Finite Group Databasebeta

← #358293

Subgroups — #358293

Order 512.

1726 conjugacy classes of subgroups.

The subgroup lattice has 745 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34052C211yesmaximal, characteristic
2C2×#1740C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4C2×#1740C211yesmaximal, characteristic
5C2×#1740C211yesmaximal, characteristic
6C2×#1740C211yesmaximal, characteristic
7C2×#1740C211yesmaximal, characteristic
8#11279C218yesmaximal
9C22×#117C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C22×#117C2211yescharacteristic
16#2317—22no—
17#2317—22no—
18#2316—22no—
19#2315C2214yes—
20#2296—22no—
21#2296—22no—
22#2285—22no—
23#1740—22no—
24#1740—22no—
25#1740—24no—
26#1740—22no—
27#1740—22no—
28#1740—22no—
29#1740—22no—
30#1740—24no—
31#1740C418yescomplemented
32C2×#342C2214yes—
33C2×#342C2214yes—
34C2×#342C2214yes—
35C2×#342C2214yes—
36C2×#342C2214yes—
37C2×#342C2214yes—
38C24×C4C2311yescharacteristic
39C2×#117—21no—
40C2×#117—21no—
41C2×#117—22no—
42C2×#117—22no—
43C2×#117—21no—
44C2×#117—21no—
45C2×#117—22no—
46C2×#117—21no—
47C2×#117—21no—
48C2×#117—21no—
49C2×#117—21no—
50C2×#117—21no—
51C2×#117—21no—
52C2×#117—21no—
53C2×#117—21no—
54C2×#117—22no—
55C2×#117—21no—
56C2×#117—21no—
57C2×#117—21no—
58C2×#117—21no—
59C2×#117—21no—
60C2×#117—21no—
61C2×#117—22no—
62C2×#117—22no—
63C2×#117—22no—
64C2×#117—22no—
65C2×#117—21no—
66C2×#117—21no—
67C2×#117—21no—
68C2×#117—21no—
69C2×#117—21no—
70C2×#117—21no—
71C2×#117—22no—
72C2×#117—22no—
73C2×#117—22no—
74C2×#117—22no—
75C2×#117—22no—
76C2×#117—21no—
77C2×#117—21no—
78C2×#117—21no—
79C2×#117—21no—
80C2×#117—22no—
81C2×#117—22no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117C2×C414yes—
89C2×#117C2×C414yes—
90C2×#117C2×C414yes—
91C2×#117D412yes—
92C2×#117D412yes—
93C2×#117D414yes—
94C2×#117D412yes—
95C2×#117D412yes—
96C2×#117D412yes—
97C2×#117D412yes—
98C2×#117Q814yes—
99C22×C4⋊C4—21no—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4Q812yes—
106C22×C22⋊C4C2312yes—
107C22×C22⋊C4C2312yes—
108C22×C22⋊C4C2312yes—
109C22×C22⋊C4C2312yes—
110C22×C22⋊C4C2312yes—
111C22×C22⋊C4C2312yes—
112C22×C22⋊C4C2312yes—
113C22×C42—21no—
114C22×C42—21no—
115C22×C42—21no—
116C22×C42—21no—
117C22×C42—21no—
118C22×C42—21no—
119C22×C42Q812yes—
120#389—28no—
121#389—28no—
122#385—28no—
123#385—28no—
124#384—24no—
125#382—24no—
126#380—28no—
127C4×C4⋊C4—28no—
128#342—28no—
129#342—28no—
130#342—28no—
131#342—28no—
132#342—28no—
133#342C2×C4116yes—
134C25C2411yescharacteristic
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4C22×C412yes—
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D412yes—
149C23×C4C2×Q814yes—
150C23×C4C2×Q812yes—
151C23×C4C2×Q811yescharacteristic
152C23×C4C2×Q811yescharacteristic
153C23×C4#4112yes—
154C23×C4#4112yes—
155C23×C4#4111yescharacteristic
156C23×C4#4111yescharacteristic
157C23×C4#4111yescharacteristic
158C23×C4#4111yescharacteristic
159C23×C4#4112yes—
160C23×C4#4112yes—
161C23×C4#4111yescharacteristic
162C23×C4#4111yescharacteristic
163C23×C4#4112yes—
164#117—24no—
165#117—24no—
166#117—24no—
167#117—24no—
168#117—24no—
169#117—24no—
170#117—24no—
171#117—24no—
172#117—24no—
173#117—24no—
174#117—24no—
175#117—24no—
176#117—24no—
177#117—24no—
178#117—24no—
179#117—24no—
180#117—24no—
181#117—24no—
182#117—24no—
183#117—24no—
184#117—24no—
185#117—24no—
186#117—24no—
187#117—24no—
188#117—24no—
189#117—24no—
190#117—41no—
191#117—41no—
192#117—41no—
193#117—41no—
194#117—42no—
195#117—42no—
196#117—42no—
197#117—42no—
198#117—42no—
199#117—42no—
200#117—42no—
201#117—42no—
202#117—42no—
203#117—42no—
204#117—42no—
205#117—42no—
206#117—42no—
207#117—42no—
208#117—41no—
209#117—41no—
210#117—41no—
211#117—41no—
212#117—41no—
213#117—41no—
214#117—41no—
215#117—41no—
216#117—41no—
217#117—41no—
218#117—41no—
219#117—41no—
220#117—42no—
221#117—42no—
222#117—42no—
223#117—42no—
224#117—42no—
225#117—42no—
226#117C4⋊C418yes—
227#117C4⋊C418yes—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—216no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4—41no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—41no—
256C2×C4⋊C4—41no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4C22×C414yes—
294C2×C22⋊C4C22×C414yes—
295C2×C22⋊C4C22×C414yes—
296C2×C22⋊C4C2×D414yes—
297C2×C22⋊C4C2×D414yes—
298C2×C22⋊C4C2×D414yes—
299C2×C22⋊C4C2×D414yes—
300C2×C22⋊C4C2×Q814yes—
301C2×C42—24no—
302C2×C42—22no—
303C2×C42—22no—
304C2×C42—24no—
305C2×C42—24no—
306C2×C42—24no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—24no—
318C2×C42—42no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—41no—
323C2×C42—41no—
324C2×C42—41no—
325C2×C42—41no—
326C2×C42—42no—
327C2×C42—41no—
328C2×C42—41no—
329C2×C42—42no—
330C2×C42—42no—
331#95—216no—
332C24—82no—
333C24C23×C411yescharacteristic
334C24C22×D411yescharacteristic
335C24C22×D411yescharacteristic
336C24C22×D411yescharacteristic
337C24C22×D411yescharacteristic
338C24C22×Q811yescharacteristic
339C24C22×Q811yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4111yescharacteristic
342C24C2×#4111yescharacteristic
343C24C2×#4111yescharacteristic
344C24C2×#4111yescharacteristic
345C24C2×#4111yescharacteristic
346C24C2×#4111yescharacteristic
347C24C2×#4111yescharacteristic
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—84no—
370C22×C4—84no—
371C22×C4—84no—
372C22×C4—84no—
373C22×C4—84no—
374C22×C4—84no—
375C22×C4—84no—
376C22×C4C2×C4⋊C412yes—
377C22×C4C2×C4⋊C412yes—
378C22×C4#11712yes—
379C22×C4#11712yes—
380C22×C4#11712yes—
381C22×C4#11712yes—
382C22×C4C4×D412yes—
383C22×C4C4×D412yes—
384C22×C4C4×D412yes—
385C22×C4C4×D412yes—
386C22×C4C4×D412yes—
387C22×C4C4×D412yes—
388C22×C4C4×Q812yes—
389C22×C4C4×Q812yes—
390C22×C4#12011yescharacteristic
391C22×C4#12011yescharacteristic
392C22×C4#12011yescharacteristic
393C22×C4#12011yescharacteristic
394C22×C4#12112yes—
395C22×C4#12112yes—
396C22×C4#12112yes—
397C22×C4#12112yes—
398C22×C4#12112yes—
399C22×C4#12112yes—
400C22×C4C22⋊Q812yes—
401C22×C4C22⋊Q812yes—
402C22×C4C22⋊Q812yes—
403C22×C4C22⋊Q812yes—
404C22×C4C22⋊Q811yescharacteristic
405C22×C4C22⋊Q811yescharacteristic
406C22×C4C22⋊Q811yescharacteristic
407C22×C4C22⋊Q811yescharacteristic
408C22×C4C22⋊Q811yescharacteristic
409C22×C4C22⋊Q811yescharacteristic
410C22×C4C22⋊Q811yescharacteristic
411C22×C4C22⋊Q811yescharacteristic
412C22×C4C22⋊Q811yescharacteristic
413C22×C4C22⋊Q811yescharacteristic
414C22×C4C22⋊Q811yescharacteristic
415C22×C4C22⋊Q811yescharacteristic
416C22×C4#12312yes—
417C22×C4#12312yes—
418C22×C4#12312yes—
419C22×C4#12312yes—
420C22×C4#12312yes—
421C22×C4#12312yes—
422C22×C4#12312yes—
423C22×C4#12312yes—
424C22×C4#12312yes—
425C22×C4#12312yes—
426C22×C4#12411yescharacteristic
427C22×C4#12411yescharacteristic
428C22×C4#12411yescharacteristic
429C22×C4#12411yescharacteristic
430C22×C4#12412yes—
431C22×C4#12412yes—
432C22×C4#12411yescharacteristic
433C22×C4#12411yescharacteristic
434C22×C4#12411yescharacteristic
435C22×C4#12411yescharacteristic
436C22×C4#12411yescharacteristic
437C22×C4#12411yescharacteristic
438C22×C4#12411yescharacteristic
439C22×C4#12411yescharacteristic
440C22×C4#12512yes—
441C22×C4#12512yes—
442C22×C4#12512yes—
443C22×C4#12512yes—
444C22×C4#12512yes—
445C22×C4#12512yes—
446C22×C4#12512yes—
447C22×C4#12512yes—
448C22×C4#12512yes—
449C22×C4#12512yes—
450C22×C4#12612yes—
451C22×C4#12612yes—
452C22×C4#12612yes—
453C22×C4#12612yes—
454C22×C4#12612yes—
455C22×C4#12612yes—
456C22×C4#12612yes—
457C22×C4#12612yes—
458C22×C4C4⋊Q812yes—
459C22×C4C4⋊Q812yes—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—44no—
463C4⋊C4—44no—
464C4⋊C4—44no—
465C4⋊C4—44no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—44no—
472C4⋊C4—44no—
473C4⋊C4—44no—
474C4⋊C4—44no—
475C4⋊C4—44no—
476C4⋊C4—816no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4C2×C4⋊C418yes—
505C42—28no—
506C42—28no—
507C42—44no—
508C42—44no—
509C42—44no—
510C42—44no—
511C42—42no—
512C42—42no—
513C42—42no—
514C42—42no—
515C42—44no—
516C42—44no—
517C42—44no—
518C42—44no—
519C42—44no—
520C42—44no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—81no—
529C23—81no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23C22×C4⋊C411yescharacteristic
537C23C2×#11711yescharacteristic
538C23C2×#11711yescharacteristic
539C23C2×C4×D411yescharacteristic
540C23C2×C4×D411yescharacteristic
541C23C2×C4×D411yescharacteristic
542C23C2×C4×Q811yescharacteristic
543C23C2×#12011yescharacteristic
544C23C2×#12111yescharacteristic
545C23C2×#12111yescharacteristic
546C23C2×#12111yescharacteristic
547C23C2×C22⋊Q811yescharacteristic
548C23C2×C22⋊Q811yescharacteristic
549C23C2×C22⋊Q811yescharacteristic
550C23C2×C22⋊Q811yescharacteristic
551C23C2×C22⋊Q811yescharacteristic
552C23C2×#12311yescharacteristic
553C23C2×#12311yescharacteristic
554C23C2×#12311yescharacteristic
555C23C2×#12311yescharacteristic
556C23C2×#12311yescharacteristic
557C23C2×#12411yescharacteristic
558C23C2×#12411yescharacteristic
559C23C2×#12411yescharacteristic
560C23C2×#12411yescharacteristic
561C23C2×#12511yescharacteristic
562C23C2×#12511yescharacteristic
563C23C2×#12511yescharacteristic
564C23C2×#12511yescharacteristic
565C23C2×#12511yescharacteristic
566C23C2×#12611yescharacteristic
567C23C2×#12611yescharacteristic
568C23C2×#12611yescharacteristic
569C23C2×#12611yescharacteristic
570C23C2×C4⋊Q811yescharacteristic
571C2×C4—28no—
572C2×C4—48no—
573C2×C4—48no—
574C2×C4—48no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—84no—
582C2×C4—84no—
583C2×C4—84no—
584C2×C4—84no—
585C2×C4—84no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4—84no—
593C2×C4—84no—
594C2×C4—84no—
595C2×C4—84no—
596C2×C4—84no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4#38212yes—
600C2×C4#38212yes—
601C2×C4#38212yes—
602C2×C4#38212yes—
603C2×C4#38512yes—
604C2×C4#38512yes—
605C2×C4#38512yes—
606C2×C4#38512yes—
607C2×C4#38712yes—
608C2×C4#38712yes—
609C2×C4#38712yes—
610C2×C4#38712yes—
611C2×C4#38712yes—
612C2×C4#38712yes—
613C2×C4#38712yes—
614C2×C4#38712yes—
615C2×C4#38812yes—
616C2×C4#38812yes—
617C2×C4#38812yes—
618C2×C4#38812yes—
619C2×C4#38812yes—
620C2×C4#38812yes—
621C2×C4#38812yes—
622C2×C4#38812yes—
623C2×C4#38912yes—
624C2×C4#38912yes—
625C2×C4#38912yes—
626C2×C4#38912yes—
627C2×C4#39311yescharacteristic
628C2×C4#39311yescharacteristic
629C2×C4#39311yescharacteristic
630C2×C4#39311yescharacteristic
631C2×C4#39311yescharacteristic
632C2×C4#39311yescharacteristic
633C2×C4#39311yescharacteristic
634C2×C4#39311yescharacteristic
635C2×C4#39412yes—
636C2×C4#39412yes—
637C2×C4#39412yes—
638C2×C4#39412yes—
639C2×C4#39712yes—
640C2×C4#39712yes—
641C2×C4#39712yes—
642C2×C4#39712yes—
643C2×C4#39812yes—
644C2×C4#39812yes—
645C2×C4#39812yes—
646C2×C4#39812yes—
647C2×C4#39812yes—
648C2×C4#39812yes—
649C2×C4#39812yes—
650C2×C4#39812yes—
651C2×C4#40012yes—
652C2×C4#40012yes—
653C2×C4#40012yes—
654C2×C4#40012yes—
655C2×C4#40012yes—
656C2×C4#40012yes—
657C2×C4#40012yes—
658C2×C4#40012yes—
659C2×C4#40012yes—
660C2×C4#40012yes—
661C2×C4#40012yes—
662C2×C4#40012yes—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22C2×#38211yescharacteristic
699C22C2×#38511yescharacteristic
700C22C2×#38711yescharacteristic
701C22C2×#38711yescharacteristic
702C22C2×#38811yescharacteristic
703C22C2×#38811yescharacteristic
704C22C2×#38911yescharacteristic
705C22C2×#39311yescharacteristic
706C22C2×#39411yescharacteristic
707C22C2×#39711yescharacteristic
708C22C2×#39811yescharacteristic
709C22C2×#39811yescharacteristic
710C22C2×#40011yescharacteristic
711C22C2×#40011yescharacteristic
712C22C2×#40011yescharacteristic
713C4—48no—
714C4—84no—
715C4—84no—
716C4—84no—
717C4—84no—
718C4—84no—
719C4—84no—
720C4#144212yes—
721C4#144212yes—
722C4#144212yes—
723C4#144212yes—
724C4#144212yes—
725C4#144212yes—
726C4#144212yes—
727C4#144212yes—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—21no—
741C2—21no—
742C2C2×#144211yescharacteristic
743C2#2347412yes—
subgroupG/H
centerC2×C4#393
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
socleC22C2×#393
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
31. #1740C4semidirect

Maximal subgroups

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

subgroupindex
#340522
C2×#17402
#112792