Finite Group Databasebeta

← #6524821

Subgroups — #6524821

Order 512.

3196 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic
2C2×#3232C212yesmaximal, complemented
3C2×#2562C211yesmaximal, characteristic, complemented
4#25890C214yesmaximal, complemented
5#25889C214yesmaximal, complemented
6#25708C214yesmaximal, complemented
7#25707C214yesmaximal, complemented
8#24007C212yesmaximal, complemented
9#24006C211yesmaximal, characteristic, complemented
10#24005C211yesmaximal, characteristic, complemented
11#24004C212yesmaximal, complemented
12#24003C211yesmaximal, characteristic, complemented
13#24002C211yesmaximal, characteristic, complemented
14#21786C211yesmaximal, characteristic, complemented
15#21388C212yesmaximal, 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—
27C22×#125C2211yescharacteristic, complemented
28C2×#525C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C2×#518—21no—
32C22×C4×D4C2211yescharacteristic
33#3232—216no—
34C2×#499C2214yescomplemented
35C2×#488C2214yescomplemented
36C2×#484C2212yescomplemented
37C2×#481C2212yes—
38C2×#483C2212yescomplemented
39C2×#480C2212yes—
40C2×#479C2214yescomplemented
41C2×#478C2214yescomplemented
42C2×#431C2212yescomplemented
43#2562—22no—
44#2562—22no—
45#2562C2214yes—
46#2562C2214yescomplemented
47C2×#400—21no—
48C2×#394—21no—
49C2×#388—21no—
50C2×#388—21no—
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic, complemented
55C2×C4×C4⋊C4C2211yescharacteristic, complemented
56#2036C2214yescomplemented
57#2036C2214yescomplemented
58#2035C2214yescomplemented
59#2035C2214yescomplemented
60#2034C2214yescomplemented
61#2034C2214yescomplemented
62#2033C2214yescomplemented
63#2033C2214yescomplemented
64#1989C2214yescomplemented
65#1983C2214yescomplemented
66#1954C2214yes—
67#1954C2214yescomplemented
68#1874C2212yes—
69#1874C2212yes—
70#1872C2212yescomplemented
71#1872C2212yescomplemented
72#1854C2214yescomplemented
73#1854C2214yescomplemented
74#1853C2212yescomplemented
75#1853C2212yescomplemented
76#1852C2212yescomplemented
77#1852C2212yescomplemented
78#1788C2214yescomplemented
79#1788C2214yescomplemented
80#1787C2212yescomplemented
81#1787C2212yescomplemented
82#1786C2212yescomplemented
83#1786C2212yescomplemented
84#1779C2211yescharacteristic
85#1779C2211yescharacteristic
86#1779C2212yescomplemented
87C4×#103C2214yescomplemented
88C4×#102C2214yescomplemented
89C22×#41C2312yes—
90C23×Q8C2311yescharacteristic
91C23×D4—21no—
92C23×D4D411yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96#553—232no—
97#553—28no—
98#553—28no—
99#552—28no—
100#552—28no—
101#551—232no—
102#548—28no—
103#548—28no—
104#546—28no—
105#546—28no—
106#539—216no—
107#538—216no—
108#534—216no—
109#529—28no—
110#529D4116yes—
111C2×#126—22no—
112C2×#126—22no—
113C2×#126—22no—
114C2×#125—22no—
115C2×#125—22no—
116C2×#125—28no—
117C2×#125C2314yes—
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—22no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C22⋊Q8C2312yes—
135C2×#121—22no—
136C2×#121—22no—
137C2×#121—21no—
138C2×#121—21no—
139C2×#121—28no—
140C2×#121—22no—
141C2×#121C2312yes—
142C2×#121C2312yes—
143C2×#121C2312yes—
144C2×#120—22no—
145C2×#120—22no—
146#518—216no—
147C2×C4×Q8C2312yes—
148C2×C4×D4—22no—
149C2×C4×D4—22no—
150C2×C4×D4—22no—
151C2×C4×D4—22no—
152C2×C4×D4—22no—
153C2×C4×D4—28no—
154C2×C4×D4D412yes—
155C2×C4×D4D412yes—
156C2×C4×D4C2312yes—
157C2×C4×D4C2312yes—
158C2×C4×D4C2312yes—
159C2×#117—22no—
160C2×#117—22no—
161C2×#117C2312yes—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4D411yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C22⋊C4—21no—
173C22×C22⋊C4—21no—
174C22×C22⋊C4—22no—
175C22×C22⋊C4—21no—
176C22×C22⋊C4—21no—
177C22×C22⋊C4—21no—
178C22×C22⋊C4—21no—
179C22×C22⋊C4D411yescharacteristic
180C22×C22⋊C4D411yescharacteristic
181C22×C42—21no—
182C22×C42C2311yescharacteristic
183#499—216no—
184#488—216no—
185#484—28no—
186#483—28no—
187#481—28no—
188#480—28no—
189#479—216no—
190#478—216no—
191#431—28no—
192C2×#107C2314yes—
193C2×#107C2314yes—
194C2×#106C2314yes—
195C2×#106C2314yes—
196C2×C4⋊C8C2314yes—
197C2×#103C2314yes—
198C2×#103C2314yes—
199C2×#103C2314yes—
200C2×#103C2314yes—
201C2×#102C2314yes—
202C2×#102C2314yes—
203C2×#102C2314yes—
204C2×#102C2314yes—
205C2×C22⋊C8C2312yes—
206C2×C22⋊C8C2312yes—
207C2×C22⋊C8C2312yes—
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2314yes—
212C2×C22⋊C8C2314yes—
213C2×C4×C8C2314yes—
214#400—24no—
215#400—24no—
216#394—24no—
217#394—24no—
218#388—24no—
219#388—24no—
220#388—24no—
221#388—24no—
222#380—21no—
223#380—21no—
224#380—21no—
225#380—21no—
226#380—22no—
227#380—22no—
228#380C2312yes—
229#380C2312yes—
230#380C2314yes—
231#380C2314yes—
232#380C2312yes—
233#380C2312yes—
234C4×C4⋊C4—22no—
235C4×C4⋊C4C2314yes—
236C2×#95—21no—
237C2×#95—21no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95—21no—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245C25—21no—
246C25C2×D411yescharacteristic
247C25C2×D411yescharacteristic
248C2×#41—24no—
249C2×#41—24no—
250C2×#41—44no—
251C2×#41—44no—
252C22×Q8—24no—
253C22×Q8—21no—
254C22×Q8—42no—
255C22×Q8—42no—
256C22×Q8C2412yes—
257C22×D4—28no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4C2×D412yes—
272C22×D4C2×D412yes—
273C22×D4C2412yes—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D412yes—
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C22×C8C2414yes—
301C22×C8C2414yes—
302#126—216no—
303#126—216no—
304#126—216no—
305#125—216no—
306#125—24no—
307#125—28no—
308#125—28no—
309#125—48no—
310#125C2×D418yes—
311#124—216no—
312#124—24no—
313#124C2×D418yes—
314#123—216no—
315#123—216no—
316#123—216no—
317#123—216no—
318#123—216no—
319C22⋊Q8—28no—
320C22⋊Q8—28no—
321C22⋊Q8—216no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324C22⋊Q8—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327C22⋊Q8C2×D418yes—
328#121—28no—
329#121—28no—
330#121—216no—
331#121—216no—
332#121—216no—
333#121—24no—
334#121—24no—
335#121—24no—
336#121—24no—
337#121—24no—
338#121C2×D418yes—
339#120—216no—
340#120—216no—
341C4×Q8—24no—
342C4×Q8C2×D418yes—
343C4×D4—216no—
344C4×D4—216no—
345C4×D4—216no—
346C4×D4—216no—
347C4×D4—216no—
348C4×D4—28no—
349C4×D4—28no—
350C4×D4—24no—
351C4×D4—24no—
352C4×D4—24no—
353C4×D4—24no—
354C4×D4—24no—
355C4×D4C2×D418yes—
356#117—216no—
357#117—24no—
358#117—24no—
359#117—216no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—216no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—44no—
415C2×C22⋊C4—82no—
416C2×C22⋊C4—82no—
417C2×C22⋊C4C2×D412yes—
418C2×C22⋊C4C2×D412yes—
419C2×C22⋊C4C2×D412yes—
420C2×C22⋊C4C2×D412yes—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—24no—
424C2×C42—82no—
425C2×C42C2×D412yes—
426C2×C42C2×D418yes—
427C2×C42C2412yes—
428#107—28no—
429#107—28no—
430#106—28no—
431#106—28no—
432C4⋊C8—28no—
433#103—28no—
434#103—28no—
435#103—44no—
436#103—44no—
437#102—28no—
438#102—28no—
439#102—44no—
440#102—44no—
441C22⋊C8—24no—
442C22⋊C8—24no—
443C22⋊C8—42no—
444C22⋊C8—42no—
445C22⋊C8—44no—
446C22⋊C8—44no—
447C22⋊C8—42no—
448C22⋊C8—42no—
449C4×C8—28no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—41no—
465C24—41no—
466C24—41no—
467C24—41no—
468C24—41no—
469C24—41no—
470C24—41no—
471C24—41no—
472C24—42no—
473C24—42no—
474C24—81no—
475C24—81no—
476C24—81no—
477C24—81no—
478C24#13514yes—
479C24C22×D412yes—
480C24C22×D411yescharacteristic
481C24C22×D411yescharacteristic
482C24C22×D411yescharacteristic
483#41—88no—
484#41—88no—
485C2×Q8—24no—
486C2×Q8—22no—
487C2×Q8—24no—
488C2×Q8—24no—
489C2×Q8—81no—
490C2×Q8—81no—
491C2×Q8—88no—
492C2×Q8C22×D414yes—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—24no—
496C2×D4—24no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—24no—
500C2×D4—24no—
501C2×D4—24no—
502C2×D4—22no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—416no—
508C2×D4—432no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4—88no—
516C2×D4—82no—
517C2×D4—82no—
518C2×D4—82no—
519C2×D4—82no—
520C2×D4C22×D414yes—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—28no—
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—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
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—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—82no—
583C22×C4—82no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4#12014yes—
589C22×C4#12014yes—
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D411yescharacteristic
596C22×C4C22×D414yes—
597C22×C4C2511yescharacteristic
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—24no—
601C2×C8—24no—
602C2×C8—24no—
603C2×C8—24no—
604C4⋊C4—24no—
605C4⋊C4—28no—
606C4⋊C4—24no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4C22×D414yes—
627C4⋊C4C22×D414yes—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—24no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—48no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—82no—
646C22⋊C4—82no—
647C22⋊C4—84no—
648C42—28no—
649C42—28no—
650C42—84no—
651C42#12018yes—
652C42C22×D414yes—
653C42C22×D414yes—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—28no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—48no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—82no—
692C23—82no—
693C23—82no—
694C23—82no—
695C23—82no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23—84no—
700C23—84no—
701C23—162no—
702C23—162no—
703C23—162no—
704C23—162no—
705C23C2×#12012yes—
706C23C2×#13512yes—
707C23C2×#13512yes—
708C23C2×#13512yes—
709C23#57512yes—
710C23C23×D411yescharacteristic
711Q8—28no—
712Q8—44no—
713Q8—84no—
714D4—28no—
715D4—48no—
716D4—48no—
717D4—416no—
718D4—416no—
719D4—44no—
720D4—88no—
721D4—84no—
722D4—88no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—28no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—44no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
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—84no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—88no—
771C2×C4—82no—
772C2×C4—82no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—88no—
776C2×C4—84no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4C2×#12014yes—
781C2×C4C2×#12012yes—
782C2×C4C2×#12014yes—
783C2×C4C23×D412yes—
784C2×C4#58512yes—
785C2×C4#58512yes—
786C8—44no—
787C8—44no—
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—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—44no—
814C22—42no—
815C22—44no—
816C22—44no—
817C22—42no—
818C22—88no—
819C22—88no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—168no—
825C22#300214yes—
826C22C22×#12011yescharacteristic
827C22#348511yescharacteristic
828C22#348511yescharacteristic
829C22C22×#13511yescharacteristic
830C22C2×#57511yescharacteristic
831C22#358511yescharacteristic
832C22#358611yescharacteristic
833C4—22no—
834C4—24no—
835C4—24no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—44no—
840C4—44no—
841C4—44no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4#350014yes—
847C2—24no—
848C2—42no—
849C2—42no—
850C2—82no—
851C2—84no—
852C2#3561611yescharacteristic
853C2C2×#300211yescharacteristic
854C2#6037111yescharacteristic
855C2#6169611yescharacteristic
856C2#6169911yescharacteristic
857C2#6171611yescharacteristic
858C2#6171811yescharacteristic
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×#3232C2semidirect
3. C2×#2562C2semidirect
4. #25890C2semidirect
5. #25889C2semidirect
6. #25708C2semidirect
7. #25707C2semidirect
8. #24007C2semidirect
9. #24006C2semidirect
10. #24005C2semidirect
11. #24004C2semidirect
12. #24003C2semidirect
13. #24002C2semidirect
14. #21786C2semidirect
15. #21388C2semidirect
27. C22×#125C22semidirect
34. C2×#499C22semidirect
35. C2×#488C22semidirect
36. C2×#484C22semidirect
38. C2×#483C22semidirect
40. C2×#479C22semidirect
41. C2×#478C22semidirect
42. C2×#431C22semidirect
46. #2562C22semidirect
53. C2×#380C22semidirect
54. C2×#380C22semidirect
55. C2×C4×C4⋊C4C22semidirect
56. #2036C22semidirect
57. #2036C22semidirect
58. #2035C22semidirect
59. #2035C22semidirect
60. #2034C22semidirect
61. #2034C22semidirect
62. #2033C22semidirect
63. #2033C22semidirect
64. #1989C22semidirect
65. #1983C22semidirect
67. #1954C22semidirect
70. #1872C22semidirect
71. #1872C22semidirect
72. #1854C22semidirect
73. #1854C22semidirect
74. #1853C22semidirect
75. #1853C22semidirect
76. #1852C22semidirect
77. #1852C22semidirect
78. #1788C22semidirect
79. #1788C22semidirect
80. #1787C22semidirect
81. #1787C22semidirect
82. #1786C22semidirect
83. #1786C22semidirect
86. #1779C22semidirect
87. C4×#103C22semidirect
88. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C2×#32322
C2×#25622
#258902
#258892
#257082
#257072
#240072
#240062
#240052
#240042
#240032
#240022
#217862
#213882