Finite Group Databasebeta

← #190485

Subgroups — #190485

Order 512.

1208 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2276C211yesmaximal, characteristic
2#21916C212yesmaximal
3#8699C212yesmaximal
4#8560C212yesmaximal
5#8558C212yesmaximal
6#8303C212yesmaximal
7#8153C212yesmaximal
8#8153C212yesmaximal
9C22×C4×Q8C411yescharacteristic
10C22×C4×Q8C411yescharacteristic
11C22×C4×Q8C2211yescharacteristic
12#2276—28no—
13C2×C4×C4⋊C4C411yescharacteristic
14C2×C4×C4⋊C4C411yescharacteristic
15C2×C4×C4⋊C4C411yescharacteristic
16C2×C4×C4⋊C4C411yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×#376C411yescharacteristic
23C2×#376C411yescharacteristic
24C2×#376C2211yescharacteristic
25#1917—28no—
26#1817C2214yes—
27#1797C2214yes—
28#1749C2214yes—
29C2×#324C2214yes—
30C2×#324C2214yes—
31#1280C2214yes—
32#1280C2214yes—
33C23×Q8C2×C411yescharacteristic
34C2×C4×Q8—24no—
35C2×C4×Q8—24no—
36C2×C4×Q8—24no—
37C2×C4×Q8—24no—
38C2×C4×Q8—24no—
39C2×C4×Q8—24no—
40C2×C4×Q8—24no—
41C2×C4×Q8—24no—
42C2×C4×Q8—24no—
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⋊C4C2311yescharacteristic
51C22×C4⋊C4C2311yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42C2×C411yescharacteristic
55C22×C42C2×C411yescharacteristic
56C22×C42C2×C411yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42C2×C411yescharacteristic
61C22×C42C2×C411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42C2×C411yescharacteristic
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C2×C4⋊C8—24no—
68C2×C22⋊C8C2318yes—
69C2×#97—24no—
70C4×C4⋊C4—24no—
71C4×C4⋊C4—24no—
72C4×C4⋊C4—24no—
73C4×C4⋊C4—24no—
74C4×C4⋊C4—24no—
75C4×C4⋊C4—24no—
76C4×C4⋊C4—24no—
77C4×C4⋊C4—24no—
78C4×C4⋊C4D418yes—
79#376—24no—
80#376—24no—
81#376—24no—
82C2×#95C2×C411yescharacteristic
83C2×#95C2×C411yescharacteristic
84C2×#95C2×C411yescharacteristic
85C2×#95C2×C411yescharacteristic
86C2×#95C2×C411yescharacteristic
87C2×#95C2×C411yescharacteristic
88C2×#95C2×C411yescharacteristic
89C2×#95C2×C411yescharacteristic
90C2×#95C2311yescharacteristic
91C2×#95C2311yescharacteristic
92#336—24no—
93#336—28no—
94#336—24no—
95#324—28no—
96#324—28no—
97C22×Q8—22no—
98C22×Q8—22no—
99C22×Q8—22no—
100C22×Q8—22no—
101C22×Q8—22no—
102C22×Q8—22no—
103C22×Q8M1614yes—
104C23×C4C22×C411yescharacteristic
105C23×C4C22×C411yescharacteristic
106C23×C4C22×C411yescharacteristic
107C23×C4C22×C411yescharacteristic
108C23×C4C22×C411yescharacteristic
109C23×C4C22×C411yescharacteristic
110C23×C4C22×C411yescharacteristic
111C23×C4C22×C411yescharacteristic
112C23×C4C22×C411yescharacteristic
113C23×C4C22×C411yescharacteristic
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C411yescharacteristic
116C23×C4C22×C411yescharacteristic
117C23×C4C22×C411yescharacteristic
118C23×C4C2411yescharacteristic
119C22×C8—28no—
120C4×Q8—232no—
121C4×Q8—232no—
122C4×Q8—232no—
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—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4C22⋊C414yes—
146C2×C4⋊C4C22⋊C414yes—
147C2×C4⋊C4M1614yes—
148C2×C4⋊C4#4114yes—
149C2×C4⋊C4#4114yes—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—22no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—22no—
176C2×C42—22no—
177C2×C42—22no—
178C2×C42—81no—
179C2×C42—81no—
180C2×C42—81no—
181C2×C42—81no—
182C2×C42—81no—
183C2×C42—81no—
184C2×C42M1614yes—
185C2×C42M1614yes—
186C2×C42C2×D414yes—
187C2×C42C2×D414yes—
188C2×C42C2×D414yes—
189C4⋊C8—84no—
190C22⋊C8—28no—
191C22⋊C8—28no—
192#97—84no—
193#95—22no—
194#95—22no—
195#95—22no—
196#95—22no—
197#95—22no—
198#95—22no—
199#95—22no—
200#95—22no—
201#95C22⋊C414yes—
202#95C22⋊C414yes—
203C24C23×C411yescharacteristic
204C2×Q8—28no—
205C2×Q8—28no—
206C2×Q8—28no—
207C2×Q8—28no—
208C2×Q8—28no—
209C2×Q8—28no—
210C2×Q8—28no—
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—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
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×C4C2×C22⋊C412yes—
268C22×C4C2×C22⋊C412yes—
269C22×C4C2×C22⋊C412yes—
270C22×C4C2×C22⋊C412yes—
271C22×C4C2×C22⋊C412yes—
272C22×C4C2×C22⋊C412yes—
273C22×C4#11712yes—
274C22×C4#11712yes—
275C22×C4#11712yes—
276C22×C4#11712yes—
277C22×C4C2×M1612yes—
278C22×C4C2×M1612yes—
279C22×C4C2×M1612yes—
280C22×C4C2×M1612yes—
281C22×C4C2×M1612yes—
282C22×C4C2×M1612yes—
283C22×C4C2×M1612yes—
284C22×C4C2×M1612yes—
285C22×C4C2×M1612yes—
286C22×C4C2×M1612yes—
287C22×C4C2×M1612yes—
288C22×C4C2×M1612yes—
289C22×C4C22×D412yes—
290C22×C4C2×#4112yes—
291C22×C4C2×#4112yes—
292C2×C8—48no—
293C2×C8—48no—
294C2×C8—48no—
295C4⋊C4—28no—
296C4⋊C4—28no—
297C4⋊C4—28no—
298C4⋊C4—28no—
299C4⋊C4—28no—
300C4⋊C4—28no—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C42—28no—
305C42—28no—
306C42—28no—
307C42—28no—
308C42—28no—
309C42—28no—
310C42—28no—
311C42—28no—
312C42—28no—
313C42—44no—
314C42—44no—
315C42—82no—
316C42—82no—
317C42—82no—
318C42—82no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C22×C22⋊C411yescharacteristic
324C23C2×#11711yescharacteristic
325C23C2×#11711yescharacteristic
326C23C22×M1611yescharacteristic
327C23C22×M1611yescharacteristic
328C23C22×M1611yescharacteristic
329C23C22×M1611yescharacteristic
330Q8—232no—
331C2×C4—22no—
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—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4#40714yes—
408C2×C4#40714yes—
409C2×C4#43214yes—
410C2×C4#43214yes—
411C2×C4#52514yes—
412C8—88no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22#228011yescharacteristic
426C22C2×#40711yescharacteristic
427C22C2×#40711yescharacteristic
428C22#288311yescharacteristic
429C22#288411yescharacteristic
430C22#288911yescharacteristic
431C22#288911yescharacteristic
432C22C2×#43211yescharacteristic
433C22C2×#43211yescharacteristic
434C22#292011yescharacteristic
435C22#292011yescharacteristic
436C4—24no—
437C4—24no—
438C4—24no—
439C4—24no—
440C4—24no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—42no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2#1736811yescharacteristic
456C2#1737011yescharacteristic
457C2#1737111yescharacteristic
458C2#1737111yescharacteristic
459C2#2071511yescharacteristic
460C2#2072511yescharacteristic
461C2#2073011yescharacteristic
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×#22762
#219162
#86992
#85602
#85582
#83032
#81532