Finite Group Databasebeta

← #6494161

Subgroups — #6494161

Order 512.

2020 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3248C212yesmaximal, complemented
2#36631C211yesmaximal, characteristic
3C4×#533C211yesmaximal, characteristic, complemented
4#33200C212yesmaximal, complemented
5#33165C212yesmaximal, complemented
6#29833C214yesmaximal, complemented
7#28283C211yesmaximal, characteristic, complemented
8#28281C212yesmaximal, complemented
9#28279C211yesmaximal, characteristic, complemented
10#28255C211yesmaximal, characteristic, complemented
11#28254C212yesmaximal, complemented
12#28252C211yesmaximal, characteristic, complemented
13#24755C214yesmaximal, complemented
14#24753C212yesmaximal
15#24752C212yesmaximal, complemented
16#21887C212yesmaximal, complemented
17C2×#1842C211yesmaximal, characteristic, complemented
18C2×#533C2211yescharacteristic
19C2×#529C2212yes—
20#3248—216no—
21C2×#479C2214yes—
22C2×#475C2212yes—
23C2×#474C2212yes—
24C2×#467C2214yes—
25C2×#465C2214yes—
26C2×#464C2214yes—
27C2×#464C2214yes—
28C2×#462C2212yes—
29C2×#462C2212yes—
30C2×#460C2212yes—
31C2×#461C2212yes—
32C22×C4⋊C8C2212yes—
33C22×C4⋊C8C2212yes—
34C22×C4⋊C8C2212yes—
35#2861C2212yes—
36#2860—21no—
37#2860—21no—
38#2859C2211yescharacteristic
39#2858C2211yescharacteristic
40#2857C2211yescharacteristic
41#2856C2211yescharacteristic
42#2854—21no—
43#2854—21no—
44#2850C2212yes—
45C4×C4⋊Q8C2211yescharacteristic
46C4×C4⋊Q8C2211yescharacteristic
47C4×C4⋊Q8C2211yescharacteristic
48C4×C4⋊Q8C2211yescharacteristic
49C4×C4⋊Q8C2211yescharacteristic
50C4×#127C2211yescharacteristic
51C4×#125—21no—
52C4×#125—21no—
53C4×#124C2212yes—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8—21no—
56C4×C22⋊Q8C2212yes—
57C4×C22⋊Q8C2212yes—
58C4×#121—21no—
59C4×#121—21no—
60#2296—21no—
61#2295—21no—
62#2295C2212yes—
63#2293—21no—
64#2293—21no—
65#2285C2211yescharacteristic
66C42×Q8—21no—
67C42×Q8C2212yes—
68C4×#117—21no—
69C2×C43C2211yescharacteristic
70#2068C2214yes—
71#2067C2214yes—
72#2066C2214yes—
73#2065C2214yes—
74#2056C2214yes—
75#2056C2214yes—
76#2055C2214yes—
77#2055C2214yes—
78#1989C2214yes—
79#1983C2214yes—
80#1983C2214yes—
81#1982C2212yes—
82#1981C2212yes—
83#1949C2214yes—
84#1948C2212yes—
85#1947C2212yes—
86#1893C2214yes—
87#1892C2214yes—
88#1842C2211yescharacteristic
89#1842C2212yes—
90#1842C2211yescharacteristic
91#1842C2212yes—
92#1842C2212yes—
93#1805C2214yes—
94#1803C2212yes—
95#1803C2212yes—
96#1803C2212yes—
97#1803C2212yes—
98#1802C2212yes—
99#1802C2212yes—
100C22×Q16C2314yes—
101C22×SD16C2314yes—
102C23×C8C2314yes—
103#533—24no—
104#533D418yescomplemented
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×C4⋊Q8C2311yescharacteristic
108C2×#127C2311yescharacteristic
109#529—28no—
110#529—28no—
111C2×#126—22no—
112C2×#125—21no—
113C2×#125C2312yes—
114C2×#124C2312yes—
115C2×#124C2312yes—
116C2×#123—22no—
117C2×C22⋊Q8—21no—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×#121—21no—
121C2×#121—21no—
122C2×#121C2312yes—
123C2×C4×Q8—21no—
124C2×C4×Q8—21no—
125C2×C4×Q8—21no—
126C2×C4×Q8C2312yes—
127C2×C4×Q8C2312yes—
128C2×C4×Q8C2312yes—
129C2×C4×Q8C2312yes—
130C2×C4×D4—22no—
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4C2312yes—
134C2×#117—21no—
135C2×#117—21no—
136C2×#117—22no—
137C22×C42D411yescharacteristic
138C22×C42D411yescharacteristic
139C22×C42D411yescharacteristic
140C22×C42D411yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#479—216no—
145#475—28no—
146#474—28no—
147#467—216no—
148#465—216no—
149#464—216no—
150#464—48no—
151#462—28no—
152#462—44no—
153#461—28no—
154#460—44no—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8—28no—
158C2×C4⋊C8—44no—
159C2×C4⋊C8—44no—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2314yes—
162C2×C4⋊C8C2312yes—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2314yes—
168C2×C4⋊C8C2312yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177#391—21no—
178#391—21no—
179#391C2312yes—
180#391C2312yes—
181#391C2312yes—
182#391C2312yes—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390C2312yes—
192#390C2312yes—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389—21no—
205#389—21no—
206#389—21no—
207#389C2312yes—
208#389C2312yes—
209#388—22no—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#387—22no—
218#387—22no—
219#387—22no—
220#387—22no—
221#386—22no—
222#386—22no—
223#385—22no—
224#385—22no—
225#384C2311yescharacteristic
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#382—21no—
230#382C2312yes—
231#380—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—22no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—21no—
244C4×C4⋊C4—21no—
245C4×C4⋊C4—21no—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—22no—
249C4×C4⋊C4—22no—
250C4×C4⋊C4C2312yes—
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256C4×C22⋊C4—22no—
257#376—22no—
258C43—22no—
259C43D411yescharacteristic
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43D411yescharacteristic
263C43C2311yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271C22×Q8—21no—
272C22×Q8C2412yes—
273C22×Q8C2412yes—
274C22×D4—22no—
275C22×D4—21no—
276C22×D4—21no—
277C22×D4C2412yes—
278C23×C4—22no—
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286C2×Q16—28no—
287C2×Q16—44no—
288C2×Q16—44no—
289C2×SD16—28no—
290C2×SD16—44no—
291C2×SD16—44no—
292C22×C8—28no—
293C22×C8—44no—
294C22×C8—44no—
295C22×C8C2414yes—
296C22×C8C2414yes—
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301C4⋊Q8C2×D414yes—
302C4⋊Q8C2×D414yes—
303#127—22no—
304#127—22no—
305#126—48no—
306#125—28no—
307#125—24no—
308#125—24no—
309#124—24no—
310#124—24no—
311#124—24no—
312#124—24no—
313#123—48no—
314C22⋊Q8—28no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8C2×D418yes—
319#121—24no—
320#121—24no—
321#121—44no—
322#121—44no—
323C4×Q8—28no—
324C4×Q8—24no—
325C4×Q8—24no—
326C4×Q8—24no—
327C4×Q8—24no—
328C4×Q8—24no—
329C4×Q8—24no—
330C4×Q8—24no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×Q8C2×D418yes—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—44no—
337C4×D4—48no—
338C4×D4—44no—
339#117—28no—
340#117—44no—
341#117—48no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2412yes—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
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×C42—24no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
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×D414yes—
420C2×C42C2×D411yescharacteristic
421C2×C42#4114yes—
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—28no—
429#106—28no—
430C4⋊C8—24no—
431C4⋊C8—24no—
432C4⋊C8—28no—
433C4⋊C8—24no—
434C4⋊C8—24no—
435C4⋊C8—28no—
436C4⋊C8—44no—
437C4⋊C8—42no—
438C4⋊C8—42no—
439#103—28no—
440#103—28no—
441#103—28no—
442#103—44no—
443#103—44no—
444#102—28no—
445#102—44no—
446#102—44no—
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—
462#95—22no—
463C24—22no—
464C24C22×D411yescharacteristic
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8C22×D414yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4#12114yes—
525C22×C4#12114yes—
526C22×C4#13714yes—
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D412yes—
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C2×#4112yes—
542C22×C4C2511yescharacteristic
543Q16—88no—
544SD16—88no—
545C2×C8—24no—
546C2×C8—24no—
547C2×C8—24no—
548C2×C8—24no—
549C2×C8—24no—
550C2×C8—24no—
551C2×C8—88no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4C22×D414yes—
585C22⋊C4—28no—
586C22⋊C4—44no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C42—28no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42#12114yes—
629C42#12114yes—
630C42#13514yes—
631C42C22×D412yes—
632C42C22×D412yes—
633C42C2×#4112yes—
634C42C2×#4112yes—
635C42H(5,𝔽2)12yes—
636C42H(5,𝔽2)12yes—
637C422−1+412yes—
638C422−1+412yes—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23C2×#12112yes—
651C23C2×#13712yes—
652C23#57512yes—
653C23C23×D411yescharacteristic
654Q8—24no—
655Q8—24no—
656Q8—42no—
657Q8—42no—
658Q8—48no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—84no—
668D4—88no—
669D4—84no—
670C2×C4—28no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—28no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—88no—
726C2×C4C2×#12112yes—
727C2×C4C2×#12112yes—
728C2×C4C2×#12112yes—
729C2×C4C2×#12112yes—
730C2×C4C2×#12112yes—
731C2×C4#53712yes—
732C2×C4#53712yes—
733C2×C4#53712yes—
734C2×C4#53712yes—
735C2×C4C2×#13512yes—
736C2×C4C2×#13512yes—
737C2×C4C2×#13512yes—
738C2×C4C2×#13712yes—
739C2×C4C2×#13712yes—
740C2×C4#57512yes—
741C2×C4C23×D411yescharacteristic
742C2×C4C22×#4111yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C2×C4C2×2−1+411yescharacteristic
746C2×C4C2×2−1+411yescharacteristic
747C8—44no—
748C8—44no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22#303714yes—
763C22C22×#12111yescharacteristic
764C22C2×#53711yescharacteristic
765C22C2×#53711yescharacteristic
766C22C22×#13511yescharacteristic
767C22C22×#13711yescharacteristic
768C22C2×#57511yescharacteristic
769C22C2×#57511yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—44no—
780C4—41no—
781C4—41no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4#303514yes—
789C4#324814yescomplemented
790C4#349811yescharacteristic
791C4#349911yescharacteristic
792C4#351111yescharacteristic
793C4#351111yescharacteristic
794C2—24no—
795C2—162no—
796C2#3527311yescharacteristic
797C2C2×#303511yescharacteristic
798C2C2×#303711yescharacteristic
799C2C2×#324811yescharacteristic
800C2#6090011yescharacteristic
801C2#6091711yescharacteristic
802C2#6091811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2856C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3248C2semidirect
3. C4×#533C2semidirect
4. #33200C2semidirect
5. #33165C2semidirect
6. #29833C2semidirect
7. #28283C2semidirect
8. #28281C2semidirect
9. #28279C2semidirect
10. #28255C2semidirect
11. #28254C2semidirect
12. #28252C2semidirect
13. #24755C2semidirect
15. #24752C2semidirect
16. #21887C2semidirect
17. C2×#1842C2semidirect
104. #533D4semidirect
789. C4#3248semidirect

Maximal subgroups

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

subgroupindex
C2×#32482
#366312
C4×#5332
#332002
#331652
#298332
#282832
#282812
#282792
#282552
#282542
#282522
#247552
#247532
#247522
#218872
C2×#18422