Finite Group Databasebeta

← #6512631

Subgroups — #6512631

Order 512.

3420 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#3117C212yesmaximal, complemented
3C2×#2538C211yesmaximal, characteristic, complemented
4#24259C214yesmaximal, complemented
5#24258C214yesmaximal, complemented
6#24139C214yesmaximal, complemented
7#24138C214yesmaximal, complemented
8#24007C212yesmaximal, complemented
9#24006C211yesmaximal, characteristic, complemented
10#24005C211yesmaximal, characteristic, complemented
11#23922C212yesmaximal, complemented
12#23921C211yesmaximal, characteristic, complemented
13#23919C211yesmaximal, characteristic, complemented
14#21867C212yesmaximal, complemented
15#21790C211yesmaximal, characteristic, complemented
16#3505—216no—
17C2×#553—22no—
18C2×#553C2212yes—
19C2×#552C2212yes—
20C2×#551—22no—
21C2×#548C2212yes—
22C2×#546C2212yes—
23C2×#539—21no—
24C2×#538—21no—
25C2×#534—21no—
26C2×#529C2212yes—
27C2×#525C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic, complemented
31C22×#121C2211yescharacteristic
32C2×#518—21no—
33C22×C4×Q8C2211yescharacteristic, complemented
34C22×C4×D4C2211yescharacteristic
35#3117—216no—
36C2×#484C2212yescomplemented
37C2×#481C2212yes—
38C2×#479C2214yescomplemented
39C2×#464C2214yescomplemented
40C2×#452C2214yescomplemented
41C2×#451C2212yescomplemented
42C2×#451C2212yescomplemented
43C2×#448C2212yes—
44C2×#450C2212yescomplemented
45C2×#441C2214yescomplemented
46C2×#440C2214yescomplemented
47C2×#432C2212yescomplemented
48#2538—22no—
49#2538—22no—
50#2538C2214yes—
51#2538C2214yescomplemented
52C2×#396—21no—
53C2×#396—21no—
54C2×#390—21no—
55C2×#389—21no—
56C2×#384C2211yescharacteristic, complemented
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic, complemented
59#2036C2214yescomplemented
60#2035C2214yescomplemented
61#2034C2214yescomplemented
62#2033C2214yescomplemented
63#2001C2214yescomplemented
64#2001C2214yescomplemented
65#2000C2214yescomplemented
66#2000C2214yescomplemented
67#1992C2214yescomplemented
68#1959C2214yescomplemented
69#1955C2214yes—
70#1955C2214yescomplemented
71#1874C2212yes—
72#1874C2212yes—
73#1873C2214yescomplemented
74#1872C2212yescomplemented
75#1872C2212yescomplemented
76#1872C2212yescomplemented
77#1872C2212yescomplemented
78#1854C2214yescomplemented
79#1853C2212yescomplemented
80#1852C2212yescomplemented
81#1803C2214yescomplemented
82#1802C2214yescomplemented
83#1788C2214yescomplemented
84#1787C2212yescomplemented
85#1786C2212yescomplemented
86#1779C2211yescharacteristic
87#1779C2211yescharacteristic
88#1779C2212yescomplemented
89C22×#41C2312yes—
90C23×Q8C2311yescharacteristic
91C23×Q8C2311yescharacteristic
92C23×D4—21no—
93C23×D4D411yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C22×Q16C2314yes—
98C22×SD16C2314yes—
99#553—232no—
100#553—28no—
101#553—28no—
102#552—28no—
103#552—28no—
104#551—232no—
105#548—28no—
106#548—28no—
107#546—28no—
108#546—28no—
109#539—216no—
110#538—216no—
111#534—216no—
112#529—28no—
113#529D4116yes—
114C2×#126—22no—
115C2×#126—22no—
116C2×#126—22no—
117C2×#125—22no—
118C2×#125C2312yes—
119C2×#124—22no—
120C2×#124C2312yes—
121#525—28no—
122#525—28no—
123C2×#123—22no—
124C2×#123—22no—
125C2×#123—22no—
126C2×#123—22no—
127C2×#123—22no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—28no—
131C2×C22⋊Q8—21no—
132C2×C22⋊Q8—21no—
133C2×C22⋊Q8—22no—
134C2×C22⋊Q8—22no—
135C2×C22⋊Q8—44no—
136C2×C22⋊Q8—44no—
137C2×C22⋊Q8C2312yes—
138C2×C22⋊Q8C2312yes—
139C2×C22⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2314yes—
142C2×C22⋊Q8C2312yes—
143C2×#121—22no—
144C2×#121—22no—
145C2×#121—21no—
146C2×#121—21no—
147C2×#121—28no—
148C2×#121—22no—
149C2×#121C2312yes—
150C2×#121C2312yes—
151C2×#121C2312yes—
152C2×#120—22no—
153C2×#120—22no—
154#518—216no—
155C2×C4×Q8—22no—
156C2×C4×Q8—28no—
157C2×C4×Q8C2314yes—
158C2×C4×Q8C2312yes—
159C2×C4×D4—22no—
160C2×C4×D4—22no—
161C2×C4×D4—22no—
162C2×C4×D4—22no—
163C2×C4×D4—22no—
164C2×C4×D4—28no—
165C2×C4×D4D412yes—
166C2×C4×D4D412yes—
167C2×C4×D4C2312yes—
168C2×C4×D4C2312yes—
169C2×C4×D4C2312yes—
170C2×#117—22no—
171C2×#117—22no—
172C2×#117C2312yes—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4—21no—
179C22×C4⋊C4D411yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C22⋊C4—21no—
186C22×C22⋊C4—21no—
187C22×C22⋊C4—22no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—21no—
190C22×C22⋊C4—21no—
191C22×C22⋊C4—21no—
192C22×C22⋊C4D411yescharacteristic
193C22×C22⋊C4D411yescharacteristic
194C22×C42—21no—
195C22×C42C2311yescharacteristic
196#484—28no—
197#481—28no—
198#479—216no—
199#464—216no—
200#452—48no—
201#451—28no—
202#451—44no—
203#450—44no—
204#448—28no—
205#441—216no—
206#440—216no—
207#432—28no—
208C2×#107C2314yes—
209C2×#106C2314yes—
210C2×C4⋊C8C2314yes—
211C2×#103C2314yes—
212C2×#103C2314yes—
213C2×#103C2314yes—
214C2×#103C2314yes—
215C2×#103C2314yes—
216C2×#102C2314yes—
217C2×#102C2314yes—
218C2×#102C2314yes—
219C2×C22⋊C8C2312yes—
220C2×C22⋊C8C2312yes—
221C2×C22⋊C8C2312yes—
222C2×C22⋊C8C2312yes—
223C2×C22⋊C8C2314yes—
224C2×C22⋊C8C2312yes—
225C2×C22⋊C8C2312yes—
226C2×C22⋊C8C2314yes—
227C2×#97C2314yes—
228#396—24no—
229#396—24no—
230#396—24no—
231#396—24no—
232#390—24no—
233#390—24no—
234#389—24no—
235#389—24no—
236#384—22no—
237#384C2314yes—
238#380—21no—
239#380—21no—
240#380—22no—
241#380C2312yes—
242#380C2312yes—
243#380C2314yes—
244C2×#95—21no—
245C2×#95—21no—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#340C2314yes—
250C25—21no—
251C25C2×D411yescharacteristic
252C25C2×D411yescharacteristic
253C2×#41—24no—
254C2×#41—24no—
255C2×#41—44no—
256C2×#41—44no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—21no—
260C22×Q8—21no—
261C22×Q8—24no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8C2412yes—
266C22×Q8C2412yes—
267C22×D4—28no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—21no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4C2×D412yes—
282C22×D4C2×D412yes—
283C22×D4C2412yes—
284C23×C4—21no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—21no—
293C23×C4—21no—
294C23×C4—21no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D412yes—
305C23×C4C2×D411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C2×Q16—28no—
311C2×Q16—28no—
312C2×Q16—44no—
313C2×SD16—28no—
314C2×SD16—28no—
315C2×SD16—44no—
316C22×C8C2414yes—
317C22×C8C2414yes—
318#126—216no—
319#126—216no—
320#126—216no—
321#125—216no—
322#125—24no—
323#125C2×D418yes—
324#124—216no—
325#124—24no—
326#124C2×D418yes—
327#123—216no—
328#123—216no—
329#123—216no—
330#123—216no—
331#123—216no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—216no—
335C22⋊Q8—24no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342C22⋊Q8—28no—
343C22⋊Q8—42no—
344C22⋊Q8—44no—
345C22⋊Q8—42no—
346C22⋊Q8—44no—
347C22⋊Q8—44no—
348C22⋊Q8—48no—
349C22⋊Q8C2×D418yes—
350#121—28no—
351#121—28no—
352#121—216no—
353#121—216no—
354#121—216no—
355#121—24no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121—24no—
360#121C2×D418yes—
361#120—216no—
362#120—216no—
363C4×Q8—24no—
364C4×Q8—28no—
365C4×Q8—28no—
366C4×Q8—48no—
367C4×Q8C2×D418yes—
368C4×D4—216no—
369C4×D4—216no—
370C4×D4—216no—
371C4×D4—216no—
372C4×D4—216no—
373C4×D4—28no—
374C4×D4—28no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4C2×D418yes—
381#117—216no—
382#117—24no—
383#117—24no—
384#117—216no—
385C2×C4⋊C4—28no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—44no—
410C2×C4⋊C4—44no—
411C2×C4⋊C4—44no—
412C2×C4⋊C4—44no—
413C2×C4⋊C4—82no—
414C2×C4⋊C4C2×D412yes—
415C2×C4⋊C4C2×D412yes—
416C2×C4⋊C4C2412yes—
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—216no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—82no—
445C2×C22⋊C4—82no—
446C2×C22⋊C4C2×D412yes—
447C2×C22⋊C4C2×D412yes—
448C2×C22⋊C4C2×D412yes—
449C2×C22⋊C4C2×D412yes—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—24no—
453C2×C42—44no—
454C2×C42C2×D412yes—
455C2×C42C2×D418yes—
456C2×C42C2412yes—
457#107—28no—
458#106—28no—
459C4⋊C8—28no—
460#103—28no—
461#103—28no—
462#103—28no—
463#103—44no—
464#103—44no—
465#102—28no—
466#102—44no—
467#102—44no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—42no—
471C22⋊C8—44no—
472C22⋊C8—42no—
473C22⋊C8—42no—
474C22⋊C8—42no—
475C22⋊C8—44no—
476#97—28no—
477#95—24no—
478#95—22no—
479#95—22no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—41no—
488C24—41no—
489C24—41no—
490C24—41no—
491C24—41no—
492C24—41no—
493C24—41no—
494C24—41no—
495C24—42no—
496C24—42no—
497C24—81no—
498C24—81no—
499C24—81no—
500C24—81no—
501C24#13714yes—
502C24C22×D412yes—
503C24C22×D411yescharacteristic
504C24C22×D411yescharacteristic
505C24C22×D411yescharacteristic
506#41—88no—
507#41—88no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—24no—
515C2×Q8—24no—
516C2×Q8—416no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—81no—
520C2×Q8—81no—
521C2×Q8—88no—
522C2×Q8C22×D414yes—
523C2×Q8H(5,𝔽2)14yes—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—416no—
539C2×D4—432no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4—88no—
547C2×D4—82no—
548C2×D4—82no—
549C2×D4—82no—
550C2×D4—82no—
551C2×D4C22×D414yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—42no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
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—42no—
609C22×C4—88no—
610C22×C4—88no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4#12014yes—
620C22×C4#12014yes—
621C22×C4C22×D412yes—
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D414yes—
628C22×C4C2511yescharacteristic
629Q16—416no—
630SD16—416no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C4⋊C4—24no—
638C4⋊C4—28no—
639C4⋊C4—24no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—28no—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—48no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—48no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—48no—
661C4⋊C4—84no—
662C4⋊C4C22×D414yes—
663C4⋊C4C22×D414yes—
664C22⋊C4—28no—
665C22⋊C4—28no—
666C22⋊C4—28no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—24no—
671C22⋊C4—28no—
672C22⋊C4—28no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—82no—
682C22⋊C4—82no—
683C22⋊C4—84no—
684C42—28no—
685C42—28no—
686C42—48no—
687C42#12018yes—
688C42C22×D414yes—
689C42C22×D414yes—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—48no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—42no—
726C23—42no—
727C23—82no—
728C23—82no—
729C23—82no—
730C23—82no—
731C23—82no—
732C23—82no—
733C23—82no—
734C23—82no—
735C23—84no—
736C23—84no—
737C23—162no—
738C23—162no—
739C23—162no—
740C23—162no—
741C23C2×#12012yes—
742C23C2×#13712yes—
743C23C2×#13712yes—
744C23C2×#13712yes—
745C23#57512yes—
746C23C23×D411yescharacteristic
747Q8—28no—
748Q8—28no—
749Q8—48no—
750Q8—44no—
751Q8—44no—
752Q8—84no—
753D4—28no—
754D4—48no—
755D4—48no—
756D4—416no—
757D4—416no—
758D4—44no—
759D4—88no—
760D4—84no—
761D4—88no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—44no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
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—84no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—88no—
811C2×C4—82no—
812C2×C4—82no—
813C2×C4—84no—
814C2×C4—84no—
815C2×C4—88no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—84no—
819C2×C4C2×#12014yes—
820C2×C4C2×#12014yes—
821C2×C4C2×#12012yes—
822C2×C4C23×D412yes—
823C2×C4C2×H(5,𝔽2)12yes—
824C2×C4#58512yes—
825C8—44no—
826C8—44no—
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—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—42no—
857C22—88no—
858C22—88no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—168no—
864C22#300714yes—
865C22C22×#12011yescharacteristic
866C22#348411yescharacteristic
867C22#348511yescharacteristic
868C22C22×#13711yescharacteristic
869C22C2×#57511yescharacteristic
870C22#358511yescharacteristic
871C22#358611yescharacteristic
872C4—22no—
873C4—24no—
874C4—24no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4#348814yes—
886C2—24no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—84no—
891C2#3551211yescharacteristic
892C2C2×#300711yescharacteristic
893C2#6037111yescharacteristic
894C2#6157411yescharacteristic
895C2#6157711yescharacteristic
896C2#6170911yescharacteristic
897C2#6171211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3505C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3117C2semidirect
3. C2×#2538C2semidirect
4. #24259C2semidirect
5. #24258C2semidirect
6. #24139C2semidirect
7. #24138C2semidirect
8. #24007C2semidirect
9. #24006C2semidirect
10. #24005C2semidirect
11. #23922C2semidirect
12. #23921C2semidirect
13. #23919C2semidirect
14. #21867C2semidirect
15. #21790C2semidirect
30. C22×C22⋊Q8C22semidirect
33. C22×C4×Q8C22semidirect
36. C2×#484C22semidirect
38. C2×#479C22semidirect
39. C2×#464C22semidirect
40. C2×#452C22semidirect
41. C2×#451C22semidirect
42. C2×#451C22semidirect
44. C2×#450C22semidirect
45. C2×#441C22semidirect
46. C2×#440C22semidirect
47. C2×#432C22semidirect
51. #2538C22semidirect
56. C2×#384C22semidirect
58. C2×#380C22semidirect
59. #2036C22semidirect
60. #2035C22semidirect
61. #2034C22semidirect
62. #2033C22semidirect
63. #2001C22semidirect
64. #2001C22semidirect
65. #2000C22semidirect
66. #2000C22semidirect
67. #1992C22semidirect
68. #1959C22semidirect
70. #1955C22semidirect
73. #1873C22semidirect
74. #1872C22semidirect
75. #1872C22semidirect
76. #1872C22semidirect
77. #1872C22semidirect
78. #1854C22semidirect
79. #1853C22semidirect
80. #1852C22semidirect
81. #1803C22semidirect
82. #1802C22semidirect
83. #1788C22semidirect
84. #1787C22semidirect
85. #1786C22semidirect
88. #1779C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#31172
C2×#25382
#242592
#242582
#241392
#241382
#240072
#240062
#240052
#239222
#239212
#239192
#218672
#217902