Finite Group Databasebeta

← #475662

Subgroups — #475662

Order 512.

1044 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2100C211yesmaximal, characteristic
2C2×#2099C211yesmaximal, characteristic
3C2×#2096C211yesmaximal, characteristic
4C2×#2095C211yesmaximal, characteristic
5#14703C211yesmaximal, characteristic
6#14687C211yesmaximal, characteristic
7#11325C212yesmaximal
8#11325C212yesmaximal
9#11052C212yesmaximal
10#11052C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×#107C2212yes—
13C22×#106C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C2×#391C2211yescharacteristic
17C2×#391C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×#382C2212yes—
23C2×#382C2212yes—
24C2×C43C2211yescharacteristic
25#2100—24no—
26#2099—24no—
27#2096—24no—
28#2095—24no—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#336C2212yes—
34C2×#336C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37#1436—22no—
38C4⋊#95—22no—
39C4⋊#95—22no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2211yescharacteristic
42#1434—22no—
43C23×Q8C2311yescharacteristic
44C23×C8C2312yes—
45C23×C8C2312yes—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2311yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C42D412yes—
57C22×C42D412yes—
58C22×C42C2311yescharacteristic
59C22×C42C2311yescharacteristic
60C22×C42C2311yescharacteristic
61C2×#107—24no—
62C2×#107—42no—
63C2×#107—42no—
64C2×#106—24no—
65C2×#106—42no—
66C2×#106—42no—
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—42no—
70C2×#103—42no—
71C2×#103—42no—
72C2×#103—42no—
73#391—22no—
74#391—22no—
75#391—22no—
76#391—24no—
77#391Q814yes—
78#389—22no—
79#389—22no—
80#384—22no—
81#384—22no—
82#384—22no—
83#384—22no—
84#382—42no—
85#382—42no—
86#382—42no—
87#382—42no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—24no—
95C2×#95—24no—
96C2×#95—21no—
97C43—24no—
98#340—24no—
99#340—24no—
100#340—24no—
101#340—24no—
102#336—24no—
103#336—24no—
104#336D414yes—
105#336D414yes—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—21no—
113C22×Q8—21no—
114C22×Q8—22no—
115C22×Q8C2×Q812yes—
116C23×C4—21no—
117C23×C4—21no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4C2×D412yes—
123C23×C4C2×D412yes—
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2411yescharacteristic
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8C2×D414yes—
140C22×C8C2×D414yes—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—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—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4C2×Q812yes—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—21no—
182C2×C42—21no—
183C2×C42—22no—
184C2×C42—24no—
185C2×C42—24no—
186C2×C42—24no—
187C2×C42—24no—
188C2×C42—42no—
189C2×C42—42no—
190C2×C42C2×D412yes—
191C2×C42C2×D412yes—
192C2×C42C2×Q812yes—
193C2×C42#4112yes—
194C2×C42#4114yes—
195#107—48no—
196#106—48no—
197#103—48no—
198#103—48no—
199#95—28no—
200#95—44no—
201#95—44no—
202#95—48no—
203#95—48no—
204#95—44no—
205#95—42no—
206#95—42no—
207#95—42no—
208C24C22×D411yescharacteristic
209C2×Q8—24no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—24no—
213C2×Q8—42no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8—42no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4C22⋊Q814yes—
276C22×C4#12314yes—
277C22×C4#12712yes—
278C22×C4#12712yes—
279C22×C4#13514yes—
280C22×C4#13714yes—
281C22×C4C22×D411yescharacteristic
282C22×C4C22×D411yescharacteristic
283C22×C4C22×Q811yescharacteristic
284C22×C4C2×#4112yes—
285C22×C4C2×#4111yescharacteristic
286C22×C4H(5,𝔽2)12yes—
287C22×C4H(5,𝔽2)12yes—
288C22×C42−1+411yescharacteristic
289C22×C42−1+411yescharacteristic
290C22×C42−1+412yes—
291C2×C8—24no—
292C2×C8—24no—
293C2×C8—24no—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—24no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—42no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—84no—
322C4⋊C4—84no—
323C4⋊C4—84no—
324C4⋊C4—84no—
325C4⋊C4—84no—
326C42—24no—
327C42—24no—
328C42—24no—
329C42—24no—
330C42—24no—
331C42—24no—
332C42—48no—
333C42—48no—
334C23C2×C22⋊Q811yescharacteristic
335C23C2×#12311yescharacteristic
336C23C2×#12711yescharacteristic
337C23#53511yescharacteristic
338C23#53511yescharacteristic
339C23#53611yescharacteristic
340C23#53611yescharacteristic
341C23C2×#13512yes—
342C23C2×#13712yes—
343C23#57512yes—
344C23#57512yes—
345Q8—44no—
346Q8—44no—
347Q8—82no—
348Q8—82no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—82no—
382C2×C4—81no—
383C2×C4—82no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4—84no—
396C2×C4—84no—
397C2×C4—84no—
398C2×C4—82no—
399C2×C4—84no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—81no—
403C2×C4#49514yes—
404C2×C4#49714yes—
405C2×C4#53512yes—
406C2×C4#53512yes—
407C2×C4#53912yes—
408C2×C4#53912yes—
409C2×C4#54212yes—
410C2×C4#54412yes—
411C2×C4#54711yescharacteristic
412C2×C4#54711yescharacteristic
413C2×C4#54712yes—
414C2×C4#54712yes—
415C2×C4D4×Q811yescharacteristic
416C2×C4D4×Q811yescharacteristic
417C2×C4#55312yes—
418C2×C4#55412yes—
419C2×C4#56312yes—
420C2×C4#56312yes—
421C8—44no—
422C8—44no—
423C22#248711yescharacteristic
424C22#250111yescharacteristic
425C22#254211yescharacteristic
426C22#262311yescharacteristic
427C22#262811yescharacteristic
428C22#265711yescharacteristic
429C22#282111yescharacteristic
430C22#307612yes—
431C22#307812yes—
432C22#309112yes—
433C22#309512yes—
434C22C2×#49511yescharacteristic
435C22C2×#49711yescharacteristic
436C22#315311yescharacteristic
437C22#315311yescharacteristic
438C22#321012yes—
439C22#321012yes—
440C22#321912yes—
441C22#321912yes—
442C22#323212yes—
443C22#323312yes—
444C22#323612yes—
445C22#323712yes—
446C4—24no—
447C4—24no—
448C4—44no—
449C4—44no—
450C4—82no—
451C4—82no—
452C4—161no—
453C4—162no—
454C4—162no—
455C4—161no—
456C4#271812yes—
457C4#271812yes—
458C4#272012yes—
459C4#272012yes—
460C2#1706411yescharacteristic
461C2#2768512yes—
462C2#2791211yescharacteristic
463C2#2791911yescharacteristic
464C2#2851011yescharacteristic
465C2#2852211yescharacteristic
466C2#2991512yes—
467C2#2998912yes—
468C2#3026111yescharacteristic
469C2#3026611yescharacteristic
470C2#3284312yes—
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×#21002
C2×#20992
C2×#20962
C2×#20952
#147032
#146872
#113252
#110522
#107952