Finite Group Databasebeta

← #478646

Subgroups — #478646

Order 512.

986 conjugacy classes of subgroups.

The subgroup lattice has 461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15185C212yesmaximal
2#11267C212yesmaximal
3#11256C211yesmaximal, characteristic
4#11255C211yesmaximal, characteristic
5#11124C212yesmaximal
6#11077C212yesmaximal
7#11050C212yesmaximal
8#11024C211yesmaximal, characteristic
9#11024C212yesmaximal
10C23×Q16C2211yescharacteristic
11C22×#107C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C2×#391C2212yes—
17C2×#391C2212yes—
18C2×#391C2212yes—
19C2×#384C2212yes—
20C2×#340C2211yescharacteristic
21C2×#340C2211yescharacteristic
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#336C2212yes—
26C2×#336C2211yescharacteristic
27C2×#336C2212yes—
28#1445—22no—
29#1445—22no—
30#1442—22no—
31#1442—22no—
32C4⋊#95C2212yes—
33C4⋊#95C2212yes—
34C4×#95C2211yescharacteristic
35C23×Q8C2312yes—
36C22×Q16—24no—
37C22×Q16—22no—
38C22×Q16—41no—
39C22×Q16—42no—
40C22×Q16—41no—
41C23×C8C2312yes—
42C23×C8C2311yescharacteristic
43C23×C8C2311yescharacteristic
44C22×C4⋊C4—22no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C42C2311yescharacteristic
50C22×C42C2312yes—
51C2×#107—42no—
52C2×#107—41no—
53C2×C4⋊C8—41no—
54C2×C4⋊C8—42no—
55C2×#103—24no—
56C2×#103—42no—
57C2×#103—42no—
58C2×#103—42no—
59C2×#103—42no—
60C2×#103—42no—
61C2×#103—42no—
62C2×#103—42no—
63C2×#103—42no—
64#391—24no—
65#391—24no—
66#391—42no—
67#391—42no—
68#391—42no—
69#391—42no—
70#384—42no—
71#384—42no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95D412yes—
83C2×#95D411yescharacteristic
84C2×#95D411yescharacteristic
85#340—22no—
86#340—41no—
87#340—42no—
88#340—42no—
89#340—42no—
90#336—24no—
91#336—42no—
92#336—41no—
93C22×Q8—22no—
94C22×Q8—22no—
95C22×Q8—22no—
96C22×Q8—22no—
97C22×Q8—22no—
98C22×Q8—22no—
99C22×Q8—22no—
100C22×Q8—22no—
101C22×Q8—22no—
102C22×Q8—22no—
103C22×Q8—22no—
104C22×Q8—22no—
105C22×Q8—22no—
106C22×Q8#4114yes—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—22no—
110C23×C4—22no—
111C23×C4C2×D411yescharacteristic
112C23×C4C2×D412yes—
113C23×C4C2×D411yescharacteristic
114C23×C4C2×D412yes—
115C23×C4C2411yescharacteristic
116C2×Q16—48no—
117C2×Q16—44no—
118C2×Q16—44no—
119C2×Q16—48no—
120C2×Q16—44no—
121C22×C8—22no—
122C22×C8—21no—
123C22×C8—21no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—21no—
127C22×C8—22no—
128C22×C8—21no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8#4112yes—
137C22×C8#4112yes—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4—82no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—21no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—21no—
171C2×C42—22no—
172#107—44no—
173C4⋊C8—44no—
174#103—48no—
175#103—48no—
176#103—48no—
177#95—24no—
178#95—41no—
179#95—44no—
180#95—44no—
181#95—44no—
182#95—44no—
183#95—44no—
184#95—44no—
185#95—82no—
186#95—82no—
187#95—82no—
188#95—82no—
189#95Q1614yescomplemented
190C24C22×D411yescharacteristic
191C2×Q8—24no—
192C2×Q8—24no—
193C2×Q8—24no—
194C2×Q8—24no—
195C2×Q8—24no—
196C2×Q8—24no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—42no—
209C2×Q8—42no—
210C2×Q8—42no—
211C2×Q8—42no—
212C2×Q8—42no—
213C2×Q8—42no—
214C2×Q8—42no—
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—42no—
218C2×Q8—42no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4C2×Q1614yes—
269C22×C4C2×Q1612yes—
270C22×C4#13714yes—
271C22×C4C2×#4111yescharacteristic
272C22×C4C2×#4112yes—
273C22×C4C2×#4111yescharacteristic
274C22×C4H(5,𝔽2)11yescharacteristic
275C22×C4H(5,𝔽2)12yes—
276C22×C4H(5,𝔽2)12yes—
277C22×C4H(5,𝔽2)11yescharacteristic
278C22×C4H(5,𝔽2)12yes—
279C22×C42−1+411yescharacteristic
280C22×C42−1+411yescharacteristic
281Q16—416no—
282C2×C8—24no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—24no—
286C2×C8—42no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—88no—
312C4⋊C4—88no—
313C42—42no—
314C42—42no—
315C42—42no—
316C42—41no—
317C42—42no—
318C42—41no—
319C42—42no—
320C23#53512yes—
321C23#53711yescharacteristic
322C23#54612yes—
323C23#54711yescharacteristic
324C23#55011yescharacteristic
325C23C22×Q1611yescharacteristic
326C23C2×#13712yes—
327C23#57511yescharacteristic
328C23#57611yescharacteristic
329C23#57712yes—
330C23#57811yescharacteristic
331Q8—44no—
332Q8—44no—
333Q8—44no—
334Q8—44no—
335Q8—82no—
336Q8—82no—
337Q8—82no—
338Q8—82no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4#53812yes—
392C2×C4#53812yes—
393C2×C4#53811yescharacteristic
394C2×C4#53911yescharacteristic
395C2×C4#53912yes—
396C2×C4#53912yes—
397C2×C4#54012yes—
398C2×C4#55111yescharacteristic
399C2×C4#55112yes—
400C2×C4#55312yes—
401C2×C4#55611yescharacteristic
402C2×C4#56011yescharacteristic
403C2×C4#56012yes—
404C2×C4H(3,𝔽4)11yescharacteristic
405C2×C4H(3,𝔽4)11yescharacteristic
406C2×C4#56212yes—
407C2×C4#56212yes—
408C2×C4#56311yescharacteristic
409C8—42no—
410C8—42no—
411C8—82no—
412C22#269311yescharacteristic
413C22#270612yes—
414C22#271412yes—
415C22#272711yescharacteristic
416C22#281911yescharacteristic
417C22#320912yes—
418C22#321512yes—
419C22#322412yes—
420C22#322512yes—
421C22#324911yescharacteristic
422C22#325511yescharacteristic
423C22#326211yescharacteristic
424C22#326311yescharacteristic
425C22#329912yes—
426C22#331212yes—
427C22#331712yes—
428C22#333312yes—
429C22#333811yescharacteristic
430C22#334412yes—
431C22#335211yescharacteristic
432C22#339511yescharacteristic
433C22#340012yes—
434C22#340311yescharacteristic
435C4—42no—
436C4—44no—
437C4—44no—
438C4—84no—
439C4—81no—
440C4—162no—
441C4—162no—
442C4—162no—
443C4#273611yescharacteristic
444C4#278211yescharacteristic
445C4#278612yes—
446C4#282411yescharacteristic
447C4#282712yes—
448C4#282811yescharacteristic
449C2#1715911yescharacteristic
450C2#3155411yescharacteristic
451C2#3156811yescharacteristic
452C2#3193612yes—
453C2#3195112yes—
454C2#3216812yes—
455C2#3219112yes—
456C2#3252611yescharacteristic
457C2#3253511yescharacteristic
458C2#3280811yescharacteristic
459C2#3281711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
189. #95Q16semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#151852
#112672
#112562
#112552
#111242
#110772
#110502
#110242