Finite Group Databasebeta

← #472098

Subgroups — #472098

Order 512.

1002 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2085C211yesmaximal, characteristic
2C2×#2026C211yesmaximal, characteristic
3C2×#1991C211yesmaximal, characteristic
4C2×#1933C211yesmaximal, characteristic
5#15241C211yesmaximal, characteristic
6#15228C211yesmaximal, characteristic
7#11378C211yesmaximal, characteristic
8#11377C211yesmaximal, characteristic
9#11373C211yesmaximal, characteristic
10#11372C211yesmaximal, characteristic
11#11124C211yesmaximal, characteristic
12#11122C211yesmaximal, characteristic
13#11052C211yesmaximal, characteristic
14#11050C211yesmaximal, characteristic
15#10797C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×C4×C8C2211yescharacteristic
24C2×#391C2211yescharacteristic
25C2×#391C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#384C2211yescharacteristic
29C2×#382C2211yescharacteristic
30C2×#382C2211yescharacteristic
31#2085—24no—
32#2026—24no—
33#1991—24no—
34#1933—24no—
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1444—22no—
51#1443—22no—
52#1443—22no—
53#1441—22no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4×#95C2211yescharacteristic
59C23×Q8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C2×#125—22no—
65C2×#125—22no—
66C2×#125—22no—
67C2×#125—22no—
68C2×#125—41no—
69C2×#125—41no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—22no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C42C2311yescharacteristic
82C22×C42C2311yescharacteristic
83C22×C42C2311yescharacteristic
84C2×#107—22no—
85C2×#107—22no—
86C2×#107—41no—
87C2×#106—22no—
88C2×#106—22no—
89C2×#106—41no—
90C2×#103—22no—
91C2×#103—22no—
92C2×#103—22no—
93C2×#103—22no—
94C2×#103—22no—
95C2×#103—22no—
96C2×#103—22no—
97C2×#103—22no—
98C2×#103—41no—
99C2×#103—41no—
100C2×#103—41no—
101C2×#103—41no—
102C2×C4×C8—41no—
103C2×C4×C8—41no—
104C2×C4×C8D414yes—
105#391—22no—
106#391—22no—
107#391—22no—
108#391—22no—
109#391—41no—
110#391—41no—
111#389—22no—
112#389—22no—
113#384—22no—
114#384—41no—
115#382—22no—
116#382—22no—
117#382—22no—
118#382—41no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—21no—
123C2×#95—22no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—22no—
131C2×#95D412yes—
132C2×#95D412yes—
133#340—22no—
134#340—22no—
135#340—22no—
136#340—22no—
137#340—22no—
138#340—22no—
139#340—22no—
140#340—22no—
141#340—22no—
142#340—22no—
143#336—41no—
144#336—41no—
145#336—41no—
146#336—41no—
147#336D414yes—
148C22×Q8—21no—
149C22×Q8—21no—
150C22×Q8—21no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—21no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8—21no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8#4112yes—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4C2×D412yes—
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D412yes—
174C23×C4C2411yescharacteristic
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8C2×D412yes—
200C22×C8C2×D412yes—
201C22×C8C2×D412yes—
202C22×C8C2×D412yes—
203#125—28no—
204#125—44no—
205#125—44no—
206#125—44no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—82no—
256C2×C4⋊C4—82no—
257C2×C4⋊C4#4112yes—
258C2×C4⋊C4#4112yes—
259C2×C4⋊C4#4112yes—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42—21no—
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42C2×D412yes—
277C2×C42C2×D412yes—
278#107—44no—
279#106—44no—
280#103—28no—
281#103—44no—
282#103—44no—
283#103—44no—
284C4×C8—44no—
285#95—24no—
286#95—42no—
287#95—44no—
288#95—44no—
289#95—44no—
290#95—44no—
291#95—44no—
292#95—42no—
293#95—42no—
294#95—42no—
295#95—42no—
296#95—42no—
297#95—44no—
298#95—82no—
299C24C22×D411yescharacteristic
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×Q8—41no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—41no—
326C2×Q8—41no—
327C2×Q8—41no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4#12712yes—
392C22×C4#12712yes—
393C22×C4#13514yes—
394C22×C4C22×D411yescharacteristic
395C22×C4C22×D411yescharacteristic
396C22×C4C2×#4111yescharacteristic
397C22×C4C2×#4111yescharacteristic
398C22×C4C2×#4111yescharacteristic
399C22×C4C2×#4111yescharacteristic
400C22×C4H(5,𝔽2)11yescharacteristic
401C22×C4H(5,𝔽2)11yescharacteristic
402C22×C4H(5,𝔽2)11yescharacteristic
403C22×C42−1+411yescharacteristic
404C22×C42−1+411yescharacteristic
405C22×C42−1+411yescharacteristic
406C22×C42−1+411yescharacteristic
407C22×C42−1+411yescharacteristic
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—41no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—88no—
467C4⋊C4—84no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—22no—
472C42—41no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42—41no—
477C42—41no—
478C42—41no—
479C42—41no—
480C23C2×#12711yescharacteristic
481C23#53611yescharacteristic
482C23#53611yescharacteristic
483C23#54611yescharacteristic
484C23#54611yescharacteristic
485C23#54611yescharacteristic
486C23#54811yescharacteristic
487C23C2×#13512yes—
488C23#57512yes—
489C23#57712yes—
490C23#57812yes—
491Q8—42no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495Q8—81no—
496Q8—81no—
497Q8—81no—
498Q8—81no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—82no—
542C2×C4—81no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—82no—
565C2×C4#52511yescharacteristic
566C2×C4#52511yescharacteristic
567C2×C4#53411yescharacteristic
568C2×C4#53611yescharacteristic
569C2×C4#53611yescharacteristic
570C2×C4#53611yescharacteristic
571C2×C4#53611yescharacteristic
572C2×C4#53711yescharacteristic
573C2×C4#53911yescharacteristic
574C2×C4#53911yescharacteristic
575C2×C4#54111yescharacteristic
576C2×C4#54111yescharacteristic
577C2×C4#54211yescharacteristic
578C2×C4#54211yescharacteristic
579C2×C4#54211yescharacteristic
580C2×C4#54211yescharacteristic
581C2×C4#54611yescharacteristic
582C2×C4#54611yescharacteristic
583C2×C4#54611yescharacteristic
584C2×C4#54811yescharacteristic
585C2×C4#55211yescharacteristic
586C2×C4#55211yescharacteristic
587C2×C4#55611yescharacteristic
588C2×C4#55611yescharacteristic
589C2×C4#56211yescharacteristic
590C2×C4#56211yescharacteristic
591C2×C4#56311yescharacteristic
592C2×C4#56311yescharacteristic
593C8—42no—
594C8—42no—
595C8—42no—
596C8—42no—
597C22#253911yescharacteristic
598C22#254011yescharacteristic
599C22#265811yescharacteristic
600C22#268711yescharacteristic
601C22#268711yescharacteristic
602C22#271611yescharacteristic
603C22#271611yescharacteristic
604C22#314711yescharacteristic
605C22#315011yescharacteristic
606C22#315411yescharacteristic
607C22#315611yescharacteristic
608C22#323212yes—
609C22#323312yes—
610C22#324212yes—
611C22#324212yes—
612C22#329612yes—
613C22#330012yes—
614C22#330412yes—
615C22#331312yes—
616C22#331512yes—
617C22#332612yes—
618C22#336412yes—
619C22#337612yes—
620C4—44no—
621C4—42no—
622C4—42no—
623C4—82no—
624C4—82no—
625C4—82no—
626C4—82no—
627C4—82no—
628C4—161no—
629C4—161no—
630C4—161no—
631C4—161no—
632C4#259911yescharacteristic
633C4#263711yescharacteristic
634C4#263811yescharacteristic
635C4#269011yescharacteristic
636C4#269011yescharacteristic
637C4#270011yescharacteristic
638C4#270011yescharacteristic
639C4#281411yescharacteristic
640C2#1681211yescharacteristic
641C2#2834011yescharacteristic
642C2#2835011yescharacteristic
643C2#2840711yescharacteristic
644C2#2841011yescharacteristic
645C2#3028211yescharacteristic
646C2#3028811yescharacteristic
647C2#3135812yes—
648C2#3136312yes—
649C2#3223412yes—
650C2#3223912yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#20852
C2×#20262
C2×#19912
C2×#19332
#152412
#152282
#113782
#113772
#113732
#113722
#111242
#111222
#110522
#110502
#107972