C2×C4#53412yes—
794C2×C4C2×AGL(1,ℤ/8)12yes—
795C2×C4C2×AGL(1,ℤ/8)12yes—
796C2×C4#57512yes—
797C2×C4C22×#4112yes—
798C2×C4C2×H(5,𝔽2)12yes—
799C2×C4#58512yes—
800C8—44no—
801C8—44no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—416no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—168no—
830C22#311714yes—
831C22#319314yes—
832C22C2×#52511yescharacteristic
833C22C2×#53411yescharacteristic
834C22#344911yescharacteristic
835C22C22×AGL(1,ℤ/8)11yescharacteristic
836C22C22×#13711yescharacteristic
837C22C2×#57511yescharacteristic
838C22C2×#57511yescharacteristic
839C4—22no—
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—44no—
850C4—41no—
851C4—44no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4#351314yes—
858C2—24no—
859C2—24no—
860C2—42no—
861C2—162no—
862C2#3506211yescharacteristic
863C2C2×#311711yescharacteristic
864C2#6056111yescharacteristic
865C2C2×#319311yescharacteristic
866C2#6075211yescharacteristic
867C2#6094911yescharacteristic
868C2#6096011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
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. #33094C2semidirect
4. #33005C2semidirect
5. #30019C2semidirect
6. #29482C2semidirect
7. #29243C2semidirect
8. #28123C2semidirect
9. #27603C2semidirect
10. #24607C2semidirect
11. #24509C2semidirect
12. #24006C2semidirect
15. #22085C2semidirect
16. #22049C2semidirect
17. #20715C2semidirect
21. C22×C4×Q8C22semidirect
27. C2×#432C22semidirect
42. C4×C22⋊Q8C22semidirect
43. C4×C22⋊Q8C22semidirect
44. C2×#391C22semidirect
49. C2×#389C22semidirect
58. C2×C4×C4⋊C4C22semidirect
60. #2088C22semidirect
61. #2076C22semidirect
62. #2068C22semidirect
63. #2067C22semidirect
64. #2055C22semidirect
65. #2036C22semidirect
68. #1973C22semidirect
69. #1943C22semidirect
70. #1936C22semidirect
71. #1935C22semidirect
72. #1925C22semidirect
73. #1925C22semidirect
74. #1918C22semidirect
75. #1918C22semidirect
76. #1880C22semidirect
77. #1880C22semidirect
82. #1865C22semidirect
83. #1865C22semidirect
86. #1852C22semidirect
87. #1852C22semidirect
89. #1824C22semidirect
90. #1817C22semidirect
92. #1797C22semidirect
93. #1787C22semidirect
98. #1749C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×C4×C22⋊Q82
#330942
#330052
#300192
#294822
#292432
#281232
#276032
#246072
#245092
#240062
#240052
#239192
#220852
#220492
#207152