Finite Group Databasebeta

← #415488

Subgroups — #415488

Order 512.

1094 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1805C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#14354C211yesmaximal, characteristic
4#13786C211yesmaximal, characteristic
5#11268C212yesmaximal
6#11267C212yesmaximal
7#11052C212yesmaximal
8#11050C212yesmaximal
9#10850C211yesmaximal, characteristic
10#10849C211yesmaximal, characteristic
11#10833C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2212yes—
17C22×#103C2211yescharacteristic
18C2×#391C2212yes—
19C2×#384C2211yescharacteristic
20C2×#384C2212yes—
21C2×#382C2211yescharacteristic
22C2×#382C2212yes—
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×#376C2211yescharacteristic
25#1805—24no—
26#1803—24no—
27C2×#340C2211yescharacteristic
28C2×#340C2212yes—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2212yes—
35C2×#336C2212yes—
36#1444—21no—
37#1444—21no—
38#1444—22no—
39#1436—22no—
40C4⋊#95C2212yes—
41#1434—21no—
42#1434—21no—
43C23×Q8C2311yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C2×C4×Q8—22no—
48C2×C4×Q8—22no—
49C2×C4×Q8—22no—
50C2×C4×Q8—22no—
51C2×C4×Q8—22no—
52C2×C4×Q8D414yes—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2312yes—
63C22×C42—21no—
64C22×C42—21no—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67C2×C4⋊C8—22no—
68C2×C4⋊C8—22no—
69C2×C4⋊C8—22no—
70C2×C4⋊C8—22no—
71C2×C4⋊C8—22no—
72C2×C4⋊C8—22no—
73C2×#103—24no—
74C2×#103—22no—
75C2×#103—22no—
76C2×#103—42no—
77C2×#103—42no—
78C2×#103—42no—
79C2×#103—42no—
80#391—24no—
81#391Q818yes—
82#384—22no—
83#384—22no—
84#384—42no—
85#384—42no—
86#382—22no—
87#382—22no—
88#382—42no—
89#382—42no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—22no—
92#376—22no—
93#376—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95D411yescharacteristic
104C2×#95D411yescharacteristic
105C2×#95D412yes—
106#340—24no—
107#340—22no—
108#340—22no—
109#340—42no—
110#340—42no—
111#340—42no—
112#340—42no—
113#336—24no—
114#336—24no—
115C22×Q8—21no—
116C22×Q8—22no—
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8C2×D412yes—
124C22×Q8C2×Q814yes—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—22no—
130C23×C4—21no—
131C23×C4C2×D412yes—
132C23×C4C2×D412yes—
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2411yescharacteristic
136C22×C8—22no—
137C22×C8—21no—
138C22×C8—21no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—21no—
144C22×C8—22no—
145C22×C8—21no—
146C22×C8—21no—
147C22×C8—22no—
148C22×C8—21no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C4×Q8—28no—
154C4×Q8—28no—
155C4×Q8—44no—
156C4×Q8—44no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—81no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4—81no—
191C2×C4⋊C4—82no—
192C2×C4⋊C4—82no—
193C2×C4⋊C4—82no—
194C2×C4⋊C4—82no—
195C2×C4⋊C4C2×D412yes—
196C2×C4⋊C4C2×Q814yes—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—24no—
202C2×C42—42no—
203C2×C42—42no—
204C2×C42—42no—
205C2×C42—81no—
206C2×C42—81no—
207C2×C42C2×D412yes—
208C2×C42C2×Q814yes—
209C2×C42#4114yes—
210C2×C42#4112yes—
211C2×C42#4112yes—
212C2×C42#4112yes—
213C2×C42#4112yes—
214C2×C42#4112yes—
215C4⋊C8—44no—
216C4⋊C8—44no—
217#103—48no—
218#103—44no—
219#103—44no—
220#95—28no—
221#95—28no—
222#95—22no—
223#95—22no—
224#95—24no—
225#95—44no—
226#95—44no—
227#95—42no—
228#95—42no—
229#95—42no—
230#95—82no—
231#95—82no—
232C24C22×D411yescharacteristic
233C2×Q8—22no—
234C2×Q8—24no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—24no—
240C2×Q8—24no—
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×Q8C4⋊Q814yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4#12112yes—
306C22×C4#12112yes—
307C22×C4C22⋊Q814yes—
308C22×C4C22⋊Q814yes—
309C22×C4#12312yes—
310C22×C4#12312yes—
311C22×C4#12412yes—
312C22×C4#12412yes—
313C22×C4C22×D411yescharacteristic
314C22×C4C22×Q812yes—
315C22×C4C2×#4111yescharacteristic
316C22×C4C2×#4111yescharacteristic
317C22×C4C2×#4111yescharacteristic
318C22×C4C2×#4111yescharacteristic
319C22×C4C2×#4111yescharacteristic
320C22×C4C2×#4112yes—
321C22×C4H(5,𝔽2)12yes—
322C22×C4H(5,𝔽2)12yes—
323C2×C8—42no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—42no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—42no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—24no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—48no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—42no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—84no—
360C4⋊C4—84no—
361C4⋊C4—88no—
362C4⋊C4—88no—
363C42—24no—
364C42—24no—
365C42—24no—
366C42—24no—
367C42—48no—
368C42—84no—
369C42#12314yes—
370C42#12314yes—
371C42#12614yes—
372C42#12614yes—
373C23C2×#12111yescharacteristic
374C23C2×C22⋊Q812yes—
375C23C2×#12311yescharacteristic
376C23C2×#12411yescharacteristic
377C23#53512yes—
378C23#57611yescharacteristic
379C23#57711yescharacteristic
380C23#57712yes—
381C23#57711yescharacteristic
382C23#57811yescharacteristic
383C23#57812yes—
384Q8—24no—
385Q8—24no—
386Q8—44no—
387Q8—44no—
388Q8—42no—
389Q8—42no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—81no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4#39714yes—
451C2×C4#39714yes—
452C2×C4C2×#12311yescharacteristic
453C2×C4C2×#12311yescharacteristic
454C2×C4C2×#12611yescharacteristic
455C2×C4C2×#12611yescharacteristic
456C2×C4C2×C4⋊Q811yescharacteristic
457C2×C4#53211yescharacteristic
458C2×C4#53312yes—
459C2×C4#53511yescharacteristic
460C2×C4#53511yescharacteristic
461C2×C4#54012yes—
462C2×C4#55312yes—
463C2×C4#55312yes—
464C2×C4#55412yes—
465C2×C4#55412yes—
466C2×C4#55412yes—
467C2×C4#55412yes—
468C2×C4#55512yes—
469C2×C4#55512yes—
470C8—82no—
471C8—81no—
472C8—81no—
473C22C2×#39711yescharacteristic
474C22#248712yes—
475C22#256312yes—
476C22#261911yescharacteristic
477C22#285711yescharacteristic
478C22#304311yescharacteristic
479C22#304411yescharacteristic
480C22#304511yescharacteristic
481C22#304611yescharacteristic
482C22#308212yes—
483C22#308212yes—
484C22#308312yes—
485C22#308412yes—
486C22#309712yes—
487C22#309811yescharacteristic
488C22#309911yescharacteristic
489C22#313611yescharacteristic
490C22#313712yes—
491C22#313711yescharacteristic
492C22#322212yes—
493C22#322312yes—
494C22#322412yes—
495C22#322512yes—
496C4—24no—
497C4—24no—
498C4—44no—
499C4—44no—
500C4—44no—
501C4—82no—
502C4—84no—
503C4—161no—
504C4—162no—
505C4—161no—
506C4#249712yes—
507C4#249712yes—
508C4#250011yescharacteristic
509C4#250011yescharacteristic
510C4#250211yescharacteristic
511C4#250211yescharacteristic
512C2#1519511yescharacteristic
513C2#2363311yescharacteristic
514C2#2363411yescharacteristic
515C2#2768912yes—
516C2#2769012yes—
517C2#2915112yes—
518C2#2915312yes—
519C2#2980311yescharacteristic
520C2#2980511yescharacteristic
521C2#3320411yescharacteristic
522C2#3320611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#18052
C2×#18032
#143542
#137862
#112682
#112672
#110522
#110502
#108502
#108492
#108332