Finite Group Databasebeta

← #1394379

Subgroups — #1394379

Order 512.

2226 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic
2C2×#2365C211yesmaximal, characteristic
3#17048C212yesmaximal
4#16663C212yesmaximal
5#16461C214yesmaximal
6#16388C214yesmaximal
7#15193C212yesmaximal
8#15191C212yesmaximal
9#15188C211yesmaximal, characteristic
10#15180C211yesmaximal, characteristic
11#15158C211yesmaximal, characteristic
12#14881C212yesmaximal
13#14346C212yesmaximal
14#14142C212yesmaximal
15#14021C212yesmaximal
16#13921C211yesmaximal, characteristic
17C4×#395C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4⋊Q8C2211yescharacteristic
20C22×C4×Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22#2568—28no—
23C2×#400C2214yes—
24C2×#395C2211yescharacteristic
25C2×#395C2212yes—
26#2365—28no—
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#387C2212yes—
39C2×#387C2212yes—
40C2×#383C2212yes—
41C2×#382C2212yes—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47#1446C2214yes—
48#1446C2214yes—
49#1446C2211yescharacteristic
50#1445C2214yes—
51#1445C2214yes—
52#1445C2214yes—
53#1444C2212yes—
54#1444C2214yes—
55#1444C2211yescharacteristic
56#1443C2214yes—
57#1443C2214yes—
58#1443C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2212yes—
63#1442C2214yes—
64#1442C2212yes—
65#1442C2214yes—
66#1441C2212yes—
67#1441C2214yes—
68#1441C2211yescharacteristic
69#1441C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1436C2214yes—
75#1436C2214yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80#1434C2214yes—
81#1434C2214yes—
82#1434C2212yes—
83C4×#95C2212yes—
84C4×#95C2211yescharacteristic
85C23×Q8C2312yes—
86C23×Q8C2311yescharacteristic
87C23×Q8C2312yes—
88C2×C4⋊Q8—24no—
89C2×C4⋊Q8—24no—
90C2×C4⋊Q8—24no—
91C2×C4⋊Q8—24no—
92C2×C4⋊Q8—44no—
93C2×C4×Q8—28no—
94C2×C4×Q8—24no—
95C2×C4×Q8—28no—
96C2×C4×Q8—44no—
97C2×C4×Q8—44no—
98C22×C4⋊C4C2312yes—
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C42C2312yes—
116C22×C42C2312yes—
117C22×C42C2311yescharacteristic
118C22×C42C2312yes—
119C22×C42C2312yes—
120C22×C42C2311yescharacteristic
121C22×C42C2312yes—
122C22×C42C2311yescharacteristic
123#400—216no—
124#395—24no—
125#395—44no—
126#391—28no—
127#391—28no—
128#391—28no—
129#391—28no—
130#391—28no—
131#391—28no—
132#391—44no—
133#391—44no—
134#389—24no—
135#389—24no—
136#389—44no—
137#387—28no—
138#387—28no—
139#383—44no—
140#382—28no—
141C4×C4⋊C4—24no—
142C4×C4⋊C4—24no—
143C4×C4⋊C4—24no—
144C4×C4⋊C4—44no—
145C4×C4⋊C4D418yes—
146C2×#95C2311yescharacteristic
147C2×#95C2312yes—
148C2×#95C2312yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2312yes—
154C2×#95C2311yescharacteristic
155C2×#95C2312yes—
156C2×#95C2312yes—
157C2×#95C2312yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2311yescharacteristic
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2311yescharacteristic
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C22×Q8—24no—
184C22×Q8—22no—
185C22×Q8—24no—
186C22×Q8—24no—
187C22×Q8—24no—
188C22×Q8—24no—
189C22×Q8—24no—
190C22×Q8—24no—
191C22×Q8—22no—
192C22×Q8—24no—
193C22×Q8—24no—
194C22×Q8—22no—
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8—24no—
198C22×Q8—24no—
199C22×Q8—42no—
200C22×Q8—42no—
201C22×Q8—42no—
202C23×C4C2412yes—
203C23×C4C2411yescharacteristic
204C23×C4C2412yes—
205C23×C4C2414yes—
206C23×C4C2414yes—
207C23×C4C2412yes—
208C23×C4C2411yescharacteristic
209C23×C4C2412yes—
210C23×C4C2412yes—
211C23×C4C2411yescharacteristic
212C23×C4C2412yes—
213C23×C4C2411yescharacteristic
214C23×C4C2412yes—
215C23×C4C2412yes—
216C23×C4C2411yescharacteristic
217C23×C4C2411yescharacteristic
218C23×C4C2411yescharacteristic
219C4⋊Q8—232no—
220C4⋊Q8—416no—
221C4×Q8—432no—
222C4×Q8—416no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—22no—
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—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—41no—
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⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4C2×D414yes—
266C2×C4⋊C4C2×D414yes—
267C2×C4⋊C4#4114yes—
268C2×C4⋊C4#4114yes—
269C2×C42—22no—
270C2×C42—24no—
271C2×C42—22no—
272C2×C42—24no—
273C2×C42—24no—
274C2×C42—24no—
275C2×C42—24no—
276C2×C42—24no—
277C2×C42—22no—
278C2×C42—24no—
279C2×C42—24no—
280C2×C42—24no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—24no—
284C2×C42—24no—
285C2×C42—24no—
286C2×C42—42no—
287C2×C42—42no—
288C2×C42C2×D414yes—
289C2×C42C2×D418yes—
290C2×C42#4114yes—
291#95—22no—
292#95—22no—
293#95—24no—
294#95—24no—
295#95—28no—
296#95—28no—
297#95—24no—
298#95—24no—
299#95—28no—
300#95—28no—
301#95—28no—
302#95—28no—
303#95—28no—
304#95—28no—
305#95—22no—
306#95—24no—
307#95—22no—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—28no—
312#95—24no—
313#95—24no—
314#95—44no—
315#95—42no—
316#95—44no—
317#95—42no—
318#95—42no—
319#95—44no—
320#95—44no—
321#95—44no—
322#95—44no—
323#95—44no—
324#95—44no—
325#95—44no—
326#95—44no—
327#95C2×D418yes—
328C24C2511yescharacteristic
329C2×Q8—216no—
330C2×Q8—28no—
331C2×Q8—48no—
332C2×Q8—48no—
333C2×Q8—48no—
334C2×Q8—48no—
335C2×Q8—48no—
336C2×Q8—48no—
337C2×Q8—44no—
338C2×Q8—48no—
339C2×Q8—48no—
340C2×Q8—48no—
341C2×Q8—48no—
342C2×Q8—48no—
343C2×Q8—48no—
344C2×Q8—48no—
345C2×Q8—48no—
346C2×Q8—44no—
347C2×Q8—48no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
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—21no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4C22×D414yes—
433C22×C4C22×D414yes—
434C22×C4C22×D412yes—
435C22×C4C22×D412yes—
436C22×C4C22×D412yes—
437C22×C4C2×#4112yes—
438C22×C4C2×#4114yes—
439C22×C4C2×#4112yes—
440C22×C4C2×#4112yes—
441C22×C4C2×#4112yes—
442C22×C4C2×#4112yes—
443C22×C4C2×#4112yes—
444C22×C4C2×#4112yes—
445C22×C4H(5,𝔽2)12yes—
446C22×C4H(5,𝔽2)14yes—
447C22×C42−1+414yes—
448C22×C42−1+414yes—
449C22×C42−1+412yes—
450C22×C42−1+414yes—
451C4⋊C4—216no—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—28no—
456C4⋊C4—44no—
457C4⋊C4—48no—
458C4⋊C4—48no—
459C4⋊C4—48no—
460C4⋊C4—44no—
461C4⋊C4—48no—
462C4⋊C4—48no—
463C4⋊C4—48no—
464C4⋊C4—44no—
465C4⋊C4—48no—
466C4⋊C4—48no—
467C4⋊C4—88no—
468C42—28no—
469C42—28no—
470C42—216no—
471C42—48no—
472C42—48no—
473C42—44no—
474C42—48no—
475C42—48no—
476C23C23×D411yescharacteristic
477C23C22×#4111yescharacteristic
478C23C22×#4111yescharacteristic
479C23C22×#4111yescharacteristic
480C23C2×H(5,𝔽2)12yes—
481C23C2×H(5,𝔽2)11yescharacteristic
482C23C2×2−1+412yes—
483C23C2×2−1+411yescharacteristic
484C23C2×2−1+412yes—
485C23C2×2−1+412yes—
486C23#58511yescharacteristic
487Q8—432no—
488Q8—416no—
489Q8—816no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—44no—
556C2×C4—44no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—44no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—44no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4#52514yes—
587C2×C4#53514yes—
588C2×C4#53614yes—
589C2×C4#54218yes—
590C2×C4#54218yes—
591C2×C4#54614yes—
592C2×C4#55614yes—
593C22C2×#52511yescharacteristic
594C22C2×#53511yescharacteristic
595C22C2×#53611yescharacteristic
596C22C2×#54212yes—
597C22C2×#54212yes—
598C22C2×#54611yescharacteristic
599C22C2×#55611yescharacteristic
600C22#347511yescharacteristic
601C22#348611yescharacteristic
602C22#348911yescharacteristic
603C22#349911yescharacteristic
604C22#350611yescharacteristic
605C22#350912yes—
606C22#352011yescharacteristic
607C22#352012yes—
608C22#352312yes—
609C22#352312yes—
610C22#353612yes—
611C22#354112yes—
612C22#355012yes—
613C22#355012yes—
614C22#355512yes—
615C22#355612yes—
616C4—24no—
617C4—24no—
618C4—44no—
619C4—44no—
620C4—44no—
621C4—44no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—44no—
626C4—84no—
627C4—84no—
628C4—82no—
629C4—82no—
630C4—81no—
631C4—82no—
632C4#263218yes—
633C2C2×#263211yescharacteristic
634C2#3574911yescharacteristic
635C2#3616111yescharacteristic
636C2#3890511yescharacteristic
637C2#3895411yescharacteristic
638C2#3898412yes—
639C2#3900712yes—
640C2#4252612yes—
641C2#4255812yes—
642C2#4281111yescharacteristic
643C2#4291111yescharacteristic
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×#23652
#170482
#166632
#164612
#163882
#151932
#151912
#151882
#151802
#151582
#148812
#143462
#141422
#140212
#139212
C4×#3952