Finite Group Databasebeta

← #403586

Subgroups — #403586

Order 512.

1126 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2330C211yesmaximal, characteristic
2C2×#2087C211yesmaximal, characteristic
3C2×#2086C211yesmaximal, characteristic
4#14266C211yesmaximal, characteristic
5#11385C211yesmaximal, characteristic
6#11385C211yesmaximal, characteristic
7#11324C211yesmaximal, characteristic
8#11267C211yesmaximal, characteristic
9#11228C211yesmaximal, characteristic
10#11227C211yesmaximal, characteristic
11#10907C211yesmaximal, characteristic
12#10907C211yesmaximal, characteristic
13#10885C211yesmaximal, characteristic
14#10884C211yesmaximal, characteristic
15#10833C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21#2330—24no—
22#2330—24no—
23C2×#389—21no—
24C2×#389—21no—
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#387—21no—
30C2×#387—21no—
31C2×#384C2211yescharacteristic
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×#376C2211yescharacteristic
35#2087—24no—
36#2086—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1445—21no—
56#1443—21no—
57#1442—21no—
58#1441—21no—
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×#125—22no—
68C2×#125—22no—
69C2×#125—22no—
70C2×#125—22no—
71C2×#125—22no—
72C2×#125Q814yes—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C42—21no—
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C2×#107—22no—
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#107—41no—
99C2×#107—41no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8—41no—
105C2×C4⋊C8—41no—
106#389—28no—
107#389—28no—
108#389—22no—
109#389—22no—
110#389—22no—
111#389—22no—
112#389—22no—
113#389D414yes—
114#389D414yes—
115#389Q814yes—
116#387—28no—
117#387—28no—
118#384—22no—
119#384—22no—
120C4×C4⋊C4—22no—
121C4×C4⋊C4—22no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124#376—22no—
125#376—22no—
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×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95D411yescharacteristic
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—41no—
157#340—41no—
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
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×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2411yescharacteristic
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×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8#4112yes—
204C22×C8#4112yes—
205#125—28no—
206#125—28no—
207#125—28no—
208#125—28no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
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—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—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—81no—
260C2×C4⋊C4—81no—
261C2×C4⋊C4—81no—
262C2×C4⋊C4—81no—
263C2×C4⋊C4—81no—
264C2×C4⋊C4—81no—
265C2×C4⋊C4—81no—
266C2×C4⋊C4—81no—
267C2×C4⋊C4—81no—
268C2×C4⋊C4—81no—
269C2×C4⋊C4—81no—
270C2×C4⋊C4—81no—
271C2×C4⋊C4C2×D412yes—
272C2×C4⋊C4C2×D412yes—
273C2×C4⋊C4C2×D412yes—
274C2×C4⋊C4C2×D412yes—
275C2×C4⋊C4C2×Q812yes—
276C2×C4⋊C4C2×Q812yes—
277C2×C4⋊C4C2×Q812yes—
278C2×C4⋊C4C2×Q812yes—
279C2×C4⋊C4#4112yes—
280C2×C4⋊C4#4112yes—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—24no—
294C2×C42—24no—
295C2×C42—81no—
296C2×C42—81no—
297C2×C42—81no—
298C2×C42—81no—
299C2×C42C2×D412yes—
300C2×C42C2×D412yes—
301C2×C42C2×Q812yes—
302C2×C42C2×Q812yes—
303C2×C42#4112yes—
304C2×C42#4112yes—
305#107—44no—
306#107—44no—
307C4⋊C8—44no—
308C4⋊C8—44no—
309#95—24no—
310#95—24no—
311#95—24no—
312#95—24no—
313#95—22no—
314#95—22no—
315#95—22no—
316#95—22no—
317#95—24no—
318#95—42no—
319#95—81no—
320#95—81no—
321#95—81no—
322#95—81no—
323#95—81no—
324#95—81no—
325#95—81no—
326#95—81no—
327C24C22×D411yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
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—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
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—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
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#12012yes—
421C22×C4#12012yes—
422C22×C4C22⋊Q812yes—
423C22×C4C22⋊Q812yes—
424C22×C4C22⋊Q812yes—
425C22×C4C22⋊Q812yes—
426C22×C4C22×D411yescharacteristic
427C22×C4C22×D411yescharacteristic
428C22×C4C22×Q811yescharacteristic
429C22×C4C22×Q811yescharacteristic
430C22×C4C2×#4111yescharacteristic
431C22×C4C2×#4111yescharacteristic
432C22×C4C2×#4111yescharacteristic
433C22×C4C2×#4111yescharacteristic
434C22×C4C2×#4111yescharacteristic
435C22×C4C2×#4111yescharacteristic
436C22×C4H(5,𝔽2)11yescharacteristic
437C22×C42−1+411yescharacteristic
438C22×C42−1+411yescharacteristic
439C22×C42−1+411yescharacteristic
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—41no—
447C2×C8—41no—
448C2×C8—41no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—41no—
468C4⋊C4—216no—
469C4⋊C4—216no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—84no—
501C4⋊C4—84no—
502C4⋊C4—84no—
503C4⋊C4—84no—
504C4⋊C4—84no—
505C4⋊C4—84no—
506C4⋊C4C22⋊Q814yes—
507C4⋊C4C22⋊Q814yes—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—84no—
521C42—84no—
522C23C2×#12011yescharacteristic
523C23C2×C22⋊Q811yescharacteristic
524C23C2×C22⋊Q811yescharacteristic
525C23#52511yescharacteristic
526C23#53211yescharacteristic
527C23#53611yescharacteristic
528C23#53711yescharacteristic
529C23#57611yescharacteristic
530C23#57611yescharacteristic
531C23#57611yescharacteristic
532C23#57711yescharacteristic
533C23#57711yescharacteristic
534C23#57811yescharacteristic
535C23#57811yescharacteristic
536C23#57811yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
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—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—81no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
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×C4C2×C22⋊Q811yescharacteristic
636C2×C4C2×C22⋊Q811yescharacteristic
637C2×C4#52511yescharacteristic
638C2×C4#52511yescharacteristic
639C2×C4#52911yescharacteristic
640C2×C4#52911yescharacteristic
641C2×C4#53311yescharacteristic
642C2×C4#53311yescharacteristic
643C2×C4#54111yescharacteristic
644C2×C4#54111yescharacteristic
645C2×C4#54211yescharacteristic
646C2×C4#54211yescharacteristic
647C2×C4#54611yescharacteristic
648C2×C4#54611yescharacteristic
649C2×C4#54711yescharacteristic
650C2×C4#54711yescharacteristic
651C2×C4#54811yescharacteristic
652C2×C4#54811yescharacteristic
653C2×C4D4×Q811yescharacteristic
654C2×C4D4×Q811yescharacteristic
655C2×C4#55211yescharacteristic
656C2×C4#55211yescharacteristic
657C2×C4#55711yescharacteristic
658C2×C4#55711yescharacteristic
659C2×C4#55711yescharacteristic
660C2×C4#55711yescharacteristic
661C2×C4Q8211yescharacteristic
662C2×C4#55911yescharacteristic
663C8—42no—
664C8—42no—
665C8—81no—
666C8—81no—
667C22#239611yescharacteristic
668C22#240911yescharacteristic
669C22#243011yescharacteristic
670C22#256511yescharacteristic
671C22#258211yescharacteristic
672C22#263711yescharacteristic
673C22#284811yescharacteristic
674C22#300811yescharacteristic
675C22#301111yescharacteristic
676C22#301211yescharacteristic
677C22#301311yescharacteristic
678C22#308111yescharacteristic
679C22#308211yescharacteristic
680C22#308311yescharacteristic
681C22#308311yescharacteristic
682C22#308311yescharacteristic
683C22#308311yescharacteristic
684C22#308311yescharacteristic
685C22#308411yescharacteristic
686C22#311911yescharacteristic
687C22#312011yescharacteristic
688C22#312411yescharacteristic
689C22#312411yescharacteristic
690C22#317611yescharacteristic
691C22#317711yescharacteristic
692C22#317811yescharacteristic
693C22#317911yescharacteristic
694C22#324111yescharacteristic
695C22#324211yescharacteristic
696C22#324311yescharacteristic
697C22#324311yescharacteristic
698C22#325711yescharacteristic
699C22#325811yescharacteristic
700C22#325911yescharacteristic
701C22#326111yescharacteristic
702C4—42no—
703C4—42no—
704C4—42no—
705C4—44no—
706C4—42no—
707C4—44no—
708C4—42no—
709C4—42no—
710C4—82no—
711C4—82no—
712C4—82no—
713C4—82no—
714C4—161no—
715C4—161no—
716C4#245111yescharacteristic
717C4#245111yescharacteristic
718C4#245311yescharacteristic
719C4#245311yescharacteristic
720C4#245811yescharacteristic
721C4#245811yescharacteristic
722C4#246211yescharacteristic
723C4#246211yescharacteristic
724C2#1487811yescharacteristic
725C2#2379111yescharacteristic
726C2#2379211yescharacteristic
727C2#2430811yescharacteristic
728C2#2431111yescharacteristic
729C2#2550811yescharacteristic
730C2#2551211yescharacteristic
731C2#2918611yescharacteristic
732C2#2918811yescharacteristic
733C2#2929211yescharacteristic
734C2#2929411yescharacteristic
735C2#3016111yescharacteristic
736C2#3016411yescharacteristic
737C2#3296311yescharacteristic
738C2#3296811yescharacteristic
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×#23302
C2×#20872
C2×#20862
#142662
#113852
#113242
#112672
#112282
#112272
#109072
#108852
#108842
#108332