Finite Group Databasebeta

← #6578249

Subgroups — #6578249

Order 512.

2521 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3110C212yesmaximal, complemented
2#36134C211yesmaximal, characteristic, complemented
3C4×D42C211yesmaximal, characteristic
4#33162C211yesmaximal, characteristic, complemented
5#32905C212yesmaximal, complemented
6#28438C211yesmaximal, characteristic, complemented
7#28279C211yesmaximal, characteristic, complemented
8#26641C214yesmaximal, complemented
9#26236C212yesmaximal, complemented
10#25753C212yesmaximal
11#25176C214yesmaximal, complemented
12#24659C212yesmaximal, complemented
13#24153C212yesmaximal, complemented
14#23190C212yesmaximal, complemented
15#23002C212yesmaximal, complemented
16#22799C211yesmaximal, characteristic, complemented
17C4×#474C211yesmaximal, characteristic, complemented
18C2×D42C2211yescharacteristic
19C2×#533C2212yescomplemented
20C22×C4×D4—21no—
21C22×C4×D4C2212yes—
22C2×#492C2212yes—
23#3110—216no—
24C2×#484C2214yescomplemented
25C2×#474C2211yescharacteristic
26C2×#474C2212yescomplemented
27C2×#461C2212yes—
28C2×#461C2212yes—
29C2×#461C2212yes—
30C2×#461C2212yescomplemented
31C2×#461C2212yescomplemented
32C2×#450C2214yes—
33C2×#450C2214yes—
34C2×#440C2214yes—
35C2×#440C2214yescomplemented
36C2×#432C2212yescomplemented
37#2868C2211yescharacteristic, complemented
38#2857C2212yescomplemented
39#2552—21no—
40#2542C2212yes—
41#2538—21no—
42#2441—22no—
43#2429C2214yescomplemented
44#2423—22no—
45#2366C2211yescharacteristic
46#2365C2212yescomplemented
47#2361—21no—
48#2361C2212yes—
49#2358—22no—
50#2354—21no—
51Q8×C4⋊C4—21no—
52D4×C4⋊C4C2211yescharacteristic
53D4×C4⋊C4C2211yescharacteristic
54D4×C22⋊C4—21no—
55D4×C22⋊C4C2212yes—
56C4×C4⋊Q8C2211yescharacteristic, complemented
57C4×#127C2211yescharacteristic
58C4×#121—21no—
59C4×#121C2212yes—
60C4×#120—22no—
61C42×D4C2211yescharacteristic
62C42×D4C2211yescharacteristic
63#2067C2214yescomplemented
64#2036C2214yescomplemented
65#2036C2214yescomplemented
66#2013C2214yescomplemented
67#2000C2214yes—
68#2000C2214yes—
69#1988C2211yescharacteristic, complemented
70#1982C2212yes—
71#1981C2212yescomplemented
72#1981C2212yescomplemented
73#1981C2212yescomplemented
74#1973C2214yescomplemented
75#1956C2212yescomplemented
76#1954C2212yes—
77#1947C2211yescharacteristic, complemented
78#1947C2212yescomplemented
79#1935C2214yescomplemented
80#1924C2214yescomplemented
81#1918C2212yescomplemented
82#1880C2214yescomplemented
83#1877C2214yes—
84#1877C2214yescomplemented
85#1872C2214yescomplemented
86#1863C2214yescomplemented
87#1862C2212yes—
88#1842C2211yescharacteristic, complemented
89#1802C2211yescharacteristic
90#1802C2212yescomplemented
91#1797C2212yescomplemented
92C4×#107C2212yescomplemented
93#1770C2212yescomplemented
94C4×C4⋊C8C2211yescharacteristic, complemented
95C4×#102C2212yes—
96C23×D4—21no—
97C23×D4C2312yes—
98C24×C4—22no—
99C22×SD16C2314yes—
100C22×SD16C2314yes—
101C22×SD16C2314yes—
102D42—24no—
103D42—24no—
104#533—28no—
105#533—44no—
106C2×C4⋊Q8C2312yes—
107C2×C4⋊Q8C2312yes—
108C2×C4⋊Q8C2312yes—
109C2×C4⋊Q8C2311yescharacteristic
110C2×#127C2311yescharacteristic
111C2×#125—22no—
112C2×C22⋊Q8—22no—
113C2×C22⋊Q8C2314yes—
114C2×C22⋊Q8C2314yes—
115C2×#121—21no—
116C2×#121C2312yes—
117C2×#120—22no—
118C2×C4×Q8—21no—
119C2×C4×Q8—22no—
120C2×C4×Q8C2314yes—
121C2×C4×D4—21no—
122C2×C4×D4—22no—
123C2×C4×D4—21no—
124C2×C4×D4—22no—
125C2×C4×D4—28no—
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×D4C2311yescharacteristic
136C2×C4×D4C2312yes—
137C2×C4×D4C2312yes—
138C2×C4×D4C2311yescharacteristic
139C2×C4×D4C2311yescharacteristic
140C2×C4×D4C2311yescharacteristic
141C2×#117—22no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4—22no—
145C22×C22⋊C4—22no—
146C22×C42—21no—
147C22×C42C2312yes—
148#492—28no—
149#484—216no—
150#474—28no—
151#474D418yescomplemented
152#461—28no—
153#461—28no—
154#461—28no—
155#461—44no—
156#461—44no—
157#450—216no—
158#450—48no—
159#440—216no—
160#440—216no—
161#432—28no—
162C2×#107C2314yes—
163C2×#107C2312yes—
164C2×#107C2312yes—
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2311yescharacteristic
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×#103C2314yes—
173C2×#103C2314yes—
174C2×#103C2314yes—
175C2×#102C2312yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2312yes—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×#97C2314yes—
182C2×C4×C8C2312yes—
183#399—24no—
184#398—24no—
185#396—24no—
186#391—21no—
187#391C2314yes—
188#390—22no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#389—21no—
195#389—22no—
196#389—21no—
197#389—22no—
198#389—22no—
199#389—24no—
200#389C2312yes—
201#389C2312yes—
202#388—24no—
203#388—22no—
204#388—22no—
205#387—24no—
206#386—22no—
207#386—22no—
208#386—22no—
209#386—22no—
210#386—22no—
211#385—22no—
212#385—22no—
213#385—22no—
214#384—22no—
215#384—21no—
216#384—21no—
217#384—21no—
218#384—21no—
219#384C2311yescharacteristic
220#384C2311yescharacteristic
221#380—22no—
222#380—22no—
223#380—21no—
224#380C2312yes—
225#379—22no—
226C4×C4⋊C4—22no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4D411yescharacteristic
229C4×C4⋊C4D411yescharacteristic
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2311yescharacteristic
232C4×C4⋊C4C2311yescharacteristic
233C4×C4⋊C4C2311yescharacteristic
234C4×C4⋊C4C2311yescharacteristic
235C4×C22⋊C4—21no—
236C4×C22⋊C4—21no—
237C4×C22⋊C4—21no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4D412yes—
240C4×C22⋊C4D412yes—
241C4×C22⋊C4C2312yes—
242C43C2311yescharacteristic
243#340C2312yes—
244#340C2314yes—
245#340C2312yes—
246#340C2312yes—
247#340C2312yes—
248#336C2314yes—
249#336C2312yes—
250C25—22no—
251C22×Q8—21no—
252C22×Q8C2414yes—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4C2×D411yescharacteristic
267C22×D4C2412yes—
268C22×D4C2411yescharacteristic
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—21no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—48no—
277C23×C4—48no—
278C23×C4—84no—
279C23×C4C2×D412yes—
280C23×C4C2×D412yes—
281C23×C4C2412yes—
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—28no—
285C2×SD16—28no—
286C2×SD16—28no—
287C2×SD16—28no—
288C2×SD16—44no—
289C2×SD16—44no—
290C2×SD16—44no—
291C22×C8C2412yes—
292C22×C8C2414yes—
293C22×C8C2412yes—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—22no—
298C4⋊Q8—24no—
299C4⋊Q8—42no—
300C4⋊Q8—42no—
301C4⋊Q8C2×D414yescomplemented
302#127—22no—
303#127#4114yes—
304#125—48no—
305C22⋊Q8—28no—
306C22⋊Q8—44no—
307C22⋊Q8—48no—
308C22⋊Q8—44no—
309C22⋊Q8—44no—
310#121—28no—
311#121—24no—
312#121—24no—
313#120—216no—
314C4×Q8—28no—
315C4×Q8—44no—
316C4×Q8—48no—
317C4×Q8—44no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—24no—
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—22no—
328C4×D4—24no—
329C4×D4—48no—
330C4×D4—42no—
331C4×D4—42no—
332C4×D4—41no—
333C4×D4—48no—
334C4×D4—48no—
335C4×D4—44no—
336C4×D4—48no—
337C4×D4—44no—
338C4×D4—44no—
339C4×D4—82no—
340C4×D4C2×D414yes—
341C4×D4#4114yes—
342#117—48no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4C2×D411yescharacteristic
364C2×C4⋊C4C2×D411yescharacteristic
365C2×C4⋊C4C2×D411yescharacteristic
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2411yescharacteristic
368C2×C4⋊C4C2412yes—
369C2×C4⋊C4C2411yescharacteristic
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2411yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—48no—
387C2×C22⋊C4—48no—
388C2×C22⋊C4C2×D412yes—
389C2×C22⋊C4C2×D412yes—
390C2×C22⋊C4C2×D412yes—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—22no—
398C2×C42—44no—
399C2×C42C2×D412yes—
400C2×C42C2×D412yes—
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2412yes—
406C2×C42C2411yescharacteristic
407C2×C42C2411yescharacteristic
408C2×C42C2411yescharacteristic
409#107—28no—
410#107—42no—
411#107C2×D418yescomplemented
412C4⋊C8—24no—
413C4⋊C8—24no—
414C4⋊C8—22no—
415C4⋊C8—42no—
416C4⋊C8C2×D414yescomplemented
417#103—28no—
418#103—28no—
419#103—28no—
420#103—44no—
421#103—44no—
422#102—24no—
423#102—28no—
424#102—44no—
425#102C2×D418yes—
426C22⋊C8—28no—
427C22⋊C8—44no—
428#97—28no—
429C4×C8—24no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—22no—
434#95—22no—
435#95—24no—
436#95—22no—
437#95—22no—
438#95—24no—
439#95C2×D412yes—
440#95C2×D412yes—
441#95C2×D412yes—
442C24—21no—
443C24—28no—
444C24—22no—
445C24—44no—
446C24—44no—
447C24—44no—
448C24—44no—
449C24—82no—
450C24—82no—
451C24C22×D412yes—
452C2×Q8—24no—
453C2×Q8—24no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—24no—
458C2×Q8—24no—
459C2×Q8—42no—
460C2×Q8—42no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—24no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—432no—
480C2×D4—48no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4#13714yes—
489C2×D4C22×D412yes—
490C2×D4C2×#4114yes—
491C2×D4C2×#4112yes—
492C2×D4H(5,𝔽2)12yes—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—42no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—42no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—81no—
530C22×C4—82no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4—832no—
534C22×C4C22×D412yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C2511yescharacteristic
544SD16—416no—
545SD16—416no—
546SD16—88no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—24no—
550C2×C8—22no—
551C2×C8—24no—
552C2×C8—22no—
553C2×C8—24no—
554C2×C8—22no—
555C2×C8C22×D414yes—
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—42no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—81no—
582C4⋊C4—84no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4C22×D414yes—
586C4⋊C4C22×D412yes—
587C4⋊C4C2×#4112yes—
588C22⋊C4—28no—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—48no—
597C22⋊C4—42no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—82no—
603C22⋊C4—82no—
604C22⋊C4—84no—
605C42—24no—
606C42—24no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—21no—
611C42—22no—
612C42—21no—
613C42—41no—
614C42—48no—
615C42—42no—
616C42—42no—
617C42—42no—
618C42—44no—
619C42AGL(1,ℤ/8)14yes—
620C42C22×D412yes—
621C42C2×#4112yes—
622C42C2×#4112yes—
623C42H(5,𝔽2)12yes—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—416no—
635C23—416no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—88no—
647C23—88no—
648C23—88no—
649C23—88no—
650C23—88no—
651C23C2×#13714yes—
652C23C23×D411yescharacteristic
653Q8—48no—
654Q8—44no—
655Q8—44no—
656Q8—44no—
657Q8—44no—
658D4—28no—
659D4—22no—
660D4—24no—
661D4—22no—
662D4—22no—
663D4—24no—
664D4—416no—
665D4—416no—
666D4—48no—
667D4—42no—
668D4—42no—
669D4—84no—
670D4#55014yes—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—48no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—48no—
705C2×C4—48no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—88no—
720C2×C4—88no—
721C2×C4—88no—
722C2×C4—88no—
723C2×C4#52512yes—
724C2×C4#52512yes—
725C2×C4D4212yes—
726C2×C4D4212yes—
727C2×C4C2×AGL(1,ℤ/8)12yes—
728C2×C4C2×AGL(1,ℤ/8)12yes—
729C2×C4C2×AGL(1,ℤ/8)12yes—
730C2×C4C2×#13712yes—
731C2×C4#57712yes—
732C2×C4C23×D411yescharacteristic
733C2×C4C22×#4111yescharacteristic
734C2×C4C22×#4111yescharacteristic
735C2×C4C2×H(5,𝔽2)11yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4#58511yescharacteristic
738C8—24no—
739C8—44no—
740C8—42no—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—832no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22C2×#52511yescharacteristic
764C22C2×D4211yescharacteristic
765C22#348811yescharacteristic
766C22C22×AGL(1,ℤ/8)11yescharacteristic
767C22C22×#13711yescharacteristic
768C22C2×#57711yescharacteristic
769C22#358611yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—42no—
774C4—41no—
775C4—42no—
776C4—42no—
777C4—44no—
778C4—42no—
779C4—42no—
780C4—84no—
781C4—82no—
782C4—81no—
783C4—82no—
784C4#311014yescomplemented
785C4#327214yes—
786C4C2×#55011yescharacteristic
787C4D4×#4111yescharacteristic
788C4#350611yescharacteristic
789C4#351911yescharacteristic
790C2—44no—
791C2—44no—
792C2—84no—
793C2#3610111yescharacteristic
794C2C2×#311011yescharacteristic
795C2#6059111yescharacteristic
796C2C2×#327211yescharacteristic
797C2D4×#13711yescharacteristic
798C2#6196211yescharacteristic
799C2#6198011yescharacteristic
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
1. C2×#3110C2semidirect
2. #36134C2semidirect
4. #33162C2semidirect
5. #32905C2semidirect
6. #28438C2semidirect
7. #28279C2semidirect
8. #26641C2semidirect
9. #26236C2semidirect
11. #25176C2semidirect
12. #24659C2semidirect
13. #24153C2semidirect
14. #23190C2semidirect
15. #23002C2semidirect
16. #22799C2semidirect
17. C4×#474C2semidirect
19. C2×#533C22semidirect
24. C2×#484C22semidirect
26. C2×#474C22semidirect
30. C2×#461C22semidirect
31. C2×#461C22semidirect
35. C2×#440C22semidirect
36. C2×#432C22semidirect
37. #2868C22semidirect
38. #2857C22semidirect
43. #2429C22semidirect
46. #2365C22semidirect
56. C4×C4⋊Q8C22semidirect
63. #2067C22semidirect
64. #2036C22semidirect
65. #2036C22semidirect
66. #2013C22semidirect
69. #1988C22semidirect
71. #1981C22semidirect
72. #1981C22semidirect
73. #1981C22semidirect
74. #1973C22semidirect
75. #1956C22semidirect
77. #1947C22semidirect
78. #1947C22semidirect
79. #1935C22semidirect
80. #1924C22semidirect
81. #1918C22semidirect
82. #1880C22semidirect
84. #1877C22semidirect
85. #1872C22semidirect
86. #1863C22semidirect
88. #1842C22semidirect
90. #1802C22semidirect
91. #1797C22semidirect
92. C4×#107C22semidirect
93. #1770C22semidirect
94. C4×C4⋊C8C22semidirect
151. #474D4semidirect
301. C4⋊Q8C2×D4semidirect
411. #107C2×D4semidirect
416. C4⋊C8C2×D4semidirect
784. C4#3110semidirect

Maximal subgroups

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

subgroupindex
C2×#31102
#361342
C4×D422
#331622
#329052
#284382
#282792
#266412
#262362
#257532
#251762
#246592
#241532
#231902
#230022
#227992
C4×#4742