Finite Group Databasebeta

← #719567

Subgroups — #719567

Order 512.

2014 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2511C212yesmaximal
2#16421C214yesmaximal
3#15876C214yesmaximal
4#15663C214yesmaximal
5#15192C212yesmaximal
6#15156C212yesmaximal
7#14967C214yesmaximal
8#14276C211yesmaximal, characteristic
9#13942C211yesmaximal, characteristic
10#13926C211yesmaximal, characteristic
11#13910C211yesmaximal, characteristic
12#13884C212yesmaximal
13#13856C211yesmaximal, characteristic
14#13804C211yesmaximal, characteristic
15#13786C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17#2511—216no—
18C2×#400C2214yes—
19C2×#400C2214yes—
20C2×#400C2214yes—
21C2×#391C2211yescharacteristic
22C2×#391C2212yes—
23C2×#391C2212yes—
24C2×#391C2211yescharacteristic
25C2×#389C2212yes—
26C2×#389C2214yes—
27C2×#387C2214yes—
28C2×#387C2214yes—
29C2×#387C2214yes—
30C2×#384C2212yes—
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4C2212yes—
34C2×C4×C4⋊C4C2212yes—
35C2×C4×C4⋊C4C2211yescharacteristic
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2212yes—
38C2×C4×C4⋊C4C2211yescharacteristic
39C2×#376C2211yescharacteristic
40#1445C2214yes—
41#1444C2212yes—
42#1444C2212yes—
43#1444C2212yes—
44#1444C2212yes—
45#1444C2212yes—
46#1444C2212yes—
47#1443C2214yes—
48#1443C2214yes—
49#1443C2214yes—
50#1443C2214yes—
51#1442C2214yes—
52#1442C2214yes—
53#1441C2214yes—
54#1441C2214yes—
55#1441C2214yes—
56#1441C2212yes—
57#1441C2214yes—
58#1441C2214yes—
59#1441C2212yes—
60#1436C2214yes—
61#1436C2214yes—
62#1436C2214yes—
63C4⋊#95C2214yes—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2212yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2211yescharacteristic
70C4⋊#95C2212yes—
71#1434C2212yes—
72#1434C2214yes—
73#1434C2212yes—
74#1434C2212yes—
75C4×#95C2212yes—
76C23×Q8C2311yescharacteristic
77C2×C4×Q8—24no—
78C2×C4×Q8—24no—
79C2×C4×Q8—24no—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2312yes—
84C22×C4⋊C4C2312yes—
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2312yes—
88C22×C4⋊C4C2312yes—
89C22×C4⋊C4C2314yes—
90C22×C4⋊C4C2312yes—
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2314yes—
94C22×C4⋊C4C2314yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C42C2312yes—
98C22×C42C2312yes—
99C22×C42C2312yes—
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C22×C42C2312yes—
103C22×C42C2314yes—
104C22×C42C2311yescharacteristic
105#400—216no—
106#400—216no—
107#400—48no—
108#391—28no—
109#391—28no—
110#391—24no—
111#391D418yes—
112#389—28no—
113#389—48no—
114#387—216no—
115#387—216no—
116#387—48no—
117#384—28no—
118#384—24no—
119#382—24no—
120C4×C4⋊C4—28no—
121C4×C4⋊C4—28no—
122C4×C4⋊C4—28no—
123C4×C4⋊C4—24no—
124C4×C4⋊C4—24no—
125C4×C4⋊C4—24no—
126#376—24no—
127C2×#95C2314yes—
128C2×#95C2314yes—
129C2×#95C2312yes—
130C2×#95C2314yes—
131C2×#95C2314yes—
132C2×#95C2314yes—
133C2×#95C2314yes—
134C2×#95C2314yes—
135C2×#95C2311yescharacteristic
136C2×#95C2312yes—
137C2×#95C2314yes—
138C2×#95C2312yes—
139C2×#95C2312yes—
140C2×#95C2312yes—
141C2×#95C2311yescharacteristic
142C2×#95C2311yescharacteristic
143C2×#95C2311yescharacteristic
144C2×#95C2314yes—
145C2×#95C2314yes—
146C2×#95C2314yes—
147C2×#95C2312yes—
148C2×#95C2312yes—
149C2×#95C2312yes—
150C2×#95C2312yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C22×Q8—22no—
161C22×Q8—22no—
162C22×Q8—22no—
163C22×Q8—22no—
164C22×Q8—22no—
165C22×Q8—22no—
166C22×Q8C2×D414yes—
167C23×C4C2414yes—
168C23×C4C2412yes—
169C23×C4C2414yes—
170C23×C4C2412yes—
171C23×C4C2412yes—
172C23×C4C2412yes—
173C23×C4C2412yes—
174C23×C4C2412yes—
175C23×C4C2412yes—
176C23×C4C2412yes—
177C23×C4C2412yes—
178C23×C4C2412yes—
179C23×C4C2411yescharacteristic
180C23×C4C2411yescharacteristic
181C23×C4C2411yescharacteristic
182C4×Q8—416no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—24no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—28no—
218C2×C4⋊C4—28no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—44no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—44no—
226C2×C4⋊C4—44no—
227C2×C4⋊C4—44no—
228C2×C4⋊C4—44no—
229C2×C4⋊C4—44no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4C2×D414yes—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42—22no—
235C2×C42—22no—
236C2×C42—24no—
237C2×C42—24no—
238C2×C42—24no—
239C2×C42—24no—
240C2×C42—24no—
241C2×C42—24no—
242C2×C42—24no—
243C2×C42—24no—
244C2×C42—24no—
245C2×C42—28no—
246C2×C42—24no—
247C2×C42—44no—
248C2×C42—44no—
249C2×C42—44no—
250C2×C42C2×D414yes—
251C2×C42#4114yes—
252C2×C42#4114yes—
253C2×C42#4114yes—
254C2×C42#4114yes—
255#95—24no—
256#95—24no—
257#95—28no—
258#95—28no—
259#95—28no—
260#95—28no—
261#95—28no—
262#95—28no—
263#95—24no—
264#95—24no—
265#95—24no—
266#95—22no—
267#95—22no—
268#95—22no—
269#95—24no—
270#95—24no—
271#95—22no—
272#95—24no—
273#95—24no—
274#95—28no—
275#95—28no—
276#95—28no—
277#95—28no—
278#95—28no—
279#95—44no—
280#95—44no—
281#95—44no—
282#95—44no—
283#95—44no—
284#95—44no—
285#95—44no—
286#95—44no—
287#95C2×D4116yes—
288C24C2511yescharacteristic
289C2×Q8—28no—
290C2×Q8—28no—
291C2×Q8—28no—
292C2×Q8—44no—
293C2×Q8—44no—
294C2×Q8—44no—
295C2×Q8—44no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4C22×D414yes—
372C22×C4C22×D414yes—
373C22×C4C22×D414yes—
374C22×C4C22×D412yes—
375C22×C4C2×#4114yes—
376C22×C4C2×#4112yes—
377C22×C4C2×#4112yes—
378C22×C4C2×#4112yes—
379C22×C4C2×#4112yes—
380C22×C4C2×#4112yes—
381C22×C4C2×#4112yes—
382C22×C4C2×#4112yes—
383C22×C4C2×#4112yes—
384C22×C4C2×#4112yes—
385C22×C4C2×#4112yes—
386C22×C4H(5,𝔽2)14yes—
387C22×C42−1+414yes—
388C22×C42−1+414yes—
389C22×C42−1+412yes—
390C22×C42−1+412yes—
391C4⋊C4—216no—
392C4⋊C4—216no—
393C4⋊C4—216no—
394C4⋊C4—28no—
395C4⋊C4—48no—
396C4⋊C4—416no—
397C4⋊C4—48no—
398C4⋊C4—48no—
399C4⋊C4—48no—
400C4⋊C4—44no—
401C4⋊C4—48no—
402C4⋊C4—48no—
403C4⋊C4—44no—
404C4⋊C4—84no—
405C4⋊C4—84no—
406C4⋊C4—88no—
407C4⋊C4—88no—
408C42—28no—
409C42—28no—
410C42—48no—
411C42—48no—
412C42—48no—
413C42—84no—
414C42—88no—
415C42#126116yes—
416C23C23×D411yescharacteristic
417C23C22×#4111yescharacteristic
418C23C22×#4111yescharacteristic
419C23C22×#4111yescharacteristic
420C23C22×#4111yescharacteristic
421C23C2×H(5,𝔽2)12yes—
422C23C2×2−1+411yescharacteristic
423C23C2×2−1+411yescharacteristic
424C23C2×2−1+412yes—
425C23C2×2−1+412yes—
426C23#58512yes—
427Q8—416no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—28no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4C2×#12614yes—
515C2×C4C2×#12614yes—
516C2×C4C2×#12614yes—
517C2×C4#53214yes—
518C2×C4#54114yes—
519C2×C4#54714yes—
520C2×C4#54714yes—
521C2×C4#55214yes—
522C2×C4#55614yes—
523C22C22×#12611yescharacteristic
524C22C2×#53211yescharacteristic
525C22C2×#54111yescharacteristic
526C22#346112yes—
527C22C2×#54711yescharacteristic
528C22C2×#54711yescharacteristic
529C22C2×#55211yescharacteristic
530C22C2×#55611yescharacteristic
531C22#348612yes—
532C22#348812yes—
533C22#349212yes—
534C22#349212yes—
535C22#349512yes—
536C22#349512yes—
537C22#350811yescharacteristic
538C22#350911yescharacteristic
539C22#350911yescharacteristic
540C22#351011yescharacteristic
541C22#351112yes—
542C22#355012yes—
543C22#355412yes—
544C22#355512yes—
545C22#355612yes—
546C4—24no—
547C4—24no—
548C4—44no—
549C4—44no—
550C4—44no—
551C4—44no—
552C4—44no—
553C4—44no—
554C4—44no—
555C4—82no—
556C4—84no—
557C4—84no—
558C4—82no—
559C4—82no—
560C4#249618yes—
561C2C2×#249611yescharacteristic
562C2#3531311yescharacteristic
563C2#3555711yescharacteristic
564C2#3592612yes—
565C2#3779512yes—
566C2#3798212yes—
567C2#4251112yes—
568C2#4497911yescharacteristic
569C2#4533411yescharacteristic
570C2#4542111yescharacteristic
571C2#4543111yescharacteristic
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×#25112
#164212
#158762
#156632
#151922
#151562
#149672
#142762
#139422
#139262
#139102
#138842
#138562
#138042
#137862