Finite Group Databasebeta

← #215730

Subgroups — #215730

Order 512.

978 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×#2295C211yesmaximal, characteristic
2#20778C211yesmaximal, characteristic
3#20777C211yesmaximal, characteristic
4#9883C212yesmaximal
5#9882C212yesmaximal
6#9880C214yesmaximal
7#8699C214yesmaximal
8C22×C4×Q8C411yescharacteristic
9#2295—21no—
10#2295—21no—
11#2295—21no—
12#2295—21no—
13#2295—21no—
14#2295—21no—
15#2295—21no—
16#2295—21no—
17C2×#391C411yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#389C411yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#387C412yes—
22C2×#387C2212yes—
23C2×C4×C4⋊C4C412yes—
24C2×C4×C4⋊C4C411yescharacteristic
25C2×#376C2212yes—
26C2×C43C2211yescharacteristic
27#1839—21no—
28#1839—21no—
29#1831—21no—
30#1831—21no—
31#1817C2212yes—
32#1817C2212yes—
33#1797C2212yes—
34#1797C2212yes—
35#1767—21no—
36C4×C4⋊C8—21no—
37#1749C2212yes—
38C4×C22⋊C8C2212yes—
39#1745—21no—
40#1744—21no—
41#1280C2218yes—
42#1280C2218yes—
43C23×Q8C2×C411yescharacteristic
44C2×C4×Q8—28no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8—21no—
48C2×C4×Q8—21no—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C412yes—
51C22×C4⋊C4C2×C412yes—
52C22×C4⋊C4C2×C412yes—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C42C2×C412yes—
56C22×C42C2×C412yes—
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42C2×C411yescharacteristic
61C22×C42C2311yescharacteristic
62C22×C42C2311yescharacteristic
63C22×C42C2311yescharacteristic
64C2×C4⋊C8—22no—
65C2×C4⋊C8—22no—
66C2×C22⋊C8C2314yes—
67C2×C22⋊C8C2314yes—
68C2×#97—22no—
69C2×C4×C8—22no—
70#391—21no—
71#391—21no—
72#391—21no—
73#391—21no—
74#391—21no—
75#391—21no—
76#391—21no—
77#391—21no—
78#389—21no—
79#389—21no—
80#389—21no—
81#389—21no—
82#389—21no—
83#389—21no—
84#389—21no—
85#389—21no—
86#387—22no—
87#387—22no—
88#387—22no—
89#387—22no—
90#387—22no—
91#387—22no—
92#387—22no—
93#387—22no—
94C4×C4⋊C4—21no—
95C4×C4⋊C4—21no—
96C4×C4⋊C4—21no—
97C4×C4⋊C4—21no—
98C4×C4⋊C4—22no—
99C4×C4⋊C4—22no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—22no—
102#376—22no—
103#376—22no—
104#376—22no—
105#376—22no—
106C2×#95C2×C412yes—
107C2×#95C2×C412yes—
108C2×#95C2×C412yes—
109C2×#95C2×C412yes—
110C2×#95C2×C412yes—
111C2×#95C2312yes—
112C2×#95C2312yes—
113C43D411yescharacteristic
114C43D411yescharacteristic
115C43D411yescharacteristic
116C43D411yescharacteristic
117C43D411yescharacteristic
118C43D411yescharacteristic
119C43D411yescharacteristic
120C43D411yescharacteristic
121#336—22no—
122#336—22no—
123#336—22no—
124#336—22no—
125#336—22no—
126#336—22no—
127#336—22no—
128#336—22no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—24no—
132C22×Q8—42no—
133C22×Q8—42no—
134C23×C4C22×C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C22×C411yescharacteristic
137C23×C4C22×C411yescharacteristic
138C23×C4C22×C412yes—
139C23×C4C22×C412yes—
140C23×C4C22×C411yescharacteristic
141C23×C4C22×C412yes—
142C23×C4C22×C412yes—
143C23×C4C22×C411yescharacteristic
144C23×C4C2411yescharacteristic
145C22×C8—24no—
146C22×C8—24no—
147C4×Q8—28no—
148C4×Q8—28no—
149C4×Q8—28no—
150C4×Q8—28no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4M1618yes—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—24no—
173C2×C42—24no—
174C2×C42—24no—
175C2×C42—24no—
176C2×C42—24no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—28no—
180C2×C42—42no—
181C2×C42—42no—
182C2×C42—42no—
183C2×C42—42no—
184C2×C42C22⋊C411yescharacteristic
185C2×C42C22⋊C411yescharacteristic
186C2×C42C22⋊C411yescharacteristic
187C2×C42C22⋊C411yescharacteristic
188C2×C42C22⋊C411yescharacteristic
189C2×C42C22⋊C411yescharacteristic
190C2×C42C22⋊C411yescharacteristic
191C2×C42C22⋊C411yescharacteristic
192C2×C42C22⋊C411yescharacteristic
193C2×C42C22⋊C411yescharacteristic
194C2×C42C22⋊C411yescharacteristic
195C2×C42C22⋊C411yescharacteristic
196C2×C42C22⋊C411yescharacteristic
197C2×C42C22⋊C411yescharacteristic
198C2×C42C22⋊C411yescharacteristic
199C2×C42C22⋊C411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204C2×C42C2×D411yescharacteristic
205C2×C42C2×D411yescharacteristic
206C2×C42C2×D411yescharacteristic
207C2×C42C2×D411yescharacteristic
208C2×C42C2×D411yescharacteristic
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42C2×D411yescharacteristic
212C4⋊C8—44no—
213C4⋊C8—44no—
214C22⋊C8—28no—
215C22⋊C8—28no—
216#97—44no—
217C4×C8—44no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95—22no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95—22no—
232C24C23×C411yescharacteristic
233C2×Q8—24no—
234C2×Q8—24no—
235C2×Q8—416no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
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—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C2×C22⋊C411yescharacteristic
279C22×C4C2×C22⋊C411yescharacteristic
280C22×C4C2×C22⋊C411yescharacteristic
281C22×C4C2×C22⋊C411yescharacteristic
282C22×C4C2×C22⋊C411yescharacteristic
283C22×C4C2×C22⋊C411yescharacteristic
284C22×C4C2×C22⋊C411yescharacteristic
285C22×C4C2×C22⋊C411yescharacteristic
286C22×C4C2×M1614yes—
287C22×C4C2×M1614yes—
288C22×C4C2×M1614yes—
289C22×C4#13114yes—
290C22×C4C22×D411yescharacteristic
291C22×C4C22×D411yescharacteristic
292C22×C42−1+414yes—
293C2×C8—44no—
294C2×C8—44no—
295C2×C8—44no—
296C2×C8—44no—
297C2×C8—44no—
298C2×C8—44no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—28no—
302C4⋊C4—28no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—44no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—42no—
309C4⋊C4—44no—
310C4⋊C4—42no—
311C42—28no—
312C42—28no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—22no—
331C42—22no—
332C42—22no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—44no—
342C42—44no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23C22×C22⋊C411yescharacteristic
348C23#51912yes—
349C23C22×M1612yes—
350C23C2×#13112yes—
351Q8—48no—
352Q8—48no—
353C2×C4—28no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4#40712yes—
411C2×C4#40712yes—
412C2×C4#40812yes—
413C2×C4#40812yes—
414C2×C4#41012yes—
415C2×C4#41012yes—
416C2×C4#41312yes—
417C2×C4#41312yes—
418C2×C4#53612yes—
419C2×C4#53612yes—
420C8—84no—
421C8—84no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22#231011yescharacteristic
429C22C2×#40711yescharacteristic
430C22C2×#40811yescharacteristic
431C22C2×#41011yescharacteristic
432C22C2×#41011yescharacteristic
433C22C2×#41311yescharacteristic
434C22C2×#41311yescharacteristic
435C22#298414yes—
436C4—22no—
437C4—22no—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—22no—
446C4—41no—
447C4—41no—
448C4—44no—
449C4—44no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—82no—
454C2—24no—
455C2#1735711yescharacteristic
456C2#1736311yescharacteristic
457C2#1737611yescharacteristic
458C2#1738011yescharacteristic
459C2#2182011yescharacteristic
460C2#2182611yescharacteristic
461C2#2183111yescharacteristic
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 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#22952
#207782
#207772
#98832
#98822
#98802
#86992