Finite Group Databasebeta

← #6476678

Subgroups — #6476678

Order 512.

2270 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2850C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3#33111C212yesmaximal, complemented
4#32909C212yesmaximal, complemented
5#30110C214yesmaximal, complemented
6#29330C212yesmaximal, complemented
7#28306C212yesmaximal, complemented
8#27686C212yesmaximal, complemented
9#24655C214yesmaximal, complemented
10#24217C212yesmaximal, complemented
11#24003C211yesmaximal, characteristic, complemented
12#24002C211yesmaximal, characteristic
13#23921C211yesmaximal, characteristic, complemented
14#23919C211yesmaximal, characteristic
15#22044C212yesmaximal, complemented
16#22043C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic, complemented
23C23×C42C2211yescharacteristic
24C2×#483C2212yescomplemented
25C2×#480C2212yes—
26C2×#464C2214yescomplemented
27C2×#451C2212yes—
28C2×#451C2212yescomplemented
29C2×#448C2212yes—
30C2×#450C2212yes—
31C2×#431C2212yescomplemented
32#2850—21no—
33#2850—21no—
34#2850—21no—
35#2850—21no—
36#2850C2212yes—
37#2850C2212yes—
38#2850C2212yes—
39#2850C2212yes—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8—21no—
43C4×C22⋊Q8—21no—
44C4×C22⋊Q8C2212yes—
45C4×C22⋊Q8C2212yes—
46C4×C22⋊Q8C2212yescomplemented
47C4×C22⋊Q8C2212yescomplemented
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic, complemented
50C2×#390C2211yescharacteristic
51C2×#389C2211yescharacteristic, complemented
52C2×#388—21no—
53C2×#388—21no—
54C2×#387—21no—
55C2×#386—21no—
56C2×#386—21no—
57C2×#385—21no—
58C2×#382C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4—21no—
61C2×C4×C4⋊C4C2211yescharacteristic, complemented
62C2×C4×C22⋊C4—21no—
63#2101C2214yescomplemented
64#2097C2214yescomplemented
65#2042C2214yescomplemented
66#2035C2214yescomplemented
67#2033C2214yes—
68#2015C2214yescomplemented
69#2001C2214yescomplemented
70#2000C2214yes—
71#1983C2214yescomplemented
72#1969C2214yescomplemented
73#1968C2214yescomplemented
74#1949C2214yescomplemented
75#1934C2214yescomplemented
76#1933C2214yescomplemented
77#1928C2214yescomplemented
78#1926C2214yescomplemented
79#1880C2214yescomplemented
80#1878C2214yescomplemented
81#1874C2212yes—
82#1874C2212yes—
83#1872C2212yes—
84#1872C2212yes—
85#1872C2212yescomplemented
86#1872C2212yescomplemented
87#1853C2212yes—
88#1852C2212yes—
89#1817C2212yescomplemented
90#1805C2214yescomplemented
91#1797C2212yes—
92#1797C2212yescomplemented
93#1787C2212yes—
94#1786C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97C4×C22⋊C8C2212yes—
98C4×C22⋊C8C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×Q8C2311yescharacteristic
101C23×D4—21no—
102C23×D4C2311yescharacteristic
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×Q16C2314yes—
107C22×SD16C2314yes—
108C2×#124—21no—
109C2×#124—21no—
110C2×#124—44no—
111C2×#124C2312yes—
112C2×#124C2312yes—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—21no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—21no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8—44no—
119C2×C22⋊Q8C2312yes—
120C2×C22⋊Q8C2312yes—
121C2×C22⋊Q8C2312yes—
122C2×C22⋊Q8C2312yes—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—44no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—44no—
131C2×C4×Q8C2312yes—
132C2×C4×Q8C2312yes—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4—21no—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C22⋊C4—21no—
150C22×C42—21no—
151C22×C42—21no—
152C22×C42—44no—
153C22×C42D411yescharacteristic
154C22×C42D411yescharacteristic
155C22×C42D411yescharacteristic
156C22×C42D411yescharacteristic
157C22×C42D411yescharacteristic
158C22×C42D411yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#483—44no—
166#480—44no—
167#464—48no—
168#451—28no—
169#451—44no—
170#450—28no—
171#448—44no—
172#431—44no—
173C2×#107C2314yes—
174C2×#106C2314yes—
175C2×C4⋊C8C2314yes—
176C2×#103C2314yes—
177C2×#103C2314yes—
178C2×#103C2314yes—
179C2×#103C2314yes—
180C2×#103C2314yes—
181C2×#102C2314yes—
182C2×#102C2314yes—
183C2×#102C2314yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C4×C8C2314yes—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#391C2312yes—
199#390—21no—
200#390—21no—
201#390C2312yes—
202#390C2312yes—
203#389—21no—
204#389—21no—
205#389C2312yes—
206#389C2312yes—
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#387—22no—
216#387—22no—
217#387—22no—
218#387—22no—
219#386—22no—
220#386—22no—
221#386—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#382—21no—
232#382—21no—
233#382C2312yes—
234#382C2312yes—
235#380—21no—
236#380—21no—
237#380C2312yes—
238#380C2312yes—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C2×#95—21no—
252C2×#95—21no—
253C2×#95—21no—
254C2×#95—21no—
255C2×#95—21no—
256C2×#95—21no—
257C2×#95—21no—
258C2×#95—21no—
259C2×#95—21no—
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#336C2314yes—
265#336C2314yes—
266C25—21no—
267C25C2×D411yescharacteristic
268C22×Q8—24no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—24no—
272C22×Q8—24no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8C2412yes—
277C22×Q8C2412yes—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—21no—
281C22×D4—24no—
282C22×D4—42no—
283C22×D4—42no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4—44no—
287C22×D4C2412yes—
288C23×C4—24no—
289C23×C4—21no—
290C23×C4—21no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—21no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2×D411yescharacteristic
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C2×Q16—28no—
323C2×Q16—44no—
324C2×Q16—44no—
325C2×SD16—28no—
326C2×SD16—44no—
327C2×SD16—44no—
328C22×C8C2414yes—
329C22×C8C2414yes—
330#124—28no—
331#124—44no—
332#124—44no—
333#124—44no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—42no—
342C22⋊Q8—42no—
343C22⋊Q8—44no—
344C22⋊Q8—44no—
345C22⋊Q8#4118yes—
346#121—24no—
347#121—24no—
348#121—42no—
349#121—42no—
350#121—44no—
351#121—44no—
352C4×Q8—28no—
353C4×Q8—44no—
354C4×Q8—44no—
355C4×Q8—44no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
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—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C22⋊C4—28no—
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—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—44no—
424C2×C42—44no—
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×C42C2×D411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441#107—44no—
442#106—44no—
443C4⋊C8—28no—
444#103—28no—
445#103—44no—
446#103—44no—
447#103—44no—
448#103—44no—
449#102—28no—
450#102—44no—
451#102—44no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—42no—
457C22⋊C8—42no—
458C4×C8—44no—
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—
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—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—41no—
483C24—41no—
484C24—42no—
485C24—42no—
486C24—42no—
487C24—42no—
488C24—42no—
489C24—42no—
490C24—42no—
491C24#13514yes—
492C24C22×D411yescharacteristic
493C24C22×D411yescharacteristic
494C24C22×D411yescharacteristic
495C2×Q8—24no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—22no—
501C2×Q8—24no—
502C2×Q8—22no—
503C2×Q8—416no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—88no—
510C2×Q8C2×#4114yes—
511C2×D4—24no—
512C2×D4—22no—
513C2×D4—24no—
514C2×D4—22no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—42no—
524C2×D4—88no—
525C2×D4—816no—
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—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4#13714yes—
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C2×#4114yes—
621C22×C4H(5,𝔽2)14yes—
622C22×C4C2511yescharacteristic
623Q16—88no—
624SD16—88no—
625C2×C8—24no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—24no—
630C2×C8—24no—
631C4⋊C4—24no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—44no—
642C4⋊C4—42no—
643C4⋊C4—44no—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—44no—
647C4⋊C4—44no—
648C4⋊C4—42no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4C2×#4114yes—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—44no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—22no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C42—44no—
684C42—44no—
685C42—44no—
686C42—44no—
687C42H(5,𝔽2)14yes—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—28no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—28no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23#52512yes—
724C23#53512yes—
725C23C2×#13512yes—
726C23C2×#13512yes—
727C23C2×#13512yes—
728C23C2×#13712yes—
729C23#57512yes—
730C23C23×D411yescharacteristic
731Q8—28no—
732Q8—48no—
733Q8—44no—
734Q8—44no—
735Q8—44no—
736Q8—84no—
737D4—44no—
738D4—44no—
739D4—84no—
740D4—88no—
741D4—88no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—48no—
787C2×C4—44no—
788C2×C4—48no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4#52512yes—
815C2×C4#53412yes—
816C2×C4#53412yes—
817C2×C4#53512yes—
818C2×C4C2×#13712yes—
819C2×C4C2×#13712yes—
820C2×C4#57512yes—
821C2×C4C22×#4112yes—
822C2×C4C2×H(5,𝔽2)12yes—
823C2×C4C2×H(5,𝔽2)12yes—
824C8—44no—
825C8—44no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—416no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—168no—
854C22#310814yes—
855C22#321114yes—
856C22C2×#52511yescharacteristic
857C22C2×#53411yescharacteristic
858C22C2×#53511yescharacteristic
859C22C22×#13511yescharacteristic
860C22C22×#13711yescharacteristic
861C22C2×#57511yescharacteristic
862C22C2×#57511yescharacteristic
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—41no—
871C4—44no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—44no—
876C4—82no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4#351914yes—
882C2—24no—
883C2—24no—
884C2—42no—
885C2—162no—
886C2#3507611yescharacteristic
887C2C2×#310811yescharacteristic
888C2#6056311yescharacteristic
889C2#6073411yescharacteristic
890C2#6075111yescharacteristic
891C2C2×#321111yescharacteristic
892C2#6080411yescharacteristic
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. #33111C2semidirect
4. #32909C2semidirect
5. #30110C2semidirect
6. #29330C2semidirect
7. #28306C2semidirect
8. #27686C2semidirect
9. #24655C2semidirect
10. #24217C2semidirect
11. #24003C2semidirect
13. #23921C2semidirect
15. #22044C2semidirect
16. #22043C2semidirect
17. #20714C2semidirect
22. C22×C4×Q8C22semidirect
24. C2×#483C22semidirect
26. C2×#464C22semidirect
28. C2×#451C22semidirect
31. C2×#431C22semidirect
46. C4×C22⋊Q8C22semidirect
47. C4×C22⋊Q8C22semidirect
49. C2×#391C22semidirect
51. C2×#389C22semidirect
61. C2×C4×C4⋊C4C22semidirect
63. #2101C22semidirect
64. #2097C22semidirect
65. #2042C22semidirect
66. #2035C22semidirect
68. #2015C22semidirect
69. #2001C22semidirect
71. #1983C22semidirect
72. #1969C22semidirect
73. #1968C22semidirect
74. #1949C22semidirect
75. #1934C22semidirect
76. #1933C22semidirect
77. #1928C22semidirect
78. #1926C22semidirect
79. #1880C22semidirect
80. #1878C22semidirect
85. #1872C22semidirect
86. #1872C22semidirect
89. #1817C22semidirect
90. #1805C22semidirect
92. #1797C22semidirect
98. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28502
C2×C4×C22⋊Q82
#331112
#329092
#301102
#293302
#283062
#276862
#246552
#242172
#240032
#240022
#239212
#239192
#220442
#220432
#207142