Finite Group Databasebeta

← #6591603

Subgroups — #6591603

Order 512.

2541 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3325C212yesmaximal, complemented
2#36187C211yesmaximal, characteristic, complemented
3C4×D42C211yesmaximal, characteristic, complemented
4#33197C211yesmaximal, characteristic, complemented
5#32902C212yesmaximal, complemented
6#28716C211yesmaximal, characteristic, complemented
7#28251C211yesmaximal, characteristic, complemented
8#27646C212yesmaximal, complemented
9#25321C212yesmaximal, complemented
10#25228C214yesmaximal, complemented
11#24812C212yesmaximal, complemented
12#24758C212yesmaximal, complemented
13#24539C214yesmaximal, complemented
14#22650C211yesmaximal, characteristic, complemented
15#22503C212yesmaximal, complemented
16C4×#459C211yesmaximal, characteristic, complemented
17#20646C212yesmaximal, complemented
18C2×#555C2212yes—
19C2×D42C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2212yes—
22#3325—216no—
23C2×#486C2212yes—
24C2×#482C2214yes—
25C2×#476C2212yes—
26C2×#469C2214yes—
27C2×#459C2212yes—
28C2×#459C2211yescharacteristic
29C2×#459C2212yescomplemented
30C2×#447C2214yes—
31C2×C4×D8C2212yes—
32C2×#436C2212yes—
33C2×#423C2212yescomplemented
34C2×#418C2214yes—
35#2868C2211yescharacteristic, complemented
36#2856C2212yescomplemented
37#2563C2212yescomplemented
38#2537—21no—
39#2537—21no—
40#2500C2214yescomplemented
41#2491—22no—
42#2491—22no—
43#2366C2211yescharacteristic
44#2361—21no—
45#2361C2212yes—
46#2358—22no—
47#2354—21no—
48#2354—21no—
49D4×C4⋊C4C2211yescharacteristic
50D4×C4⋊C4C2211yescharacteristic
51D4×C22⋊C4—21no—
52D4×C22⋊C4C2212yes—
53C4×#127C2211yescharacteristic
54C4×#127C2211yescharacteristic, complemented
55C4×#121—21no—
56C4×#121C2212yes—
57C4×#120—22no—
58#2285C2212yescomplemented
59C42×D4C2211yescharacteristic
60C42×D4C2211yescharacteristic
61#2085C2214yescomplemented
62#2073C2214yescomplemented
63#2071C2214yescomplemented
64#2065C2214yescomplemented
65#2054C2214yescomplemented
66#2054C2214yescomplemented
67#1990C2212yescomplemented
68#1987C2212yescomplemented
69#1982C2211yescharacteristic, complemented
70#1948C2212yescomplemented
71#1948C2212yescomplemented
72#1947C2211yescharacteristic, complemented
73#1939C2212yescomplemented
74#1925C2212yescomplemented
75#1895C2214yescomplemented
76#1879C2214yes—
77#1879C2212yes—
78#1879C2214yescomplemented
79#1874C2214yescomplemented
80#1851C2214yescomplemented
81#1842C2211yescharacteristic, complemented
82#1825C2214yescomplemented
83#1804C2214yes—
84#1804C2214yescomplemented
85#1802C2212yes—
86#1802C2211yescharacteristic
87#1802C2212yes—
88#1802C2212yescomplemented
89#1802C2212yescomplemented
90#1802C2212yescomplemented
91#1802C2212yescomplemented
92#1797C2212yescomplemented
93C4×C4⋊C8C2211yescharacteristic, complemented
94C4×#102C2212yescomplemented
95#1736C2214yescomplemented
96C23×D4—21no—
97C23×D4C2312yes—
98C24×C4—22no—
99C22×D8C2312yes—
100C22×D8C2314yes—
101C22×M16C2314yes—
102#555—28no—
103#555—28no—
104D42—24no—
105D42D418yescomplemented
106C2×C4⋊Q8—21no—
107C2×C4⋊Q8—21no—
108C2×C4⋊Q8C2312yes—
109C2×#127C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#124—24no—
112C2×#121—22no—
113C2×#121—22no—
114C2×#121—22no—
115C2×#121—21no—
116C2×#121C2314yes—
117C2×#121C2312yes—
118C2×#120—22no—
119C2×C4×D4—21no—
120C2×C4×D4—22no—
121C2×C4×D4—21no—
122C2×C4×D4—22no—
123C2×C4×D4—28no—
124C2×C4×D4—21no—
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—22no—
128C2×C4×D4—22no—
129C2×C4×D4—21no—
130C2×C4×D4—44no—
131C2×C4×D4—48no—
132C2×C4×D4D411yescharacteristic
133C2×C4×D4D411yescharacteristic
134C2×C4×D4C2312yes—
135C2×C4×D4C2312yes—
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2312yes—
138C2×C4×D4C2312yes—
139C2×C4×D4C2311yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×C4×D4C2311yescharacteristic
142C2×#117—22no—
143C2×#117C2314yes—
144C22×C4⋊C4—21no—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4—22no—
147C22×C22⋊C4—22no—
148C22×C42—21no—
149C22×C42C2312yes—
150#486—28no—
151#482—216no—
152#476—28no—
153#469—216no—
154#459—28no—
155#459—24no—
156#459—44no—
157#447—216no—
158C4×D8—28no—
159#436—28no—
160C2×#107C2312yes—
161C2×#106C2314yes—
162#423—44no—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2314yes—
169#418—216no—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2312yes—
174C2×#102C2314yes—
175C2×#102C2312yes—
176C2×#102C2312yes—
177C2×#102C2312yes—
178C2×#102C2314yes—
179C2×C22⋊C8C2314yes—
180C2×C4×C8C2312yes—
181#394—24no—
182#394—24no—
183#393—24no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—22no—
190#390—22no—
191#390C2312yes—
192#390C2312yes—
193#390C2314yes—
194#390C2312yes—
195#389—21no—
196#389C2312yes—
197#388—22no—
198#388—24no—
199#388—24no—
200#388—22no—
201#386—22no—
202#386—22no—
203#386—22no—
204#386—22no—
205#386—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#384—21no—
210#384—21no—
211#384C2311yescharacteristic
212#384C2311yescharacteristic
213#384C2312yes—
214#384C2312yes—
215#382C2314yes—
216#380—22no—
217#380—22no—
218#380—22no—
219#380—22no—
220#380—21no—
221#380C2312yes—
222#379—22no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4—22no—
225C4×C4⋊C4D411yescharacteristic
226C4×C4⋊C4D411yescharacteristic
227C4×C4⋊C4C2311yescharacteristic
228C4×C4⋊C4C2311yescharacteristic
229C4×C4⋊C4C2311yescharacteristic
230C4×C4⋊C4C2311yescharacteristic
231C4×C22⋊C4—21no—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—21no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4D412yes—
236C4×C22⋊C4D412yes—
237C4×C22⋊C4C2312yes—
238C43C2311yescharacteristic
239#340C2314yes—
240#340C2314yes—
241#340C2312yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2312yes—
246#336C2314yes—
247#336C2312yes—
248C25—22no—
249C22×Q8—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—28no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—24no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4C2×D411yescharacteristic
266C22×D4C2×D418yes—
267C22×D4C2412yes—
268C22×D4C2412yes—
269C22×D4C2411yescharacteristic
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—48no—
279C23×C4—48no—
280C23×C4—84no—
281C23×C4C2×D412yes—
282C23×C4C2×D412yes—
283C23×C4C2412yes—
284C2×D8—24no—
285C2×D8—24no—
286C2×D8—24no—
287C2×D8—28no—
288C2×D8—44no—
289C2×D8—44no—
290C2×M16—28no—
291C2×M16—44no—
292C2×M16—44no—
293C22×C8C2412yes—
294C22×C8C2414yes—
295C22×C8C2412yes—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8—82no—
299C4⋊Q8—82no—
300#127—22no—
301#127—22no—
302#127—22no—
303#127C2×D414yes—
304#124—416no—
305#121—24no—
306#121—28no—
307#121—28no—
308#121—28no—
309#121—48no—
310#121—84no—
311#121—84no—
312#121C2×D418yes—
313#120—216no—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—24no—
319C4×D4—22no—
320C4×D4—24no—
321C4×D4—24no—
322C4×D4—22no—
323C4×D4—24no—
324C4×D4—48no—
325C4×D4—42no—
326C4×D4—42no—
327C4×D4—42no—
328C4×D4—41no—
329C4×D4—48no—
330C4×D4—44no—
331C4×D4—48no—
332C4×D4—44no—
333C4×D4—48no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—82no—
338C4×D4C2×D414yes—
339C4×D4C2×D414yes—
340C4×D4#4114yes—
341C4×D4#4114yes—
342#117—28no—
343#117—28no—
344#117—48no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4C2×D411yescharacteristic
360C2×C4⋊C4C2×D411yescharacteristic
361C2×C4⋊C4C2×D411yescharacteristic
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2414yes—
365C2×C4⋊C4C2411yescharacteristic
366C2×C4⋊C4C2411yescharacteristic
367C2×C4⋊C4C2411yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—48no—
388C2×C22⋊C4—48no—
389C2×C22⋊C4C2×D412yes—
390C2×C22⋊C4C2×D412yes—
391C2×C22⋊C4C2×D412yes—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—44no—
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2412yes—
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409#107—24no—
410#106—28no—
411C4⋊C8—24no—
412C4⋊C8—22no—
413C4⋊C8—22no—
414C4⋊C8—24no—
415C4⋊C8—42no—
416C4⋊C8—44no—
417#102—24no—
418#102—28no—
419#102—28no—
420#102—28no—
421#102—28no—
422#102—24no—
423#102—24no—
424#102—42no—
425#102—44no—
426C22⋊C8—28no—
427C4×C8—24no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—22no—
432#95—22no—
433#95—24no—
434#95—24no—
435#95C2×D412yes—
436#95C2×D412yes—
437#95C2×D412yes—
438C24—21no—
439C24—22no—
440C24—28no—
441C24—22no—
442C24—44no—
443C24—44no—
444C24—44no—
445C24—44no—
446C24—82no—
447C24—82no—
448C24C22×D412yes—
449C2×Q8—44no—
450C2×Q8—82no—
451C2×Q8—82no—
452C2×D4—216no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—432no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—81no—
491C2×D4—81no—
492C2×D4—84no—
493C2×D4—84no—
494C2×D4#12114yes—
495C2×D4C22×D414yes—
496C2×D4C22×D412yes—
497C2×D4C2×#4112yes—
498C2×D42−1+412yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—42no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—81no—
536C22×C4—82no—
537C22×C4—82no—
538C22×C4—82no—
539C22×C4—832no—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D412yes—
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D414yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C2×#4114yes—
551C22×C4C2511yescharacteristic
552D8—48no—
553D8—88no—
554M16—88no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—24no—
558C2×C8—22no—
559C2×C8—24no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—81no—
585C4⋊C4—82no—
586C4⋊C4—82no—
587C4⋊C4#12114yes—
588C4⋊C4C22×D412yes—
589C4⋊C4C2×#4112yes—
590C22⋊C4—24no—
591C22⋊C4—28no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—42no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—42no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4#12118yes—
612C42—24no—
613C42—24no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42—48no—
622C42—42no—
623C42—42no—
624C42—42no—
625C42AGL(1,ℤ/8)14yes—
626C42C22×D412yes—
627C42C2×#4112yes—
628C42C2×#4112yes—
629C42H(5,𝔽2)12yes—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—416no—
641C23—416no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—88no—
660C23—88no—
661C23—88no—
662C23—88no—
663C23—88no—
664C23C2×#12114yes—
665C23C23×D411yescharacteristic
666Q8—164no—
667D4—24no—
668D4—22no—
669D4—22no—
670D4—24no—
671D4—22no—
672D4—28no—
673D4—416no—
674D4—416no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—48no—
682D4—84no—
683D4—84no—
684D4—84no—
685D4—168no—
686D4#54714yes—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—88no—
732C2×C4—88no—
733C2×C4—88no—
734C2×C4—88no—
735C2×C4—88no—
736C2×C4C2×#12114yes—
737C2×C4C2×#12112yes—
738C2×C4C2×#12112yes—
739C2×C4#54612yes—
740C2×C4#54612yes—
741C2×C4C2×AGL(1,ℤ/8)12yes—
742C2×C4C2×AGL(1,ℤ/8)12yes—
743C2×C4C2×AGL(1,ℤ/8)12yes—
744C2×C4#57512yes—
745C2×C4#57612yes—
746C2×C4C23×D411yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4111yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×2−1+411yescharacteristic
751C2×C4#58511yescharacteristic
752C8—42no—
753C8—42no—
754C8—44no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—832no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22C22×#12111yescharacteristic
785C22C2×#54611yescharacteristic
786C22#348911yescharacteristic
787C22C22×AGL(1,ℤ/8)11yescharacteristic
788C22C2×#57511yescharacteristic
789C22C2×#57611yescharacteristic
790C22#358511yescharacteristic
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—42no—
800C4—84no—
801C4—81no—
802C4—82no—
803C4—82no—
804C4#303614yes—
805C4#332514yescomplemented
806C4C2×#54711yescharacteristic
807C4#347511yescharacteristic
808C4#349611yescharacteristic
809C4#352011yescharacteristic
810C2—44no—
811C2—44no—
812C2—84no—
813C2—162no—
814C2#3615311yescharacteristic
815C2C2×#303611yescharacteristic
816C2#6042811yescharacteristic
817C2C2×#332511yescharacteristic
818C2#6116611yescharacteristic
819C2#6211011yescharacteristic
820C2#6214311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3325C2semidirect
2. #36187C2semidirect
3. C4×D42C2semidirect
4. #33197C2semidirect
5. #32902C2semidirect
6. #28716C2semidirect
7. #28251C2semidirect
8. #27646C2semidirect
9. #25321C2semidirect
10. #25228C2semidirect
11. #24812C2semidirect
12. #24758C2semidirect
13. #24539C2semidirect
14. #22650C2semidirect
15. #22503C2semidirect
16. C4×#459C2semidirect
17. #20646C2semidirect
29. C2×#459C22semidirect
33. C2×#423C22semidirect
35. #2868C22semidirect
36. #2856C22semidirect
37. #2563C22semidirect
40. #2500C22semidirect
54. C4×#127C22semidirect
58. #2285C22semidirect
61. #2085C22semidirect
62. #2073C22semidirect
63. #2071C22semidirect
64. #2065C22semidirect
65. #2054C22semidirect
66. #2054C22semidirect
67. #1990C22semidirect
68. #1987C22semidirect
69. #1982C22semidirect
70. #1948C22semidirect
71. #1948C22semidirect
72. #1947C22semidirect
73. #1939C22semidirect
74. #1925C22semidirect
75. #1895C22semidirect
78. #1879C22semidirect
79. #1874C22semidirect
80. #1851C22semidirect
81. #1842C22semidirect
82. #1825C22semidirect
84. #1804C22semidirect
88. #1802C22semidirect
89. #1802C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
92. #1797C22semidirect
93. C4×C4⋊C8C22semidirect
94. C4×#102C22semidirect
95. #1736C22semidirect
105. D42D4semidirect
805. C4#3325semidirect

Maximal subgroups

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

subgroupindex
C2×#33252
#361872
C4×D422
#331972
#329022
#287162
#282512
#276462
#253212
#252282
#248122
#247582
#245392
#226502
#225032
C4×#4592
#206462