Finite Group Databasebeta

← #453791

Subgroups — #453791

Order 512.

822 conjugacy classes of subgroups.

The subgroup lattice has 689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13936C211yesmaximal, characteristic
2#13936C211yesmaximal, characteristic
3#11379C211yesmaximal, characteristic
4#11378C211yesmaximal, characteristic
5#11378C211yesmaximal, characteristic
6#11257C211yesmaximal, characteristic
7#11257C211yesmaximal, characteristic
8#11256C211yesmaximal, characteristic
9#11255C211yesmaximal, characteristic
10#11232C211yesmaximal, characteristic
11#11231C211yesmaximal, characteristic
12#10908C211yesmaximal, characteristic
13#10907C211yesmaximal, characteristic
14#10907C211yesmaximal, characteristic
15#10907C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×C4×C4⋊C4C2211yescharacteristic
23C2×#340C2211yescharacteristic
24C2×#340C2211yescharacteristic
25C2×#340C2211yescharacteristic
26C2×#340C2211yescharacteristic
27C2×#340C2211yescharacteristic
28C2×#340C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38C2×#336C2211yescharacteristic
39C2×#336C2211yescharacteristic
40#1443—21no—
41#1443—21no—
42#1443—21no—
43#1443—21no—
44C4⋊#95C2211yescharacteristic
45C4⋊#95C2211yescharacteristic
46C4⋊#95C2211yescharacteristic
47C4⋊#95C2211yescharacteristic
48C4⋊#95C2211yescharacteristic
49C4⋊#95C2211yescharacteristic
50C4⋊#95C2211yescharacteristic
51C4⋊#95C2211yescharacteristic
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54#1434—21no—
55#1434—21no—
56#1434—21no—
57#1434—21no—
58C4×#95C2211yescharacteristic
59C23×C8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2311yescharacteristic
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C42—21no—
72C22×C42—21no—
73C22×C42C2311yescharacteristic
74C22×C42C2311yescharacteristic
75C22×C42C2311yescharacteristic
76C2×#107—22no—
77C2×#107—22no—
78C2×#107—22no—
79C2×#107—22no—
80C2×#107—41no—
81C2×#107—41no—
82C2×#106—22no—
83C2×#106—22no—
84C2×#106—22no—
85C2×#106—41no—
86C2×#106—41no—
87C2×#106—41no—
88C2×C4⋊C8—22no—
89C2×C4⋊C8—22no—
90C2×C4⋊C8—41no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—22no—
94C4×C4⋊C4—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95D411yescharacteristic
118C2×#95D411yescharacteristic
119C2×#95D411yescharacteristic
120C2×#95D411yescharacteristic
121#340—22no—
122#340—22no—
123#340—22no—
124#340—22no—
125#340—22no—
126#340—22no—
127#340—22no—
128#340—41no—
129#340—41no—
130#340—41no—
131#340—41no—
132#340—41no—
133#336—22no—
134#336—22no—
135#336—22no—
136#336—22no—
137#336—41no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2411yescharacteristic
153C22×C8—21no—
154C22×C8—21no—
155C22×C8—21no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—21no—
161C22×C8—21no—
162C22×C8—21no—
163C22×C8—21no—
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8#4112yes—
178C22×C8#4112yes—
179C22×C8#4112yes—
180C22×C8#4112yes—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
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#4112yes—
226C2×C4⋊C4#4112yes—
227C2×C4⋊C4#4112yes—
228C2×C4⋊C4#4112yes—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—24no—
248C2×C42—24no—
249C2×C42—81no—
250C2×C42—81no—
251C2×C42—81no—
252C2×C42—81no—
253#107—44no—
254#107—44no—
255#106—44no—
256#106—44no—
257C4⋊C8—44no—
258#95—24no—
259#95—24no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—41no—
264#95—42no—
265#95—42no—
266#95—42no—
267#95—42no—
268#95—42no—
269#95—42no—
270#95—81no—
271#95—81no—
272#95—81no—
273#95—81no—
274#95—81no—
275#95—81no—
276#95—81no—
277#95—81no—
278#95—81no—
279#95—81no—
280#95—81no—
281#95—81no—
282#95—81no—
283#95—81no—
284C24C22×D411yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
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—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
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#13512yes—
381C22×C4#13712yes—
382C22×C4#13712yes—
383C22×C4C2×#4111yescharacteristic
384C22×C4C2×#4111yescharacteristic
385C22×C4C2×#4111yescharacteristic
386C22×C4C2×#4111yescharacteristic
387C22×C4C2×#4111yescharacteristic
388C22×C4C2×#4111yescharacteristic
389C22×C4C2×#4111yescharacteristic
390C22×C4C2×#4111yescharacteristic
391C22×C4H(5,𝔽2)11yescharacteristic
392C22×C4H(5,𝔽2)11yescharacteristic
393C22×C42−1+411yescharacteristic
394C22×C42−1+411yescharacteristic
395C22×C42−1+411yescharacteristic
396C22×C42−1+411yescharacteristic
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4—41no—
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—
457C42—41no—
458C42—41no—
459C42—41no—
460C42—41no—
461C42—41no—
462C42—41no—
463C42—41no—
464C42—41no—
465C42—41no—
466C42—41no—
467C42—41no—
468C42—41no—
469C42—84no—
470C42—84no—
471C23#52511yescharacteristic
472C23#52511yescharacteristic
473C23#53711yescharacteristic
474C23#54711yescharacteristic
475C23#54711yescharacteristic
476C23#54711yescharacteristic
477C23#55011yescharacteristic
478C23C2×#13511yescharacteristic
479C23C2×#13711yescharacteristic
480C23C2×#13711yescharacteristic
481C23#57511yescharacteristic
482C23#57611yescharacteristic
483C23#57611yescharacteristic
484C23#57711yescharacteristic
485C23#57711yescharacteristic
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
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—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4#52911yescharacteristic
585C2×C4#52911yescharacteristic
586C2×C4#52911yescharacteristic
587C2×C4#52911yescharacteristic
588C2×C4#53811yescharacteristic
589C2×C4#53911yescharacteristic
590C2×C4#54111yescharacteristic
591C2×C4#54111yescharacteristic
592C2×C4#54111yescharacteristic
593C2×C4#54111yescharacteristic
594C2×C4#54211yescharacteristic
595C2×C4#54211yescharacteristic
596C2×C4#55111yescharacteristic
597C2×C4#55111yescharacteristic
598C2×C4#55111yescharacteristic
599C2×C4#55111yescharacteristic
600C2×C4#55211yescharacteristic
601C2×C4#55211yescharacteristic
602C2×C4#55211yescharacteristic
603C2×C4#55211yescharacteristic
604C2×C4#55211yescharacteristic
605C2×C4#55211yescharacteristic
606C2×C4#55511yescharacteristic
607C2×C4#55611yescharacteristic
608C2×C4#55611yescharacteristic
609C2×C4#55611yescharacteristic
610C2×C4#56311yescharacteristic
611C2×C4#56311yescharacteristic
612C8—42no—
613C8—42no—
614C8—42no—
615C8—42no—
616C22#247811yescharacteristic
617C22#247811yescharacteristic
618C22#247911yescharacteristic
619C22#247911yescharacteristic
620C22#260911yescharacteristic
621C22#272211yescharacteristic
622C22#272711yescharacteristic
623C22#310211yescharacteristic
624C22#310811yescharacteristic
625C22#311311yescharacteristic
626C22#311611yescharacteristic
627C22#311811yescharacteristic
628C22#311911yescharacteristic
629C22#312211yescharacteristic
630C22#312511yescharacteristic
631C22#324811yescharacteristic
632C22#325211yescharacteristic
633C22#325711yescharacteristic
634C22#325711yescharacteristic
635C22#333711yescharacteristic
636C22#333911yescharacteristic
637C22#334011yescharacteristic
638C22#334411yescharacteristic
639C22#334611yescharacteristic
640C22#334611yescharacteristic
641C22#334611yescharacteristic
642C22#334711yescharacteristic
643C22#334811yescharacteristic
644C22#335111yescharacteristic
645C22#335611yescharacteristic
646C22#335711yescharacteristic
647C22#339611yescharacteristic
648C22#340011yescharacteristic
649C22#340011yescharacteristic
650C22#340311yescharacteristic
651C4—42no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—82no—
657C4—82no—
658C4—82no—
659C4—82no—
660C4—81no—
661C4—161no—
662C4—161no—
663C4—161no—
664C4—161no—
665C4#252311yescharacteristic
666C4#252411yescharacteristic
667C4#252411yescharacteristic
668C4#257211yescharacteristic
669C4#275811yescharacteristic
670C4#275811yescharacteristic
671C4#276411yescharacteristic
672C4#276911yescharacteristic
673C2#1611611yescharacteristic
674C2#2745711yescharacteristic
675C2#2746411yescharacteristic
676C2#2747311yescharacteristic
677C2#2748011yescharacteristic
678C2#2748911yescharacteristic
679C2#2750011yescharacteristic
680C2#2750511yescharacteristic
681C2#2751611yescharacteristic
682C2#2954111yescharacteristic
683C2#2954211yescharacteristic
684C2#3241511yescharacteristic
685C2#3241611yescharacteristic
686C2#3253211yescharacteristic
687C2#3254011yescharacteristic
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
#139362
#113792
#113782
#112572
#112562
#112552
#112322
#112312
#109082
#109072