Finite Group Databasebeta

← #381197

Subgroups — #381197

Order 512.

1078 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2859C211yesmaximal, characteristic
2#20772C211yesmaximal, characteristic
3C4×#423C211yesmaximal, characteristic
4#11354C212yesmaximal
5#11354C212yesmaximal
6#11204C214yesmaximal
7#10913C214yesmaximal
8C22×#125C412yes—
9C2×#423C2212yes—
10C2×C4×M16C2212yes—
11#2859—21no—
12#2859—21no—
13#2859—21no—
14#2859—21no—
15#2859—21no—
16#2859—21no—
17#2859—21no—
18#2859—21no—
19C2×#389C412yes—
20C2×#389C412yes—
21C2×#389C2212yes—
22C2×#389C2212yes—
23C2×#384C2211yescharacteristic
24C2×#384C2211yescharacteristic
25C2×#382C412yes—
26C2×C43C2211yescharacteristic
27#1839—21no—
28#1839—21no—
29#1839—21no—
30#1839—21no—
31#1767—21no—
32#1767—21no—
33C4×C4⋊C8—21no—
34C4×C4⋊C8—21no—
35C2×#343C2218yes—
36C2×#343C2218yes—
37#1728C2212yes—
38#1728C2212yes—
39#1728C2212yes—
40#1728C2212yes—
41C22×M16C2314yes—
42C22×M16C2314yes—
43C2×#125—22no—
44C2×#125—22no—
45C2×#125—22no—
46C2×#125—22no—
47C2×#125—48no—
48C22×C4⋊C4C2×C412yes—
49C22×C4⋊C4C2×C412yes—
50C22×C4⋊C4C2×C414yes—
51C22×C4⋊C4C2×C414yes—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C412yes—
54C22×C4⋊C4C2312yes—
55C22×C4⋊C4C2312yes—
56C22×C42C2×C411yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42C2311yescharacteristic
61C22×C42C2311yescharacteristic
62C22×C42C2311yescharacteristic
63#423—28no—
64C2×C4⋊C8—22no—
65C2×C4⋊C8—22no—
66C4×M16—44no—
67C2×#97—22no—
68C2×C4×C8—22no—
69#389—22no—
70#389—22no—
71#389—22no—
72#389—22no—
73#389—22no—
74#389—22no—
75#389—22no—
76#389—22no—
77#389—22no—
78#389—22no—
79#389—22no—
80#389—22no—
81#389—22no—
82#389—22no—
83#389—22no—
84#389—22no—
85#384—21no—
86#384—21no—
87#384—21no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384—21no—
92#384—21no—
93#382—22no—
94#382—22no—
95#382—22no—
96#382—22no—
97C2×#95C2×C414yes—
98C2×#95C2×C414yes—
99C43D411yescharacteristic
100C43D411yescharacteristic
101C43D411yescharacteristic
102C43D411yescharacteristic
103C43D411yescharacteristic
104C43D411yescharacteristic
105C43D411yescharacteristic
106C43D411yescharacteristic
107#343—216no—
108#343—48no—
109#336—22no—
110#336—22no—
111#336—22no—
112#336—22no—
113#336—22no—
114#336—22no—
115#336—22no—
116#336—22no—
117C23×C4C22×C411yescharacteristic
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C414yes—
124C23×C4C22×C414yes—
125C23×C4C2411yescharacteristic
126C2×M16—24no—
127C2×M16—28no—
128C2×M16—28no—
129C2×M16—28no—
130C2×M16—24no—
131C2×M16—28no—
132C2×M16—24no—
133C2×M16#4118yes—
134C22×C8—24no—
135C22×C8—24no—
136#125—48no—
137#125—48no—
138#125—48no—
139#125—48no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
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—28no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—48no—
164C2×C4⋊C4—48no—
165C2×C42—24no—
166C2×C42—22no—
167C2×C42—24no—
168C2×C42—22no—
169C2×C42—24no—
170C2×C42—24no—
171C2×C42—42no—
172C2×C42—42no—
173C2×C42C22⋊C411yescharacteristic
174C2×C42C22⋊C411yescharacteristic
175C2×C42C22⋊C411yescharacteristic
176C2×C42C22⋊C411yescharacteristic
177C2×C42C22⋊C411yescharacteristic
178C2×C42C22⋊C411yescharacteristic
179C2×C42C22⋊C411yescharacteristic
180C2×C42C22⋊C411yescharacteristic
181C2×C42C22⋊C411yescharacteristic
182C2×C42C22⋊C411yescharacteristic
183C2×C42C22⋊C411yescharacteristic
184C2×C42C22⋊C411yescharacteristic
185C2×C42C22⋊C411yescharacteristic
186C2×C42C22⋊C411yescharacteristic
187C2×C42C22⋊C411yescharacteristic
188C2×C42C22⋊C411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C4⋊C8—28no—
202C4⋊C8—28no—
203#97—44no—
204C4×C8—44no—
205#95—24no—
206#95—24no—
207#95—24no—
208#95—24no—
209C24C23×C411yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—24no—
226C22×C4—28no—
227C22×C4—28no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4C2×C22⋊C411yescharacteristic
237C22×C4C2×C22⋊C411yescharacteristic
238C22×C4C2×C22⋊C411yescharacteristic
239C22×C4C2×C22⋊C411yescharacteristic
240C22×C4C2×C22⋊C411yescharacteristic
241C22×C4C2×C22⋊C411yescharacteristic
242C22×C4C2×C22⋊C411yescharacteristic
243C22×C4C2×C22⋊C411yescharacteristic
244C22×C4C2×C22⋊C411yescharacteristic
245C22×C4C2×C22⋊C411yescharacteristic
246C22×C4C2×C22⋊C411yescharacteristic
247C22×C4C2×C22⋊C411yescharacteristic
248C22×C4C22×D411yescharacteristic
249C22×C4C22×D411yescharacteristic
250C22×C4C2×#4114yes—
251C22×C4H(5,𝔽2)12yes—
252C22×C42−1+414yes—
253C22×C42−1+412yes—
254M16—216no—
255M16—48no—
256M16—48no—
257M16—48no—
258C2×C8—28no—
259C2×C8—44no—
260C2×C8—44no—
261C2×C8—44no—
262C2×C8—44no—
263C2×C8—44no—
264C4⋊C4—44no—
265C4⋊C4—44no—
266C4⋊C4—44no—
267C4⋊C4—44no—
268C4⋊C4—48no—
269C4⋊C4—48no—
270C4⋊C4—44no—
271C4⋊C4—44no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—44no—
275C4⋊C4—44no—
276C4⋊C4—44no—
277C4⋊C4—48no—
278C4⋊C4—48no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—21no—
286C42—21no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—21no—
292C42—21no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—22no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C42—22no—
304C42—22no—
305C42—41no—
306C42—41no—
307C42—41no—
308C42—41no—
309C42#10014yes—
310C42#10114yes—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23C22×C22⋊C411yescharacteristic
316C23C4×#4112yes—
317C23#51912yes—
318C23#52012yes—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—88no—
360C2×C4—88no—
361C2×C4C2×#10012yes—
362C2×C4C2×#10012yes—
363C2×C4C2×#10012yes—
364C2×C4C2×#10112yes—
365C2×C4C2×#10112yes—
366C2×C4C2×#10112yes—
367C2×C4#41312yes—
368C2×C4#41312yes—
369C2×C4#52512yes—
370C2×C4#53212yes—
371C2×C4#53511yescharacteristic
372C2×C4#53612yes—
373C2×C4#53611yescharacteristic
374C2×C4#53612yes—
375C2×C4#53712yes—
376C2×C4#53918yes—
377C2×C4#54118yes—
378C8—48no—
379C8—84no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22#229711yescharacteristic
387C22#231011yescharacteristic
388C22#231111yescharacteristic
389C22#233614yes—
390C22C22×#10011yescharacteristic
391C22C22×#10111yescharacteristic
392C22C2×#41311yescharacteristic
393C22C2×#41311yescharacteristic
394C4—22no—
395C4—22no—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—84no—
407C4—84no—
408C4#263312yes—
409C4#263412yes—
410C4#266414yes—
411C2—24no—
412C2#1428911yescharacteristic
413C2#2142411yescharacteristic
414C2#2142511yescharacteristic
415C2#2182911yescharacteristic
416C2#2183011yescharacteristic
417C2#2187811yescharacteristic
418C2#2187911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ 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×#28592
#207722
C4×#4232
#113542
#112042
#109132