Finite Group Databasebeta

← #719447

Subgroups — #719447

Order 512.

2470 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C212yesmaximal
2C2×#2546C211yesmaximal, characteristic
3C2×#2399C211yesmaximal, characteristic
4#16835C214yesmaximal
5#15767C214yesmaximal
6#15699C214yesmaximal
7#15201C212yesmaximal
8#15180C212yesmaximal
9#14937C214yesmaximal
10#14274C211yesmaximal, characteristic
11#14155C211yesmaximal, characteristic
12#14021C212yesmaximal
13#13942C211yesmaximal, characteristic
14#13804C211yesmaximal, characteristic
15#13786C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4⋊Q8C2212yes—
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2212yes—
20#2568—216no—
21#2546—28no—
22#2399—28no—
23C2×#400C2214yes—
24C2×#400C2214yes—
25C2×#398C2212yes—
26C2×#398C2212yes—
27C2×#398C2212yes—
28C2×#398C2212yes—
29C2×#395C2212yes—
30C2×#395C2212yes—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#391C2214yes—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2211yescharacteristic
40C2×#389C2214yes—
41C2×#382C2214yes—
42C2×#382C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2212yes—
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×#376C2211yescharacteristic
49#1446C2214yes—
50#1445C2212yes—
51#1445C2212yes—
52#1445C2214yes—
53#1445C2214yes—
54#1443C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1436C2214yes—
65#1436C2214yes—
66#1436C2214yes—
67C4⋊#95C2214yes—
68C4⋊#95C2212yes—
69C4⋊#95C2211yescharacteristic
70C4⋊#95C2212yes—
71C4⋊#95C2211yescharacteristic
72#1434C2212yes—
73#1434C2214yes—
74#1434C2214yes—
75#1434C2212yes—
76#1434C2212yes—
77C4×#95C2212yes—
78C23×Q8C2312yes—
79C23×Q8C2311yescharacteristic
80C23×Q8C2312yes—
81C2×C4⋊Q8—28no—
82C2×C4⋊Q8—28no—
83C2×C4⋊Q8—24no—
84C2×C4⋊Q8—24no—
85C2×C4⋊Q8—24no—
86C2×C4⋊Q8—44no—
87C2×C4×Q8—28no—
88C2×C4×Q8—28no—
89C2×C4×Q8—24no—
90C2×C4×Q8—24no—
91C2×C4×Q8—24no—
92C2×C4×Q8—44no—
93C22×C4⋊C4C2312yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C42C2312yes—
110C22×C42C2312yes—
111C22×C42C2314yes—
112C22×C42C2311yescharacteristic
113C22×C42C2312yes—
114C22×C42C2311yescharacteristic
115C22×C42C2312yes—
116C22×C42C2311yescharacteristic
117#400—216no—
118#400—216no—
119#398—28no—
120#398—28no—
121#398—28no—
122#398—28no—
123#395—28no—
124#395—28no—
125#391—28no—
126#391—28no—
127#391—28no—
128#391—28no—
129#391—24no—
130#391—28no—
131#391—216no—
132#391—44no—
133#391D418yes—
134#389—216no—
135#382—24no—
136#382—216no—
137C4×C4⋊C4—28no—
138C4×C4⋊C4—28no—
139C4×C4⋊C4—24no—
140C4×C4⋊C4—24no—
141C4×C4⋊C4D418yes—
142#376—24no—
143C2×#95C2312yes—
144C2×#95C2311yescharacteristic
145C2×#95C2312yes—
146C2×#95C2312yes—
147C2×#95C2311yescharacteristic
148C2×#95C2312yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2314yes—
154C2×#95C2314yes—
155C2×#95C2314yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2312yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2312yes—
162C2×#95C2312yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2311yescharacteristic
173C2×#95C2311yescharacteristic
174C2×#95C2314yes—
175C22×Q8—22no—
176C22×Q8—24no—
177C22×Q8—24no—
178C22×Q8—24no—
179C22×Q8—24no—
180C22×Q8—22no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—24no—
184C22×Q8—24no—
185C22×Q8—24no—
186C22×Q8—22no—
187C22×Q8—24no—
188C22×Q8—24no—
189C22×Q8—24no—
190C22×Q8—22no—
191C22×Q8—24no—
192C22×Q8—24no—
193C22×Q8—42no—
194C22×Q8—42no—
195C22×Q8C2×D414yes—
196C23×C4C2414yes—
197C23×C4C2412yes—
198C23×C4C2412yes—
199C23×C4C2414yes—
200C23×C4C2412yes—
201C23×C4C2412yes—
202C23×C4C2412yes—
203C23×C4C2412yes—
204C23×C4C2412yes—
205C23×C4C2412yes—
206C23×C4C2412yes—
207C23×C4C2411yescharacteristic
208C23×C4C2411yescharacteristic
209C23×C4C2412yes—
210C23×C4C2411yescharacteristic
211C4⋊Q8—432no—
212C4⋊Q8—416no—
213C4×Q8—432no—
214C4×Q8—416no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—28no—
231C2×C4⋊C4—24no—
232C2×C4⋊C4—28no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4C2×D414yes—
262C2×C4⋊C4C2×D418yes—
263C2×C42—22no—
264C2×C42—24no—
265C2×C42—22no—
266C2×C42—22no—
267C2×C42—24no—
268C2×C42—22no—
269C2×C42—24no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—28no—
273C2×C42—24no—
274C2×C42—24no—
275C2×C42—24no—
276C2×C42—28no—
277C2×C42—24no—
278C2×C42—44no—
279C2×C42—44no—
280C2×C42C2×D414yes—
281C2×C42C2×D418yes—
282C2×C42C2×D414yes—
283C2×C42#4114yes—
284C2×C42#4114yes—
285C2×C42#4114yes—
286#95—24no—
287#95—24no—
288#95—24no—
289#95—22no—
290#95—24no—
291#95—22no—
292#95—28no—
293#95—28no—
294#95—28no—
295#95—28no—
296#95—28no—
297#95—28no—
298#95—28no—
299#95—28no—
300#95—28no—
301#95—24no—
302#95—24no—
303#95—24no—
304#95—28no—
305#95—28no—
306#95—28no—
307#95—28no—
308#95—28no—
309#95—44no—
310#95—44no—
311#95—44no—
312#95—44no—
313#95—44no—
314#95—44no—
315#95C2×D414yes—
316#95C2×D414yes—
317#95C2×D4116yes—
318C24C2511yescharacteristic
319C2×Q8—216no—
320C2×Q8—28no—
321C2×Q8—28no—
322C2×Q8—28no—
323C2×Q8—48no—
324C2×Q8—48no—
325C2×Q8—48no—
326C2×Q8—48no—
327C2×Q8—48no—
328C2×Q8—44no—
329C2×Q8—48no—
330C2×Q8—48no—
331C2×Q8—48no—
332C2×Q8—44no—
333C2×Q8—48no—
334C2×Q8—48no—
335C2×Q8—48no—
336C2×Q8—44no—
337C2×Q8—48no—
338C2×Q8—44no—
339C2×Q8—48no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
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—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—24no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4C22×D414yes—
414C22×C4C22×D414yes—
415C22×C4C22×D414yes—
416C22×C4C22×D414yes—
417C22×C4C22×D412yes—
418C22×C4C22×D412yes—
419C22×C4C22×D414yes—
420C22×C4C22×D412yes—
421C22×C4C22×D412yes—
422C22×C4C2×#4114yes—
423C22×C4C2×#4112yes—
424C22×C4C2×#4112yes—
425C22×C4C2×#4112yes—
426C22×C4C2×#4112yes—
427C22×C4C2×#4112yes—
428C22×C4C2×#4112yes—
429C22×C4C2×#4112yes—
430C22×C4H(5,𝔽2)12yes—
431C22×C42−1+414yes—
432C22×C42−1+414yes—
433C22×C42−1+414yes—
434C22×C42−1+412yes—
435C4⋊C4—216no—
436C4⋊C4—28no—
437C4⋊C4—48no—
438C4⋊C4—48no—
439C4⋊C4—48no—
440C4⋊C4—48no—
441C4⋊C4—48no—
442C4⋊C4—416no—
443C4⋊C4—416no—
444C4⋊C4—48no—
445C4⋊C4—44no—
446C4⋊C4—48no—
447C4⋊C4—48no—
448C4⋊C4—48no—
449C4⋊C4—48no—
450C4⋊C4—44no—
451C42—28no—
452C42—216no—
453C42—28no—
454C42—416no—
455C42—48no—
456C42—48no—
457C42—84no—
458C42#124116yes—
459C23C23×D411yescharacteristic
460C23C23×D411yescharacteristic
461C23C22×#4111yescharacteristic
462C23C22×#4111yescharacteristic
463C23C22×#4111yescharacteristic
464C23C2×H(5,𝔽2)11yescharacteristic
465C23C2×2−1+412yes—
466C23C2×2−1+412yes—
467C23C2×2−1+411yescharacteristic
468C23C2×2−1+412yes—
469C23#58512yes—
470Q8—432no—
471Q8—416no—
472Q8—816no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—28no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4C2×#12414yes—
559C2×C4C2×#12414yes—
560C2×C4C2×#12414yes—
561C2×C4#53214yes—
562C2×C4#53618yes—
563C2×C4#54214yes—
564C2×C4D4214yes—
565C2×C4#54714yes—
566C2×C4#54814yes—
567C2×C4#55514yes—
568C22C22×#12411yescharacteristic
569C22C2×#53211yescharacteristic
570C22C2×#53612yes—
571C22C2×#54211yescharacteristic
572C22C2×D4211yescharacteristic
573C22C2×#54711yescharacteristic
574C22C2×#54811yescharacteristic
575C22C2×#55511yescharacteristic
576C22#348612yes—
577C22#348912yes—
578C22#348912yes—
579C22#350712yes—
580C22#350712yes—
581C22#350911yescharacteristic
582C22#350911yescharacteristic
583C22#350912yes—
584C22#350912yes—
585C22#350911yescharacteristic
586C22#351011yescharacteristic
587C22#353812yes—
588C22#354112yes—
589C22#355512yes—
590C22#355612yes—
591C4—28no—
592C4—24no—
593C4—24no—
594C4—44no—
595C4—44no—
596C4—44no—
597C4—44no—
598C4—44no—
599C4—44no—
600C4—82no—
601C4—82no—
602C4—82no—
603C4—84no—
604C4—84no—
605C4#249118yes—
606C2C2×#249111yescharacteristic
607C2#3532011yescharacteristic
608C2#3562811yescharacteristic
609C2#3593812yes—
610C2#3765112yes—
611C2#3972412yes—
612C2#4270112yes—
613C2#4515111yescharacteristic
614C2#4533411yescharacteristic
615C2#4542911yescharacteristic
616C2#4543611yescharacteristic
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×#25682
C2×#25462
C2×#23992
#168352
#157672
#156992
#152012
#151802
#149372
#142742
#141552
#140212
#139422
#138042
#137862