Finite Group Databasebeta

← #6380674

Subgroups — #6380674

Order 512.

2408 conjugacy classes of subgroups.

The subgroup lattice has 792 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×#2354C211yesmaximal, characteristic, complemented
4#22820C214yesmaximal, complemented
5#22817C214yesmaximal, complemented
6#22813C212yesmaximal, complemented
7#22811C212yesmaximal, complemented
8#22807C212yesmaximal, complemented
9#22805C212yesmaximal, complemented
10#21236C212yesmaximal
11#21060C212yesmaximal, complemented
12#21059C212yesmaximal, complemented
13#20800C211yesmaximal, characteristic, complemented
14#20648C211yesmaximal, characteristic, complemented
15#20646C211yesmaximal, characteristic, complemented
16C4×#428C212yesmaximal, complemented
17C4⋊C4×M16C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C4×#41C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117—21no—
22C4×AGL(1,ℤ/8)C4116yescomplemented
23C2×#442C2212yes—
24C2×#440C2212yes—
25C2×C4×SD16C2212yes—
26C2×C4×D8C2212yes—
27C2×#428C2212yes—
28C2×#428C2212yes—
29C2×#428C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C2×#417C2212yes—
32C2×#417C2211yescharacteristic
33C2×#418C2212yes—
34C2×#418C2211yescharacteristic
35C2×C4×M16C2212yes—
36C2×C4×M16C2211yescharacteristic
37#2357C2212yescomplemented
38#2356C2212yescomplemented
39#2355C2211yescharacteristic, complemented
40#2355C2211yescharacteristic, complemented
41#2354—21no—
42#2354—21no—
43#2354—22no—
44#2354C2212yes—
45#2354C2212yes—
46#2354C2214yes—
47#2354C2211yescharacteristic, complemented
48#2354C2211yescharacteristic, complemented
49#2353—22no—
50#2352—21no—
51#2352—21no—
52#2298—22no—
53#2297C2212yes—
54C2×#390C2212yes—
55C2×#388—22no—
56#2285C2211yescharacteristic
57C2×#384C2211yescharacteristic
58#2283—21no—
59C2×#380—21no—
60C4×#117—21no—
61C4×#117C2212yes—
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64#1973C2214yes—
65#1972C2214yes—
66#1970C2214yes—
67#1968C2214yes—
68#1928C2214yescomplemented
69#1927C2214yescomplemented
70#1926C2214yes—
71#1926C2214yes—
72#1926C2214yescomplemented
73#1925C2214yes—
74#1925C2214yes—
75#1925C2214yescomplemented
76#1847C2214yescomplemented
77#1845C2212yescomplemented
78#1844C2212yescomplemented
79#1804C2214yes—
80#1803C2212yescomplemented
81#1803C2212yescomplemented
82#1802C2212yes—
83#1802C2212yes—
84#1802C2212yescomplemented
85#1802C2212yescomplemented
86#1776C2214yescomplemented
87#1776C2214yescomplemented
88C4×#107C2214yescomplemented
89C4×#106C2214yescomplemented
90#1771C2214yescomplemented
91#1770C2212yescomplemented
92C8×C4⋊C4C2212yescomplemented
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×#41C2×C418yes—
109C2×C4×Q8C2311yescharacteristic
110C2×C4×Q8C2311yescharacteristic
111C2×C4×D4—21no—
112C2×C4×D4—21no—
113C2×C4×D4—21no—
114C2×C4×D4—21no—
115C2×C4×D4—24no—
116C2×C4×D4C2×C418yes—
117C2×C4×D4C2312yes—
118C2×C4×D4C2311yescharacteristic
119C2×C4×D4C2311yescharacteristic
120C2×C4×D4C2312yes—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—22no—
124C2×#117—24no—
125C2×#117—22no—
126C2×#117—21no—
127C2×#117—48no—
128C2×#117C2312yes—
129C2×#117C2311yescharacteristic
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4D411yescharacteristic
133C22×C4⋊C4D411yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4—21no—
137C22×C22⋊C4—22no—
138C22×C22⋊C4—22no—
139C22×C42—21no—
140C22×C42—22no—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143#442C2×C4116yescomplemented
144#440C2×C4116yescomplemented
145C4×SD16C2×C4116yescomplemented
146C4×D8C2×C4116yescomplemented
147#428—28no—
148#428—44no—
149#428C2×C418yes—
150C2×#107C2314yes—
151C2×#107C2314yes—
152C2×#107C2312yes—
153C2×#106C2314yes—
154C2×#106C2314yes—
155C2×#106C2312yes—
156#423—24no—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159#418—44no—
160#418C2×C418yes—
161#417—44no—
162#417C2×C418yes—
163C2×#103C2314yes—
164C2×#103C2312yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2312yes—
169C2×#102C2312yes—
170C2×#102C2312yes—
171C4×M16—28no—
172C4×M16C2×C418yes—
173C2×#97C2314yes—
174C2×#97C2312yes—
175C2×C4×C8C2314yes—
176C2×C4×C8C2312yes—
177#391C2312yes—
178#391C2312yes—
179#390—22no—
180#390—22no—
181#390C2314yes—
182#390C2314yes—
183#390C2312yes—
184#390C2312yes—
185#388—22no—
186#388—22no—
187#388—22no—
188#388—22no—
189#388—24no—
190#388—24no—
191#388—24no—
192#388—24no—
193#387—22no—
194#387—22no—
195#387—22no—
196#387—22no—
197#386—22no—
198#386—22no—
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—21no—
213#380—21no—
214#380—22no—
215#380—22no—
216#380—24no—
217C4×C4⋊C4—21no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4—22no—
220C4×C4⋊C4—22no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—21no—
223C4×C4⋊C4D411yescharacteristic
224C4×C4⋊C4D411yescharacteristic
225C4×C4⋊C4D412yes—
226C4×C4⋊C4C2314yes—
227C4×C4⋊C4C2314yes—
228C4×C4⋊C4C2312yes—
229C4×C4⋊C4C2312yes—
230C4×C4⋊C4C2312yes—
231C4×C4⋊C4C2312yes—
232C4×C4⋊C4C2311yescharacteristic
233C4×C4⋊C4C2311yescharacteristic
234C4×C4⋊C4C2312yes—
235C4×C22⋊C4—22no—
236C4×C22⋊C4—22no—
237C4×C22⋊C4—22no—
238C4×C22⋊C4—22no—
239C4×C22⋊C4—22no—
240#376—22no—
241#376—22no—
242C2×#95—22no—
243C2×#95D412yes—
244C43—22no—
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×D4—22no—
265C22×D4—22no—
266C22×D4C22×C414yes—
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—44no—
278C23×C4—44no—
279C23×C4C2×D412yes—
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D412yes—
282C23×C4C2×D411yescharacteristic
283C23×C4C2411yescharacteristic
284AGL(1,ℤ/8)—232no—
285C2×SD16—24no—
286C2×SD16—24no—
287C2×SD16C22×C418yes—
288C2×D8—24no—
289C2×D8—24no—
290C2×D8C22×C418yes—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—24no—
294C2×M16—24no—
295C2×M16—24no—
296C2×M16C22×C414yes—
297C2×M16C22×C414yes—
298C2×M16#4114yes—
299C2×M16#4114yes—
300C22×C8C2414yes—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8C22×C414yes—
306C4×Q8C22×C414yes—
307C4×D4—28no—
308C4×D4—28no—
309C4×D4—28no—
310C4×D4—28no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4C22×C418yes—
316C4×D4C22×C418yes—
317C4×D4C22×C414yes—
318C4×D4C22×C414yes—
319#117—22no—
320#117—28no—
321#117—24no—
322#117—24no—
323#117—44no—
324#117—48no—
325#117—416no—
326#117—44no—
327#117—48no—
328#117C22×C414yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—82no—
348C2×C4⋊C4C22×C414yes—
349C2×C4⋊C4C2×D411yescharacteristic
350C2×C4⋊C4C2×D412yes—
351C2×C4⋊C4C2×D411yescharacteristic
352C2×C4⋊C4C2×D411yescharacteristic
353C2×C4⋊C4C2×D412yes—
354C2×C4⋊C4C2×D411yescharacteristic
355C2×C4⋊C4C2414yes—
356C2×C4⋊C4C2412yes—
357C2×C4⋊C4C2412yes—
358C2×C4⋊C4C2412yes—
359C2×C4⋊C4C2411yescharacteristic
360C2×C4⋊C4C2411yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—48no—
377C2×C22⋊C4—84no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—28no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—48no—
392C2×C42C22×C414yes—
393C2×C42C2×D412yes—
394C2×C42C2×D412yes—
395C2×C42C2×D411yescharacteristic
396C2×C42C2×D411yescharacteristic
397C2×C42#4114yes—
398C2×C42C2412yes—
399C2×C42C2412yes—
400C2×C42C2411yescharacteristic
401C2×C42C2411yescharacteristic
402#107—28no—
403#107—44no—
404#107C22×C418yes—
405#106—28no—
406#106—44no—
407#106C22×C418yes—
408C4⋊C8—24no—
409C4⋊C8—24no—
410#103—44no—
411#103C22×C418yes—
412#102—44no—
413#102—44no—
414#102—44no—
415#102C22×C418yes—
416#102C22×C418yes—
417#102C22×C418yes—
418#97—28no—
419#97C22×C418yes—
420C4×C8—28no—
421C4×C8C22×C418yes—
422#95—24no—
423#95—24no—
424#95—22no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95C2×D412yes—
435#95C2×D412yes—
436#95C2×D412yes—
437#95C2×D412yes—
438C24—24no—
439C24—21no—
440C24—22no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24—42no—
446C24—42no—
447C24C22×D411yescharacteristic
448#41—28no—
449#41—28no—
450#41—44no—
451#41—44no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C23×C412yes—
458C2×D4—24no—
459C2×D4—28no—
460C2×D4—24no—
461C2×D4—28no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4C23×C412yes—
479C2×D4C23×C414yes—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—41no—
499C22×C4—42no—
500C22×C4—41no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—432no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—44no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4C4×D414yes—
520C22×C4C4×D414yes—
521C22×C4C23×C412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D412yes—
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C2×#4112yes—
532C22×C4C2×#4112yes—
533C22×C4C2×#4112yes—
534C22×C4H(5,𝔽2)12yes—
535C22×C42−1+412yes—
536C22×C4C2511yescharacteristic
537SD16—216no—
538D8—216no—
539M16—28no—
540M16—48no—
541M16#117116yescomplemented
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—24no—
545C2×C8—24no—
546C2×C8—24no—
547C2×C8C23×C414yes—
548C2×C8C23×C414yes—
549C2×C8C2×#4114yes—
550C2×C8C2×#4114yes—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—42no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4—82no—
576C4⋊C4—82no—
577C4⋊C4AGL(1,ℤ/8)14yescomplemented
578C4⋊C4C23×C412yes—
579C4⋊C4C23×C412yes—
580C4⋊C4C23×C414yes—
581C22⋊C4—24no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—48no—
587C22⋊C4—44no—
588C22⋊C4—44no—
589C22⋊C4—48no—
590C22⋊C4—44no—
591C22⋊C4—82no—
592C22⋊C4—82no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C42—24no—
596C42—24no—
597C42—24no—
598C42—24no—
599C42—24no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—48no—
605C42—44no—
606C42—44no—
607C42—48no—
608C42—44no—
609C42—82no—
610C42—82no—
611C42C4×D414yes—
612C42C4×D414yes—
613C42C23×C412yes—
614C42C23×C412yes—
615C42C2×#4112yes—
616C42C2×#4112yes—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—24no—
623C23—48no—
624C23—48no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—48no—
630C23—41no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—84no—
639C23—84no—
640C23—84no—
641C23—84no—
642C23C2×C4×D412yes—
643C23#54712yes—
644C23#55012yes—
645C23C23×D411yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650D4—22no—
651D4—24no—
652D4—24no—
653D4—22no—
654D4—48no—
655D4—48no—
656D4—42no—
657D4—41no—
658D4—42no—
659D4—41no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—48no—
684C2×C4—416no—
685C2×C4—48no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—48no—
695C2×C4—48no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—84no—
707C2×C4—84no—
708C2×C4—88no—
709C2×C4C2×#11714yes—
710C2×C4C2×C4×D412yes—
711C2×C4C2×C4×D412yes—
712C2×C4C2×C4×D412yes—
713C2×C4C2×C4×D412yes—
714C2×C4C2×C4×D412yes—
715C2×C4#52014yes—
716C2×C4#54712yes—
717C2×C4#55012yes—
718C2×C4#55514yes—
719C2×C4#55614yes—
720C2×C4C2×AGL(1,ℤ/8)14yes—
721C2×C4C2×AGL(1,ℤ/8)12yes—
722C2×C4#57512yes—
723C2×C4C24×C411yescharacteristic
724C2×C4C22×#4111yescharacteristic
725C2×C4C22×#4111yescharacteristic
726C2×C4C22×#4111yescharacteristic
727C2×C4C2×H(5,𝔽2)11yescharacteristic
728C2×C4C2×2−1+411yescharacteristic
729C8—24no—
730C8—44no—
731C8C2×#11718yescomplemented
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—816no—
745C22—81no—
746C22—82no—
747C22—81no—
748C22—82no—
749C22—81no—
750C22—82no—
751C22—81no—
752C22—82no—
753C22#235414yes—
754C22C22×C4×D411yescharacteristic
755C22C2×#54711yescharacteristic
756C22C2×#55011yescharacteristic
757C22C22×AGL(1,ℤ/8)11yescharacteristic
758C22C2×#57511yescharacteristic
759C22#358511yescharacteristic
760C22#358611yescharacteristic
761C4—22no—
762C4—22no—
763C4—24no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—44no—
772C4—82no—
773C4—84no—
774C4—82no—
775C4#235414yes—
776C4C4×AGL(1,ℤ/8)14yes—
777C4C22×#11711yescharacteristic
778C4C2×#52011yescharacteristic
779C4C2×#55511yescharacteristic
780C4C2×#55611yescharacteristic
781C2—24no—
782C2—82no—
783C2—84no—
784C2C2×#235411yescharacteristic
785C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
786C2#6017011yescharacteristic
787C2#6125211yescharacteristic
788C2#6125611yescharacteristic
789C2#6140211yescharacteristic
790C2#6140311yescharacteristic
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×#2354C2semidirect
4. #22820C2semidirect
5. #22817C2semidirect
6. #22813C2semidirect
7. #22811C2semidirect
8. #22807C2semidirect
9. #22805C2semidirect
11. #21060C2semidirect
12. #21059C2semidirect
13. #20800C2semidirect
14. #20648C2semidirect
15. #20646C2semidirect
16. C4×#428C2semidirect
17. C4⋊C4×M16C2semidirect
22. C4×AGL(1,ℤ/8)C4semidirect
37. #2357C22semidirect
38. #2356C22semidirect
39. #2355C22semidirect
40. #2355C22semidirect
47. #2354C22semidirect
48. #2354C22semidirect
68. #1928C22semidirect
69. #1927C22semidirect
72. #1926C22semidirect
75. #1925C22semidirect
76. #1847C22semidirect
77. #1845C22semidirect
78. #1844C22semidirect
80. #1803C22semidirect
81. #1803C22semidirect
84. #1802C22semidirect
85. #1802C22semidirect
86. #1776C22semidirect
87. #1776C22semidirect
88. C4×#107C22semidirect
89. C4×#106C22semidirect
90. #1771C22semidirect
91. #1770C22semidirect
92. C8×C4⋊C4C22semidirect
143. #442C2×C4semidirect
144. #440C2×C4semidirect
145. C4×SD16C2×C4semidirect
146. C4×D8C2×C4semidirect
541. M16#117semidirect
577. C4⋊C4AGL(1,ℤ/8)semidirect
731. C8C2×#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
#341212
C2×#23542
#228202
#228172
#228132
#228112
#228072
#228052
#212362
#210602
#210592
#208002
#206482
#206462
C4×#4282
C4⋊C4×M162