Finite Group Databasebeta

← #116802

Subgroups — #116802

Order 512.

932 conjugacy classes of subgroups.

The subgroup lattice has 677 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1948C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3C22×Q8⋊C8C211yesmaximal, characteristic
4#13926C211yesmaximal, characteristic
5#10841C211yesmaximal, characteristic
6C2×#1296C211yesmaximal, characteristic
7C2×#1279C211yesmaximal, characteristic
8C22×C4×Q8C2211yescharacteristic
9C22×#106—21no—
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×#103—21no—
13C22×C4×C8C2211yescharacteristic
14C2×#391—21no—
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18#1948—22no—
19#1948—22no—
20#1803—22no—
21#1803—22no—
22C2×#340—21no—
23C2×#340—21no—
24C2×#340—22no—
25C2×Q8⋊C8—22no—
26C2×Q8⋊C8—22no—
27C2×Q8⋊C8C414yescomplemented
28#1441—22no—
29C4⋊#95—21no—
30C4⋊#95—21no—
31C4⋊#95—21no—
32#1296—22no—
33#1279—22no—
34C23×Q8D411yescharacteristic
35C23×C8—21no—
36C23×C8—21no—
37C23×C8—21no—
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40C2×C4×Q8—21no—
41C2×C4×Q8—21no—
42C2×C4×Q8—21no—
43C2×C4×Q8—21no—
44C2×C4×Q8—21no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8C2×C412yes—
49C2×C4×Q8Q812yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4D412yes—
60C22×C42—21no—
61C22×C42—21no—
62C22×C42C2311yescharacteristic
63C2×#106—24no—
64C2×#106—42no—
65C2×#106—42no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8C2×C412yes—
75C2×C4⋊C8D412yes—
76C2×C4⋊C8D412yes—
77C2×C4⋊C8D412yes—
78C2×#103—24no—
79C2×#103—42no—
80C2×#103—42no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8—21no—
84C2×C4×C8—21no—
85C2×C4×C8—21no—
86C2×C4×C8C2×C412yes—
87#391—42no—
88#391—42no—
89#384—21no—
90#384—21no—
91#384—21no—
92#384—21no—
93#384—21no—
94#384—21no—
95#384—21no—
96#384D412yes—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—21no—
99C4×C4⋊C4—21no—
100C4×C4⋊C4—21no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—21no—
104C2×#95—22no—
105C2×#95—22no—
106#340—24no—
107#340—24no—
108#340—44no—
109Q8⋊C8—28no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8—21no—
114C22×Q8—21no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—21no—
121C22×Q8C4⋊C412yes—
122C22×Q8SD1612yes—
123C22×Q8SD1612yes—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—41no—
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—41no—
141C22×C8—41no—
142C22×C8—41no—
143C22×C8—41no—
144C22×C8—41no—
145C22×C8—41no—
146C22×C8—41no—
147C22×C8—41no—
148C22×C8—41no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8—41no—
152C22×C8—41no—
153C22×C8—41no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—22no—
162C4×Q8—41no—
163C4×Q8—41no—
164C4×Q8—41no—
165C4×Q8—41no—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—41no—
169C4×Q8—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—41no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—41no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4C4⋊C412yes—
224C2×C4⋊C4SD1612yes—
225C2×C4⋊C4Q1612yes—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—41no—
229C2×C42—41no—
230C2×C42—41no—
231C2×C42—41no—
232C2×C42—41no—
233C2×C42—41no—
234C2×C42—41no—
235C2×C42—41no—
236C2×C42—41no—
237C2×C42—41no—
238C2×C42C22×C411yescharacteristic
239C2×C42C2×D411yescharacteristic
240C2×C42C2×D411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42C2×D411yescharacteristic
243C2×C42C2×Q811yescharacteristic
244C2×C42#4111yescharacteristic
245C2×C42#4111yescharacteristic
246C2×C42#4111yescharacteristic
247C2×C42#4111yescharacteristic
248C2×C42#4111yescharacteristic
249C2×C42#4111yescharacteristic
250#106—48no—
251C4⋊C8—22no—
252C4⋊C8—22no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—22no—
256C4⋊C8—41no—
257C4⋊C8—41no—
258C4⋊C8C22⋊C414yes—
259#103—48no—
260C4×C8—22no—
261C4×C8—22no—
262C4×C8—41no—
263C4×C8—41no—
264#95—44no—
265#95—44no—
266#95—41no—
267#95—41no—
268#95—82no—
269#95—82no—
270C24#12011yescharacteristic
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—22no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8#10614yescomplemented
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—81no—
340C22×C4—81no—
341C22×C4—81no—
342C22×C4—81no—
343C22×C4—81no—
344C22×C4—81no—
345C22×C4C2×C4⋊C411yescharacteristic
346C22×C4C4×D411yescharacteristic
347C22×C4C4×D411yescharacteristic
348C22×C4#12011yescharacteristic
349C22×C4#12011yescharacteristic
350C22×C4#12111yescharacteristic
351C22×C4#12111yescharacteristic
352C22×C4#12111yescharacteristic
353C22×C4#12111yescharacteristic
354C22×C4#12111yescharacteristic
355C22×C4#12111yescharacteristic
356C22×C4C22⋊Q811yescharacteristic
357C22×C4C22⋊Q811yescharacteristic
358C22×C4#12311yescharacteristic
359C22×C4#12311yescharacteristic
360C22×C4#12311yescharacteristic
361C22×C4#12411yescharacteristic
362C22×C4#12711yescharacteristic
363C22×C4C2×SD1611yescharacteristic
364C22×C4C2×SD1611yescharacteristic
365C22×C4C2×SD1611yescharacteristic
366C22×C4C2×Q1611yescharacteristic
367C22×C4#13511yescharacteristic
368C22×C4#13511yescharacteristic
369C22×C4#13511yescharacteristic
370C22×C4#13511yescharacteristic
371C22×C4AGL(1,ℤ/8)11yescharacteristic
372C22×C4AGL(1,ℤ/8)11yescharacteristic
373C22×C4AGL(1,ℤ/8)11yescharacteristic
374C22×C4#13711yescharacteristic
375C22×C4#13711yescharacteristic
376C22×C4#13711yescharacteristic
377C22×C4#13711yescharacteristic
378C22×C4#13711yescharacteristic
379C2×C8—24no—
380C2×C8—24no—
381C2×C8—42no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—42no—
385C2×C8—42no—
386C2×C8—42no—
387C2×C8—42no—
388C2×C8—42no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—42no—
396C2×C8—81no—
397C2×C8—81no—
398C2×C8—81no—
399C2×C8—81no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—44no—
407C4⋊C4—44no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—41no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—42no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4—82no—
423C4⋊C4—82no—
424C4⋊C4—81no—
425C4⋊C4—81no—
426C4⋊C4—81no—
427C4⋊C4—81no—
428C4⋊C4—81no—
429C4⋊C4—81no—
430C4⋊C4—81no—
431C4⋊C4—81no—
432C4⋊C4—81no—
433C4⋊C4—81no—
434C4⋊C4—81no—
435C4⋊C4—81no—
436C42—42no—
437C42—42no—
438C42—42no—
439C42—42no—
440C42—81no—
441C42—81no—
442C42—81no—
443C42—81no—
444C42C2×C22⋊C411yescharacteristic
445C42#11711yescharacteristic
446C42C4×D411yescharacteristic
447C42C4×D411yescharacteristic
448C42#12111yescharacteristic
449C42#12111yescharacteristic
450C42C22⋊Q811yescharacteristic
451C42C22⋊Q811yescharacteristic
452C42C22⋊Q811yescharacteristic
453C42C22⋊Q811yescharacteristic
454C42#12311yescharacteristic
455C42#12311yescharacteristic
456C42#12411yescharacteristic
457C42#12411yescharacteristic
458C42#12611yescharacteristic
459C42#12611yescharacteristic
460C23#38511yescharacteristic
461C23#39211yescharacteristic
462C23#39411yescharacteristic
463C23#44811yescharacteristic
464C23#44811yescharacteristic
465C23#44911yescharacteristic
466C23#44911yescharacteristic
467C23#45011yescharacteristic
468C23#45111yescharacteristic
469C23#45211yescharacteristic
470C23#45211yescharacteristic
471C23#45311yescharacteristic
472C23#45411yescharacteristic
473C23#45511yescharacteristic
474C23#45611yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—42no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—42no—
482Q8—42no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—161no—
534C2×C4—161no—
535C2×C4—161no—
536C2×C4—161no—
537C2×C4#38011yescharacteristic
538C2×C4#38511yescharacteristic
539C2×C4#38611yescharacteristic
540C2×C4#38811yescharacteristic
541C2×C4#38811yescharacteristic
542C2×C4#39011yescharacteristic
543C2×C4#39311yescharacteristic
544C2×C4#39411yescharacteristic
545C2×C4#39611yescharacteristic
546C2×C4#39611yescharacteristic
547C2×C4#39711yescharacteristic
548C2×C4#39911yescharacteristic
549C2×C4C2×#10611yescharacteristic
550C2×C4#42711yescharacteristic
551C2×C4#42811yescharacteristic
552C2×C4#42811yescharacteristic
553C2×C4C4×SD1611yescharacteristic
554C2×C4C4×Q1611yescharacteristic
555C2×C4#44011yescharacteristic
556C2×C4#44111yescharacteristic
557C2×C4#44811yescharacteristic
558C2×C4#44911yescharacteristic
559C2×C4#45011yescharacteristic
560C2×C4#45011yescharacteristic
561C2×C4#45111yescharacteristic
562C2×C4#45211yescharacteristic
563C2×C4#45211yescharacteristic
564C2×C4#45211yescharacteristic
565C2×C4#46111yescharacteristic
566C2×C4#46211yescharacteristic
567C2×C4#46311yescharacteristic
568C2×C4#46411yescharacteristic
569C2×C4#46511yescharacteristic
570C2×C4#46511yescharacteristic
571C2×C4#46511yescharacteristic
572C2×C4#46511yescharacteristic
573C2×C4#46511yescharacteristic
574C2×C4#46711yescharacteristic
575C2×C4#46811yescharacteristic
576C2×C4#46811yescharacteristic
577C2×C4#46811yescharacteristic
578C2×C4#46911yescharacteristic
579C2×C4#47011yescharacteristic
580C2×C4#47011yescharacteristic
581C2×C4#47511yescharacteristic
582C2×C4#47711yescharacteristic
583C2×C4#47911yescharacteristic
584C2×C4#47911yescharacteristic
585C2×C4#48111yescharacteristic
586C2×C4#48111yescharacteristic
587C2×C4#48211yescharacteristic
588C2×C4#48211yescharacteristic
589C2×C4#48311yescharacteristic
590C2×C4#48311yescharacteristic
591C2×C4#48511yescharacteristic
592C2×C4#48511yescharacteristic
593C2×C4#48711yescharacteristic
594C2×C4#48811yescharacteristic
595C2×C4#48911yescharacteristic
596C2×C4#49111yescharacteristic
597C8—44no—
598C8—44no—
599C8—82no—
600C22#143911yescharacteristic
601C22#162011yescharacteristic
602C22#162311yescharacteristic
603C22#162611yescharacteristic
604C22#162611yescharacteristic
605C22#163111yescharacteristic
606C22#163211yescharacteristic
607C22#163711yescharacteristic
608C22#163811yescharacteristic
609C22#164011yescharacteristic
610C22#164211yescharacteristic
611C22#164311yescharacteristic
612C22#164511yescharacteristic
613C22#164811yescharacteristic
614C22#165011yescharacteristic
615C22#165111yescharacteristic
616C22#165311yescharacteristic
617C22#185311yescharacteristic
618C22#185411yescharacteristic
619C22#185911yescharacteristic
620C22#186011yescharacteristic
621C22#186311yescharacteristic
622C22#186511yescharacteristic
623C22#200011yescharacteristic
624C22#200011yescharacteristic
625C22#200011yescharacteristic
626C22#200111yescharacteristic
627C22#200611yescharacteristic
628C22#200711yescharacteristic
629C22#203411yescharacteristic
630C22#203511yescharacteristic
631C22#203711yescharacteristic
632C22#203811yescharacteristic
633C22#204211yescharacteristic
634C22#204311yescharacteristic
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—44no—
640C4—82no—
641C4—82no—
642C4—82no—
643C4—162no—
644C4—162no—
645C4#180711yescharacteristic
646C4#180911yescharacteristic
647C4#185311yescharacteristic
648C4#185411yescharacteristic
649C4#187711yescharacteristic
650C4#187811yescharacteristic
651C4#193311yescharacteristic
652C4#193511yescharacteristic
653C4#202411yescharacteristic
654C4#202611yescharacteristic
655C4#203411yescharacteristic
656C4#203511yescharacteristic
657C4#206611yescharacteristic
658C4#206811yescharacteristic
659C4#207711yescharacteristic
660C4#207711yescharacteristic
661C2#888311yescharacteristic
662C2#888811yescharacteristic
663C2#889111yescharacteristic
664C2#889611yescharacteristic
665C2#1023011yescharacteristic
666C2#1023211yescharacteristic
667C2#1023411yescharacteristic
668C2#1023611yescharacteristic
669C2#1041011yescharacteristic
670C2#1041511yescharacteristic
671C2#1041811yescharacteristic
672C2#1042311yescharacteristic
673C2#1106711yescharacteristic
674C2#1109511yescharacteristic
675C2#1111311yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
27. C2×Q8⋊C8C4semidirect
298. C2×Q8#106semidirect

Maximal subgroups

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

subgroupindex
C2×#19482
C2×#18032
C22×Q8⋊C82
#139262
#108412
C2×#12962
C2×#12792