Finite Group Databasebeta

← #449008

Subgroups — #449008

Order 512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2514C211yesmaximal, characteristic
2C2×#2100C211yesmaximal, characteristic
3C2×#2072C211yesmaximal, characteristic
4#13910C211yesmaximal, characteristic
5#11346C211yesmaximal, characteristic
6#11208C212yesmaximal
7#11067C212yesmaximal
8#11067C212yesmaximal
9#10932C211yesmaximal, characteristic
10#10884C211yesmaximal, characteristic
11#10884C212yesmaximal
12C22×#103C2212yes—
13C22×#103C2212yes—
14#2514—24no—
15#2514—24no—
16C2×#401—21no—
17C2×#400—21no—
18C2×#391C2211yescharacteristic
19C2×#391C2211yescharacteristic
20C2×#391C2211yescharacteristic
21C2×#389C2212yes—
22C2×#389C2212yes—
23C2×#389C2211yescharacteristic
24C2×#387—21no—
25C2×#384—21no—
26C2×#384C2211yescharacteristic
27C2×#383—21no—
28C2×#382C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32#2100—24no—
33#2072—24no—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#340C2212yes—
39C2×#340C2212yes—
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2212yes—
43C2×#336C2212yes—
44#1444—21no—
45#1444—21no—
46C4⋊#95—21no—
47C23×Q8C2311yescharacteristic
48C23×C8C2312yes—
49C23×C8C2312yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2312yes—
62C22×C42—21no—
63C22×C42—21no—
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—42no—
72C2×#103—42no—
73#401—28no—
74#400—28no—
75#391—22no—
76#391—22no—
77#391—22no—
78#391—22no—
79#391—22no—
80#391D414yes—
81#389—22no—
82#389—24no—
83#389—24no—
84#389—42no—
85#389—42no—
86#389D414yes—
87#387—28no—
88#384—22no—
89#384—22no—
90#384—44no—
91#383—28no—
92#382—22no—
93#382—22no—
94C4×C4⋊C4—22no—
95C4×C4⋊C4—22no—
96C4×C4⋊C4—24no—
97C4×C4⋊C4—22no—
98C4×C4⋊C4—22no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—22no—
111C2×#95—22no—
112C2×#95D411yescharacteristic
113C2×#95D411yescharacteristic
114#340—24no—
115#340—24no—
116#340—24no—
117#340—24no—
118#340—24no—
119#340—24no—
120#336—22no—
121#336—22no—
122#336—42no—
123#336—42no—
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8C2×D412yes—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2411yescharacteristic
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—82no—
195C2×C4⋊C4—82no—
196C2×C4⋊C4—82no—
197C2×C4⋊C4C2×D412yes—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4#4114yes—
201C2×C4⋊C4#4114yes—
202C2×C4⋊C4#4114yes—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—24no—
206C2×C42—24no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—42no—
216C2×C42—42no—
217C2×C42—42no—
218C2×C42—42no—
219C2×C42C2×D412yes—
220C2×C42C2×D412yes—
221#103—48no—
222#103—48no—
223#95—24no—
224#95—24no—
225#95—24no—
226#95—24no—
227#95—24no—
228#95—24no—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—24no—
233#95—24no—
234#95—22no—
235#95—22no—
236#95—44no—
237#95—44no—
238C24C22×D411yescharacteristic
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—24no—
262C22×C4—21no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—24no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4#12012yes—
319C22×C4#12012yes—
320C22×C4#13512yes—
321C22×C4AGL(1,ℤ/8)12yes—
322C22×C4#13712yes—
323C22×C4C22×D411yescharacteristic
324C22×C4C22×D411yescharacteristic
325C22×C4C2×#4112yes—
326C22×C4C2×#4112yes—
327C22×C4C2×#4112yes—
328C22×C4H(5,𝔽2)12yes—
329C22×C42−1+412yes—
330C22×C42−1+412yes—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—24no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—44no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—44no—
358C4⋊C4—48no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—88no—
364C4⋊C4—84no—
365C4⋊C4—84no—
366C4⋊C4—88no—
367C4⋊C4#12618yes—
368C42—24no—
369C42—24no—
370C42—48no—
371C42—48no—
372C42—41no—
373C42—41no—
374C42—41no—
375C42—41no—
376C42—42no—
377C42—42no—
378C23C2×#12011yescharacteristic
379C23#52511yescharacteristic
380C23#53611yescharacteristic
381C23#54612yes—
382C23#54812yes—
383C23C2×#13511yescharacteristic
384C23C2×AGL(1,ℤ/8)11yescharacteristic
385C23C2×#13711yescharacteristic
386C23#57511yescharacteristic
387C23#57712yes—
388C23#57812yes—
389Q8—44no—
390Q8—44no—
391Q8—82no—
392Q8—82no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—28no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4#45214yes—
461C2×C4C2×#12612yes—
462C2×C4#53211yescharacteristic
463C2×C4#53211yescharacteristic
464C2×C4#53511yescharacteristic
465C2×C4#53611yescharacteristic
466C2×C4#53912yes—
467C2×C4#54112yes—
468C2×C4#54212yes—
469C2×C4#54712yes—
470C2×C4#54712yes—
471C2×C4#54712yes—
472C2×C4#55012yes—
473C2×C4#55212yes—
474C2×C4#55312yes—
475C2×C4#55612yes—
476C2×C4#56312yes—
477C8—82no—
478C8—82no—
479C22#240611yescharacteristic
480C22#243111yescharacteristic
481C22#243211yescharacteristic
482C22#248112yes—
483C22#271612yes—
484C22C2×#45211yescharacteristic
485C22#300611yescharacteristic
486C22#301011yescharacteristic
487C22#301111yescharacteristic
488C22#310511yescharacteristic
489C22#311711yescharacteristic
490C22#312012yes—
491C22#323211yescharacteristic
492C22#323911yescharacteristic
493C22#324212yes—
494C22#330212yes—
495C22#331012yes—
496C22#331712yes—
497C22#332812yes—
498C22#336012yes—
499C22#336712yes—
500C22#336912yes—
501C22#337712yes—
502C4—24no—
503C4—42no—
504C4—48no—
505C4—42no—
506C4—82no—
507C4—82no—
508C4—82no—
509C4—82no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—162no—
514C4#249612yes—
515C4#251212yes—
516C4#271812yes—
517C4#272112yes—
518C2#1592811yescharacteristic
519C2#2406711yescharacteristic
520C2#2407111yescharacteristic
521C2#2557011yescharacteristic
522C2#2558311yescharacteristic
523C2#2564611yescharacteristic
524C2#2566111yescharacteristic
525C2#2755512yes—
526C2#2757012yes—
527C2#3223512yes—
528C2#3224412yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25142
C2×#21002
C2×#20722
#139102
#113462
#112082
#110672
#109322
#108842