Finite Group Databasebeta

← #479713

Subgroups — #479713

Order 512.

820 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15152C211yesmaximal, characteristic
2#15152C211yesmaximal, characteristic
3#11378C212yesmaximal
4#11346C211yesmaximal, characteristic
5#11323C212yesmaximal
6#11323C212yesmaximal
7#11316C212yesmaximal
8#11315C212yesmaximal
9#11257C212yesmaximal
10C22×#106C2212yes—
11C22×#106C2212yes—
12C2×#400—21no—
13C2×#400—21no—
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×C4×C4⋊C4C2211yescharacteristic
17C2×#340C2212yes—
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#336C2212yes—
24C2×#336C2212yes—
25C2×#336C2211yescharacteristic
26C2×#336C2211yescharacteristic
27#1445—21no—
28#1445—21no—
29#1442—21no—
30#1442—21no—
31#1441—21no—
32#1441—21no—
33C4⋊#95C2211yescharacteristic
34C4⋊#95C2212yes—
35C4⋊#95C2211yescharacteristic
36C4⋊#95C2212yes—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4D411yescharacteristic
46C22×C4⋊C4D411yescharacteristic
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C2×#106—24no—
55C2×#106—42no—
56C2×#106—42no—
57C2×#106—42no—
58C2×#106—42no—
59C2×#106—42no—
60#400—44no—
61#400—44no—
62#384—41no—
63#384—41no—
64#384—41no—
65#384—41no—
66C4×C4⋊C4—41no—
67C4×C4⋊C4—41no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—21no—
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—42no—
86#340—42no—
87#340—42no—
88#336—24no—
89#336—24no—
90#336—41no—
91#336—41no—
92C23×C4—22no—
93C23×C4—22no—
94C23×C4—22no—
95C23×C4—22no—
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2411yescharacteristic
103C22×C8—22no—
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#4114yes—
116C22×C8#4114yes—
117C2×C4⋊C4—22no—
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—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—41no—
145C2×C4⋊C4—41no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
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—82no—
155C2×C4⋊C4—82no—
156C2×C4⋊C4SD1614yes—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169#106—48no—
170#106—48no—
171#95—41no—
172#95—41no—
173#95—42no—
174#95—44no—
175#95—42no—
176#95—42no—
177#95—44no—
178#95—44no—
179#95—42no—
180#95—44no—
181#95—82no—
182#95—82no—
183#95—82no—
184#95—82no—
185C24C22×D411yescharacteristic
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
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×C4C2×SD1612yes—
242C22×C4C2×SD1612yes—
243C22×C4C2×SD1612yes—
244C22×C4AGL(1,ℤ/8)12yes—
245C22×C4#13712yes—
246C22×C4C2×#4112yes—
247C22×C4C2×#4112yes—
248C22×C4H(5,𝔽2)11yescharacteristic
249C22×C4H(5,𝔽2)12yes—
250C22×C4H(5,𝔽2)11yescharacteristic
251C22×C42−1+412yes—
252C22×C42−1+412yes—
253C22×C42−1+412yes—
254C2×C8—24no—
255C2×C8—24no—
256C2×C8—24no—
257C2×C8—24no—
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C4⋊C4—44no—
269C4⋊C4—44no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—84no—
287C4⋊C4—84no—
288C4⋊C4—84no—
289C4⋊C4—84no—
290C42—42no—
291C42—42no—
292C42—41no—
293C42—41no—
294C42—42no—
295C42—42no—
296C42—41no—
297C42—41no—
298C23#53411yescharacteristic
299C23#53611yescharacteristic
300C23#53611yescharacteristic
301C23#54712yes—
302C23#55012yes—
303C23C22×SD1611yescharacteristic
304C23C2×AGL(1,ℤ/8)11yescharacteristic
305C23C2×#13711yescharacteristic
306C23#57511yescharacteristic
307C23#57712yes—
308C23#57712yes—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
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#53812yes—
370C2×C4#53912yes—
371C2×C4#53912yes—
372C2×C4#53912yes—
373C2×C4#54112yes—
374C2×C4#54112yes—
375C2×C4#55212yes—
376C2×C4#55212yes—
377C2×C4#55511yescharacteristic
378C2×C4#55911yescharacteristic
379C2×C4H(3,𝔽4)11yescharacteristic
380C2×C4#56311yescharacteristic
381C2×C4#56312yes—
382C2×C4#56312yes—
383C2×C4#56312yes—
384C2×C4#56312yes—
385C8—44no—
386C8—44no—
387C22#272112yes—
388C22#272112yes—
389C22#272411yescharacteristic
390C22#273311yescharacteristic
391C22#281711yescharacteristic
392C22#318711yescharacteristic
393C22#319311yescharacteristic
394C22#320011yescharacteristic
395C22#320011yescharacteristic
396C22#322711yescharacteristic
397C22#322911yescharacteristic
398C22#323511yescharacteristic
399C22#323711yescharacteristic
400C22#324412yes—
401C22#324412yes—
402C22#333512yes—
403C22#334412yes—
404C22#334512yes—
405C22#335112yes—
406C22#339212yes—
407C22#339712yes—
408C22#340012yes—
409C22#340112yes—
410C4—42no—
411C4—42no—
412C4—42no—
413C4—42no—
414C4—42no—
415C4—81no—
416C4—162no—
417C4—162no—
418C4—162no—
419C4—162no—
420C4#276912yes—
421C4#277112yes—
422C4#283312yes—
423C4#283512yes—
424C2#1722811yescharacteristic
425C2#3237612yes—
426C2#3237812yes—
427C2#3240012yes—
428C2#3240212yes—
429C2#3245911yescharacteristic
430C2#3246811yescharacteristic
431C2#3266911yescharacteristic
432C2#3268011yescharacteristic
433C2#3278811yescharacteristic
434C2#3279411yescharacteristic
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
#113782
#113462
#113232
#113162
#113152
#112572