Finite Group Databasebeta

← #432768

Subgroups — #432768

Order 512.

1166 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2453C211yesmaximal, characteristic
2C2×#2072C211yesmaximal, characteristic
3C2×#1992C211yesmaximal, characteristic
4#15152C211yesmaximal, characteristic
5#11385C211yesmaximal, characteristic
6#11293C212yesmaximal
7#11292C212yesmaximal
8#11190C212yesmaximal
9#10928C211yesmaximal, characteristic
10#10875C211yesmaximal, characteristic
11#10789C212yesmaximal
12C22×#125C2211yescharacteristic
13C22×C4×Q8C2211yescharacteristic
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#97C2211yescharacteristic
17#2453—24no—
18#2453—24no—
19C2×#400—21no—
20C2×#400—21no—
21C2×#398—21no—
22C2×#391C2211yescharacteristic
23C2×#391C2211yescharacteristic
24C2×#389—21no—
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#387—21no—
28C2×#384C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30#2072—24no—
31#1992—24no—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#340C2212yes—
36C2×#340C2212yes—
37C2×#340C2212yes—
38C2×#336C2212yes—
39C2×#336C2211yescharacteristic
40C2×#336C2212yes—
41#1445—21no—
42#1442—21no—
43#1441—21no—
44C4⋊#95C2212yes—
45C4⋊#95C2212yes—
46C4⋊#95C2211yescharacteristic
47C23×Q8C2311yescharacteristic
48C23×C8C2312yes—
49C23×C8C2312yes—
50C2×#125—24no—
51C2×#125—22no—
52C2×#125—42no—
53C2×#125D414yes—
54C2×C4×Q8—22no—
55C2×C4×Q8—22no—
56C2×C4×Q8—24no—
57C2×C4×Q8—42no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4D411yescharacteristic
66C22×C4⋊C4D411yescharacteristic
67C22×C4⋊C4C2312yes—
68C22×C4⋊C4C2312yes—
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C42—21no—
73C22×C42C2311yescharacteristic
74C22×C42C2311yescharacteristic
75C22×C42C2311yescharacteristic
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—42no—
82C2×#97—22no—
83C2×#97—42no—
84#400—28no—
85#400—44no—
86#398—28no—
87#391—22no—
88#391—22no—
89#391—22no—
90#391D414yes—
91#389—28no—
92#389—22no—
93#389—22no—
94#389—22no—
95#389—22no—
96#387—28no—
97#384—22no—
98#384—22no—
99C4×C4⋊C4—22no—
100C4×C4⋊C4—22no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—22no—
112C2×#95—22no—
113C2×#95D411yescharacteristic
114C2×#95D411yescharacteristic
115#340—24no—
116#340—24no—
117#340—24no—
118#340—24no—
119#340—24no—
120#340—42no—
121#336—24no—
122#336—22no—
123#336—42no—
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8C2×D412yes—
131C22×Q8#4114yes—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—22no—
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#4114yes—
159#125—28no—
160#125—44no—
161#125—48no—
162C4×Q8—48no—
163C4×Q8—44no—
164C4×Q8—44no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—44no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—82no—
208C2×C4⋊C4C2×D412yes—
209C2×C4⋊C4C2×D412yes—
210C2×C4⋊C4C2×D412yes—
211C2×C4⋊C4#4114yes—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—24no—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—44no—
224C2×C42C2×D412yes—
225C2×C42C2×D412yes—
226#103—48no—
227#103—48no—
228#97—44no—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—24no—
233#95—24no—
234#95—24no—
235#95—22no—
236#95—22no—
237#95—42no—
238#95—42no—
239#95—44no—
240#95—44no—
241#95—82no—
242#95—82no—
243C24C22×D411yescharacteristic
244C2×Q8—22no—
245C2×Q8—24no—
246C2×Q8—24no—
247C2×Q8—24no—
248C2×Q8—24no—
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—24no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8#12414yes—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
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—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4#12012yes—
325C22×C4#12012yes—
326C22×C4AGL(1,ℤ/8)12yes—
327C22×C4#13712yes—
328C22×C4C22×D411yescharacteristic
329C22×C4C22×D411yescharacteristic
330C22×C4C2×#4112yes—
331C22×C4C2×#4112yes—
332C22×C4C2×#4112yes—
333C22×C4H(5,𝔽2)12yes—
334C22×C42−1+412yes—
335C22×C42−1+412yes—
336C2×C8—24no—
337C2×C8—24no—
338C2×C8—24no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—44no—
356C4⋊C4—44no—
357C4⋊C4—48no—
358C4⋊C4—48no—
359C4⋊C4—48no—
360C4⋊C4—48no—
361C4⋊C4—48no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—84no—
373C4⋊C4—84no—
374C4⋊C4#12314yes—
375C42—22no—
376C42—22no—
377C42—24no—
378C42—48no—
379C42—41no—
380C42—41no—
381C42—42no—
382C42—42no—
383C42—42no—
384C23C2×#12011yescharacteristic
385C23#53211yescharacteristic
386C23#53611yescharacteristic
387C23#54612yes—
388C23#54812yes—
389C23C2×AGL(1,ℤ/8)11yescharacteristic
390C23C2×#13711yescharacteristic
391C23#57511yescharacteristic
392C23#57511yescharacteristic
393C23#57712yes—
394C23#57812yes—
395Q8—28no—
396Q8—44no—
397Q8—44no—
398Q8—44no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—44no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
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—82no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4C2×#12311yescharacteristic
468C2×C4C2×#12411yescharacteristic
469C2×C4#52912yes—
470C2×C4#53411yescharacteristic
471C2×C4#53611yescharacteristic
472C2×C4#53912yes—
473C2×C4#53912yes—
474C2×C4#54112yes—
475C2×C4#54612yes—
476C2×C4#54712yes—
477C2×C4#54812yes—
478C2×C4#54812yes—
479C2×C4#55112yes—
480C2×C4#55212yes—
481C2×C4#55612yes—
482C2×C4#56312yes—
483C8—44no—
484C8—82no—
485C22#240511yescharacteristic
486C22#243211yescharacteristic
487C22#243611yescharacteristic
488C22#256012yes—
489C22#269012yes—
490C22#300611yescharacteristic
491C22#300711yescharacteristic
492C22#301011yescharacteristic
493C22#301111yescharacteristic
494C22#317211yescharacteristic
495C22#317812yes—
496C22#318011yescharacteristic
497C22#323811yescharacteristic
498C22#324011yescharacteristic
499C22#324212yes—
500C22#331512yes—
501C22#331612yes—
502C22#332612yes—
503C22#333012yes—
504C22#336812yes—
505C22#337112yes—
506C22#337412yes—
507C22#337712yes—
508C4—42no—
509C4—44no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—44no—
514C4—82no—
515C4—81no—
516C4—82no—
517C4—81no—
518C4—162no—
519C4—162no—
520C4#242112yes—
521C4#248812yes—
522C4#268912yes—
523C4#272812yes—
524C2#1546511yescharacteristic
525C2#2405211yescharacteristic
526C2#2405411yescharacteristic
527C2#2567911yescharacteristic
528C2#2568611yescharacteristic
529C2#2594311yescharacteristic
530C2#2594411yescharacteristic
531C2#2908612yes—
532C2#2909012yes—
533C2#3147212yes—
534C2#3147712yes—
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×#24532
C2×#20722
C2×#19922
#151522
#113852
#112932
#112922
#111902
#109282
#108752
#107892