Finite Group Databasebeta

← #416100

Subgroups — #416100

Order 512.

1100 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2C2×#1949C211yesmaximal, characteristic
3C2×#1948C211yesmaximal, characteristic
4#13783C211yesmaximal, characteristic
5#11328C211yesmaximal, characteristic
6#11327C211yesmaximal, characteristic
7#11327C211yesmaximal, characteristic
8#11327C211yesmaximal, characteristic
9#11220C211yesmaximal, characteristic
10#11220C211yesmaximal, characteristic
11#11220C211yesmaximal, characteristic
12#11219C211yesmaximal, characteristic
13#10850C211yesmaximal, characteristic
14#10849C211yesmaximal, characteristic
15#10833C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22#2647—24no—
23#2647—24no—
24C2×#400—21no—
25C2×#400—21no—
26C2×#398—21no—
27C2×#398—21no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×#376C2211yescharacteristic
39#1949—24no—
40#1948—24no—
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55C2×#336C2211yescharacteristic
56C2×#336C2211yescharacteristic
57#1436—21no—
58#1436—21no—
59C4⋊#95—21no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62#1434—21no—
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
83C22×C42—21no—
84C22×C42—21no—
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C2×#107—22no—
89C2×#107—22no—
90C2×#107—41no—
91C2×#106—22no—
92C2×#106—22no—
93C2×#106—22no—
94C2×#106—22no—
95C2×#106—22no—
96C2×#106—22no—
97C2×#106—41no—
98C2×#106—41no—
99C2×#106—41no—
100C2×C4⋊C8—22no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—22no—
104C2×C4⋊C8Q814yes—
105C2×C4⋊C8Q814yes—
106#400—28no—
107#400—28no—
108#398—28no—
109#398—28no—
110#389—22no—
111#389—22no—
112#389—22no—
113#389—22no—
114#389—22no—
115#389—22no—
116#389—22no—
117#389—22no—
118#389—22no—
119#389—22no—
120#389—22no—
121#389—22no—
122#384—22no—
123#384D414yes—
124#382—22no—
125#382D414yes—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
129C4×C4⋊C4Q814yes—
130#376—22no—
131#376—22no—
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×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95D411yescharacteristic
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—41no—
159#340—41no—
160#340—41no—
161#340—41no—
162#336—41no—
163#336—41no—
164#336—41no—
165#336—41no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2411yescharacteristic
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—21no—
204C22×C8—21no—
205C22×C8C2×Q812yes—
206C22×C8C2×Q812yes—
207C22×C8C2×Q812yes—
208C22×C8C2×Q812yes—
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—21no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—81no—
256C2×C4⋊C4—81no—
257C2×C4⋊C4—81no—
258C2×C4⋊C4—81no—
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⋊C4#4112yes—
278C2×C4⋊C4#4112yes—
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—42no—
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×C42C2×Q812yes—
304C2×C42#4112yes—
305#107—44no—
306#106—44no—
307#106—44no—
308#106—44no—
309C4⋊C8—28no—
310C4⋊C8—28no—
311#95—24no—
312#95—24no—
313#95—24no—
314#95—24no—
315#95—24no—
316#95—24no—
317#95—24no—
318#95—24no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—24no—
324#95—42no—
325#95—81no—
326#95—81no—
327#95—81no—
328#95—81no—
329C24C22×D411yescharacteristic
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
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—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
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—41no—
421C22×C4—41no—
422C22×C4#12012yes—
423C22×C4#12012yes—
424C22×C4C22⋊Q812yes—
425C22×C4C22⋊Q812yes—
426C22×C4C4⋊Q812yes—
427C22×C4C4⋊Q812yes—
428C22×C4C22×D411yescharacteristic
429C22×C4C22×D411yescharacteristic
430C22×C4C22×Q811yescharacteristic
431C22×C4C22×Q811yescharacteristic
432C22×C4C22×Q811yescharacteristic
433C22×C4C2×#4111yescharacteristic
434C22×C4C2×#4111yescharacteristic
435C22×C4C2×#4111yescharacteristic
436C22×C4C2×#4111yescharacteristic
437C22×C4C2×#4111yescharacteristic
438C22×C4H(5,𝔽2)11yescharacteristic
439C22×C4H(5,𝔽2)11yescharacteristic
440C22×C42−1+411yescharacteristic
441C22×C42−1+411yescharacteristic
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
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—
468C2×C8—41no—
469C2×C8—41no—
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—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
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—41no—
501C4⋊C4—84no—
502C4⋊C4—84no—
503C4⋊C4—84no—
504C4⋊C4—84no—
505C4⋊C4—84no—
506C4⋊C4—84no—
507C4⋊C4—84no—
508C4⋊C4—84no—
509C4⋊C4#12514yes—
510C42—41no—
511C42—41no—
512C42—41no—
513C42—41no—
514C42—41no—
515C42—41no—
516C42—41no—
517C42—41no—
518C42—84no—
519C42—84no—
520C42C22⋊Q814yes—
521C42C22⋊Q814yes—
522C42C4⋊Q814yes—
523C42C4⋊Q814yes—
524C23C2×#12011yescharacteristic
525C23C2×C22⋊Q811yescharacteristic
526C23#52511yescharacteristic
527C23#52511yescharacteristic
528C23C2×C4⋊Q811yescharacteristic
529C23#53711yescharacteristic
530C23#53711yescharacteristic
531C23#57611yescharacteristic
532C23#57711yescharacteristic
533C23#57711yescharacteristic
534C23#57711yescharacteristic
535C23#57711yescharacteristic
536C23#57711yescharacteristic
537C23#57711yescharacteristic
538C23#57811yescharacteristic
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—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
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×C4#39514yes—
636C2×C4#39514yes—
637C2×C4C2×C22⋊Q811yescharacteristic
638C2×C4C2×C22⋊Q811yescharacteristic
639C2×C4C2×#12511yescharacteristic
640C2×C4#52911yescharacteristic
641C2×C4#52911yescharacteristic
642C2×C4C2×C4⋊Q811yescharacteristic
643C2×C4C2×C4⋊Q811yescharacteristic
644C2×C4#53311yescharacteristic
645C2×C4#54011yescharacteristic
646C2×C4#54111yescharacteristic
647C2×C4#54411yescharacteristic
648C2×C4#54411yescharacteristic
649C2×C4#54611yescharacteristic
650C2×C4#54611yescharacteristic
651C2×C4#54711yescharacteristic
652C2×C4#54711yescharacteristic
653C2×C4#54811yescharacteristic
654C2×C4#54811yescharacteristic
655C2×C4#55011yescharacteristic
656C2×C4#55011yescharacteristic
657C2×C4#55411yescharacteristic
658C2×C4#55411yescharacteristic
659C2×C4#55411yescharacteristic
660C2×C4#55411yescharacteristic
661C2×C4#55711yescharacteristic
662C2×C4#55711yescharacteristic
663C2×C4#55711yescharacteristic
664C2×C4#55711yescharacteristic
665C8—42no—
666C8—42no—
667C8—42no—
668C8—42no—
669C22C2×#39511yescharacteristic
670C22#240711yescharacteristic
671C22#240711yescharacteristic
672C22#258411yescharacteristic
673C22#258411yescharacteristic
674C22#262911yescharacteristic
675C22#285111yescharacteristic
676C22#300911yescharacteristic
677C22#301011yescharacteristic
678C22#301211yescharacteristic
679C22#301311yescharacteristic
680C22#308111yescharacteristic
681C22#308211yescharacteristic
682C22#308411yescharacteristic
683C22#308411yescharacteristic
684C22#311811yescharacteristic
685C22#311911yescharacteristic
686C22#312011yescharacteristic
687C22#312111yescharacteristic
688C22#312311yescharacteristic
689C22#312511yescharacteristic
690C22#312511yescharacteristic
691C22#312611yescharacteristic
692C22#316311yescharacteristic
693C22#316311yescharacteristic
694C22#316311yescharacteristic
695C22#316411yescharacteristic
696C22#325711yescharacteristic
697C22#325711yescharacteristic
698C22#325811yescharacteristic
699C22#325811yescharacteristic
700C22#326011yescharacteristic
701C22#326011yescharacteristic
702C22#326311yescharacteristic
703C22#326311yescharacteristic
704C4—24no—
705C4—24no—
706C4—44no—
707C4—82no—
708C4—81no—
709C4—82no—
710C4—81no—
711C4—82no—
712C4—82no—
713C4—81no—
714C4—82no—
715C4—82no—
716C4—81no—
717C4—82no—
718C4#245311yescharacteristic
719C4#245311yescharacteristic
720C4#245411yescharacteristic
721C4#245411yescharacteristic
722C4#255011yescharacteristic
723C4#255011yescharacteristic
724C4#255211yescharacteristic
725C4#255211yescharacteristic
726C2#1521811yescharacteristic
727C2#2355611yescharacteristic
728C2#2355711yescharacteristic
729C2#2416311yescharacteristic
730C2#2416411yescharacteristic
731C2#2416611yescharacteristic
732C2#2416911yescharacteristic
733C2#2932311yescharacteristic
734C2#2932411yescharacteristic
735C2#2932511yescharacteristic
736C2#2932711yescharacteristic
737C2#3000311yescharacteristic
738C2#3000411yescharacteristic
739C2#3307511yescharacteristic
740C2#3307611yescharacteristic
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×#26472
C2×#19492
C2×#19482
#137832
#113282
#113272
#112202
#112192
#108502
#108492
#108332