Finite Group Databasebeta

← #6380512

Subgroups — #6380512

Order 512.

2538 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
2C2×#2354C211yesmaximal, characteristic, complemented
3C4⋊C4×#41C211yesmaximal, characteristic, complemented
4#22781C214yesmaximal, complemented
5#22780C214yesmaximal, complemented
6#22767C212yesmaximal, complemented
7#22766C212yesmaximal, complemented
8#22759C212yesmaximal, complemented
9#22758C212yesmaximal, complemented
10#21095C212yesmaximal, complemented
11#21033C212yesmaximal, complemented
12#20928C212yesmaximal
13#20764C211yesmaximal, characteristic, complemented
14#20648C211yesmaximal, characteristic, complemented
15#20646C211yesmaximal, characteristic, complemented
16C4⋊C4×M16C211yesmaximal, characteristic, complemented
17C4×#417C212yesmaximal, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C4×#41C2212yes—
20C2×C4×#41C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117—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#2354—21no—
37#2354—21no—
38#2354—22no—
39#2354C2212yes—
40#2354C2212yes—
41#2354C2214yes—
42#2351C2212yescomplemented
43Q8×C4⋊C4C2211yescharacteristic, complemented
44Q8×C4⋊C4C2211yescharacteristic, complemented
45#2349—22no—
46#2349C2212yescomplemented
47D4×C4⋊C4—21no—
48D4×C4⋊C4—21no—
49D4×C4⋊C4C2211yescharacteristic, complemented
50D4×C4⋊C4C2211yescharacteristic, complemented
51#2296—22no—
52#2296C2212yes—
53C2×#390C2212yes—
54C2×#388—22no—
55#2285—21no—
56#2285C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#380—21no—
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62#1936C2214yes—
63#1936C2214yes—
64#1934C2214yes—
65#1934C2214yes—
66#1921C2214yescomplemented
67#1920C2214yescomplemented
68#1919C2214yescomplemented
69#1918C2214yescomplemented
70#1880C2214yes—
71#1880C2214yes—
72#1879C2214yes—
73#1879C2214yes—
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#1763C2214yescomplemented
88#1762C2214yescomplemented
89C4×#103C2214yescomplemented
90C4×#102C2214yescomplemented
91#1736C2212yes—
92#1736C2212yes—
93#1736C2212yes—
94#1736C2212yes—
95#1728C2212yes—
96C22×#41C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4—21no—
99C2×AGL(1,ℤ/8)—24no—
100C2×AGL(1,ℤ/8)—24no—
101C2×AGL(1,ℤ/8)C2×C418yes—
102C22×SD16C2312yes—
103C22×D8C2312yes—
104C22×M16C2312yes—
105C22×M16C2311yescharacteristic
106C22×M16C2311yescharacteristic
107C4×#41—24no—
108C4×#41—28no—
109C4×#41—44no—
110C4×#41C2×C418yes—
111C2×C4×Q8C2312yes—
112C2×C4×Q8C2312yes—
113C2×C4×Q8C2311yescharacteristic
114C2×C4×Q8C2311yescharacteristic
115C2×C4×D4—21no—
116C2×C4×D4—21no—
117C2×C4×D4—22no—
118C2×C4×D4—22no—
119C2×C4×D4—21no—
120C2×C4×D4—21no—
121C2×C4×D4—24no—
122C2×C4×D4C2×C418yescomplemented
123C2×C4×D4C2312yes—
124C2×C4×D4C2312yes—
125C2×C4×D4C2312yes—
126C2×C4×D4C2311yescharacteristic
127C2×C4×D4C2311yescharacteristic
128C2×C4×D4C2312yes—
129C2×#117—22no—
130C2×#117—24no—
131C2×#117—22no—
132C2×#117—21no—
133C2×#117—22no—
134C2×#117—48no—
135C2×#117C2312yes—
136C2×#117C2311yescharacteristic
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4—21no—
141C22×C4⋊C4D411yescharacteristic
142C22×C4⋊C4D411yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C22⋊C4—21no—
146C22×C22⋊C4—22no—
147C22×C22⋊C4—22no—
148C22×C42—21no—
149C22×C42—22no—
150C22×C42—22no—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153#442C2×C4116yescomplemented
154#440C2×C4116yescomplemented
155C4×SD16C2×C4116yescomplemented
156C4×D8C2×C4116yescomplemented
157#428C2×C418yescomplemented
158C2×#107C2312yes—
159C2×#106C2312yes—
160#423—24no—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163#418—44no—
164#418C2×C418yescomplemented
165#417—28no—
166#417C2×C418yes—
167C2×#103C2314yes—
168C2×#103C2312yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2312yes—
173C2×#102C2312yes—
174C2×#102C2312yes—
175C4×M16—44no—
176C4×M16C2×C418yescomplemented
177C2×#97C2314yes—
178C2×#97C2312yes—
179C2×C4×C8C2314yes—
180C2×C4×C8C2312yes—
181#390—22no—
182#390—22no—
183#390C2314yes—
184#390C2314yes—
185#389—22no—
186#389—22no—
187#389—22no—
188#389—22no—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#389C2312yes—
193#388—24no—
194#388—24no—
195#388—24no—
196#388—24no—
197#385—22no—
198#385—22no—
199#385—22no—
200#385—22no—
201#385—22no—
202#385—22no—
203#384—21no—
204#384—21no—
205#384—21no—
206#384—21no—
207#384C2311yescharacteristic
208#384C2311yescharacteristic
209#384C2312yes—
210#384C2312yes—
211#382—22no—
212#382C2312yes—
213#380—21no—
214#380—21no—
215#380—21no—
216#380—21no—
217#380—22no—
218#380—22no—
219#380—24no—
220#380—22no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4—22no—
224C4×C4⋊C4—22no—
225C4×C4⋊C4—21no—
226C4×C4⋊C4—22no—
227C4×C4⋊C4—22no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4D411yescharacteristic
231C4×C4⋊C4D411yescharacteristic
232C4×C4⋊C4D412yes—
233C4×C4⋊C4C2314yes—
234C4×C4⋊C4C2314yes—
235C4×C4⋊C4C2311yescharacteristic
236C4×C4⋊C4C2311yescharacteristic
237C4×C4⋊C4C2312yes—
238C2×#95—22no—
239C2×#95—22no—
240C2×#95D412yes—
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×#41C22×C414yes—
256C2×#41#4114yes—
257C2×#41#4114yes—
258C22×Q8C2411yescharacteristic
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4C22×C414yes—
267C22×D4C2412yes—
268C22×D4C2411yescharacteristic
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—28no—
272C23×C4—21no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—21no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4C2×D412yes—
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D412yes—
284C23×C4C2×D411yescharacteristic
285C23×C4C2411yescharacteristic
286AGL(1,ℤ/8)—232no—
287C2×SD16—24no—
288C2×SD16—24no—
289C2×SD16C22×C418yes—
290C2×D8—24no—
291C2×D8—24no—
292C2×D8C22×C418yes—
293C2×M16—22no—
294C2×M16—22no—
295C2×M16—22no—
296C2×M16—22no—
297C2×M16—24no—
298C2×M16—24no—
299C2×M16—24no—
300C2×M16C22×C414yes—
301C2×M16C22×C414yes—
302C22×C8C2414yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4×Q8—22no—
306C4×Q8—22no—
307C4×Q8—24no—
308C4×Q8—24no—
309C4×Q8—42no—
310C4×Q8—42no—
311C4×Q8C22×C414yes—
312C4×Q8C22×C414yes—
313C4×D4—28no—
314C4×D4—28no—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—28no—
318C4×D4—28no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4—22no—
323C4×D4—42no—
324C4×D4—42no—
325C4×D4—48no—
326C4×D4—48no—
327C4×D4C22×C418yes—
328C4×D4C22×C418yes—
329C4×D4C22×C414yes—
330C4×D4C22×C414yes—
331#117—22no—
332#117—28no—
333#117—24no—
334#117—24no—
335#117—48no—
336#117—48no—
337#117—416no—
338#117—48no—
339#117C22×C414yes—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—82no—
367C2×C4⋊C4C22×C414yes—
368C2×C4⋊C4C2×D411yescharacteristic
369C2×C4⋊C4C2×D411yescharacteristic
370C2×C4⋊C4C2×D412yes—
371C2×C4⋊C4C2×D411yescharacteristic
372C2×C4⋊C4C2×D412yes—
373C2×C4⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2414yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2411yescharacteristic
379C2×C4⋊C4C2411yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—48no—
394C2×C22⋊C4—84no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—28no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—48no—
407C2×C42—48no—
408C2×C42C22×C414yes—
409C2×C42C2×D412yes—
410C2×C42C2×D412yes—
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42#4114yes—
414C2×C42C2412yes—
415C2×C42C2412yes—
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418#107C22×C418yes—
419#106C22×C418yes—
420C4⋊C8—24no—
421C4⋊C8—24no—
422#103—28no—
423#103C22×C418yes—
424#102—28no—
425#102—44no—
426#102—44no—
427#102C22×C418yes—
428#102C22×C418yes—
429#102C22×C418yes—
430#97—44no—
431#97C22×C418yes—
432C4×C8—44no—
433C4×C8C22×C418yes—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—24no—
438#95—24no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95C2×D412yes—
443#95C2×D412yes—
444#95C2×D412yes—
445#95C2×D412yes—
446C24—21no—
447C24—24no—
448C24—22no—
449C24—42no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—42no—
454C24—42no—
455C24C22×D411yescharacteristic
456#41—28no—
457#41—28no—
458#41—28no—
459#41#117116yescomplemented
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C23×C412yes—
464C2×Q8C2×#4112yes—
465C2×Q8C2×#4112yes—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—28no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4C23×C414yes—
485C2×D4C23×C412yes—
486C2×D4C2×#4112yes—
487C2×D4C2×#4112yes—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—432no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—82no—
532C22×C4—82no—
533C22×C4C4×D414yes—
534C22×C4C4×D414yes—
535C22×C4C23×C412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D412yes—
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4H(5,𝔽2)12yes—
549C22×C42−1+412yes—
550C22×C4C2511yescharacteristic
551SD16—216no—
552D8—216no—
553M16—28no—
554M16—28no—
555M16—48no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—24no—
561C2×C8—24no—
562C2×C8—24no—
563C2×C8C23×C414yes—
564C2×C8C23×C414yes—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—42no—
589C4⋊C4—44no—
590C4⋊C4—42no—
591C4⋊C4—81no—
592C4⋊C4—81no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C4⋊C4AGL(1,ℤ/8)14yescomplemented
598C4⋊C4C23×C412yes—
599C4⋊C4C23×C412yes—
600C4⋊C4C23×C414yes—
601C22⋊C4—24no—
602C22⋊C4—28no—
603C22⋊C4—28no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C42—24no—
614C42—24no—
615C42—24no—
616C42—24no—
617C42—24no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—44no—
623C42—44no—
624C42—48no—
625C42—44no—
626C42—48no—
627C42C4×D414yes—
628C42C4×D414yes—
629C42C23×C412yes—
630C42C23×C412yes—
631C42C2×#4112yes—
632C42C2×#4112yes—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—48no—
642C23—48no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23C2×C4×D412yes—
659C23#54612yes—
660C23#54812yes—
661C23C23×D411yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8C2×#11714yescomplemented
666D4—216no—
667D4—24no—
668D4—22no—
669D4—24no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—42no—
675D4C2×#11714yescomplemented
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—216no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—44no—
702C2×C4—48no—
703C2×C4—416no—
704C2×C4—48no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—416no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—84no—
723C2×C4—88no—
724C2×C4—84no—
725C2×C4—88no—
726C2×C4—88no—
727C2×C4C2×#11714yes—
728C2×C4C2×C4×D412yes—
729C2×C4C2×C4×D412yes—
730C2×C4C2×C4×D412yes—
731C2×C4C2×C4×D412yes—
732C2×C4C2×C4×D412yes—
733C2×C4#52014yes—
734C2×C4#54612yes—
735C2×C4#54812yes—
736C2×C4#55214yes—
737C2×C4#55314yes—
738C2×C4C2×AGL(1,ℤ/8)14yes—
739C2×C4C2×AGL(1,ℤ/8)12yes—
740C2×C4#57512yes—
741C2×C4C24×C411yescharacteristic
742C2×C4C22×#4111yescharacteristic
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4C2×H(5,𝔽2)11yescharacteristic
746C2×C4C2×2−1+411yescharacteristic
747C8—24no—
748C8—24no—
749C8—44no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—816no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#235214yes—
772C22C22×C4×D411yescharacteristic
773C22C2×#54611yescharacteristic
774C22C2×#54811yescharacteristic
775C22C22×AGL(1,ℤ/8)11yescharacteristic
776C22C2×#57511yescharacteristic
777C22#358511yescharacteristic
778C22#358611yescharacteristic
779C4—22no—
780C4—22no—
781C4—24no—
782C4—24no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—44no—
790C4—84no—
791C4—82no—
792C4—82no—
793C4#235214yes—
794C4C4×AGL(1,ℤ/8)14yes—
795C4C22×#11711yescharacteristic
796C4C2×#52011yescharacteristic
797C4C2×#55211yescharacteristic
798C4C2×#55311yescharacteristic
799C2—24no—
800C2—44no—
801C2—84no—
802C2C2×#235211yescharacteristic
803C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
804C2#6017011yescharacteristic
805C2#6116111yescharacteristic
806C2#6116611yescharacteristic
807C2#6132111yescharacteristic
808C2#6132311yescharacteristic
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. C2×#2354C2semidirect
3. C4⋊C4×#41C2semidirect
4. #22781C2semidirect
5. #22780C2semidirect
6. #22767C2semidirect
7. #22766C2semidirect
8. #22759C2semidirect
9. #22758C2semidirect
10. #21095C2semidirect
11. #21033C2semidirect
13. #20764C2semidirect
14. #20648C2semidirect
15. #20646C2semidirect
16. C4⋊C4×M16C2semidirect
17. C4×#417C2semidirect
23. C4×AGL(1,ℤ/8)C4semidirect
42. #2351C22semidirect
43. Q8×C4⋊C4C22semidirect
44. Q8×C4⋊C4C22semidirect
46. #2349C22semidirect
49. D4×C4⋊C4C22semidirect
50. D4×C4⋊C4C22semidirect
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
87. #1763C22semidirect
88. #1762C22semidirect
89. C4×#103C22semidirect
90. C4×#102C22semidirect
122. C2×C4×D4C2×C4semidirect
153. #442C2×C4semidirect
154. #440C2×C4semidirect
155. C4×SD16C2×C4semidirect
156. C4×D8C2×C4semidirect
157. #428C2×C4semidirect
164. #418C2×C4semidirect
176. C4×M16C2×C4semidirect
459. #41#117semidirect
597. C4⋊C4AGL(1,ℤ/8)semidirect
665. Q8C2×#117semidirect
675. D4C2×#117semidirect

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
C2×#23542
C4⋊C4×#412
#227812
#227802
#227672
#227662
#227592
#227582
#210952
#210332
#209282
#207642
#206482
#206462
C4⋊C4×M162
C4×#4172