Finite Group Databasebeta

← #1395718

Subgroups — #1395718

Order 512.

2006 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2506C211yesmaximal, characteristic
2C2×#2369C211yesmaximal, characteristic
3#16678C212yesmaximal
4#16634C212yesmaximal
5#16387C214yesmaximal
6#16279C214yesmaximal
7#15230C211yesmaximal, characteristic
8#15225C212yesmaximal
9#15187C212yesmaximal
10#15156C211yesmaximal, characteristic
11#15128C211yesmaximal, characteristic
12#15080C212yesmaximal
13#14289C212yesmaximal
14#14030C212yesmaximal
15#13981C212yesmaximal
16#13921C211yesmaximal, characteristic
17C4×#400C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×#125C2212yes—
20#2506—28no—
21C2×#400C2212yes—
22C2×#400C2211yescharacteristic
23C2×#400C2212yes—
24C2×#398C2212yes—
25C2×#395C2212yes—
26#2369—28no—
27C2×#391C2214yes—
28C2×#389C2212yes—
29C2×#389C2212yes—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#387C2212yes—
36C2×#387C2214yes—
37C2×#384C2211yescharacteristic
38C2×#383C2212yes—
39C2×#382C2212yes—
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2212yes—
43C2×C4×C4⋊C4C2212yes—
44C2×C4×C4⋊C4C2211yescharacteristic
45#1446C2212yes—
46#1446C2214yes—
47#1445C2214yes—
48#1445C2211yescharacteristic
49#1445C2214yes—
50#1444C2212yes—
51#1443C2212yes—
52#1443C2214yes—
53#1443C2214yes—
54#1443C2214yes—
55#1443C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1442C2212yes—
59#1442C2211yescharacteristic
60#1442C2214yes—
61#1442C2214yes—
62#1441C2214yes—
63#1441C2212yes—
64#1441C2214yes—
65#1441C2212yes—
66#1441C2214yes—
67#1441C2211yescharacteristic
68#1441C2212yes—
69#1441C2214yes—
70#1441C2212yes—
71#1436C2214yes—
72#1436C2214yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80#1434C2214yes—
81#1434C2212yes—
82C4×#95C2212yes—
83C4×#95C2211yescharacteristic
84C4×#95C2212yes—
85C23×Q8C2312yes—
86C2×C4⋊Q8—28no—
87C2×C4⋊Q8—24no—
88C2×#125—28no—
89C2×#125—28no—
90C2×#125—44no—
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2314yes—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C42C2312yes—
111C22×C42C2312yes—
112C22×C42C2311yescharacteristic
113C22×C42C2311yescharacteristic
114C22×C42C2312yes—
115C22×C42C2311yescharacteristic
116C22×C42C2314yes—
117#400—24no—
118#400—28no—
119#400—44no—
120#398—28no—
121#395—44no—
122#391—216no—
123#389—28no—
124#389—24no—
125#389—24no—
126#389—24no—
127#389—28no—
128#389—28no—
129#389—24no—
130#387—28no—
131#387—48no—
132#384—24no—
133#383—44no—
134#382—28no—
135C4×C4⋊C4—28no—
136C4×C4⋊C4—28no—
137C4×C4⋊C4—24no—
138C4×C4⋊C4—24no—
139C4×C4⋊C4D418yes—
140C2×#95C2312yes—
141C2×#95C2312yes—
142C2×#95C2311yescharacteristic
143C2×#95C2311yescharacteristic
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2312yes—
147C2×#95C2312yes—
148C2×#95C2312yes—
149C2×#95C2312yes—
150C2×#95C2312yes—
151C2×#95C2311yescharacteristic
152C2×#95C2312yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2312yes—
159C2×#95C2314yes—
160C2×#95C2311yescharacteristic
161C2×#95C2314yes—
162C2×#95C2312yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C22×Q8—24no—
179C22×Q8—28no—
180C22×Q8—42no—
181C22×Q8—44no—
182C22×Q8—42no—
183C23×C4C2412yes—
184C23×C4C2412yes—
185C23×C4C2412yes—
186C23×C4C2414yes—
187C23×C4C2411yescharacteristic
188C23×C4C2412yes—
189C23×C4C2412yes—
190C23×C4C2412yes—
191C23×C4C2412yes—
192C23×C4C2411yescharacteristic
193C23×C4C2411yescharacteristic
194C23×C4C2411yescharacteristic
195C23×C4C2414yes—
196C23×C4C2411yescharacteristic
197C23×C4C2412yes—
198C23×C4C2411yescharacteristic
199C23×C4C2411yescharacteristic
200C4⋊Q8—232no—
201#125—432no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—28no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—28no—
242C2×C4⋊C4—41no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—42no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4C2×D414yes—
252C2×C4⋊C4C2×D414yes—
253C2×C4⋊C4#4114yes—
254C2×C4⋊C4#4118yes—
255C2×C42—24no—
256C2×C42—24no—
257C2×C42—24no—
258C2×C42—24no—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42—24no—
262C2×C42—24no—
263C2×C42—24no—
264C2×C42—24no—
265C2×C42—22no—
266C2×C42—22no—
267C2×C42—24no—
268C2×C42—24no—
269C2×C42—28no—
270C2×C42—44no—
271C2×C42—44no—
272C2×C42C2×D418yes—
273C2×C42C2×D414yes—
274#95—22no—
275#95—28no—
276#95—28no—
277#95—24no—
278#95—22no—
279#95—24no—
280#95—24no—
281#95—24no—
282#95—24no—
283#95—28no—
284#95—28no—
285#95—28no—
286#95—22no—
287#95—24no—
288#95—24no—
289#95—22no—
290#95—24no—
291#95—24no—
292#95—24no—
293#95—24no—
294#95—28no—
295#95—42no—
296#95—44no—
297#95—44no—
298#95—42no—
299#95—44no—
300#95—42no—
301#95—42no—
302#95—44no—
303#95—44no—
304#95—44no—
305#95—44no—
306#95—44no—
307#95—44no—
308#95—42no—
309#95—44no—
310#95—44no—
311#95C2×D418yes—
312C24C2511yescharacteristic
313C2×Q8—216no—
314C2×Q8—84no—
315C2×Q8—84no—
316C2×Q8—88no—
317C2×Q8—88no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—24no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—24no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—22no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4C22×D412yes—
406C22×C4C22×D414yes—
407C22×C4C22×D414yes—
408C22×C4C22×D412yes—
409C22×C4C22×D412yes—
410C22×C4C2×#4118yes—
411C22×C4C2×#4112yes—
412C22×C4C2×#4112yes—
413C22×C4C2×#4112yes—
414C22×C4C2×#4114yes—
415C22×C4H(5,𝔽2)12yes—
416C22×C4H(5,𝔽2)12yes—
417C22×C42−1+414yes—
418C22×C42−1+414yes—
419C22×C42−1+412yes—
420C22×C42−1+412yes—
421C4⋊C4—28no—
422C4⋊C4—216no—
423C4⋊C4—216no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—48no—
428C4⋊C4—44no—
429C4⋊C4—416no—
430C4⋊C4—48no—
431C4⋊C4—48no—
432C4⋊C4—48no—
433C4⋊C4—48no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C4⋊C4—48no—
437C4⋊C4—44no—
438C4⋊C4—48no—
439C4⋊C4—88no—
440C42—28no—
441C42—216no—
442C42—44no—
443C42—48no—
444C42—44no—
445C42—48no—
446C42—88no—
447C23C23×D411yescharacteristic
448C23C22×#4112yes—
449C23C22×#4111yescharacteristic
450C23C2×H(5,𝔽2)11yescharacteristic
451C23C2×H(5,𝔽2)11yescharacteristic
452C23C2×2−1+411yescharacteristic
453C23C2×2−1+411yescharacteristic
454C23C2×2−1+412yes—
455C23C2×2−1+412yes—
456C23#58511yescharacteristic
457C23#58512yes—
458Q8—816no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—28no—
482C2×C4—28no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—41no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4#52514yes—
557C2×C4#53614yes—
558C2×C4#53614yes—
559C2×C4#54118yes—
560C2×C4#54118yes—
561C2×C4#54614yes—
562C22C2×#52511yescharacteristic
563C22C2×#53611yescharacteristic
564C22C2×#53611yescharacteristic
565C22C2×#54112yes—
566C22C2×#54112yes—
567C22C2×#54611yescharacteristic
568C22#348212yes—
569C22#348611yescharacteristic
570C22#348811yescharacteristic
571C22#350011yescharacteristic
572C22#350711yescharacteristic
573C22#351111yescharacteristic
574C22#351312yes—
575C22#351812yes—
576C22#352112yes—
577C22#352212yes—
578C22#354711yescharacteristic
579C22#354712yes—
580C22#354811yescharacteristic
581C22#355212yes—
582C22#355512yes—
583C22#355512yes—
584C22#356312yes—
585C4—24no—
586C4—44no—
587C4—44no—
588C4—42no—
589C4—44no—
590C4—42no—
591C4—42no—
592C4—48no—
593C4—42no—
594C4—82no—
595C4—82no—
596C4—81no—
597C4—82no—
598C4—82no—
599C4—82no—
600C4—84no—
601C4#263418yes—
602C2C2×#263411yescharacteristic
603C2#3598211yescharacteristic
604C2#3642211yescharacteristic
605C2#3895811yescharacteristic
606C2#3947011yescharacteristic
607C2#4010712yes—
608C2#4022712yes—
609C2#4262612yes—
610C2#4278012yes—
611C2#4279311yescharacteristic
612C2#4281411yescharacteristic
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
C2×#25062
C2×#23692
#166782
#166342
#163872
#162792
#152302
#152252
#151872
#151562
#151282
#150802
#142892
#140302
#139812
#139212
C4×#4002