Finite Group Databasebeta

← #215985

Subgroups — #215985

Order 512.

910 conjugacy classes of subgroups.

The subgroup lattice has 437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2331C211yesmaximal, characteristic
2#21916C211yesmaximal, characteristic
3#21912C211yesmaximal, characteristic
4#9882C212yesmaximal
5#9881C212yesmaximal
6#9880C212yesmaximal
7#9878C212yesmaximal
8#8701C212yesmaximal
9#8699C212yesmaximal
10C22×C4⋊Q8C411yescharacteristic
11#2331—24no—
12#2331—24no—
13C2×#391C411yescharacteristic
14C2×#391C411yescharacteristic
15C2×#391C2211yescharacteristic
16C2×#391C2211yescharacteristic
17C2×#389C411yescharacteristic
18C2×#389C411yescharacteristic
19C2×#387C411yescharacteristic
20C2×#387C411yescharacteristic
21C2×#387C2211yescharacteristic
22C2×#387C2211yescharacteristic
23C2×#382C411yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×#376C2211yescharacteristic
27#1917—24no—
28#1916—24no—
29#1817C2212yes—
30#1817C2212yes—
31#1797C2212yes—
32#1797C2212yes—
33#1749C2212yes—
34C4×C22⋊C8C2212yes—
35#1280C2214yes—
36#1280C2214yes—
37#1280C2214yes—
38#1280C2214yes—
39C23×Q8C2×C411yescharacteristic
40C23×Q8C2×C411yescharacteristic
41C2×C4⋊Q8—24no—
42C2×C4⋊Q8—24no—
43C2×C4⋊Q8—24no—
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×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C42C2×C411yescharacteristic
55C22×C42C2×C411yescharacteristic
56C22×C42C2×C411yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2311yescharacteristic
59C22×C42C2311yescharacteristic
60C22×C42C2311yescharacteristic
61C2×C4⋊C8—22no—
62C2×C4⋊C8—22no—
63C2×C22⋊C8C2314yes—
64C2×C22⋊C8C2314yes—
65C2×#97—22no—
66C2×C4×C8—22no—
67#391—22no—
68#391—22no—
69#391—22no—
70#391—22no—
71#391—24no—
72#391—24no—
73#389—24no—
74#389—24no—
75#387—22no—
76#387—22no—
77#387—22no—
78#387—22no—
79#387—24no—
80#387—24no—
81#382—24no—
82C4×C4⋊C4—22no—
83C4×C4⋊C4—22no—
84C4×C4⋊C4D414yes—
85C4×C4⋊C4D414yes—
86#376—22no—
87#376—22no—
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×#95C2311yescharacteristic
101C2×#95C2311yescharacteristic
102C2×#95C2311yescharacteristic
103C2×#95C2311yescharacteristic
104#336—22no—
105#336—22no—
106#336—24no—
107#336—24no—
108#336—22no—
109#336—22no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—81no—
116C22×Q8—81no—
117C22×Q8—81no—
118C22×Q8—81no—
119C22×Q8M1614yes—
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C22×C411yescharacteristic
128C23×C4C22×C411yescharacteristic
129C23×C4C22×C411yescharacteristic
130C23×C4C22×C411yescharacteristic
131C23×C4C22×C411yescharacteristic
132C23×C4C22×C411yescharacteristic
133C23×C4C22×C411yescharacteristic
134C23×C4C2411yescharacteristic
135C22×C8—24no—
136C22×C8—24no—
137C4⋊Q8—232no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—24no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—81no—
156C2×C4⋊C4—81no—
157C2×C4⋊C4—81no—
158C2×C4⋊C4—81no—
159C2×C4⋊C4C22⋊C414yes—
160C2×C4⋊C4C22⋊C414yes—
161C2×C4⋊C4M1614yes—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—24no—
166C2×C42—22no—
167C2×C42—24no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—81no—
171C2×C42—81no—
172C2×C42—81no—
173C2×C42—81no—
174C2×C42C2×D412yes—
175C2×C42C2×D412yes—
176C2×C42C2×D412yes—
177C2×C42C2×D412yes—
178C2×C42C2×D412yes—
179C2×C42C2×D412yes—
180C4⋊C8—82no—
181C4⋊C8—82no—
182C22⋊C8—28no—
183C22⋊C8—28no—
184#97—82no—
185C4×C8—82no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—22no—
190#95—22no—
191#95—22no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95C22⋊C414yes—
205#95C22⋊C414yes—
206C24C23×C411yescharacteristic
207C2×Q8—28no—
208C2×Q8—28no—
209C2×Q8—82no—
210C2×Q8—82no—
211C2×Q8—82no—
212C2×Q8—82no—
213C2×Q8—84no—
214C2×Q8—84no—
215C2×Q8—84no—
216C2×Q8—84no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
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×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4C2×C22⋊C412yes—
270C22×C4C2×C22⋊C412yes—
271C22×C4C2×C22⋊C412yes—
272C22×C4C2×C22⋊C412yes—
273C22×C4C2×C22⋊C412yes—
274C22×C4C2×C22⋊C412yes—
275C22×C4C2×M1612yes—
276C22×C4C2×M1612yes—
277C22×C4C2×M1612yes—
278C22×C4C2×M1612yes—
279C22×C4C2×M1612yes—
280C22×C4C2×M1612yes—
281C22×C4#13114yes—
282C22×C4C22×D411yescharacteristic
283C22×C4C22×D411yescharacteristic
284C22×C42−1+414yes—
285C2×C8—44no—
286C2×C8—44no—
287C2×C8—44no—
288C2×C8—44no—
289C2×C8—44no—
290C2×C8—44no—
291C4⋊C4—28no—
292C4⋊C4—28no—
293C4⋊C4—28no—
294C4⋊C4—28no—
295C4⋊C4—28no—
296C4⋊C4—44no—
297C4⋊C4—82no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C4⋊C4—82no—
301C42—28no—
302C42—24no—
303C42—24no—
304C42—42no—
305C42—42no—
306C42—42no—
307C42—42no—
308C42—44no—
309C42—82no—
310C42—82no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23C22×C22⋊C411yescharacteristic
316C23#51912yes—
317C23C22×M1611yescharacteristic
318C23C22×M1611yescharacteristic
319C23C2×#13112yes—
320Q8—88no—
321Q8—88no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4#40714yes—
389C2×C4#40814yes—
390C2×C4#53612yes—
391C2×C4#53612yes—
392C8—84no—
393C8—84no—
394C22—22no—
395C22—22no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—22no—
402C22#231011yescharacteristic
403C22C2×#40711yescharacteristic
404C22C2×#40811yescharacteristic
405C22#288311yescharacteristic
406C22#288411yescharacteristic
407C22#288811yescharacteristic
408C22#288911yescharacteristic
409C22#298412yes—
410C22#298412yes—
411C4—24no—
412C4—22no—
413C4—22no—
414C4—24no—
415C4—42no—
416C4—42no—
417C4—42no—
418C4—42no—
419C4—42no—
420C4—42no—
421C4—42no—
422C4—42no—
423C4—81no—
424C4—81no—
425C4—81no—
426C4—81no—
427C2—22no—
428C2—22no—
429C2#1736711yescharacteristic
430C2#1737111yescharacteristic
431C2#1738811yescharacteristic
432C2#1739011yescharacteristic
433C2#2182011yescharacteristic
434C2#2182811yescharacteristic
435C2#2183211yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ 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×#23312
#219162
#219122
#98822
#98812
#98802
#98782
#87012
#86992