Finite Group Databasebeta

← #467421

Subgroups — #467421

Order 512.

910 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15152C211yesmaximal, characteristic
2#13910C211yesmaximal, characteristic
3#11292C212yesmaximal
4#11292C212yesmaximal
5#11267C212yesmaximal
6#11227C212yesmaximal
7#11207C212yesmaximal
8#11202C211yesmaximal, characteristic
9#10806C212yesmaximal
10C22×C4⋊C8C2211yescharacteristic
11C2×#400—21no—
12C2×#389C2212yes—
13C2×#389C2212yes—
14C2×#384—21no—
15C2×#384C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2212yes—
30#1445—21no—
31#1444—21no—
32#1444—21no—
33#1442—21no—
34#1441—21no—
35C4⋊#95—21no—
36C4⋊#95C2212yes—
37C4⋊#95C2211yescharacteristic
38C4⋊#95C2212yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4D411yescharacteristic
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C4⋊C4C2312yes—
53C22×C42—21no—
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C2×C4⋊C8—41no—
58C2×C4⋊C8—42no—
59#400—44no—
60#389—24no—
61#389—24no—
62#389—42no—
63#389—42no—
64#384—41no—
65#384—41no—
66#384—41no—
67#384—41no—
68#384—44no—
69C4×C4⋊C4—22no—
70C4×C4⋊C4—41no—
71C4×C4⋊C4—41no—
72C4×C4⋊C4Q814yes—
73C2×#95—21no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—21no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—21no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95D411yescharacteristic
83C2×#95D411yescharacteristic
84#340—24no—
85#340—24no—
86#340—24no—
87#340—24no—
88#340—42no—
89#340—42no—
90#340—42no—
91#340—42no—
92#336—24no—
93#336—41no—
94#336—42no—
95C23×C4—22no—
96C23×C4—22no—
97C23×C4—22no—
98C23×C4—22no—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2411yescharacteristic
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—44no—
147C2×C4⋊C4—44no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—42no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4—82no—
162C2×C4⋊C4D814yes—
163C2×C4⋊C4C2×Q814yes—
164C2×C4⋊C4#4114yes—
165C2×C4⋊C4#4114yes—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—24no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—21no—
174C2×C42—22no—
175C2×C42—21no—
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—22no—
179C2×C42—42no—
180C2×C42—42no—
181C2×C42C2×Q812yes—
182C2×C42#4112yes—
183C4⋊C8—44no—
184#95—24no—
185#95—41no—
186#95—41no—
187#95—44no—
188#95—44no—
189#95—42no—
190#95—44no—
191#95—44no—
192#95—42no—
193#95—82no—
194#95—82no—
195C24C22×D411yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—24no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—24no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
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×C4C22⋊Q812yes—
250C22×C4C22⋊Q812yes—
251C22×C4C2×D812yes—
252C22×C4C2×D812yes—
253C22×C4C2×D812yes—
254C22×C4#13712yes—
255C22×C4#13712yes—
256C22×C4C22×Q811yescharacteristic
257C22×C4C2×#4112yes—
258C22×C4C2×#4112yes—
259C22×C4C2×#4111yescharacteristic
260C22×C4H(5,𝔽2)11yescharacteristic
261C22×C4H(5,𝔽2)11yescharacteristic
262C22×C4H(5,𝔽2)12yes—
263C22×C42−1+411yescharacteristic
264C22×C42−1+411yescharacteristic
265C22×C42−1+412yes—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—24no—
283C4⋊C4—44no—
284C4⋊C4—44no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—88no—
298C4⋊C4—88no—
299C4⋊C4—84no—
300C4⋊C4—84no—
301C4⋊C4—84no—
302C4⋊C4—84no—
303C4⋊C4#12518yes—
304C42—22no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—42no—
309C42—42no—
310C42—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—48no—
315C23C2×C22⋊Q811yescharacteristic
316C23#53411yescharacteristic
317C23#53611yescharacteristic
318C23#54612yes—
319C23#54812yes—
320C23C22×D811yescharacteristic
321C23C2×#13711yescharacteristic
322C23C2×#13711yescharacteristic
323C23#57511yescharacteristic
324C23#57712yes—
325C23#57712yes—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—28no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—82no—
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#47414yes—
386C2×C4C2×#12512yes—
387C2×C4#53911yescharacteristic
388C2×C4#53911yescharacteristic
389C2×C4#54012yes—
390C2×C4#54112yes—
391C2×C4#54212yes—
392C2×C4#54212yes—
393C2×C4#54411yescharacteristic
394C2×C4#54412yes—
395C2×C4#54411yescharacteristic
396C2×C4#55212yes—
397C2×C4#55312yes—
398C2×C4#55511yescharacteristic
399C2×C4#55612yes—
400C2×C4#55911yescharacteristic
401C2×C4#56011yescharacteristic
402C2×C4#56312yes—
403C2×C4#56311yescharacteristic
404C8—82no—
405C8—82no—
406C22#244212yes—
407C22#262711yescharacteristic
408C22#270911yescharacteristic
409C22#271612yes—
410C22#273111yescharacteristic
411C22C2×#47411yescharacteristic
412C22#307811yescharacteristic
413C22#308412yes—
414C22#318611yescharacteristic
415C22#319511yescharacteristic
416C22#320011yescharacteristic
417C22#320011yescharacteristic
418C22#322611yescharacteristic
419C22#323611yescharacteristic
420C22#324412yes—
421C22#329412yes—
422C22#331712yes—
423C22#332012yes—
424C22#333112yes—
425C22#335812yes—
426C22#336912yes—
427C22#337112yes—
428C22#337212yes—
429C4—24no—
430C4—42no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—48no—
435C4—81no—
436C4—162no—
437C4—162no—
438C4—162no—
439C4#257111yescharacteristic
440C4#264712yes—
441C4#279312yes—
442C4#279411yescharacteristic
443C4#279511yescharacteristic
444C4#284311yescharacteristic
445C2#1657011yescharacteristic
446C2#2610612yes—
447C2#2612112yes—
448C2#2996611yescharacteristic
449C2#2997711yescharacteristic
450C2#3202611yescharacteristic
451C2#3203711yescharacteristic
452C2#3222612yes—
453C2#3225512yes—
454C2#3262811yescharacteristic
455C2#3264511yescharacteristic
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
#151522
#139102
#112922
#112672
#112272
#112072
#112022
#108062