Finite Group Databasebeta

← #158374

Subgroups — #158374

Order 512.

3260 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#398C212yesmaximal
2C22×#389C211yesmaximal, characteristic
3C2×#1444C212yesmaximal
4C2×#1441C212yesmaximal
5C2×C4⋊#95C211yesmaximal, characteristic
6#7557C214yesmaximal
7#7557C212yesmaximal
8#7554C211yesmaximal, characteristic
9C23×C4⋊C4C2212yes—
10C23×C4⋊C4C2211yescharacteristic
11C23×C4⋊C4C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2214yes—
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#398—28no—
17C2×#398—28no—
18C2×#398—28no—
19C2×#389—24no—
20C2×#389—28no—
21C22×#95C2212yes—
22C22×#95C2212yes—
23C22×#95C2214yes—
24C22×#95C2214yes—
25C22×#95C2214yes—
26C22×#95C2212yes—
27C22×#95C2212yes—
28C22×#95C2212yes—
29C22×#95C2212yes—
30#1444—28no—
31#1441—28no—
32C4⋊#95—24no—
33C24×C4C2312yes—
34C24×C4C2312yes—
35C24×C4C2312yes—
36C24×C4C2312yes—
37C24×C4C2311yescharacteristic
38C24×C4C2314yes—
39C24×C4C2311yescharacteristic
40C24×C4C2311yescharacteristic
41C22×C4⋊C4—24no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—24no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—28no—
46C22×C4⋊C4—28no—
47C22×C4⋊C4—28no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—24no—
55C22×C4⋊C4—24no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—24no—
58C22×C4⋊C4—24no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—24no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—24no—
63C22×C4⋊C4—28no—
64C22×C4⋊C4—28no—
65C22×C4⋊C4—24no—
66C22×C4⋊C4—42no—
67C22×C4⋊C4—42no—
68C22×C4⋊C4—44no—
69C22×C4⋊C4—44no—
70C22×C4⋊C4D414yes—
71C22×C4⋊C4D418yes—
72C22×C4⋊C4D414yes—
73C22×C42—24no—
74C22×C42—24no—
75C22×C42—42no—
76C22×C42D414yes—
77#398—264no—
78#389—232no—
79C2×#95—28no—
80C2×#95—28no—
81C2×#95—28no—
82C2×#95—24no—
83C2×#95—24no—
84C2×#95—24no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—24no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—24no—
91C2×#95—28no—
92C2×#95—28no—
93C2×#95—28no—
94C2×#95—24no—
95C2×#95—28no—
96C2×#95—24no—
97C2×#95—42no—
98C2×#95—42no—
99C2×#95—44no—
100C2×#95—44no—
101C2×#95—44no—
102C2×#95D418yes—
103C2×#95Q818yes—
104C2×#95Q818yes—
105C25C2411yescharacteristic
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—22no—
111C23×C4—22no—
112C23×C4—22no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—22no—
118C23×C4—24no—
119C23×C4—24no—
120C23×C4—22no—
121C23×C4—24no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—22no—
125C23×C4—22no—
126C23×C4—24no—
127C23×C4—24no—
128C23×C4—24no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—24no—
133C23×C4—24no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4—22no—
137C23×C4—24no—
138C23×C4—22no—
139C23×C4—24no—
140C23×C4—24no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—24no—
145C23×C4—24no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—24no—
149C23×C4—22no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—24no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—24no—
161C23×C4—24no—
162C23×C4—22no—
163C23×C4—24no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—24no—
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4C2×D414yes—
176C23×C4C2×D414yes—
177C23×C4C2×D414yes—
178C23×C4C2×D414yes—
179C23×C4C2×D418yes—
180C23×C4C2×D412yes—
181C23×C4C2×D412yes—
182C23×C4C2×D414yes—
183C23×C4C2×D414yes—
184C23×C4C2×D412yes—
185C23×C4C2×D412yes—
186C23×C4C2×D412yes—
187C23×C4C2×Q818yes—
188C23×C4C2×Q818yes—
189C23×C4C2×Q814yes—
190C23×C4C2×Q814yes—
191C23×C4#4114yes—
192C23×C4#4114yes—
193C23×C4#4112yes—
194C23×C4#4112yes—
195C23×C4#4114yes—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—216no—
198C2×C4⋊C4—28no—
199C2×C4⋊C4—216no—
200C2×C4⋊C4—28no—
201C2×C4⋊C4—28no—
202C2×C4⋊C4—28no—
203C2×C4⋊C4—232no—
204C2×C4⋊C4—216no—
205C2×C4⋊C4—216no—
206C2×C4⋊C4—216no—
207C2×C4⋊C4—216no—
208C2×C4⋊C4—28no—
209C2×C4⋊C4—416no—
210C2×C4⋊C4—416no—
211C2×C4⋊C4—416no—
212C2×C4⋊C4—416no—
213C2×C4⋊C4—416no—
214C2×C4⋊C4—416no—
215C2×C4⋊C4—44no—
216C2×C4⋊C4—44no—
217C2×C4⋊C4—416no—
218C2×C4⋊C4—48no—
219C2×C4⋊C4—44no—
220C2×C4⋊C4—416no—
221C2×C4⋊C4—48no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4—48no—
224C2×C4⋊C4—44no—
225C2×C4⋊C4—44no—
226C2×C4⋊C4—48no—
227C2×C4⋊C4—44no—
228C2×C42—28no—
229C2×C42—28no—
230C2×C42—44no—
231C2×C42—416no—
232#95—216no—
233#95—232no—
234#95—216no—
235#95—216no—
236#95—48no—
237#95—416no—
238#95—416no—
239#95—48no—
240#95—48no—
241C24C22×D412yes—
242C24C22×D411yescharacteristic
243C24C22×D411yescharacteristic
244C24C22×D412yes—
245C24C22×D411yescharacteristic
246C24C22×Q812yes—
247C24C22×Q812yes—
248C24C2×#4111yescharacteristic
249C24C2×#4111yescharacteristic
250C24C2×#4112yes—
251C24C2×#4112yes—
252C24C2×#4112yes—
253C24H(5,𝔽2)12yes—
254C24H(5,𝔽2)12yes—
255C24H(5,𝔽2)11yescharacteristic
256C242−1+412yes—
257C242−1+412yes—
258C242−1+412yes—
259C242−1+411yescharacteristic
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—28no—
277C22×C4—28no—
278C22×C4—28no—
279C22×C4—28no—
280C22×C4—28no—
281C22×C4—28no—
282C22×C4—28no—
283C22×C4—28no—
284C22×C4—22no—
285C22×C4—28no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—28no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—28no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—28no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—28no—
306C22×C4—24no—
307C22×C4—28no—
308C22×C4—24no—
309C22×C4—28no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—28no—
316C22×C4—24no—
317C22×C4—28no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—28no—
322C22×C4—28no—
323C22×C4—28no—
324C22×C4—28no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—28no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—28no—
337C22×C4—24no—
338C22×C4—28no—
339C22×C4—28no—
340C22×C4—28no—
341C22×C4—28no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—42no—
362C22×C4—44no—
363C22×C4—42no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—44no—
371C22×C4—42no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—44no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—42no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—44no—
394C22×C4—42no—
395C22×C4—44no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—44no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—44no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—42no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—44no—
427C22×C4—42no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—44no—
434C22×C4—42no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4#12018yes—
438C22×C4#12014yes—
439C22×C4#12118yes—
440C22×C4#12114yes—
441C22×C4#12118yes—
442C22×C4#12114yes—
443C22×C4C22⋊Q818yes—
444C22×C4#12314yes—
445C22×C4#12518yes—
446C22×C4#12714yes—
447C22×C4C4⋊Q814yes—
448C22×C4C4⋊Q8116yes—
449C22×C4C4⋊Q814yes—
450C4⋊C4—232no—
451C4⋊C4—416no—
452C4⋊C4—416no—
453C4⋊C4—464no—
454C4⋊C4—432no—
455C4⋊C4—416no—
456C42—416no—
457C23C2×#12011yescharacteristic
458C23C2×#12012yes—
459C23C2×#12111yescharacteristic
460C23C2×#12112yes—
461C23C2×#12111yescharacteristic
462C23C2×#12112yes—
463C23C2×C22⋊Q812yes—
464C23C2×#12311yescharacteristic
465C23#52511yescharacteristic
466C23#52511yescharacteristic
467C23#52512yes—
468C23C2×#12512yes—
469C23#52912yes—
470C23C2×#12711yescharacteristic
471C23C2×C4⋊Q811yescharacteristic
472C23C2×C4⋊Q811yescharacteristic
473C23C2×C4⋊Q814yes—
474C23#53212yes—
475C23#53314yes—
476C23#53411yescharacteristic
477C23#53511yescharacteristic
478C23#53512yes—
479C23#53611yescharacteristic
480C23#53611yescharacteristic
481C23#53611yescharacteristic
482C23#53614yes—
483C23#53711yescharacteristic
484C23#53712yes—
485C23#53712yes—
486C23#53712yes—
487C23#53914yes—
488C23#53912yes—
489C23#53912yes—
490C23#54112yes—
491C23#54114yes—
492C23#54212yes—
493C23#54312yes—
494C23#54412yes—
495C23#54414yes—
496C23D4211yescharacteristic
497C23D4212yes—
498C23#54614yes—
499C23#54612yes—
500C23#54612yes—
501C23#54614yes—
502C23#54714yes—
503C23#54711yescharacteristic
504C23#54711yescharacteristic
505C23#54714yes—
506C23#54812yes—
507C23#54812yes—
508C23D4×Q814yes—
509C23D4×Q812yes—
510C23D4×Q812yes—
511C23D4×Q814yes—
512C23D4×Q812yes—
513C23#55012yes—
514C23#55214yes—
515C23#55212yes—
516C23#55312yes—
517C23#55414yes—
518C23#55412yes—
519C23#55414yes—
520C23#55511yescharacteristic
521C23#55712yes—
522C23#55712yes—
523C23#55712yes—
524C23#55712yes—
525C23#56214yes—
526C23#56312yes—
527C23#56412yes—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—216no—
537C2×C4—216no—
538C2×C4—216no—
539C2×C4—24no—
540C2×C4—216no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—28no—
545C2×C4—24no—
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—216no—
550C2×C4—216no—
551C2×C4—24no—
552C2×C4—216no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—48no—
573C2×C4—48no—
574C2×C4—48no—
575C2×C4—48no—
576C2×C4—48no—
577C2×C4—48no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—48no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—48no—
589C2×C4—48no—
590C2×C4—48no—
591C2×C4—48no—
592C2×C4—48no—
593C2×C4—48no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—82no—
614C2×C4—82no—
615C2×C4—82no—
616C2×C4#39218yes—
617C2×C4#39818yescomplemented
618C22C2×#39211yescharacteristic
619C22C2×#39811yescharacteristic
620C22#239911yescharacteristic
621C22#240511yescharacteristic
622C22#240611yescharacteristic
623C22#240712yes—
624C22#240812yes—
625C22#241412yes—
626C22#241612yes—
627C22#241714yes—
628C22#242514yes—
629C22#242914yes—
630C22#243014yes—
631C22#243411yescharacteristic
632C22#243411yescharacteristic
633C22#243414yes—
634C22#244014yes—
635C22#245212yes—
636C22#245312yes—
637C22#246214yes—
638C22#247314yes—
639C22#248411yescharacteristic
640C22#250111yescharacteristic
641C22#250211yescharacteristic
642C22#250612yes—
643C22#250812yes—
644C22#253511yescharacteristic
645C22#253611yescharacteristic
646C22#253711yescharacteristic
647C22#253911yescharacteristic
648C22#254011yescharacteristic
649C22#254111yescharacteristic
650C22#254611yescharacteristic
651C22#254614yes—
652C22#254611yescharacteristic
653C22#254611yescharacteristic
654C22#254914yes—
655C22#255014yes—
656C22#255214yes—
657C22#255614yes—
658C22#258311yescharacteristic
659C22#258411yescharacteristic
660C22#259014yes—
661C22#261511yescharacteristic
662C22#261811yescharacteristic
663C22#261811yescharacteristic
664C22#262511yescharacteristic
665C22#263311yescharacteristic
666C22#263411yescharacteristic
667C22#265811yescharacteristic
668C22#265911yescharacteristic
669C22#266011yescharacteristic
670C22#268114yes—
671C22#268312yes—
672C22#269214yes—
673C22#269414yes—
674C22#269814yes—
675C22#270414yes—
676C22#270414yes—
677C22#271914yes—
678C22#272014yes—
679C22#272612yes—
680C22#272614yes—
681C22#272612yes—
682C22#280214yes—
683C22#280912yes—
684C22#281611yescharacteristic
685C22#282211yescharacteristic
686C22#284711yescharacteristic
687C22#285411yescharacteristic
688C22#286811yescharacteristic
689C4—28no—
690C4—28no—
691C4—48no—
692C4—44no—
693C4—416no—
694C4—84no—
695C4—84no—
696C4—84no—
697C2#1482111yescharacteristic
698C2#1488011yescharacteristic
699C2#1492611yescharacteristic
700C2#1510611yescharacteristic
701C2#1512311yescharacteristic
702C2#1514511yescharacteristic
703C2#1514911yescharacteristic
704C2#1517311yescharacteristic
705C2#1519011yescharacteristic
706C2#1551714yes—
707C2#1561414yes—
708C2#1561814yes—
709C2#1584814yes—
710C2#1636511yescharacteristic
711C2#1660711yescharacteristic
712C2#1681111yescharacteristic
713C2#1696411yescharacteristic
714C2#1699211yescharacteristic
715C2#1707011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
617. C2×C4#398semidirect

Maximal subgroups

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

subgroupindex
C22×#3982
C22×#3892
C2×#14442
C2×#14412
C2×C4⋊#952
#75572
#75542