Finite Group Databasebeta

← #6591585

Subgroups — #6591585

Order 512.

2539 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3295C212yesmaximal
2#36180C211yesmaximal, characteristic, complemented
3C4×D42C211yesmaximal, characteristic
4#33197C211yesmaximal, characteristic, complemented
5#32905C212yesmaximal, complemented
6#28716C211yesmaximal, characteristic, complemented
7#28252C211yesmaximal, characteristic, complemented
8#27645C212yesmaximal, complemented
9#25322C212yesmaximal, complemented
10#25202C214yesmaximal, complemented
11#24815C212yesmaximal, complemented
12#24751C212yesmaximal, complemented
13#24530C214yesmaximal, complemented
14D4×C4⋊C8C211yesmaximal, characteristic, complemented
15#22487C212yesmaximal, complemented
16C4×#461C211yesmaximal, characteristic, complemented
17C2×#1802C212yesmaximal, complemented
18C2×#554C2212yes—
19C2×D42C2211yescharacteristic
20C22×C4×D4—21no—
21C22×C4×D4C2212yes—
22#3295—216no—
23C2×#486C2212yes—
24C2×#481C2214yes—
25C2×#476C2212yes—
26C2×#465C2214yes—
27C2×#460C2212yes—
28C2×#461C2211yescharacteristic
29C2×#461C2212yescomplemented
30C2×#450C2214yes—
31C2×C4×SD16C2212yes—
32C2×C8×D4C2212yes—
33C22×C4⋊C8C2212yescomplemented
34C22×#102C2214yes—
35#2868C2211yescharacteristic, complemented
36#2857C2212yescomplemented
37#2567C2212yescomplemented
38#2552—21no—
39#2552—21no—
40#2502C2214yescomplemented
41#2440—22no—
42#2440—22no—
43#2366C2211yescharacteristic
44#2361—21no—
45#2361C2212yes—
46#2358—22no—
47D4×C4⋊C4—21no—
48D4×C4⋊C4—21no—
49D4×C4⋊C4C2211yescharacteristic
50D4×C4⋊C4C2211yescharacteristic
51D4×C22⋊C4—21no—
52D4×C22⋊C4C2212yes—
53C4×C4⋊Q8C2211yescharacteristic, complemented
54C4×#127C2211yescharacteristic
55C4×#121—21no—
56C4×#121C2212yes—
57C4×#120—22no—
58C2×#384C2212yescomplemented
59C42×D4C2211yescharacteristic
60C42×D4C2211yescharacteristic
61#2084C2214yescomplemented
62#2071C2214yescomplemented
63#2071C2214yescomplemented
64#2066C2214yescomplemented
65#2055C2214yescomplemented
66#2055C2214yescomplemented
67#1990C2212yescomplemented
68#1987C2212yescomplemented
69#1981C2211yescharacteristic, complemented
70#1948C2212yescomplemented
71#1948C2212yescomplemented
72#1948C2211yescharacteristic, complemented
73#1939C2212yescomplemented
74#1927C2212yescomplemented
75#1892C2214yescomplemented
76#1877C2214yes—
77#1877C2212yes—
78#1877C2214yescomplemented
79#1872C2214yescomplemented
80#1850C2214yescomplemented
81#1842C2211yescharacteristic, complemented
82#1824C2214yescomplemented
83#1803C2212yescomplemented
84#1802C2212yes—
85#1802C2211yescharacteristic
86#1802C2214yes—
87#1802C2212yes—
88#1802C2212yescomplemented
89#1802C2212yescomplemented
90#1802C2212yescomplemented
91#1802C2214yescomplemented
92#1797C2212yescomplemented
93C4×C4⋊C8C2211yescharacteristic, complemented
94C4×#103C2212yescomplemented
95C2×#340C2214yescomplemented
96C23×D4—21no—
97C23×D4C2312yes—
98C24×C4—22no—
99C22×SD16C2312yes—
100C22×SD16C2314yes—
101C23×C8C2314yes—
102#554—28no—
103#554—28no—
104D42—24no—
105D42D418yes—
106C2×C4⋊Q8—21no—
107C2×C4⋊Q8—21no—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2312yes—
110C2×#127C2311yescharacteristic
111C2×#125—22no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8C2314yes—
114C2×#121—21no—
115C2×#121C2312yes—
116C2×#120—22no—
117C2×C4×Q8C2312yes—
118C2×C4×D4—21no—
119C2×C4×D4—22no—
120C2×C4×D4—22no—
121C2×C4×D4—21no—
122C2×C4×D4—22no—
123C2×C4×D4—28no—
124C2×C4×D4—21no—
125C2×C4×D4—22no—
126C2×C4×D4—22no—
127C2×C4×D4—21no—
128C2×C4×D4—44no—
129C2×C4×D4—48no—
130C2×C4×D4D411yescharacteristic
131C2×C4×D4D411yescharacteristic
132C2×C4×D4C2312yes—
133C2×C4×D4C2311yescharacteristic
134C2×C4×D4C2312yes—
135C2×C4×D4C2312yes—
136C2×C4×D4C2311yescharacteristic
137C2×C4×D4C2311yescharacteristic
138C2×C4×D4C2311yescharacteristic
139C22×C4⋊C4—22no—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4—22no—
145C22×C22⋊C4—22no—
146C22×C42—21no—
147C22×C42C2312yes—
148#486—28no—
149#481—216no—
150#476—28no—
151#465—216no—
152#461—24no—
153#461—44no—
154#460—28no—
155#450—216no—
156C4×SD16—28no—
157C8×D4—28no—
158C2×#106C2312yes—
159C2×#106C2314yes—
160C2×C4⋊C8—44no—
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2314yes—
167C2×#103C2312yes—
168C2×#103C2312yes—
169C2×#103C2312yes—
170C2×#103C2314yes—
171C2×#102—216no—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2312yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8C2314yes—
178C2×C4×C8C2312yes—
179#398—24no—
180#398—24no—
181#395—24no—
182#391C2312yes—
183#391C2314yes—
184#390—21no—
185#390—21no—
186#390—21no—
187#390C2312yes—
188#390C2312yes—
189#389—22no—
190#389—22no—
191#389—21no—
192#389—21no—
193#389—21no—
194#389—22no—
195#389—22no—
196#389C2312yes—
197#388—22no—
198#388—22no—
199#386—22no—
200#386—22no—
201#386—22no—
202#386—22no—
203#386—22no—
204#385—24no—
205#385—24no—
206#385—22no—
207#385—22no—
208#385—22no—
209#384—21no—
210#384—21no—
211#384—22no—
212#384—22no—
213#384C2311yescharacteristic
214#384C2311yescharacteristic
215#384C2314yes—
216#384C2312yes—
217#384C2312yes—
218#380—22no—
219#380—22no—
220#380—21no—
221#380C2312yes—
222#379—22no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4—21no—
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×Q8C2412yes—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—22no—
254C22×D4—28no—
255C22×D4—22no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—24no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4C2×D418yes—
264C22×D4C2×D411yescharacteristic
265C22×D4C2412yes—
266C22×D4C2411yescharacteristic
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—48no—
276C23×C4—48no—
277C23×C4—84no—
278C23×C4C2×D412yes—
279C23×C4C2×D412yes—
280C23×C4C2412yes—
281C2×SD16—24no—
282C2×SD16—24no—
283C2×SD16—24no—
284C2×SD16—28no—
285C2×SD16—44no—
286C2×SD16—44no—
287C22×C8—28no—
288C22×C8—44no—
289C22×C8—44no—
290C22×C8C2412yes—
291C22×C8C2414yes—
292C22×C8C2412yes—
293C4⋊Q8—24no—
294C4⋊Q8—24no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—82no—
298C4⋊Q8—82no—
299#127—22no—
300#127C2×D414yes—
301#125—48no—
302C22⋊Q8—28no—
303C22⋊Q8—28no—
304C22⋊Q8—416no—
305#121—24no—
306#121—28no—
307#121C2×D418yes—
308#120—216no—
309C4×Q8—24no—
310C4×Q8—24no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—24no—
315C4×D4—22no—
316C4×D4—24no—
317C4×D4—22no—
318C4×D4—24no—
319C4×D4—48no—
320C4×D4—42no—
321C4×D4—42no—
322C4×D4—41no—
323C4×D4—48no—
324C4×D4—48no—
325C4×D4—44no—
326C4×D4—48no—
327C4×D4—44no—
328C4×D4—48no—
329C4×D4—44no—
330C4×D4—82no—
331C4×D4SD1618yescomplemented
332C4×D4C2×D414yes—
333C4×D4C2×D414yes—
334C4×D4#4114yes—
335C4×D4#4114yes—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—84no—
360C2×C4⋊C4—84no—
361C2×C4⋊C4C2×D411yescharacteristic
362C2×C4⋊C4C2×D411yescharacteristic
363C2×C4⋊C4C2×D411yescharacteristic
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2414yes—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2411yescharacteristic
369C2×C4⋊C4C2411yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—48no—
384C2×C22⋊C4—48no—
385C2×C22⋊C4C2×D412yes—
386C2×C22⋊C4C2×D412yes—
387C2×C22⋊C4C2×D412yes—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—22no—
394C2×C42—44no—
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D412yes—
397C2×C42C2×D412yes—
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2412yes—
402C2×C42C2411yescharacteristic
403C2×C42C2411yescharacteristic
404C2×C42C2411yescharacteristic
405#106—24no—
406#106—28no—
407C4⋊C8—24no—
408C4⋊C8—22no—
409C4⋊C8—22no—
410C4⋊C8—24no—
411C4⋊C8—44no—
412C4⋊C8—42no—
413#103—24no—
414#103—24no—
415#103—42no—
416#103—44no—
417#102—24no—
418#102—28no—
419#102—28no—
420#102—28no—
421#102—28no—
422C22⋊C8—28no—
423C4×C8—24no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—24no—
433#95C2×D412yes—
434#95C2×D412yes—
435#95C2×D412yes—
436C24—21no—
437C24—22no—
438C24—28no—
439C24—44no—
440C24—44no—
441C24—44no—
442C24—44no—
443C24—82no—
444C24—82no—
445C24C22×D412yes—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—44no—
453C2×Q8—82no—
454C2×Q8—82no—
455C2×D4—216no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—432no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4#12114yes—
481C2×D4C2×SD1614yes—
482C2×D4#13714yes—
483C2×D4C22×D414yes—
484C2×D4C22×D412yes—
485C2×D4C2×#4112yes—
486C2×D42−1+412yes—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—42no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—48no—
515C22×C4—44no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—81no—
522C22×C4—82no—
523C22×C4—82no—
524C22×C4—832no—
525C22×C4—82no—
526C22×C4—84no—
527C22×C4—84no—
528C22×C4C2×SD1618yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D412yes—
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D412yes—
533C22×C4C22×D414yes—
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D412yes—
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C2×#4114yes—
540C22×C4C2511yescharacteristic
541SD16—48no—
542SD16—88no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—24no—
546C2×C8—22no—
547C2×C8—24no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—24no—
552C2×C8—88no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—44no—
565C4⋊C4—42no—
566C4⋊C4—44no—
567C4⋊C4—48no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—44no—
577C4⋊C4—84no—
578C4⋊C4—84no—
579C4⋊C4—81no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4#12114yes—
583C4⋊C4C2×SD1614yes—
584C4⋊C4C22×D412yes—
585C4⋊C4C2×#4112yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—28no—
589C22⋊C4—24no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—42no—
593C22⋊C4—48no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—82no—
599C22⋊C4—82no—
600C22⋊C4#12118yes—
601C22⋊C4C2×SD1618yes—
602C42—24no—
603C42—24no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—21no—
609C42—21no—
610C42—41no—
611C42—44no—
612C42—42no—
613C42—42no—
614C42—42no—
615C42C2×SD1614yes—
616C42C22×D412yes—
617C42C2×#4112yes—
618C42C2×#4112yes—
619C42H(5,𝔽2)12yes—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—416no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—416no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—88no—
641C23—88no—
642C23—88no—
643C23—88no—
644C23—88no—
645C23C2×#12114yes—
646C23C22×SD1614yes—
647C23C2×#13714yes—
648C23C23×D411yescharacteristic
649Q8—42no—
650Q8—42no—
651Q8—42no—
652Q8—42no—
653Q8—164no—
654D4—24no—
655D4—22no—
656D4—22no—
657D4—24no—
658D4—22no—
659D4—416no—
660D4—416no—
661D4—42no—
662D4—42no—
663D4—48no—
664D4—84no—
665D4#461116yescomplemented
666D4#54714yes—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—216no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—48no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—88no—
713C2×C4—84no—
714C2×C4—88no—
715C2×C4—88no—
716C2×C4—88no—
717C2×C4—168no—
718C2×C4C2×#12112yes—
719C2×C4C2×#12114yes—
720C2×C4C2×#12112yes—
721C2×C4#54612yes—
722C2×C4#54612yes—
723C2×C4C22×SD1612yes—
724C2×C4C22×SD1614yes—
725C2×C4C22×SD1612yes—
726C2×C4C22×SD1612yes—
727C2×C4C2×#13712yes—
728C2×C4#57612yes—
729C2×C4C23×D411yescharacteristic
730C2×C4C22×#4111yescharacteristic
731C2×C4C22×#4111yescharacteristic
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4C2×2−1+411yescharacteristic
734C2×C4#58511yescharacteristic
735C8—42no—
736C8—42no—
737C8—44no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—832no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22C2×#46118yes—
760C22C22×#12111yescharacteristic
761C22C2×#54611yescharacteristic
762C22#348911yescharacteristic
763C22C23×SD1611yescharacteristic
764C22C22×#13711yescharacteristic
765C22C2×#57611yescharacteristic
766C22#358511yescharacteristic
767C4—22no—
768C4—24no—
769C4—22no—
770C4—24no—
771C4—22no—
772C4—41no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—82no—
777C4—84no—
778C4—82no—
779C4—81no—
780C4—82no—
781C4C2×#46114yes—
782C4#329514yescomplemented
783C4C2×#54711yescharacteristic
784C4#347511yescharacteristic
785C4#349611yescharacteristic
786C4#352011yescharacteristic
787C2—28no—
788C2—44no—
789C2—84no—
790C2#3615311yescharacteristic
791C2C22×#46111yescharacteristic
792C2#6042811yescharacteristic
793C2C2×#329511yescharacteristic
794C2#6116211yescharacteristic
795C2#6209611yescharacteristic
796C2#6212711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
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
2. #36180C2semidirect
4. #33197C2semidirect
5. #32905C2semidirect
6. #28716C2semidirect
7. #28252C2semidirect
8. #27645C2semidirect
9. #25322C2semidirect
10. #25202C2semidirect
11. #24815C2semidirect
12. #24751C2semidirect
13. #24530C2semidirect
14. D4×C4⋊C8C2semidirect
15. #22487C2semidirect
16. C4×#461C2semidirect
17. C2×#1802C2semidirect
29. C2×#461C22semidirect
33. C22×C4⋊C8C22semidirect
35. #2868C22semidirect
36. #2857C22semidirect
37. #2567C22semidirect
40. #2502C22semidirect
53. C4×C4⋊Q8C22semidirect
58. C2×#384C22semidirect
61. #2084C22semidirect
62. #2071C22semidirect
63. #2071C22semidirect
64. #2066C22semidirect
65. #2055C22semidirect
66. #2055C22semidirect
67. #1990C22semidirect
68. #1987C22semidirect
69. #1981C22semidirect
70. #1948C22semidirect
71. #1948C22semidirect
72. #1948C22semidirect
73. #1939C22semidirect
74. #1927C22semidirect
75. #1892C22semidirect
78. #1877C22semidirect
79. #1872C22semidirect
80. #1850C22semidirect
81. #1842C22semidirect
82. #1824C22semidirect
83. #1803C22semidirect
88. #1802C22semidirect
89. #1802C22semidirect
90. #1802C22semidirect
91. #1802C22semidirect
92. #1797C22semidirect
93. C4×C4⋊C8C22semidirect
94. C4×#103C22semidirect
95. C2×#340C22semidirect
331. C4×D4SD16semidirect
665. D4#461semidirect
782. C4#3295semidirect

Maximal subgroups

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

subgroupindex
C2×#32952
#361802
C4×D422
#331972
#329052
#287162
#282522
#276452
#253222
#252022
#248152
#247512
#245302
D4×C4⋊C82
#224872
C4×#4612
C2×#18022