Finite Group Databasebeta

← #476184

Subgroups — #476184

Order 512.

1164 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2043C212yesmaximal
2C2×#2024C212yesmaximal
3#15180C211yesmaximal, characteristic
4#15128C211yesmaximal, characteristic
5#11346C211yesmaximal, characteristic
6#11220C212yesmaximal
7#11190C212yesmaximal
8#11122C212yesmaximal
9#11122C212yesmaximal
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4⋊Q8C2211yescharacteristic
12C22×#106C2212yes—
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C2×#395—21no—
18C2×#391C2212yes—
19C2×#391C2212yes—
20C2×#389C2212yes—
21C2×C4×C4⋊C4C2211yescharacteristic
22#2043—28no—
23#2024—28no—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2212yes—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1446—21no—
32#1444—21no—
33#1442—21no—
34#1442—21no—
35#1441—21no—
36#1441—21no—
37#1441—21no—
38C4⋊#95C2211yescharacteristic
39C4⋊#95C2212yes—
40C4⋊#95C2211yescharacteristic
41C23×Q8—21no—
42C23×Q8C2312yes—
43C23×C8C2312yes—
44C23×C8C2312yes—
45C2×C4⋊Q8—24no—
46C2×C4⋊Q8—24no—
47C2×C4⋊Q8—41no—
48C2×C4⋊Q8—41no—
49C2×C4⋊Q8—42no—
50C2×C4⋊Q8—41no—
51C2×C4⋊Q8—41no—
52C2×C4⋊Q8—42no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4D411yescharacteristic
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2312yes—
62C22×C42C2311yescharacteristic
63C22×C42C2311yescharacteristic
64C22×C42C2311yescharacteristic
65C2×#106—24no—
66C2×#106—42no—
67C2×#106—42no—
68C2×#103—24no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—24no—
74C2×#103—42no—
75C2×#103—42no—
76C2×#103—42no—
77C2×#103—42no—
78C2×#103—42no—
79C2×#103D418yes—
80#395—44no—
81#391—24no—
82#391—42no—
83#391—42no—
84#391—42no—
85#389—24no—
86#389—42no—
87C4×C4⋊C4—41no—
88C4×C4⋊C4—41no—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95D411yescharacteristic
101C2×#95D411yescharacteristic
102#340—24no—
103#340—24no—
104#340—42no—
105#336—24no—
106#336—24no—
107#336—41no—
108#336—41no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—44no—
123C22×Q8—42no—
124C22×Q8—42no—
125C22×Q8—42no—
126C22×Q8—82no—
127C22×Q8C2×D414yes—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4C2×D411yescharacteristic
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2411yescharacteristic
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8C2×D414yes—
153C4⋊Q8—44no—
154C4⋊Q8—48no—
155C4⋊Q8—44no—
156C4⋊Q8—48no—
157C4⋊Q8—44no—
158C4⋊Q8—44no—
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—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—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4SD1614yes—
190C2×C4⋊C4C2×D414yes—
191C2×C4⋊C4#4114yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—22no—
203C2×C42—22no—
204#106—48no—
205#103—48no—
206#103—48no—
207#103—48no—
208#103—48no—
209#95—41no—
210#95—41no—
211#95—44no—
212#95—44no—
213#95—44no—
214#95—42no—
215#95—44no—
216#95—44no—
217#95—42no—
218#95—44no—
219#95—42no—
220#95—42no—
221#95—82no—
222C24C22×D411yescharacteristic
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—48no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—88no—
253C2×Q8—84no—
254C2×Q8—88no—
255C2×Q8—84no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
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×C4C2×SD1612yes—
312C22×C4C2×SD1612yes—
313C22×C4C2×SD1612yes—
314C22×C4#13712yes—
315C22×C4#13712yes—
316C22×C4C22×D412yes—
317C22×C4C2×#4112yes—
318C22×C4H(5,𝔽2)11yescharacteristic
319C22×C4H(5,𝔽2)12yes—
320C22×C4H(5,𝔽2)12yes—
321C22×C4H(5,𝔽2)11yescharacteristic
322C22×C42−1+412yes—
323C22×C42−1+412yes—
324C2×C8—24no—
325C2×C8—24no—
326C2×C8—24no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—42no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—44no—
343C4⋊C4—44no—
344C4⋊C4—48no—
345C4⋊C4—48no—
346C4⋊C4—48no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—88no—
356C42—42no—
357C42—42no—
358C42—41no—
359C42—41no—
360C42—41no—
361C42—41no—
362C42—42no—
363C42—42no—
364C23#53411yescharacteristic
365C23#53511yescharacteristic
366C23#53611yescharacteristic
367C23D4212yes—
368C23#54812yes—
369C23C22×SD1611yescharacteristic
370C23C2×#13711yescharacteristic
371C23C2×#13711yescharacteristic
372C23#57511yescharacteristic
373C23#57712yes—
374C23#57812yes—
375Q8—44no—
376Q8—44no—
377Q8—44no—
378Q8—44no—
379Q8—816no—
380Q8—82no—
381Q8—82no—
382Q8—82no—
383Q8—82no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
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#53412yes—
445C2×C4#53612yes—
446C2×C4#53712yes—
447C2×C4#53812yes—
448C2×C4#54212yes—
449C2×C4#54212yes—
450C2×C4D4211yescharacteristic
451C2×C4#54612yes—
452C2×C4#54712yes—
453C2×C4#55511yescharacteristic
454C2×C4H(3,𝔽4)11yescharacteristic
455C2×C4#56212yes—
456C2×C4#56212yes—
457C2×C4#56212yes—
458C2×C4#56312yes—
459C2×C4#56311yescharacteristic
460C8—44no—
461C8—82no—
462C22#267412yes—
463C22#267612yes—
464C22#267911yescharacteristic
465C22#273111yescharacteristic
466C22#281611yescharacteristic
467C22#318711yescharacteristic
468C22#319511yescharacteristic
469C22#320011yescharacteristic
470C22#320211yescharacteristic
471C22#320611yescharacteristic
472C22#321611yescharacteristic
473C22#322512yes—
474C22#322911yescharacteristic
475C22#323711yescharacteristic
476C22#324212yes—
477C22#327012yes—
478C22#327012yes—
479C22#327512yes—
480C22D4×SD1612yes—
481C22#335912yes—
482C22#336912yes—
483C22#337212yes—
484C22#337712yes—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—42no—
489C4—42no—
490C4—81no—
491C4—84no—
492C4—84no—
493C4—84no—
494C4—162no—
495C4#267212yes—
496C4#268612yes—
497C4#281412yes—
498C4#283212yes—
499C2#1708411yescharacteristic
500C2#3080812yes—
501C2#3083612yes—
502C2#3087812yes—
503C2#3090412yes—
504C2#3105811yescharacteristic
505C2#3106911yescharacteristic
506C2#3263011yescharacteristic
507C2#3264511yescharacteristic
508C2#3277111yescharacteristic
509C2#3278011yescharacteristic
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×#20432
C2×#20242
#151802
#151282
#113462
#112202
#111902
#111222