Finite Group Databasebeta

← #6476157

Subgroups — #6476157

Order 512.

2276 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#33098C212yesmaximal, complemented
4#33007C212yesmaximal, complemented
5#30008C214yesmaximal, complemented
6#29464C214yesmaximal, complemented
7#29235C212yesmaximal, complemented
8#28115C212yesmaximal, complemented
9#27601C211yesmaximal, characteristic, complemented
10#24601C212yesmaximal, complemented
11#24501C212yesmaximal, complemented
12#24005C211yesmaximal, characteristic
13#24003C211yesmaximal, characteristic, complemented
14#23919C211yesmaximal, characteristic
15#22076C212yesmaximal, complemented
16#22041C212yesmaximal, complemented
17#20714C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2211yescharacteristic
22C23×C42C2211yescharacteristic
23C2×#481C2212yes—
24C2×#483C2212yes—
25C2×#448C2212yes—
26C2×#450C2212yes—
27C2×#431C2212yes—
28#2855—21no—
29#2855—21no—
30#2855—21no—
31#2855—21no—
32#2855C2212yes—
33#2855C2212yes—
34#2855C2212yescomplemented
35#2855C2212yescomplemented
36C4×#121—21no—
37C4×#121—21no—
38C4×#121—21no—
39C4×#121—21no—
40C4×#121C2212yes—
41C4×#121C2212yes—
42C4×#121C2212yes—
43C4×#121C2212yes—
44C2×#391C2211yescharacteristic, complemented
45C2×#391C2211yescharacteristic, complemented
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic, complemented
49C2×#389C2211yescharacteristic, complemented
50C2×#388—21no—
51C2×#387—21no—
52C2×#387—21no—
53C2×#386—21no—
54C2×#385—21no—
55C2×#381—21no—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4—21no—
60#2088C2214yescomplemented
61#2077C2214yescomplemented
62#2066C2214yescomplemented
63#2065C2214yescomplemented
64#2055C2214yescomplemented
65#2035C2214yescomplemented
66#2034C2214yes—
67#2000C2214yes—
68#1968C2214yescomplemented
69#1941C2214yescomplemented
70#1934C2214yescomplemented
71#1933C2214yescomplemented
72#1927C2214yescomplemented
73#1927C2214yescomplemented
74#1920C2214yescomplemented
75#1920C2214yescomplemented
76#1877C2214yescomplemented
77#1877C2214yescomplemented
78#1874C2212yes—
79#1874C2212yes—
80#1872C2212yes—
81#1872C2212yes—
82#1864C2214yescomplemented
83#1864C2214yescomplemented
84#1853C2212yes—
85#1853C2212yes—
86#1853C2212yescomplemented
87#1853C2212yescomplemented
88#1824C2212yescomplemented
89#1823C2212yes—
90#1817C2212yes—
91#1797C2212yescomplemented
92#1797C2212yescomplemented
93#1787C2212yescomplemented
94#1786C2212yes—
95#1779C2211yescharacteristic
96#1779C2211yescharacteristic
97C4×C22⋊C8C2212yescomplemented
98C4×C22⋊C8C2212yescomplemented
99C23×Q8C2311yescharacteristic
100C23×D4—21no—
101C23×D4C2311yescharacteristic
102C24×C4—21no—
103C24×C4D411yescharacteristic
104C24×C4D411yescharacteristic
105C24×C4C2311yescharacteristic
106C22×SD16C2314yes—
107C2×C22⋊Q8—21no—
108C2×C22⋊Q8—21no—
109C2×C22⋊Q8—44no—
110C2×C22⋊Q8C2312yes—
111C2×C22⋊Q8C2312yes—
112C2×#121—21no—
113C2×#121—21no—
114C2×#121—28no—
115C2×#121C2312yes—
116C2×#121C2312yes—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—21no—
122C2×C4×D4—21no—
123C2×C4×D4—44no—
124C2×C4×D4—48no—
125C2×C4×D4C2312yes—
126C2×C4×D4C2312yes—
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×C42—21no—
145C22×C42—44no—
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#483—44no—
159#481—28no—
160#450—44no—
161#448—28no—
162#431—44no—
163C2×#106C2314yes—
164C2×#106C2314yes—
165C2×#106C2314yes—
166C2×C4⋊C8C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C4×C8C2314yes—
180#391—21no—
181#391—21no—
182#391—21no—
183#391—21no—
184#391C2312yes—
185#391C2312yes—
186#391C2312yes—
187#391C2312yes—
188#390—21no—
189#390—21no—
190#390C2312yes—
191#390C2312yes—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389C2312yes—
199#389C2312yes—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#387—22no—
213#387—22no—
214#387—22no—
215#387—22no—
216#386—22no—
217#386—22no—
218#386—22no—
219#386—22no—
220#385—22no—
221#385—22no—
222#385—22no—
223#385—22no—
224#381—22no—
225#381—22no—
226#381—22no—
227#381—22no—
228#380—21no—
229#380—21no—
230#380—21no—
231#380—21no—
232#380C2312yes—
233#380C2312yes—
234#380C2312yes—
235#380C2312yes—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
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—
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—21no—
265C22×Q8—24no—
266C22×Q8—42no—
267C22×Q8—42no—
268C22×Q8C2412yes—
269C22×D4—28no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—24no—
273C22×D4—21no—
274C22×D4—24no—
275C22×D4—42no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2412yes—
279C23×C4—21no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4SD1618yescomplemented
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×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×SD16—28no—
319C2×SD16—44no—
320C2×SD16—44no—
321C22×C8C2414yes—
322C22×C8C2414yes—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—42no—
326C22⋊Q8—42no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—28no—
330#121—28no—
331#121—24no—
332#121—24no—
333#121—24no—
334#121#4118yes—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—48no—
340C4×D4—48no—
341C4×D4—48no—
342C4×D4—48no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
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—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C22⋊C4—28no—
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×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
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×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425#106—28no—
426#106—44no—
427#106—44no—
428C4⋊C8—44no—
429#103—28no—
430#103—44no—
431#103—44no—
432#102—28no—
433#102—44no—
434#102—44no—
435C22⋊C8—24no—
436C22⋊C8—24no—
437C22⋊C8—24no—
438C22⋊C8—24no—
439C22⋊C8—42no—
440C22⋊C8—42no—
441C4×C8—44no—
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—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—24no—
467C24—22no—
468C24—41no—
469C24—41no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24—42no—
474C24—42no—
475C24—42no—
476C24C2×SD1614yes—
477C24C22×D411yescharacteristic
478C24C22×D411yescharacteristic
479C24C22×D411yescharacteristic
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—24no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—88no—
488C2×D4—24no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—416no—
495C2×D4—42no—
496C2×D4—432no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4C2×#4114yes—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
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—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—416no—
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—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—42no—
564C22×C4—416no—
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—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—44no—
585C22×C4—44no—
586C22×C4—816no—
587C22×C4C2×SD1614yes—
588C22×C4C2×SD1614yes—
589C22×C4C2×SD1614yes—
590C22×C4C2×SD1614yes—
591C22×C4C2×SD1614yes—
592C22×C4C2×SD1614yes—
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D411yescharacteristic
597C22×C4C22×D411yescharacteristic
598C22×C4C22×D411yescharacteristic
599C22×C4C22×D411yescharacteristic
600C22×C4C22×D411yescharacteristic
601C22×C4C22×D411yescharacteristic
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D411yescharacteristic
604C22×C4C2×#4114yes—
605C22×C4H(5,𝔽2)14yes—
606C22×C4C2511yescharacteristic
607SD16—88no—
608C2×C8—24no—
609C2×C8—24no—
610C2×C8—24no—
611C2×C8—24no—
612C2×C8—24no—
613C2×C8—24no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—22no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4C2×#4114yes—
636C22⋊C4—28no—
637C22⋊C4—28no—
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—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—41no—
659C42—41no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—44no—
667C42—44no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—28no—
677C23—21no—
678C23—28no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—24no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—48no—
691C23—48no—
692C23—48no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23#52512yes—
704C23#53412yes—
705C23C22×SD1612yes—
706C23C22×SD1612yes—
707C23C22×SD1612yes—
708C23#57512yes—
709C23#57512yes—
710C23C23×D411yescharacteristic
711Q8—44no—
712Q8—44no—
713Q8—84no—
714D4—28no—
715D4—48no—
716D4—416no—
717D4—416no—
718D4—44no—
719C2×C4—21no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
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—28no—
736C2×C4—28no—
737C2×C4—21no—
738C2×C4—24no—
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—44no—
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—44no—
762C2×C4—48no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—88no—
786C2×C4—88no—
787C2×C4—84no—
788C2×C4—84no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—84no—
792C2×C4—84no—
793C2×C4#52512yes—
794C2×C4#53412yes—
795C2×C4C22×SD1612yes—
796C2×C4C22×SD1612yes—
797C2×C4C22×SD1612yes—
798C2×C4C22×SD1612yes—
799C2×C4#57512yes—
800C2×C4C22×#4112yes—
801C2×C4C2×H(5,𝔽2)12yes—
802C2×C4#58512yes—
803C8—44no—
804C8—44no—
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—22no—
818C22—22no—
819C22—22no—
820C22—416no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—816no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22#310114yes—
834C22#318714yes—
835C22C2×#52511yescharacteristic
836C22C2×#53411yescharacteristic
837C22#344911yescharacteristic
838C22C23×SD1611yescharacteristic
839C22C2×#57511yescharacteristic
840C22C2×#57511yescharacteristic
841C22C2×#57511yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—44no—
853C4—41no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4#351314yes—
861C2—24no—
862C2—24no—
863C2—42no—
864C2—84no—
865C2#3506211yescharacteristic
866C2C2×#310111yescharacteristic
867C2#6056311yescharacteristic
868C2C2×#318711yescharacteristic
869C2#6075211yescharacteristic
870C2#6094111yescharacteristic
871C2#6096411yescharacteristic
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
1. C2×#2855C2semidirect
3. #33098C2semidirect
4. #33007C2semidirect
5. #30008C2semidirect
6. #29464C2semidirect
7. #29235C2semidirect
8. #28115C2semidirect
9. #27601C2semidirect
10. #24601C2semidirect
11. #24501C2semidirect
13. #24003C2semidirect
15. #22076C2semidirect
16. #22041C2semidirect
17. #20714C2semidirect
34. #2855C22semidirect
35. #2855C22semidirect
44. C2×#391C22semidirect
45. C2×#391C22semidirect
48. C2×#389C22semidirect
49. C2×#389C22semidirect
60. #2088C22semidirect
61. #2077C22semidirect
62. #2066C22semidirect
63. #2065C22semidirect
64. #2055C22semidirect
65. #2035C22semidirect
68. #1968C22semidirect
69. #1941C22semidirect
70. #1934C22semidirect
71. #1933C22semidirect
72. #1927C22semidirect
73. #1927C22semidirect
74. #1920C22semidirect
75. #1920C22semidirect
76. #1877C22semidirect
77. #1877C22semidirect
82. #1864C22semidirect
83. #1864C22semidirect
86. #1853C22semidirect
87. #1853C22semidirect
88. #1824C22semidirect
91. #1797C22semidirect
92. #1797C22semidirect
93. #1787C22semidirect
97. C4×C22⋊C8C22semidirect
98. C4×C22⋊C8C22semidirect
299. C23×C4SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×C4×#1212
#330982
#330072
#300082
#294642
#292352
#281152
#276012
#246012
#245012
#240052
#240032
#239192
#220762
#220412
#207142