Finite Group Databasebeta

← #644189

Subgroups — #644189

Order 512.

1726 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16908C214yesmaximal
2#16905C214yesmaximal
3#15242C212yesmaximal
4#15232C212yesmaximal
5#15232C212yesmaximal
6#15232C212yesmaximal
7#15231C212yesmaximal
8#15225C212yesmaximal
9#14687C211yesmaximal, characteristic
10#14266C212yesmaximal
11#14266C212yesmaximal
12#14151C211yesmaximal, characteristic
13#14151C211yesmaximal, characteristic
14#13911C211yesmaximal, characteristic
15#13910C211yesmaximal, characteristic
16C4×#382C211yesmaximal, characteristic
17#13755C211yesmaximal, characteristic
18C2×#389C2212yes—
19C2×#389C2212yes—
20C2×#389C2212yes—
21C2×#389C2212yes—
22C2×#389C2212yes—
23C2×#389C2212yes—
24C2×#384C2211yescharacteristic
25C2×#384C2211yescharacteristic
26C2×#384C2212yes—
27C2×#382C2211yescharacteristic
28C2×#382C2211yescharacteristic
29C2×#382C2212yes—
30C2×#382C2212yes—
31C2×#382C2212yes—
32C2×C4×C4⋊C4C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×#376C2212yes—
37C2×C43C2211yescharacteristic
38#1445C2214yes—
39#1445C2214yes—
40#1445C2214yes—
41#1445C2214yes—
42#1444C2214yes—
43#1443C2214yes—
44#1443C2214yes—
45#1443C2214yes—
46#1443C2214yes—
47#1442C2214yes—
48#1442C2214yes—
49#1442C2214yes—
50#1442C2214yes—
51#1442C2214yes—
52#1441C2214yes—
53#1441C2214yes—
54#1441C2214yes—
55#1441C2214yes—
56#1441C2214yes—
57#1441C2214yes—
58C4⋊#95C2212yes—
59C4⋊#95C2212yes—
60C4⋊#95C2212yes—
61C4⋊#95C2212yes—
62C4⋊#95C2212yes—
63C4⋊#95C2212yes—
64C4⋊#95C2212yes—
65C4⋊#95C2212yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2211yescharacteristic
71C4⋊#95C2211yescharacteristic
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2211yescharacteristic
76#1434C2212yes—
77#1434C2212yes—
78#1434C2212yes—
79#1434C2212yes—
80C4×#95C2212yes—
81C4×#95C2212yes—
82C4×#95C2212yes—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2314yes—
98C22×C4⋊C4C2314yes—
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2314yes—
101C22×C42C2312yes—
102C22×C42C2312yes—
103C22×C42C2312yes—
104C22×C42C2312yes—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C22×C42C2311yescharacteristic
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112#389—28no—
113#389—28no—
114#389—44no—
115#389—44no—
116#389—44no—
117#389—44no—
118#384—24no—
119#384—24no—
120#384—44no—
121#382—24no—
122#382—24no—
123#382—44no—
124#382—44no—
125#382—44no—
126C4×C4⋊C4—24no—
127C4×C4⋊C4—24no—
128C4×C4⋊C4—24no—
129C4×C4⋊C4—24no—
130#376—44no—
131C2×#95C2312yes—
132C2×#95C2312yes—
133C2×#95C2312yes—
134C2×#95C2312yes—
135C2×#95C2312yes—
136C2×#95C2312yes—
137C2×#95C2312yes—
138C2×#95C2312yes—
139C2×#95C2314yes—
140C2×#95C2314yes—
141C2×#95C2312yes—
142C2×#95C2312yes—
143C2×#95C2312yes—
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2312yes—
147C2×#95C2312yes—
148C2×#95C2312yes—
149C2×#95C2312yes—
150C2×#95C2312yes—
151C2×#95C2312yes—
152C2×#95C2312yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C43Q818yes—
168C23×C4C2414yes—
169C23×C4C2412yes—
170C23×C4C2414yes—
171C23×C4C2412yes—
172C23×C4C2412yes—
173C23×C4C2412yes—
174C23×C4C2412yes—
175C23×C4C2412yes—
176C23×C4C2411yescharacteristic
177C23×C4C2411yescharacteristic
178C23×C4C2411yescharacteristic
179C23×C4C2411yescharacteristic
180C23×C4C2412yes—
181C23×C4C2412yes—
182C23×C4C2411yescharacteristic
183C23×C4C2411yescharacteristic
184C23×C4C2411yescharacteristic
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—24no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—28no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—42no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—42no—
227C2×C4⋊C4—44no—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—44no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—44no—
232C2×C4⋊C4—44no—
233C2×C4⋊C4—44no—
234C2×C4⋊C4—44no—
235C2×C4⋊C4—44no—
236C2×C4⋊C4—44no—
237C2×C4⋊C4#4114yes—
238C2×C4⋊C4#4114yes—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—24no—
248C2×C42—24no—
249C2×C42—24no—
250C2×C42—24no—
251C2×C42—24no—
252C2×C42—24no—
253C2×C42—24no—
254C2×C42—24no—
255C2×C42—24no—
256C2×C42—24no—
257C2×C42—24no—
258C2×C42—24no—
259C2×C42—41no—
260C2×C42—41no—
261C2×C42—41no—
262C2×C42—41no—
263C2×C42C2×Q814yes—
264C2×C42C2×Q814yes—
265C2×C42C2×Q814yes—
266C2×C42C2×Q814yes—
267C2×C42C2×Q814yes—
268C2×C42C2×Q814yes—
269C2×C42C2×Q814yes—
270C2×C42#4114yes—
271C2×C42#4114yes—
272#95—24no—
273#95—24no—
274#95—24no—
275#95—24no—
276#95—24no—
277#95—24no—
278#95—24no—
279#95—24no—
280#95—28no—
281#95—28no—
282#95—42no—
283#95—44no—
284#95—42no—
285#95—42no—
286#95—42no—
287#95—42no—
288#95—42no—
289#95—42no—
290#95—42no—
291#95—44no—
292#95—44no—
293#95—44no—
294#95—42no—
295#95—42no—
296#95—42no—
297#95—42no—
298#95—44no—
299#95—44no—
300#95—44no—
301#95—44no—
302#95—44no—
303#95—44no—
304#95—44no—
305#95—44no—
306#95—44no—
307#95—44no—
308C24C2511yescharacteristic
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—22no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4C22×Q812yes—
406C22×C4C22×Q812yes—
407C22×C4C22×Q812yes—
408C22×C4C22×Q812yes—
409C22×C4C22×Q812yes—
410C22×C4C22×Q812yes—
411C22×C4C22×Q812yes—
412C22×C4C2×#4114yes—
413C22×C4C2×#4114yes—
414C22×C4C2×#4112yes—
415C22×C4C2×#4112yes—
416C22×C4C2×#4112yes—
417C22×C4C2×#4112yes—
418C22×C4C2×#4112yes—
419C22×C4C2×#4112yes—
420C22×C4C2×#4112yes—
421C22×C4C2×#4112yes—
422C22×C4H(5,𝔽2)12yes—
423C22×C4H(5,𝔽2)12yes—
424C22×C4H(5,𝔽2)12yes—
425C22×C42−1+412yes—
426C22×C42−1+412yes—
427C22×C42−1+412yes—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—44no—
431C4⋊C4—48no—
432C4⋊C4—48no—
433C4⋊C4—44no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C4⋊C4—44no—
437C4⋊C4—44no—
438C4⋊C4—48no—
439C4⋊C4—48no—
440C4⋊C4—84no—
441C4⋊C4—84no—
442C4⋊C4—88no—
443C4⋊C4—88no—
444C4⋊C4—88no—
445C4⋊C4—88no—
446C42—28no—
447C42—28no—
448C42—28no—
449C42—28no—
450C42—44no—
451C42—44no—
452C42—48no—
453C42—48no—
454C42—48no—
455C42—48no—
456C42#125116yes—
457C23C23×Q811yescharacteristic
458C23C22×#4111yescharacteristic
459C23C22×#4111yescharacteristic
460C23C22×#4111yescharacteristic
461C23C22×#4111yescharacteristic
462C23C2×H(5,𝔽2)11yescharacteristic
463C23C2×H(5,𝔽2)11yescharacteristic
464C23C2×H(5,𝔽2)11yescharacteristic
465C23C2×2−1+411yescharacteristic
466C23C2×2−1+411yescharacteristic
467C23C2×2−1+411yescharacteristic
468C23#58511yescharacteristic
469C23#58511yescharacteristic
470C23#58511yescharacteristic
471C23#58511yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
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—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—44no—
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—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—44no—
564C2×C4—44no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4C2×#12514yes—
577C2×C4C2×#12514yes—
578C2×C4C2×#12514yes—
579C2×C4#53314yes—
580C2×C4#54014yes—
581C2×C4#54114yes—
582C2×C4#54214yes—
583C2×C4#54214yes—
584C2×C4#54414yes—
585C2×C4#54414yes—
586C2×C4#54414yes—
587C2×C4#55214yes—
588C2×C4#55314yes—
589C2×C4#55614yes—
590C2×C4#55914yes—
591C22C22×#12511yescharacteristic
592C22C2×#53311yescharacteristic
593C22C2×#54011yescharacteristic
594C22C2×#54111yescharacteristic
595C22C2×#54211yescharacteristic
596C22C2×#54211yescharacteristic
597C22C2×#54411yescharacteristic
598C22C2×#54411yescharacteristic
599C22C2×#54411yescharacteristic
600C22#345811yescharacteristic
601C22#345811yescharacteristic
602C22C2×#55211yescharacteristic
603C22C2×#55311yescharacteristic
604C22C2×#55611yescharacteristic
605C22C2×#55911yescharacteristic
606C22#351011yescharacteristic
607C22#351011yescharacteristic
608C22#351211yescharacteristic
609C22#351211yescharacteristic
610C22#351411yescharacteristic
611C22#351411yescharacteristic
612C22#351511yescharacteristic
613C22#351511yescharacteristic
614C22#351711yescharacteristic
615C22#351711yescharacteristic
616C22#351811yescharacteristic
617C22#351811yescharacteristic
618C22#354611yescharacteristic
619C22#354611yescharacteristic
620C22#354711yescharacteristic
621C22#354711yescharacteristic
622C22#355411yescharacteristic
623C22#355411yescharacteristic
624C22#355511yescharacteristic
625C22#355511yescharacteristic
626C4—24no—
627C4—44no—
628C4—44no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4—84no—
638C4—82no—
639C4—82no—
640C4—84no—
641C4#257018yes—
642C4#264718yes—
643C2C2×#264711yescharacteristic
644C2C2×#257011yescharacteristic
645C2#3519211yescharacteristic
646C2#3520211yescharacteristic
647C2#3533911yescharacteristic
648C2#3762411yescharacteristic
649C2#3762411yescharacteristic
650C2#3897711yescharacteristic
651C2#3897811yescharacteristic
652C2#3898611yescharacteristic
653C2#3898711yescharacteristic
654C2#3919311yescharacteristic
655C2#3919411yescharacteristic
656C2#3920211yescharacteristic
657C2#3920311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
#169082
#169052
#152422
#152322
#152312
#152252
#146872
#142662
#141512
#139112
#139102
C4×#3822
#137552