Finite Group Databasebeta

← #449439

Subgroups — #449439

Order 512.

906 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15151C211yesmaximal, characteristic
2#13911C211yesmaximal, characteristic
3#11315C212yesmaximal
4#11315C212yesmaximal
5#11267C212yesmaximal
6#11207C212yesmaximal
7#10884C212yesmaximal
8#10874C211yesmaximal, characteristic
9#10820C212yesmaximal
10C22×C4×C8C2211yescharacteristic
11C2×#398—21no—
12C2×#398—21no—
13C2×#389C2212yes—
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#382—21no—
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×#336C2212yes—
29C2×#336C2211yescharacteristic
30#1445—21no—
31#1445—21no—
32#1442—21no—
33#1442—21no—
34C4⋊#95—21no—
35C4⋊#95C2212yes—
36C4⋊#95C2211yescharacteristic
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4D411yescharacteristic
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C42—21no—
53C22×C42C2311yescharacteristic
54C22×C42C2311yescharacteristic
55C22×C42C2311yescharacteristic
56C2×C4×C8—24no—
57C2×C4×C8—41no—
58#398—44no—
59#398—44no—
60#389—24no—
61#389—24no—
62#384—41no—
63#384—41no—
64#384—41no—
65#384—41no—
66#382—44no—
67C4×C4⋊C4—24no—
68C4×C4⋊C4—41no—
69C4×C4⋊C4—41no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—22no—
73C2×#95—21no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95D411yescharacteristic
81C2×#95D411yescharacteristic
82#340—24no—
83#340—24no—
84#340—24no—
85#340—24no—
86#340—24no—
87#340—24no—
88#340—42no—
89#340—42no—
90#336—24no—
91#336—24no—
92#336—41no—
93C23×C4—22no—
94C23×C4—22no—
95C23×C4—22no—
96C23×C4—22no—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2411yescharacteristic
104C22×C8—22no—
105C22×C8—22no—
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#4114yes—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—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—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—42no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—42no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—42no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—82no—
158C2×C4⋊C4D814yes—
159C2×C4⋊C4SD1614yes—
160C2×C4⋊C4#4114yes—
161C2×C4⋊C4#4114yes—
162C2×C42—22no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—24no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—42no—
175C2×C42—42no—
176C2×C42#4114yes—
177C4×C8—44no—
178#95—24no—
179#95—41no—
180#95—41no—
181#95—44no—
182#95—44no—
183#95—44no—
184#95—42no—
185#95—44no—
186#95—42no—
187#95—44no—
188#95—82no—
189#95—82no—
190C24C22×D411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
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#12412yes—
244C22×C4#12412yes—
245C22×C4C2×D812yes—
246C22×C4C2×D812yes—
247C22×C4C2×D812yes—
248C22×C4C2×SD1612yes—
249C22×C4C2×SD1612yes—
250C22×C4C2×SD1612yes—
251C22×C4C2×#4112yes—
252C22×C4C2×#4112yes—
253C22×C4C2×#4112yes—
254C22×C4C2×#4112yes—
255C22×C4H(5,𝔽2)11yescharacteristic
256C22×C4H(5,𝔽2)11yescharacteristic
257C22×C42−1+412yes—
258C22×C42−1+412yes—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—84no—
292C4⋊C4—84no—
293C4⋊C4—84no—
294C4⋊C4—84no—
295C4⋊C4—88no—
296C42—24no—
297C42—24no—
298C42—48no—
299C42—42no—
300C42—42no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—41no—
305C23#52511yescharacteristic
306C23C2×#12411yescharacteristic
307C23#53411yescharacteristic
308C23#54712yes—
309C23#54812yes—
310C23C22×D811yescharacteristic
311C23C22×SD1611yescharacteristic
312C23#57511yescharacteristic
313C23#57511yescharacteristic
314C23#57712yes—
315C23#57812yes—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
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#48614yes—
376C2×C4#52912yes—
377C2×C4#52912yes—
378C2×C4#54112yes—
379C2×C4#54112yes—
380C2×C4#54212yes—
381C2×C4#54212yes—
382C2×C4#55111yescharacteristic
383C2×C4#55212yes—
384C2×C4#55212yes—
385C2×C4#55212yes—
386C2×C4#55212yes—
387C2×C4#55312yes—
388C2×C4#55312yes—
389C2×C4#55511yescharacteristic
390C2×C4#56311yescharacteristic
391C2×C4#56311yescharacteristic
392C8—44no—
393C8—82no—
394C22#247512yes—
395C22#248912yes—
396C22#259111yescharacteristic
397C22#271711yescharacteristic
398C22#273111yescharacteristic
399C22#310011yescharacteristic
400C22#310311yescharacteristic
401C22#312012yes—
402C22C2×#48611yescharacteristic
403C22#313712yes—
404C22#314211yescharacteristic
405C22#318611yescharacteristic
406C22#318711yescharacteristic
407C22#320011yescharacteristic
408C22#320211yescharacteristic
409C22#333412yes—
410C22#333512yes—
411C22#334812yes—
412C22#334912yes—
413C22#335812yes—
414C22#335912yes—
415C22#337112yes—
416C22#337712yes—
417C4—24no—
418C4—42no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4—42no—
423C4—84no—
424C4—84no—
425C4—162no—
426C4—162no—
427C4#251512yes—
428C4#252912yes—
429C4#276612yes—
430C4#276612yes—
431C2#1594511yescharacteristic
432C2#2735812yes—
433C2#2736212yes—
434C2#2772712yes—
435C2#2774512yes—
436C2#2932811yescharacteristic
437C2#2934411yescharacteristic
438C2#3225811yescharacteristic
439C2#3225911yescharacteristic
440C2#3262811yescharacteristic
441C2#3263011yescharacteristic
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
#151512
#139112
#113152
#112672
#112072
#108842
#108742
#108202