Finite Group Databasebeta

← #469852

Subgroups — #469852

Order 512.

976 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2024C211yesmaximal, characteristic
2C2×#1840C211yesmaximal, characteristic
3#14282C211yesmaximal, characteristic
4#14261C211yesmaximal, characteristic
5#11384C211yesmaximal, characteristic
6#11325C211yesmaximal, characteristic
7#11316C211yesmaximal, characteristic
8#11315C211yesmaximal, characteristic
9#11220C211yesmaximal, characteristic
10#11219C211yesmaximal, characteristic
11#11190C211yesmaximal, characteristic
12#11190C211yesmaximal, characteristic
13#11124C211yesmaximal, characteristic
14#11122C211yesmaximal, characteristic
15#11052C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C2×#391C2211yescharacteristic
24C2×#391C2211yescharacteristic
25C2×#391C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#382C2211yescharacteristic
28C2×#376C2211yescharacteristic
29#2024—24no—
30#1840—24no—
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47#1446—21no—
48#1446—21no—
49#1445—21no—
50#1445—21no—
51#1443—21no—
52#1443—21no—
53#1442—21no—
54#1442—21no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C23×Q8—21no—
62C23×Q8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×C4⋊Q8—22no—
68C2×C4⋊Q8—22no—
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—41no—
72C2×C4⋊Q8—41no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C42C2311yescharacteristic
83C22×C42C2311yescharacteristic
84C22×C42C2311yescharacteristic
85C2×#107—22no—
86C2×#107—41no—
87C2×#107—41no—
88C2×#106—22no—
89C2×#106—41no—
90C2×#106—41no—
91C2×#103—22no—
92C2×#103—22no—
93C2×#103—22no—
94C2×#103—22no—
95C2×#103—22no—
96C2×#103—22no—
97C2×#103—41no—
98C2×#103—41no—
99C2×#103—41no—
100C2×#103—41no—
101C2×#103—41no—
102C2×#103—41no—
103#391—22no—
104#391—22no—
105#391—22no—
106#391—22no—
107#391—41no—
108#391—41no—
109#389—41no—
110#389—41no—
111#382—41no—
112#382—41no—
113#376—22no—
114#376—22no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95D411yescharacteristic
137C2×#95D411yescharacteristic
138C2×#95D411yescharacteristic
139C2×#95D411yescharacteristic
140#340—22no—
141#340—22no—
142#340—22no—
143#340—22no—
144#340—41no—
145#340—41no—
146#340—41no—
147#340—41no—
148#340—41no—
149#340—41no—
150#336—22no—
151#336—22no—
152#336—22no—
153#336—22no—
154#336—22no—
155#336D414yes—
156C22×Q8—24no—
157C22×Q8—21no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—21no—
161C22×Q8—21no—
162C22×Q8—21no—
163C22×Q8—21no—
164C22×Q8—21no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—81no—
173C22×Q8—81no—
174C22×Q8—81no—
175C22×Q8—81no—
176C22×Q8#4112yes—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2411yescharacteristic
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8C2×D412yes—
219C22×C8C2×D412yes—
220C4⋊Q8—44no—
221C4⋊Q8—44no—
222C4⋊Q8—44no—
223C4⋊Q8—44no—
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—24no—
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—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—42no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—81no—
268C2×C4⋊C4—81no—
269C2×C4⋊C4#4112yes—
270C2×C4⋊C4#4112yes—
271C2×C4⋊C4#4112yes—
272C2×C42—21no—
273C2×C42—21no—
274C2×C42—21no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—21no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42C2×D412yes—
289C2×C42#4112yes—
290#107—44no—
291#106—44no—
292#103—44no—
293#103—44no—
294#103—44no—
295#103—44no—
296#95—24no—
297#95—24no—
298#95—22no—
299#95—22no—
300#95—22no—
301#95—22no—
302#95—42no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—42no—
307#95—42no—
308#95—42no—
309#95—81no—
310#95—81no—
311#95—81no—
312#95—81no—
313#95—81no—
314#95—81no—
315#95—81no—
316#95—81no—
317#95—81no—
318#95—81no—
319#95—81no—
320#95—81no—
321C24C22×D411yescharacteristic
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—48no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—41no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—84no—
352C2×Q8—84no—
353C2×Q8—84no—
354C2×Q8—84no—
355C2×Q8—84no—
356C2×Q8—84no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4#12112yes—
454C22×C4#12112yes—
455C22×C4C22×D411yescharacteristic
456C22×C4C2×#4111yescharacteristic
457C22×C4C2×#4111yescharacteristic
458C22×C4C2×#4111yescharacteristic
459C22×C4C2×#4111yescharacteristic
460C22×C4C2×#4111yescharacteristic
461C22×C4H(5,𝔽2)11yescharacteristic
462C22×C4H(5,𝔽2)11yescharacteristic
463C22×C4H(5,𝔽2)11yescharacteristic
464C22×C4H(5,𝔽2)11yescharacteristic
465C22×C42−1+411yescharacteristic
466C22×C42−1+411yescharacteristic
467C22×C42−1+411yescharacteristic
468C22×C42−1+411yescharacteristic
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—48no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—84no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42—22no—
531C42—41no—
532C42—41no—
533C42—41no—
534C42—41no—
535C42—41no—
536C42—41no—
537C42—41no—
538C42—41no—
539C23C2×#12111yescharacteristic
540C23#52511yescharacteristic
541C23#52511yescharacteristic
542C23#53511yescharacteristic
543C23#53511yescharacteristic
544C23#53611yescharacteristic
545C23#53611yescharacteristic
546C23#57611yescharacteristic
547C23#57711yescharacteristic
548C23#57711yescharacteristic
549C23#57711yescharacteristic
550C23#57711yescharacteristic
551C23#57811yescharacteristic
552C23#57811yescharacteristic
553C23#57811yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—42no—
557Q8—42no—
558Q8—816no—
559Q8—81no—
560Q8—81no—
561Q8—81no—
562Q8—81no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—81no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—81no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4#53711yescharacteristic
662C2×C4#53711yescharacteristic
663C2×C4#53811yescharacteristic
664C2×C4#53811yescharacteristic
665C2×C4#53811yescharacteristic
666C2×C4#53811yescharacteristic
667C2×C4#54211yescharacteristic
668C2×C4#54211yescharacteristic
669C2×C4#54211yescharacteristic
670C2×C4#54211yescharacteristic
671C2×C4#54211yescharacteristic
672C2×C4#54211yescharacteristic
673C2×C4#54611yescharacteristic
674C2×C4#54611yescharacteristic
675C2×C4#54711yescharacteristic
676C2×C4#54811yescharacteristic
677C2×C4#55111yescharacteristic
678C2×C4#55111yescharacteristic
679C2×C4#55211yescharacteristic
680C2×C4#55211yescharacteristic
681C2×C4#55211yescharacteristic
682C2×C4#55611yescharacteristic
683C2×C4#55611yescharacteristic
684C2×C4#55611yescharacteristic
685C2×C4#56311yescharacteristic
686C2×C4#56311yescharacteristic
687C2×C4#56311yescharacteristic
688C2×C4#56311yescharacteristic
689C8—42no—
690C8—42no—
691C8—81no—
692C8—81no—
693C22#241111yescharacteristic
694C22#241511yescharacteristic
695C22#259911yescharacteristic
696C22#262011yescharacteristic
697C22#263111yescharacteristic
698C22#263211yescharacteristic
699C22#282111yescharacteristic
700C22#305711yescharacteristic
701C22#305911yescharacteristic
702C22#306211yescharacteristic
703C22#306311yescharacteristic
704C22#311811yescharacteristic
705C22#312111yescharacteristic
706C22#312111yescharacteristic
707C22#312111yescharacteristic
708C22#312311yescharacteristic
709C22#312411yescharacteristic
710C22#312511yescharacteristic
711C22#312711yescharacteristic
712C22#322211yescharacteristic
713C22#322311yescharacteristic
714C22#322411yescharacteristic
715C22#322411yescharacteristic
716C22#322511yescharacteristic
717C22#322511yescharacteristic
718C22#322511yescharacteristic
719C22#322511yescharacteristic
720C22#324211yescharacteristic
721C22#324211yescharacteristic
722C22#324211yescharacteristic
723C22#324211yescharacteristic
724C22#324311yescharacteristic
725C22#324311yescharacteristic
726C22#324411yescharacteristic
727C22#324411yescharacteristic
728C4—42no—
729C4—42no—
730C4—82no—
731C4—82no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—82no—
737C4—82no—
738C4—161no—
739C4—161no—
740C4—161no—
741C4—161no—
742C4#270211yescharacteristic
743C4#270211yescharacteristic
744C4#271511yescharacteristic
745C4#271511yescharacteristic
746C4#275911yescharacteristic
747C4#275911yescharacteristic
748C4#276411yescharacteristic
749C4#276411yescharacteristic
750C2#1666511yescharacteristic
751C2#2451411yescharacteristic
752C2#2451611yescharacteristic
753C2#2471411yescharacteristic
754C2#2471811yescharacteristic
755C2#2940211yescharacteristic
756C2#2940311yescharacteristic
757C2#2984811yescharacteristic
758C2#2985711yescharacteristic
759C2#3005011yescharacteristic
760C2#3005511yescharacteristic
761C2#3006811yescharacteristic
762C2#3007011yescharacteristic
763C2#3284611yescharacteristic
764C2#3284711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#20242
C2×#18402
#142822
#142612
#113842
#113252
#113162
#113152
#112202
#112192
#111902
#111242
#111222
#110522