Finite Group Databasebeta

← #190443

Subgroups — #190443

Order 512.

924 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2320C211yesmaximal, characteristic
2#21822C211yesmaximal, characteristic
3#21818C211yesmaximal, characteristic
4#8705C212yesmaximal
5#8703C212yesmaximal
6#8701C212yesmaximal
7#8699C212yesmaximal
8#7916C212yesmaximal
9#7914C212yesmaximal
10C22×C4×Q8C2211yescharacteristic
11C2×#432C2212yes—
12C2×#431C2212yes—
13#2320—24no—
14#2320—24no—
15C2×#391C411yescharacteristic
16C2×#391C411yescharacteristic
17C2×#389C411yescharacteristic
18C2×#389C411yescharacteristic
19C2×#387C411yescharacteristic
20C2×#387C411yescharacteristic
21C2×#387C411yescharacteristic
22C2×#387C411yescharacteristic
23C2×#383C2211yescharacteristic
24C2×#383C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×#382C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×#376C2211yescharacteristic
29#1985—24no—
30#1984—24no—
31#1817C2212yes—
32#1817C2212yes—
33#1817C2212yes—
34#1817C2212yes—
35#1280C2214yes—
36#1280C2214yes—
37#1280C2214yes—
38#1280C2214yes—
39C23×Q8C2×C411yescharacteristic
40C2×C4×Q8—28no—
41C2×C4×Q8D414yes—
42C2×C4×Q8D414yes—
43C22×C4⋊C4C2×C411yescharacteristic
44C22×C4⋊C4C2×C411yescharacteristic
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42C2×C411yescharacteristic
55C22×C42C2×C411yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58C22×C42C2311yescharacteristic
59#432—28no—
60#431—28no—
61C2×C4⋊C8—22no—
62C2×C4⋊C8—22no—
63C2×C22⋊C8C2314yes—
64C2×C22⋊C8C2314yes—
65C2×#97—22no—
66C2×C4×C8—22no—
67#391—24no—
68#391—24no—
69#389—24no—
70#389—24no—
71#387—24no—
72#387—24no—
73#387—24no—
74#387—24no—
75#383—22no—
76#383—22no—
77#383—22no—
78#383—22no—
79#382—22no—
80#382—22no—
81#382—22no—
82#382—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4—22no—
85#376—22no—
86#376—22no—
87C2×#95C2×C411yescharacteristic
88C2×#95C2×C411yescharacteristic
89C2×#95C2×C411yescharacteristic
90C2×#95C2×C411yescharacteristic
91C2×#95C2×C411yescharacteristic
92C2×#95C2×C411yescharacteristic
93C2×#95C2×C411yescharacteristic
94C2×#95C2×C411yescharacteristic
95C2×#95C2×C411yescharacteristic
96C2×#95C2×C411yescharacteristic
97C2×#95C2×C411yescharacteristic
98C2×#95C2×C411yescharacteristic
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101C2×#95C2311yescharacteristic
102C2×#95C2311yescharacteristic
103C2×#95C2311yescharacteristic
104C2×#95C2311yescharacteristic
105#336—24no—
106#336—24no—
107#336—24no—
108#336—24no—
109C22×Q8—24no—
110C22×Q8—24no—
111C22×Q8—42no—
112C22×Q8C22⋊C414yes—
113C23×C4C22×C411yescharacteristic
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C411yescharacteristic
116C23×C4C22×C411yescharacteristic
117C23×C4C22×C411yescharacteristic
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C2411yescharacteristic
128C22×C8—24no—
129C22×C8—24no—
130C4×Q8—28no—
131C4×Q8—28no—
132C4×Q8—28no—
133C4×Q8—28no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—81no—
146C2×C4⋊C4—81no—
147C2×C4⋊C4—81no—
148C2×C4⋊C4—81no—
149C2×C4⋊C4C22⋊C414yes—
150C2×C4⋊C4C22⋊C414yes—
151C2×C4⋊C4C22⋊C414yes—
152C2×C42—24no—
153C2×C42—24no—
154C2×C42—22no—
155C2×C42—22no—
156C2×C42—24no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—42no—
160C2×C42—81no—
161C2×C42—81no—
162C2×C42C2×D412yes—
163C2×C42C2×D412yes—
164C2×C42C2×D412yes—
165C2×C42C2×D412yes—
166C2×C42C2×D412yes—
167C2×C42C2×D412yes—
168C2×C42#4118yes—
169C4⋊C8—44no—
170C4⋊C8—44no—
171C22⋊C8—28no—
172C22⋊C8—28no—
173#97—44no—
174C4×C8—44no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—22no—
181#95—22no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—21no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197C24C23×C411yescharacteristic
198C2×Q8—28no—
199C2×Q8—28no—
200C2×Q8—44no—
201C2×Q8—416no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×C22⋊C412yes—
252C22×C4C2×C22⋊C412yes—
253C22×C4C2×C22⋊C412yes—
254C22×C4C2×C22⋊C412yes—
255C22×C4C2×C22⋊C412yes—
256C22×C4C2×C22⋊C412yes—
257C22×C4#11714yes—
258C22×C4#11714yes—
259C22×C4#13114yes—
260C22×C4C22×D411yescharacteristic
261C22×C4C22×D411yescharacteristic
262C22×C4C2×#4114yes—
263C2×C8—44no—
264C2×C8—44no—
265C2×C8—44no—
266C2×C8—44no—
267C2×C8—44no—
268C2×C8—44no—
269C4⋊C4—28no—
270C4⋊C4—28no—
271C4⋊C4—28no—
272C4⋊C4—44no—
273C4⋊C4—44no—
274C4⋊C4—82no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C4⋊C4—82no—
278C42—24no—
279C42—24no—
280C42—24no—
281C42—24no—
282C42—44no—
283C42—44no—
284C42—82no—
285C42—82no—
286C42#12314yes—
287C42#12314yes—
288C42#12314yes—
289C42#12314yes—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C22×C22⋊C411yescharacteristic
295C23C2×#11712yes—
296C23C2×#13112yes—
297C23#56812yes—
298Q8—416no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—44no—
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—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
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#38114yes—
358C2×C4#38114yes—
359C2×C4#40814yes—
360C2×C4C2×#12312yes—
361C2×C4C2×#12312yes—
362C8—84no—
363C8—84no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22C2×#38111yescharacteristic
371C22C2×#40811yescharacteristic
372C22#287911yescharacteristic
373C22#288411yescharacteristic
374C22#288411yescharacteristic
375C22#288811yescharacteristic
376C22#288911yescharacteristic
377C22#292414yes—
378C4—24no—
379C4—24no—
380C4—22no—
381C4—22no—
382C4—24no—
383C4—42no—
384C4—42no—
385C4—42no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—81no—
394C2—24no—
395C2#1739011yescharacteristic
396C2#1739111yescharacteristic
397C2#1740911yescharacteristic
398C2#1741011yescharacteristic
399C2#2068511yescharacteristic
400C2#2069111yescharacteristic
401C2#2069511yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#23202
#218222
#218182
#87052
#87032
#87012
#86992
#79162
#79142