Finite Group Databasebeta

← #416832

Subgroups — #416832

Order 512.

1072 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1805C211yesmaximal, characteristic
2C2×#1805C211yesmaximal, characteristic
3#14689C211yesmaximal, characteristic
4C4×#391C211yesmaximal, characteristic
5#11316C212yesmaximal
6#11315C212yesmaximal
7#11190C212yesmaximal
8#11190C212yesmaximal
9#10850C211yesmaximal, characteristic
10#10850C211yesmaximal, characteristic
11#10832C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2212yes—
16C22×#103C2212yes—
17C2×#391C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#382C2211yescharacteristic
20C2×#382C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×C43C2211yescharacteristic
23#1805—24no—
24#1805—24no—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#336C2212yes—
32C2×#336C2212yes—
33#1436—22no—
34C4⋊#95C2211yescharacteristic
35C4⋊#95C2212yes—
36C4⋊#95C2211yescharacteristic
37C4⋊#95C2212yes—
38#1434—22no—
39#1434—22no—
40C4×#95—22no—
41C23×Q8C2311yescharacteristic
42C23×C8C2312yes—
43C23×C8C2312yes—
44C2×C4×Q8—22no—
45C2×C4×Q8—22no—
46C2×C4×Q8—22no—
47C2×C4×Q8—22no—
48C2×C4×Q8—22no—
49C2×C4×Q8D414yes—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2311yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C42—21no—
57C22×C42—21no—
58C22×C42D412yes—
59C22×C42D412yes—
60C22×C42C2311yescharacteristic
61C22×C42C2311yescharacteristic
62C22×C42C2311yescharacteristic
63C2×C4⋊C8—22no—
64C2×C4⋊C8—22no—
65C2×C4⋊C8—22no—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—22no—
68C2×C4⋊C8—22no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—42no—
74C2×#103—42no—
75#391—22no—
76#391—22no—
77#391—22no—
78#391—22no—
79#382—22no—
80#382—22no—
81#382—22no—
82#382—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C43—22no—
99C43—22no—
100#340—24no—
101#340—24no—
102#340—24no—
103#340—24no—
104#340—42no—
105#340—42no—
106#336—42no—
107#336—42no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8—21no—
114C22×Q8—21no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—21no—
118C22×Q8—21no—
119C22×Q8C2×D412yes—
120C22×Q8#4112yes—
121C22×Q8#4112yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4C2×D412yes—
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C23×C4C2411yescharacteristic
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C4×Q8—28no—
148C4×Q8—28no—
149C4×Q8—44no—
150C4×Q8—44no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
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—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4C2×D412yes—
182C2×C4⋊C4#4112yes—
183C2×C4⋊C4#4112yes—
184C2×C42—24no—
185C2×C42—24no—
186C2×C42—24no—
187C2×C42—24no—
188C2×C42—24no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—42no—
202C2×C42—42no—
203C2×C42—42no—
204C2×C42—42no—
205C2×C42—44no—
206C2×C42—42no—
207C2×C42C2×D412yes—
208C2×C42#4112yes—
209C2×C42#4112yes—
210C2×C42#4112yes—
211C2×C42#4112yes—
212C2×C42#4112yes—
213C4⋊C8—44no—
214C4⋊C8—44no—
215#103—48no—
216#103—48no—
217#95—28no—
218#95—28no—
219#95—44no—
220#95—44no—
221#95—44no—
222#95—42no—
223#95—42no—
224#95—42no—
225#95—42no—
226#95—42no—
227#95—44no—
228#95—44no—
229#95—44no—
230C24C22×D411yescharacteristic
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8#12414yes—
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—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4#12112yes—
312C22×C4#12112yes—
313C22×C4#12312yes—
314C22×C4#12312yes—
315C22×C4#12412yes—
316C22×C4#12412yes—
317C22×C4#13514yes—
318C22×C4#13714yes—
319C22×C4C22×D411yescharacteristic
320C22×C4C2×#4111yescharacteristic
321C22×C4C2×#4111yescharacteristic
322C22×C4C2×#4111yescharacteristic
323C22×C4C2×#4111yescharacteristic
324C22×C4C2×#4111yescharacteristic
325C22×C4C2×#4111yescharacteristic
326C22×C4C2×#4111yescharacteristic
327C22×C4C2×#4111yescharacteristic
328C22×C4C2×#4111yescharacteristic
329C22×C4H(5,𝔽2)11yescharacteristic
330C22×C4H(5,𝔽2)11yescharacteristic
331C22×C42−1+411yescharacteristic
332C22×C42−1+411yescharacteristic
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—
345C2×C8—42no—
346C2×C8—42no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—48no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C42—48no—
369C42—48no—
370C42—41no—
371C42—41no—
372C42—41no—
373C42—41no—
374C42—41no—
375C42—41no—
376C42—41no—
377C42—41no—
378C42—48no—
379C42—84no—
380C42#12314yes—
381C42#12314yes—
382C42#12614yes—
383C42#12614yes—
384C23C2×#12111yescharacteristic
385C23C2×#12311yescharacteristic
386C23#52511yescharacteristic
387C23#52511yescharacteristic
388C23C2×#12411yescharacteristic
389C23#53711yescharacteristic
390C23#53711yescharacteristic
391C23C2×#13512yes—
392C23C2×#13712yes—
393C23#57512yes—
394C23#57512yes—
395Q8—24no—
396Q8—24no—
397Q8—42no—
398Q8—42no—
399Q8—42no—
400Q8—42no—
401Q8—42no—
402Q8—42no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—82no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
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—82no—
461C2×C4#39714yes—
462C2×C4#39714yes—
463C2×C4C2×#12311yescharacteristic
464C2×C4C2×#12311yescharacteristic
465C2×C4C2×#12411yescharacteristic
466C2×C4C2×#12611yescharacteristic
467C2×C4C2×#12611yescharacteristic
468C2×C4#52911yescharacteristic
469C2×C4#52911yescharacteristic
470C2×C4#53211yescharacteristic
471C2×C4#53511yescharacteristic
472C2×C4#53611yescharacteristic
473C2×C4#54211yescharacteristic
474C2×C4#54211yescharacteristic
475C2×C4#55211yescharacteristic
476C2×C4#55211yescharacteristic
477C2×C4#55211yescharacteristic
478C2×C4#55211yescharacteristic
479C2×C4#55211yescharacteristic
480C2×C4#55211yescharacteristic
481C2×C4#55311yescharacteristic
482C2×C4#55311yescharacteristic
483C2×C4#55311yescharacteristic
484C2×C4#55311yescharacteristic
485C2×C4#55311yescharacteristic
486C2×C4#55311yescharacteristic
487C2×C4#55511yescharacteristic
488C2×C4#55511yescharacteristic
489C2×C4#55611yescharacteristic
490C2×C4#55611yescharacteristic
491C8—82no—
492C8—82no—
493C22C2×#39711yescharacteristic
494C22#248511yescharacteristic
495C22#248511yescharacteristic
496C22#256211yescharacteristic
497C22#256211yescharacteristic
498C22#262011yescharacteristic
499C22#285011yescharacteristic
500C22#303512yes—
501C22#303712yes—
502C22#309112yes—
503C22#309512yes—
504C22#310212yes—
505C22#310812yes—
506C22#311112yes—
507C22#311712yes—
508C22#313111yescharacteristic
509C22#313511yescharacteristic
510C22#313911yescharacteristic
511C22#314011yescharacteristic
512C22#324812yes—
513C22#325012yes—
514C22#325212yes—
515C22#325612yes—
516C4—24no—
517C4—24no—
518C4—44no—
519C4—44no—
520C4—44no—
521C4—82no—
522C4—82no—
523C4—82no—
524C4—162no—
525C4—162no—
526C4#249411yescharacteristic
527C4#249411yescharacteristic
528C4#249511yescharacteristic
529C4#249511yescharacteristic
530C4#249911yescharacteristic
531C4#250011yescharacteristic
532C4#250311yescharacteristic
533C4#250411yescharacteristic
534C2#1523311yescharacteristic
535C2#2362711yescharacteristic
536C2#2362911yescharacteristic
537C2#2763412yes—
538C2#2763512yes—
539C2#2912511yescharacteristic
540C2#2912611yescharacteristic
541C2#2912811yescharacteristic
542C2#2912911yescharacteristic
543C2#2983312yes—
544C2#3302912yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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
#146892
C4×#3912
#113162
#113152
#111902
#108502
#108322