Finite Group Databasebeta

← #6463785

Subgroups — #6463785

Order 512.

2324 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×M16C211yesmaximal, characteristic, complemented
2C2×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
3#34952C211yesmaximal, characteristic, complemented
4C2×#2538C211yesmaximal, characteristic, complemented
5#28199C214yesmaximal, complemented
6#28197C214yesmaximal, complemented
7#28195C212yesmaximal, complemented
8#28194C212yesmaximal, complemented
9#28186C212yesmaximal, complemented
10#28185C212yesmaximal, complemented
11#23670C212yesmaximal, complemented
12#23546C212yesmaximal
13#21095C212yesmaximal, complemented
14#21093C212yesmaximal, complemented
15#20764C211yesmaximal, characteristic, complemented
16#20648C211yesmaximal, characteristic, complemented
17#20646C211yesmaximal, characteristic, complemented
18C22×AGL(1,ℤ/8)C2211yescharacteristic
19C22×C22⋊Q8—21no—
20C2×C4×#41C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23Q8×M16—28no—
24C2×#446C2212yescomplemented
25C2×#446C2214yescomplemented
26C2×C8×Q8C2212yescomplemented
27C4×AGL(1,ℤ/8)—28no—
28C2×#442C2212yes—
29C2×#440C2212yes—
30C2×C4×SD16C2212yes—
31C2×C4×D8C2212yes—
32C2×#428C2211yescharacteristic
33C2×#423C2212yes—
34C2×#423C2211yescharacteristic
35C2×#417C2211yescharacteristic
36C2×#417C2212yes—
37C2×#418C2211yescharacteristic
38C2×#418C2212yes—
39C2×C4×M16C2212yes—
40C2×C4×M16C2211yescharacteristic
41#2582C2211yescharacteristic, complemented
42#2582C2211yescharacteristic, complemented
43#2581C2212yescomplemented
44#2580C2212yescomplemented
45#2579—22no—
46#2538—22no—
47#2538—21no—
48#2538—21no—
49#2538C2212yes—
50#2538C2212yes—
51#2538C2214yes—
52#2538C2211yescharacteristic, complemented
53#2538C2211yescharacteristic, complemented
54#2487—21no—
55#2409—21no—
56#2396—22no—
57C2×#396—22no—
58C4×C22⋊Q8—21no—
59C4×C22⋊Q8—21no—
60#2297C2212yes—
61#2296C2212yes—
62C2×#390C2212yes—
63C2×#389C2212yes—
64#2285C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C2×#380—21no—
67#2088C2214yescomplemented
68#2088C2214yescomplemented
69#2087C2214yescomplemented
70#2086C2214yescomplemented
71#2055C2214yes—
72#2055C2214yes—
73#2054C2214yes—
74#2054C2214yes—
75#1936C2214yes—
76#1936C2214yes—
77#1936C2214yescomplemented
78#1935C2214yescomplemented
79#1934C2214yes—
80#1934C2214yes—
81#1934C2214yescomplemented
82#1933C2214yescomplemented
83#1836C2214yescomplemented
84#1834C2212yescomplemented
85#1834C2212yescomplemented
86#1804C2214yes—
87#1803C2212yescomplemented
88#1803C2212yescomplemented
89#1802C2212yes—
90#1802C2212yes—
91#1802C2212yescomplemented
92#1802C2212yescomplemented
93#1736C2212yes—
94#1736C2212yes—
95#1736C2212yes—
96#1736C2212yes—
97C22×#41C2311yescharacteristic
98C23×Q8D411yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4—21no—
101C2×AGL(1,ℤ/8)—24no—
102C2×AGL(1,ℤ/8)—24no—
103C2×AGL(1,ℤ/8)—24no—
104C22×SD16C2312yes—
105C22×D8C2312yes—
106C22×M16C2312yes—
107C22×M16C2311yescharacteristic
108C22×M16C2311yescharacteristic
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—22no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—22no—
114C2×C22⋊Q8—48no—
115C4×#41—24no—
116C4×#41—24no—
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8D412yes—
120C2×C4×Q8D411yescharacteristic
121C2×C4×Q8D411yescharacteristic
122C2×C4×Q8C2311yescharacteristic
123C2×C4×Q8C2311yescharacteristic
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2311yescharacteristic
126C2×C4×Q8C2311yescharacteristic
127C2×C4×D4—21no—
128C2×C4×D4—21no—
129C2×C4×D4—21no—
130C2×C4×D4—21no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4C2312yes—
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2312yes—
137C2×#117—21no—
138C2×#117C2311yescharacteristic
139C2×#117C2312yes—
140C22×C4⋊C4—22no—
141C22×C4⋊C4—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4D412yes—
144C22×C4⋊C4D411yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C22⋊C4—21no—
148C22×C22⋊C4—22no—
149C22×C22⋊C4—22no—
150C22×C42—21no—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153#446—216no—
154#446—28no—
155C8×Q8—28no—
156#442—28no—
157#440—28no—
158C4×SD16—28no—
159C4×D8—28no—
160#428—24no—
161C2×#107C2312yes—
162C2×#106C2312yes—
163#423—28no—
164#423—24no—
165C2×C4⋊C8C2314yes—
166C2×C4⋊C8C2314yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169#418—28no—
170#418—24no—
171#417—28no—
172#417—24no—
173C2×#103C2314yes—
174C2×#103C2312yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×#102C2314yes—
178C2×#102C2312yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C4×M16—28no—
182C4×M16D418yes—
183C2×#97C2314yes—
184C2×#97C2312yes—
185C2×C4×C8C2314yes—
186C2×C4×C8C2312yes—
187#400—22no—
188#399—22no—
189#398—22no—
190#398—22no—
191#396—22no—
192#396—22no—
193#396—24no—
194#396—24no—
195#396—24no—
196#396—24no—
197#395—22no—
198#393—22no—
199#391—21no—
200#391—21no—
201#391C2312yes—
202#391C2312yes—
203#390—22no—
204#390—22no—
205#390C2312yes—
206#390C2312yes—
207#390C2314yes—
208#390C2314yes—
209#389—21no—
210#389—21no—
211#389—22no—
212#389—22no—
213#389C2312yes—
214#389C2312yes—
215#389C2312yes—
216#389C2312yes—
217#389C2314yes—
218#389C2314yes—
219#387—22no—
220#387—22no—
221#386—22no—
222#386—22no—
223#385—22no—
224#385—22no—
225#385—22no—
226#385—22no—
227#384—21no—
228#384—21no—
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#384C2312yes—
232#384C2312yes—
233#382C2312yes—
234#380—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—22no—
239#380—22no—
240#380—24no—
241C4×C4⋊C4—21no—
242C4×C4⋊C4—22no—
243C4×C4⋊C4—22no—
244C4×C4⋊C4—21no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C2×#95—22no—
248#340C2314yes—
249#340C2314yes—
250#340C2314yes—
251#340C2314yes—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256C25—21no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41#4114yes—
263C22×Q8—24no—
264C22×Q8—24no—
265C22×Q8—42no—
266C22×Q8C2×D411yescharacteristic
267C22×Q8C2×D412yes—
268C22×Q8C2×D411yescharacteristic
269C22×Q8C2411yescharacteristic
270C22×D4—21no—
271C22×D4—22no—
272C22×D4—21no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4#4114yes—
278C22×D4C2411yescharacteristic
279C22×D4C2412yes—
280C23×C4—21no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—44no—
290C23×C4C2×D412yes—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D412yes—
293C23×C4C2×D411yescharacteristic
294C23×C4C2411yescharacteristic
295AGL(1,ℤ/8)—232no—
296C2×SD16—24no—
297C2×SD16—24no—
298C2×SD16—24no—
299C2×D8—24no—
300C2×D8—24no—
301C2×D8—24no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—24no—
307C2×M16—24no—
308C2×M16—24no—
309C2×M16C2×D414yes—
310C2×M16C2×D414yes—
311C22×C8C2414yes—
312C22×C8C2412yes—
313C22×C8C2412yes—
314C22⋊Q8—44no—
315C22⋊Q8—48no—
316C22⋊Q8—416no—
317C22⋊Q8—44no—
318C22⋊Q8—48no—
319C4×Q8—24no—
320C4×Q8—24no—
321C4×Q8—28no—
322C4×Q8—22no—
323C4×Q8—24no—
324C4×Q8—22no—
325C4×Q8—22no—
326C4×Q8—24no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×D4—24no—
333C4×D4—24no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—24no—
337C4×D4—24no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344#117—22no—
345#117—22no—
346#117—24no—
347#117—24no—
348#117—44no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—48no—
375C2×C4⋊C4—82no—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2×D412yes—
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D412yes—
382C2×C4⋊C4C2×D412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2414yes—
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—48no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—84no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—21no—
409C2×C42—22no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—44no—
413C2×C42C2×D412yes—
414C2×C42C2×D412yes—
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D414yes—
418C2×C42#4114yes—
419C2×C42C2412yes—
420C2×C42C2412yes—
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423#107—24no—
424#106—24no—
425C4⋊C8—28no—
426C4⋊C8—28no—
427C4⋊C8—24no—
428C4⋊C8—24no—
429#103—28no—
430#103—24no—
431#102—28no—
432#102—28no—
433#102—28no—
434#102—24no—
435#102—24no—
436#102—24no—
437#97—28no—
438#97C2×D418yes—
439C4×C8—28no—
440C4×C8C2×D418yes—
441#95—24no—
442#95—24no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453C24—24no—
454C24—21no—
455C24—22no—
456C24—42no—
457C24—42no—
458C24—42no—
459C24—42no—
460C24—42no—
461C24—42no—
462C24C22×D411yescharacteristic
463#41—28no—
464#41—28no—
465#41—44no—
466#41—44no—
467C2×Q8—22no—
468C2×Q8—24no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8—416no—
481C2×Q8AGL(1,ℤ/8)14yescomplemented
482C2×Q8C2×#4112yes—
483C2×D4—24no—
484C2×D4—28no—
485C2×D4—24no—
486C2×D4—28no—
487C2×D4—21no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—44no—
503C2×D4C2×#4112yes—
504C2×D4C2×#4114yes—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—44no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—816no—
544C22×C4#12114yes—
545C22×C4#12114yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D412yes—
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D412yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C42−1+412yes—
560C22×C42−1+412yes—
561C22×C4C2511yescharacteristic
562SD16—216no—
563D8—216no—
564M16—28no—
565M16—28no—
566M16—48no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8C22×D414yes—
575C2×C8C22×D414yes—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—24no—
589C4⋊C4—22no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—44no—
596C4⋊C4—48no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—48no—
604C4⋊C4—42no—
605C4⋊C4—44no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4—81no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—42no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C42—24no—
628C42—24no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—42no—
634C42—42no—
635C42—42no—
636C42—44no—
637C42#12114yes—
638C42#12114yes—
639C42C22×D412yes—
640C42C22×D412yes—
641C42C2×#4112yes—
642C42C2×#4112yes—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—24no—
649C23—48no—
650C23—48no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—42no—
659C23—48no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—84no—
665C23—84no—
666C23—84no—
667C23—84no—
668C23C2×#12112yes—
669C23#54812yes—
670C23#54812yes—
671C23C23×D411yescharacteristic
672Q8—28no—
673Q8—22no—
674Q8—22no—
675Q8—48no—
676Q8—41no—
677Q8—41no—
678Q8—44no—
679D4—22no—
680D4—24no—
681D4—24no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—41no—
686D4—42no—
687D4—41no—
688D4—48no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—48no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—88no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—88no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—88no—
738C2×C4C2×#12112yes—
739C2×C4C2×#12112yes—
740C2×C4C2×#12112yes—
741C2×C4C2×#12112yes—
742C2×C4C2×#12112yes—
743C2×C4#52514yes—
744C2×C4#53614yes—
745C2×C4#54812yes—
746C2×C4#54812yes—
747C2×C4#55214yes—
748C2×C4#55214yes—
749C2×C4C2×AGL(1,ℤ/8)14yes—
750C2×C4C2×AGL(1,ℤ/8)12yes—
751C2×C4#57512yes—
752C2×C4C23×D411yescharacteristic
753C2×C4C22×#4111yescharacteristic
754C2×C4C22×#4111yescharacteristic
755C2×C4C22×#4111yescharacteristic
756C2×C4C2×2−1+411yescharacteristic
757C2×C4C2×2−1+411yescharacteristic
758C8—24no—
759C8—24no—
760C8—44no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—42no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—82no—
778C22—81no—
779C22—81no—
780C22—82no—
781C22—82no—
782C22#253614yes—
783C22C22×#12111yescharacteristic
784C22C2×#54811yescharacteristic
785C22C2×#54811yescharacteristic
786C22C22×AGL(1,ℤ/8)11yescharacteristic
787C22C2×#57511yescharacteristic
788C22#358511yescharacteristic
789C22#358611yescharacteristic
790C4—22no—
791C4—24no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—82no—
800C4—81no—
801C4—82no—
802C4—82no—
803C4—84no—
804C4#253614yes—
805C4#305514yes—
806C4C2×#52511yescharacteristic
807C4C2×#53611yescharacteristic
808C4C2×#55211yescharacteristic
809C4C2×#55211yescharacteristic
810C2—24no—
811C2—82no—
812C2—84no—
813C2C2×#253611yescharacteristic
814C2C2×#305511yescharacteristic
815C2#6045611yescharacteristic
816C2#6131711yescharacteristic
817C2#6131811yescharacteristic
818C2#6132111yescharacteristic
819C2#6132311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×Q8×M16C2semidirect
3. #34952C2semidirect
4. C2×#2538C2semidirect
5. #28199C2semidirect
6. #28197C2semidirect
7. #28195C2semidirect
8. #28194C2semidirect
9. #28186C2semidirect
10. #28185C2semidirect
11. #23670C2semidirect
13. #21095C2semidirect
14. #21093C2semidirect
15. #20764C2semidirect
16. #20648C2semidirect
17. #20646C2semidirect
24. C2×#446C22semidirect
25. C2×#446C22semidirect
26. C2×C8×Q8C22semidirect
41. #2582C22semidirect
42. #2582C22semidirect
43. #2581C22semidirect
44. #2580C22semidirect
52. #2538C22semidirect
53. #2538C22semidirect
67. #2088C22semidirect
68. #2088C22semidirect
69. #2087C22semidirect
70. #2086C22semidirect
77. #1936C22semidirect
78. #1935C22semidirect
81. #1934C22semidirect
82. #1933C22semidirect
83. #1836C22semidirect
84. #1834C22semidirect
85. #1834C22semidirect
87. #1803C22semidirect
88. #1803C22semidirect
91. #1802C22semidirect
92. #1802C22semidirect
481. C2×Q8AGL(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×Q8×M162
C2×C4×AGL(1,ℤ/8)2
#349522
C2×#25382
#281992
#281972
#281952
#281942
#281862
#281852
#236702
#235462
#210952
#210932
#207642
#206482
#206462