Finite Group Databasebeta

← #158493

Subgroups — #158493

Order 512.

3136 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C2×#1444C212yesmaximal
3C2×#1444C212yesmaximal
4C2×#1441C214yesmaximal
5C2×C4⋊#95C211yesmaximal, characteristic
6#7557C212yesmaximal
7#7557C212yesmaximal
8#7554C211yesmaximal, characteristic
9C23×C4⋊C4C2211yescharacteristic
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2214yes—
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C23×C42C2211yescharacteristic
16C2×#389—24no—
17C2×#389—28no—
18C22×#95C2212yes—
19C22×#95C2212yes—
20C22×#95C2214yes—
21C22×#95C2214yes—
22C22×#95C2212yes—
23C22×#95C2212yes—
24C22×#95C2212yes—
25C22×#95C2214yes—
26C22×#95C2212yes—
27#1444—28no—
28#1444—28no—
29#1441—216no—
30C4⋊#95—24no—
31C24×C4C2312yes—
32C24×C4C2312yes—
33C24×C4C2312yes—
34C24×C4C2311yescharacteristic
35C24×C4C2312yes—
36C24×C4C2314yes—
37C24×C4C2311yescharacteristic
38C24×C4C2311yescharacteristic
39C22×C4⋊C4—24no—
40C22×C4⋊C4—22no—
41C22×C4⋊C4—24no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—28no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—28no—
53C22×C4⋊C4—28no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—28no—
56C22×C4⋊C4—24no—
57C22×C4⋊C4—28no—
58C22×C4⋊C4—28no—
59C22×C4⋊C4—24no—
60C22×C4⋊C4—42no—
61C22×C4⋊C4—42no—
62C22×C4⋊C4—42no—
63C22×C4⋊C4—42no—
64C22×C4⋊C4—44no—
65C22×C4⋊C4—44no—
66C22×C4⋊C4—44no—
67C22×C4⋊C4D414yes—
68C22×C4⋊C4Q814yes—
69C22×C42—24no—
70C22×C42—24no—
71C22×C42—42no—
72C22×C42D414yes—
73#389—232no—
74C2×#95—24no—
75C2×#95—24no—
76C2×#95—24no—
77C2×#95—24no—
78C2×#95—24no—
79C2×#95—24no—
80C2×#95—24no—
81C2×#95—24no—
82C2×#95—28no—
83C2×#95—28no—
84C2×#95—28no—
85C2×#95—28no—
86C2×#95—28no—
87C2×#95—28no—
88C2×#95—24no—
89C2×#95—24no—
90C2×#95—42no—
91C2×#95—42no—
92C2×#95—44no—
93C2×#95—44no—
94C2×#95—44no—
95C2×#95—44no—
96C2×#95D418yes—
97C2×#95D418yes—
98C2×#95Q818yes—
99C2×#95Q818yes—
100C25C2411yescharacteristic
101C23×C4—22no—
102C23×C4—22no—
103C23×C4—22no—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—22no—
111C23×C4—24no—
112C23×C4—22no—
113C23×C4—24no—
114C23×C4—24no—
115C23×C4—22no—
116C23×C4—22no—
117C23×C4—24no—
118C23×C4—24no—
119C23×C4—24no—
120C23×C4—24no—
121C23×C4—24no—
122C23×C4—22no—
123C23×C4—22no—
124C23×C4—24no—
125C23×C4—24no—
126C23×C4—24no—
127C23×C4—24no—
128C23×C4—24no—
129C23×C4—24no—
130C23×C4—21no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—24no—
135C23×C4—24no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—24no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—22no—
142C23×C4—24no—
143C23×C4—24no—
144C23×C4—22no—
145C23×C4—24no—
146C23×C4—22no—
147C23×C4—24no—
148C23×C4—22no—
149C23×C4—24no—
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—24no—
153C23×C4—22no—
154C23×C4—24no—
155C23×C4—24no—
156C23×C4—24no—
157C23×C4—24no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—24no—
165C23×C4—22no—
166C23×C4C2×D414yes—
167C23×C4C2×D414yes—
168C23×C4C2×D414yes—
169C23×C4C2×D414yes—
170C23×C4C2×D412yes—
171C23×C4C2×D418yes—
172C23×C4C2×D412yes—
173C23×C4C2×D414yes—
174C23×C4C2×D412yes—
175C23×C4C2×D412yes—
176C23×C4C2×Q814yes—
177C23×C4C2×Q818yes—
178C23×C4C2×Q818yes—
179C23×C4C2×Q814yes—
180C23×C4C2×Q812yes—
181C23×C4C2×Q814yes—
182C23×C4#4114yes—
183C23×C4#4114yes—
184C23×C4#4112yes—
185C23×C4#4112yes—
186C23×C4#4114yes—
187C2×C4⋊C4—28no—
188C2×C4⋊C4—216no—
189C2×C4⋊C4—28no—
190C2×C4⋊C4—216no—
191C2×C4⋊C4—28no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4—232no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—216no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—48no—
198C2×C4⋊C4—416no—
199C2×C4⋊C4—416no—
200C2×C4⋊C4—416no—
201C2×C4⋊C4—416no—
202C2×C4⋊C4—416no—
203C2×C4⋊C4—416no—
204C2×C4⋊C4—416no—
205C2×C4⋊C4—416no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4—44no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4—44no—
210C2×C4⋊C4—48no—
211C2×C4⋊C4—48no—
212C2×C4⋊C4—416no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4—416no—
215C2×C4⋊C4—44no—
216C2×C4⋊C4—48no—
217C2×C42—28no—
218C2×C42—28no—
219C2×C42—44no—
220C2×C42—416no—
221#95—216no—
222#95—216no—
223#95—216no—
224#95—48no—
225#95—416no—
226#95—416no—
227#95—416no—
228#95—48no—
229#95—48no—
230C24C22×D411yescharacteristic
231C24C22×D412yes—
232C24C22×D411yescharacteristic
233C24C22×D412yes—
234C24C22×Q812yes—
235C24C22×Q812yes—
236C24C22×Q811yescharacteristic
237C24C2×#4112yes—
238C24C2×#4111yescharacteristic
239C24C2×#4111yescharacteristic
240C24C2×#4112yes—
241C24C2×#4112yes—
242C24H(5,𝔽2)11yescharacteristic
243C24H(5,𝔽2)12yes—
244C24H(5,𝔽2)12yes—
245C24H(5,𝔽2)12yes—
246C242−1+411yescharacteristic
247C242−1+412yes—
248C242−1+412yes—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—28no—
266C22×C4—28no—
267C22×C4—28no—
268C22×C4—28no—
269C22×C4—28no—
270C22×C4—28no—
271C22×C4—28no—
272C22×C4—28no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—28no—
278C22×C4—28no—
279C22×C4—22no—
280C22×C4—28no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—28no—
293C22×C4—28no—
294C22×C4—28no—
295C22×C4—28no—
296C22×C4—28no—
297C22×C4—28no—
298C22×C4—28no—
299C22×C4—28no—
300C22×C4—28no—
301C22×C4—28no—
302C22×C4—28no—
303C22×C4—28no—
304C22×C4—28no—
305C22×C4—28no—
306C22×C4—28no—
307C22×C4—28no—
308C22×C4—28no—
309C22×C4—28no—
310C22×C4—28no—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4—24no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—28no—
317C22×C4—24no—
318C22×C4—24no—
319C22×C4—28no—
320C22×C4—28no—
321C22×C4—28no—
322C22×C4—24no—
323C22×C4—28no—
324C22×C4—24no—
325C22×C4—28no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—44no—
329C22×C4—42no—
330C22×C4—44no—
331C22×C4—44no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—44no—
340C22×C4—44no—
341C22×C4—44no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—42no—
346C22×C4—44no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4—44no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—44no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—44no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—44no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—44no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—44no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4—44no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4—44no—
414C22×C4#12014yes—
415C22×C4#12118yes—
416C22×C4#12114yes—
417C22×C4C22⋊Q818yes—
418C22×C4C22⋊Q814yes—
419C22×C4C22⋊Q818yes—
420C22×C4#12314yes—
421C22×C4#12518yes—
422C22×C4#12714yes—
423C22×C4C4⋊Q8116yes—
424C22×C4C4⋊Q814yes—
425C22×C4C4⋊Q818yes—
426C22×C4C4⋊Q814yes—
427C4⋊C4—232no—
428C4⋊C4—416no—
429C4⋊C4—416no—
430C4⋊C4—416no—
431C4⋊C4—464no—
432C4⋊C4—432no—
433C42—416no—
434C23C2×#12011yescharacteristic
435C23C2×#12111yescharacteristic
436C23C2×#12112yes—
437C23C2×C22⋊Q811yescharacteristic
438C23C2×C22⋊Q812yes—
439C23C2×C22⋊Q812yes—
440C23C2×#12311yescharacteristic
441C23#52511yescharacteristic
442C23#52512yes—
443C23#52511yescharacteristic
444C23#52514yes—
445C23C2×#12512yes—
446C23#52912yes—
447C23C2×#12711yescharacteristic
448C23C2×C4⋊Q811yescharacteristic
449C23C2×C4⋊Q811yescharacteristic
450C23C2×C4⋊Q814yes—
451C23C2×C4⋊Q812yes—
452C23#53312yes—
453C23#53411yescharacteristic
454C23#53412yes—
455C23#53511yescharacteristic
456C23#53511yescharacteristic
457C23#53611yescharacteristic
458C23#53611yescharacteristic
459C23#53612yes—
460C23#53711yescharacteristic
461C23#53712yes—
462C23#53712yes—
463C23#53712yes—
464C23#53812yes—
465C23#53814yes—
466C23#53912yes—
467C23#54012yes—
468C23#54114yes—
469C23#54212yes—
470C23#54312yes—
471C23#54414yes—
472C23#54414yes—
473C23D4214yes—
474C23D4212yes—
475C23#54614yes—
476C23#54614yes—
477C23#54612yes—
478C23#54714yes—
479C23#54712yes—
480C23D4×Q814yes—
481C23D4×Q811yescharacteristic
482C23D4×Q812yes—
483C23D4×Q812yes—
484C23#55011yescharacteristic
485C23#55012yes—
486C23#55214yes—
487C23#55312yes—
488C23#55412yes—
489C23#55412yes—
490C23#55414yes—
491C23#55412yes—
492C23#55414yes—
493C23#55411yescharacteristic
494C23#55414yes—
495C23#55611yescharacteristic
496C23#55612yes—
497C23#55712yes—
498C23#55712yes—
499C23#55712yes—
500C23#55712yes—
501C23Q8212yes—
502C23#56214yes—
503C23#56212yes—
504C23#56312yes—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—216no—
515C2×C4—24no—
516C2×C4—216no—
517C2×C4—216no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—216no—
521C2×C4—216no—
522C2×C4—28no—
523C2×C4—24no—
524C2×C4—216no—
525C2×C4—24no—
526C2×C4—216no—
527C2×C4—216no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—48no—
540C2×C4—48no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—44no—
544C2×C4—48no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—48no—
548C2×C4—48no—
549C2×C4—48no—
550C2×C4—48no—
551C2×C4—48no—
552C2×C4—48no—
553C2×C4—44no—
554C2×C4—48no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—48no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—48no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—84no—
580C2×C4—84no—
581C2×C4—84no—
582C2×C4—84no—
583C2×C4—82no—
584C2×C4—84no—
585C2×C4—84no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4#39518yes—
590C2×C4#39818yes—
591C22C2×#39511yescharacteristic
592C22C2×#39811yescharacteristic
593C22#239711yescharacteristic
594C22#240411yescharacteristic
595C22#240511yescharacteristic
596C22#241714yes—
597C22#242414yes—
598C22#243311yescharacteristic
599C22#243411yescharacteristic
600C22#244014yes—
601C22#244014yes—
602C22#245014yes—
603C22#245112yes—
604C22#245412yes—
605C22#245614yes—
606C22#246214yes—
607C22#247314yes—
608C22#247814yes—
609C22#248411yescharacteristic
610C22#250111yescharacteristic
611C22#250211yescharacteristic
612C22#250712yes—
613C22#250912yes—
614C22#253511yescharacteristic
615C22#253811yescharacteristic
616C22#253812yes—
617C22#254111yescharacteristic
618C22#254211yescharacteristic
619C22#254612yes—
620C22#254611yescharacteristic
621C22#254914yes—
622C22#255114yes—
623C22#255214yes—
624C22#256711yescharacteristic
625C22#258112yes—
626C22#258111yescharacteristic
627C22#258311yescharacteristic
628C22#258311yescharacteristic
629C22#258314yes—
630C22#258414yes—
631C22#258411yescharacteristic
632C22#258412yes—
633C22#258411yescharacteristic
634C22#261611yescharacteristic
635C22#261811yescharacteristic
636C22#262411yescharacteristic
637C22#262611yescharacteristic
638C22#263111yescharacteristic
639C22#263411yescharacteristic
640C22#265611yescharacteristic
641C22#266011yescharacteristic
642C22#266011yescharacteristic
643C22#267114yes—
644C22#267214yes—
645C22#268212yes—
646C22#268312yes—
647C22#270414yes—
648C22#270414yes—
649C22#271314yes—
650C22#272712yes—
651C22#273212yes—
652C22#276814yes—
653C22#277414yes—
654C22#278814yes—
655C22#280214yes—
656C22#280614yes—
657C22#281611yescharacteristic
658C22#282011yescharacteristic
659C22#284711yescharacteristic
660C22#285511yescharacteristic
661C22#286811yescharacteristic
662C4—28no—
663C4—28no—
664C4—416no—
665C4—48no—
666C4—44no—
667C4—84no—
668C4—84no—
669C4—84no—
670C2#1481111yescharacteristic
671C2#1482111yescharacteristic
672C2#1491411yescharacteristic
673C2#1508211yescharacteristic
674C2#1514311yescharacteristic
675C2#1514511yescharacteristic
676C2#1515811yescharacteristic
677C2#1519411yescharacteristic
678C2#1521111yescharacteristic
679C2#1530514yes—
680C2#1544914yes—
681C2#1552014yes—
682C2#1562314yes—
683C2#1636311yescharacteristic
684C2#1660811yescharacteristic
685C2#1696011yescharacteristic
686C2#1698911yescharacteristic
687C2#1699211yescharacteristic
688C2#1707111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC25C24
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Maximal subgroups

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

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