Finite Group Databasebeta

← #6380508

Subgroups — #6380508

Order 512.

2624 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#34121C211yesmaximal, characteristic, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#22778C214yesmaximal, complemented
5#22774C214yesmaximal, complemented
6#22770C212yesmaximal, complemented
7#22766C212yesmaximal, complemented
8#22762C212yesmaximal, complemented
9#22758C212yesmaximal, complemented
10#21093C212yesmaximal, complemented
11#21034C212yesmaximal, complemented
12#20925C212yesmaximal
13#20764C211yesmaximal, characteristic, complemented
14#20648C211yesmaximal, characteristic, complemented
15#20646C211yesmaximal, characteristic, complemented
16C4⋊C4×M16C211yesmaximal, characteristic, complemented
17C4×#418C212yesmaximal, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4—21no—
23C4×AGL(1,ℤ/8)C4116yescomplemented
24C2×#442C2212yes—
25C2×#440C2212yes—
26C2×C4×SD16C2212yes—
27C2×C4×D8C2212yes—
28C2×#428C2211yescharacteristic
29C2×#423C2211yescharacteristic
30C2×#417C2212yes—
31C2×#417C2211yescharacteristic
32C2×#418C2212yes—
33C2×#418C2211yescharacteristic
34C2×C4×M16C2212yes—
35C2×C4×M16C2211yescharacteristic
36#2357C2212yescomplemented
37#2356C2212yescomplemented
38#2355C2211yescharacteristic, complemented
39#2355C2211yescharacteristic, complemented
40#2354C2211yescharacteristic, complemented
41#2354C2211yescharacteristic, complemented
42#2353—22no—
43#2352—21no—
44#2352—21no—
45D4×C4⋊C4—21no—
46D4×C4⋊C4—21no—
47D4×C4⋊C4—22no—
48D4×C4⋊C4C2212yes—
49D4×C4⋊C4C2212yes—
50D4×C4⋊C4C2214yes—
51#2298—22no—
52#2297C2212yes—
53C2×#389C2212yes—
54C2×#385—22no—
55#2285C2211yescharacteristic
56C2×#384C2211yescharacteristic
57#2283—21no—
58C2×#380—21no—
59C4×#117—21no—
60C4×#117C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62#1936C2214yescomplemented
63#1935C2214yescomplemented
64#1934C2214yescomplemented
65#1933C2214yescomplemented
66#1921C2214yescomplemented
67#1920C2214yescomplemented
68#1919C2214yescomplemented
69#1918C2214yescomplemented
70#1879C2214yes—
71#1879C2214yes—
72#1877C2214yes—
73#1877C2214yes—
74#1836C2214yescomplemented
75#1834C2212yescomplemented
76#1834C2212yescomplemented
77#1804C2214yes—
78#1803C2212yescomplemented
79#1803C2212yescomplemented
80#1802C2212yes—
81#1802C2212yes—
82#1802C2212yescomplemented
83#1802C2212yescomplemented
84#1771C2214yescomplemented
85#1770C2212yescomplemented
86C8×C4⋊C4C2212yescomplemented
87#1762C2214yes—
88#1762C2214yes—
89C4×#102C2214yes—
90C4×#102C2214yes—
91#1736C2212yes—
92#1736C2212yes—
93#1736C2212yes—
94#1736C2212yes—
95#1728C2212yes—
96C22×#41C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4—21no—
99C24×C4—22no—
100C2×AGL(1,ℤ/8)—24no—
101C2×AGL(1,ℤ/8)—24no—
102C2×AGL(1,ℤ/8)C2×C418yes—
103C22×SD16C2312yes—
104C22×D8C2312yes—
105C22×M16C2312yes—
106C22×M16C2311yescharacteristic
107C22×M16C2311yescharacteristic
108C4×#41—24no—
109C4×#41C2×C418yescomplemented
110C2×C4×Q8C2311yescharacteristic
111C2×C4×Q8C2311yescharacteristic
112C2×C4×D4—21no—
113C2×C4×D4—21no—
114C2×C4×D4—28no—
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—24no—
120C2×C4×D4—44no—
121C2×C4×D4C2×C418yes—
122C2×C4×D4C2314yes—
123C2×C4×D4C2314yes—
124C2×C4×D4C2312yes—
125C2×C4×D4C2312yes—
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2311yescharacteristic
128C2×#117—21no—
129C2×#117—21no—
130C2×#117—21no—
131C2×#117C2312yes—
132C2×#117C2311yescharacteristic
133C22×C4⋊C4—21no—
134C22×C4⋊C4—22no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—22no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—22no—
139C22×C4⋊C4—48no—
140C22×C4⋊C4D411yescharacteristic
141C22×C4⋊C4D411yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4—21no—
145C22×C22⋊C4—22no—
146C22×C42—21no—
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149#442C2×C4116yescomplemented
150#440C2×C4116yescomplemented
151C4×SD16C2×C4116yescomplemented
152C4×D8C2×C4116yescomplemented
153#428C2×C418yescomplemented
154C2×#107C2312yes—
155C2×#106C2312yes—
156#423—24no—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159#418—28no—
160#418C2×C418yes—
161#417—44no—
162#417C2×C418yescomplemented
163C2×#103C2314yes—
164C2×#103C2312yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2312yes—
169C2×#102C2312yes—
170C2×#102C2312yes—
171C4×M16—44no—
172C4×M16C2×C418yescomplemented
173C2×#97C2314yes—
174C2×#97C2312yes—
175C2×C4×C8C2314yes—
176C2×C4×C8C2312yes—
177#391C2312yes—
178#391C2312yes—
179#390C2312yes—
180#390C2312yes—
181#389—22no—
182#389—22no—
183#389C2314yes—
184#389C2314yes—
185#388—22no—
186#388—22no—
187#388—22no—
188#388—22no—
189#387—22no—
190#387—22no—
191#387—22no—
192#387—22no—
193#386—22no—
194#386—22no—
195#385—24no—
196#385—24no—
197#385—24no—
198#385—24no—
199#384—21no—
200#384—21no—
201#384C2311yescharacteristic
202#384C2311yescharacteristic
203#384C2312yes—
204#384C2312yes—
205#383—22no—
206#382—21no—
207#382—21no—
208#382C2312yes—
209#381—22no—
210#380—21no—
211#380—21no—
212#380—22no—
213#380—22no—
214#380—24no—
215#380—21no—
216#380—21no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4D411yescharacteristic
222C4×C4⋊C4D411yescharacteristic
223C4×C4⋊C4D412yes—
224C4×C4⋊C4C2312yes—
225C4×C4⋊C4C2312yes—
226C4×C4⋊C4C2312yes—
227C4×C4⋊C4C2312yes—
228C4×C4⋊C4C2311yescharacteristic
229C4×C4⋊C4C2311yescharacteristic
230C4×C4⋊C4C2312yes—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C4×C22⋊C4—22no—
235C4×C22⋊C4—22no—
236#376—22no—
237#376—22no—
238C2×#95—22no—
239C2×#95D412yes—
240C43—22no—
241#340C2314yes—
242#340C2314yes—
243#340C2314yes—
244#340C2314yes—
245#340C2314yes—
246#340C2314yes—
247#340C2314yes—
248#340C2314yes—
249#336C2314yes—
250#336C2314yes—
251C25—21no—
252C2×#41—22no—
253C2×#41—22no—
254C2×#41—22no—
255C2×#41—22no—
256C2×#41—22no—
257C2×#41C22×C414yes—
258C22×Q8C2411yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4C22×C414yes—
265C22×D4#4114yes—
266C22×D4#4114yes—
267C22×D4C2411yescharacteristic
268C22×D4C2412yes—
269C23×C4—21no—
270C23×C4—28no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—48no—
282C23×C4—48no—
283C23×C4—84no—
284C23×C4C2×D412yes—
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D412yes—
287C23×C4C2×D411yescharacteristic
288C23×C4C2411yescharacteristic
289AGL(1,ℤ/8)—232no—
290C2×SD16—24no—
291C2×SD16—24no—
292C2×SD16C22×C418yes—
293C2×D8—24no—
294C2×D8—24no—
295C2×D8C22×C418yes—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—24no—
301C2×M16—24no—
302C2×M16—24no—
303C2×M16C22×C414yes—
304C2×M16C22×C414yes—
305C22×C8C2414yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8C22×C414yescomplemented
311C4×Q8C22×C414yescomplemented
312C4×D4—28no—
313C4×D4—28no—
314C4×D4—28no—
315C4×D4—28no—
316C4×D4—28no—
317C4×D4—28no—
318C4×D4—24no—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—44no—
323C4×D4—44no—
324C4×D4—48no—
325C4×D4—48no—
326C4×D4C22×C418yes—
327C4×D4C22×C418yes—
328C4×D4C22×C414yescomplemented
329C4×D4C22×C414yescomplemented
330#117—22no—
331#117—28no—
332#117—24no—
333#117—24no—
334#117—44no—
335#117—44no—
336#117C22×C414yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—416no—
357C2×C4⋊C4—48no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—48no—
360C2×C4⋊C4—48no—
361C2×C4⋊C4—82no—
362C2×C4⋊C4C22×C414yes—
363C2×C4⋊C4C2×D411yescharacteristic
364C2×C4⋊C4C2×D412yes—
365C2×C4⋊C4C2×D411yescharacteristic
366C2×C4⋊C4C2×D411yescharacteristic
367C2×C4⋊C4C2×D412yes—
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C4⋊C4C2414yes—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2411yescharacteristic
374C2×C4⋊C4C2411yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—48no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—28no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42C22×C414yes—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42#4114yes—
406C2×C42C2412yes—
407C2×C42C2412yes—
408C2×C42C2411yescharacteristic
409C2×C42C2411yescharacteristic
410#107C22×C418yescomplemented
411#106C22×C418yescomplemented
412C4⋊C8—24no—
413C4⋊C8—24no—
414#103—44no—
415#103C22×C418yescomplemented
416#102—28no—
417#102—28no—
418#102—44no—
419#102C22×C418yes—
420#102C22×C418yes—
421#102C22×C418yescomplemented
422#97—44no—
423#97C22×C418yescomplemented
424C4×C8—44no—
425C4×C8C22×C418yescomplemented
426#95—24no—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95C2×D412yes—
439#95C2×D412yes—
440#95C2×D412yes—
441#95C2×D412yes—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—22no—
446C24—21no—
447C24—42no—
448C24—42no—
449C24—42no—
450C24—42no—
451C24C22×D411yescharacteristic
452#41—28no—
453#41—28no—
454#41—44no—
455#41—44no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C23×C412yes—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—28no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4#117116yescomplemented
480C2×D4C23×C412yes—
481C2×D4C23×C414yes—
482C2×D4C2×#4114yes—
483C2×D4C2×#4114yes—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—41no—
503C22×C4—42no—
504C22×C4—41no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—432no—
510C22×C4—48no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—44no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—84no—
528C22×C4—84no—
529C22×C4—832no—
530C22×C4C4×D414yes—
531C22×C4C4×D414yes—
532C22×C4C23×C412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D412yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C42−1+412yes—
547C22×C4C2511yescharacteristic
548SD16—216no—
549D8—216no—
550M16—28no—
551M16—28no—
552M16—48no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—24no—
558C2×C8—24no—
559C2×C8—24no—
560C2×C8C23×C414yes—
561C2×C8C23×C414yes—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—48no—
581C4⋊C4—44no—
582C4⋊C4—48no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4AGL(1,ℤ/8)14yescomplemented
591C4⋊C4C23×C412yes—
592C4⋊C4C23×C412yes—
593C4⋊C4C23×C414yes—
594C22⋊C4—24no—
595C22⋊C4—28no—
596C22⋊C4—28no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—82no—
605C22⋊C4—82no—
606C42—24no—
607C42—24no—
608C42—24no—
609C42—24no—
610C42—24no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—44no—
616C42—44no—
617C42—44no—
618C42—82no—
619C42—82no—
620C42C4×D414yes—
621C42C4×D414yes—
622C42C23×C412yes—
623C42C23×C412yes—
624C42C2×#4112yes—
625C42C2×#4112yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—216no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—22no—
635C23—48no—
636C23—48no—
637C23—48no—
638C23—48no—
639C23—48no—
640C23—48no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C2×C4×D412yes—
652C23#54612yes—
653C23#54812yes—
654C23C23×D411yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—41no—
658Q8—41no—
659D4—216no—
660D4—22no—
661D4—24no—
662D4—22no—
663D4—24no—
664D4—24no—
665D4—48no—
666D4—41no—
667D4—41no—
668D4C2×#11718yes—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—44no—
692C2×C4—48no—
693C2×C4—416no—
694C2×C4—48no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—48no—
704C2×C4—48no—
705C2×C4—416no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—84no—
716C2×C4—816no—
717C2×C4—84no—
718C2×C4—816no—
719C2×C4—88no—
720C2×C4C2×#11714yes—
721C2×C4C2×C4×D412yes—
722C2×C4C2×C4×D412yes—
723C2×C4C2×C4×D412yes—
724C2×C4C2×C4×D412yes—
725C2×C4C2×C4×D412yes—
726C2×C4#52014yes—
727C2×C4#54612yes—
728C2×C4#54812yes—
729C2×C4#55214yes—
730C2×C4#55314yes—
731C2×C4C2×AGL(1,ℤ/8)14yes—
732C2×C4C2×AGL(1,ℤ/8)12yes—
733C2×C4#57512yes—
734C2×C4C24×C411yescharacteristic
735C2×C4C22×#4111yescharacteristic
736C2×C4C22×#4111yescharacteristic
737C2×C4C22×#4111yescharacteristic
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C2×C4C2×2−1+411yescharacteristic
740C8—24no—
741C8—24no—
742C8—44no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—28no—
750C22—432no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22#235214yes—
765C22C22×C4×D411yescharacteristic
766C22C2×#54611yescharacteristic
767C22C2×#54811yescharacteristic
768C22C22×AGL(1,ℤ/8)11yescharacteristic
769C22C2×#57511yescharacteristic
770C22#358511yescharacteristic
771C22#358611yescharacteristic
772C4—22no—
773C4—22no—
774C4—24no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—84no—
786C4#235214yes—
787C4C4×AGL(1,ℤ/8)14yes—
788C4C22×#11711yescharacteristic
789C4C2×#52011yescharacteristic
790C4C2×#55211yescharacteristic
791C4C2×#55311yescharacteristic
792C2—24no—
793C2—48no—
794C2—82no—
795C2C2×#235211yescharacteristic
796C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
797C2#6017011yescharacteristic
798C2#6115511yescharacteristic
799C2#6115911yescharacteristic
800C2#6131711yescharacteristic
801C2#6131811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34121C2semidirect
3. C2×D4×C4⋊C4C2semidirect
4. #22778C2semidirect
5. #22774C2semidirect
6. #22770C2semidirect
7. #22766C2semidirect
8. #22762C2semidirect
9. #22758C2semidirect
10. #21093C2semidirect
11. #21034C2semidirect
13. #20764C2semidirect
14. #20648C2semidirect
15. #20646C2semidirect
16. C4⋊C4×M16C2semidirect
17. C4×#418C2semidirect
23. C4×AGL(1,ℤ/8)C4semidirect
36. #2357C22semidirect
37. #2356C22semidirect
38. #2355C22semidirect
39. #2355C22semidirect
40. #2354C22semidirect
41. #2354C22semidirect
62. #1936C22semidirect
63. #1935C22semidirect
64. #1934C22semidirect
65. #1933C22semidirect
66. #1921C22semidirect
67. #1920C22semidirect
68. #1919C22semidirect
69. #1918C22semidirect
74. #1836C22semidirect
75. #1834C22semidirect
76. #1834C22semidirect
78. #1803C22semidirect
79. #1803C22semidirect
82. #1802C22semidirect
83. #1802C22semidirect
84. #1771C22semidirect
85. #1770C22semidirect
86. C8×C4⋊C4C22semidirect
109. C4×#41C2×C4semidirect
149. #442C2×C4semidirect
150. #440C2×C4semidirect
151. C4×SD16C2×C4semidirect
152. C4×D8C2×C4semidirect
153. #428C2×C4semidirect
162. #417C2×C4semidirect
172. C4×M16C2×C4semidirect
310. C4×Q8C22×C4semidirect
311. C4×Q8C22×C4semidirect
328. C4×D4C22×C4semidirect
329. C4×D4C22×C4semidirect
410. #107C22×C4semidirect
411. #106C22×C4semidirect
415. #103C22×C4semidirect
421. #102C22×C4semidirect
423. #97C22×C4semidirect
425. C4×C8C22×C4semidirect
479. C2×D4#117semidirect
590. C4⋊C4AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C2×C4×AGL(1,ℤ/8)2
#341212
C2×D4×C4⋊C42
#227782
#227742
#227702
#227662
#227622
#227582
#210932
#210342
#209252
#207642
#206482
#206462
C4⋊C4×M162
C4×#4182