Finite Group Databasebeta

← #461465

Subgroups — #461465

Order 512.

1048 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1865C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic
4#13931C211yesmaximal, characteristic
5#11373C211yesmaximal, characteristic
6#11357C212yesmaximal
7#11257C212yesmaximal
8#11255C211yesmaximal, characteristic
9#11227C211yesmaximal, characteristic
10#11190C212yesmaximal
11#11050C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×#103C2211yescharacteristic
16C22×#103C2211yescharacteristic
17C22×#103C2212yes—
18C2×#398—21no—
19C2×#398—21no—
20C2×#391C2212yes—
21C2×#389C2211yescharacteristic
22C2×#384C2211yescharacteristic
23C2×#384C2212yes—
24#1865—24no—
25#1803—24no—
26C2×#340C2212yes—
27C2×#340C2211yescharacteristic
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#336C2211yescharacteristic
33C2×#336C2212yes—
34C2×#336C2212yes—
35#1445—22no—
36#1444—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40#1434—21no—
41#1434—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2312yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C2×C4×Q8—22no—
48C2×C4×Q8—24no—
49C2×C4×Q8—42no—
50C2×C4×Q8D414yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C42—21no—
63C22×C42C2312yes—
64C22×C42C2311yescharacteristic
65C2×#106—22no—
66C2×#106—42no—
67C2×C4⋊C8—22no—
68C2×C4⋊C8—42no—
69C2×#103—22no—
70C2×#103—22no—
71C2×#103—22no—
72C2×#103—24no—
73C2×#103—22no—
74C2×#103—24no—
75C2×#103—42no—
76C2×#103—42no—
77#398—44no—
78#398—44no—
79#391—24no—
80#391—42no—
81#389—22no—
82#389—22no—
83#384—24no—
84#384—22no—
85#384—22no—
86#384—42no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95D411yescharacteristic
97C2×#95D412yes—
98C2×#95D411yescharacteristic
99#340—24no—
100#340—24no—
101#340—22no—
102#340—42no—
103#340—42no—
104#340—42no—
105#336—22no—
106#336—42no—
107#336—42no—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—21no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8—21no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8C2×D412yes—
117C22×Q8#4114yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—22no—
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D412yes—
126C23×C4C2×D412yes—
127C23×C4C2×D411yescharacteristic
128C23×C4C2411yescharacteristic
129C22×C8—21no—
130C22×C8—21no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—21no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—21no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8#4112yes—
146C4×Q8—28no—
147C4×Q8—44no—
148C4×Q8—48no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—42no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—82no—
187C2×C4⋊C4—81no—
188C2×C4⋊C4—81no—
189C2×C4⋊C4—82no—
190C2×C4⋊C4C2×D412yes—
191C2×C4⋊C4#4112yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—24no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—44no—
202C2×C42C2×D412yes—
203C2×C42#4112yes—
204#106—44no—
205C4⋊C8—44no—
206#103—28no—
207#103—48no—
208#103—44no—
209#95—22no—
210#95—24no—
211#95—44no—
212#95—44no—
213#95—44no—
214#95—42no—
215#95—44no—
216#95—42no—
217#95—44no—
218#95—82no—
219#95—81no—
220#95SD1614yes—
221C24C22×D411yescharacteristic
222C2×Q8—22no—
223C2×Q8—24no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—24no—
231C2×Q8—24no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8#12314yes—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4#12112yes—
295C22×C4#12112yes—
296C22×C4C2×SD1614yes—
297C22×C4C2×SD1612yes—
298C22×C4AGL(1,ℤ/8)12yes—
299C22×C4#13714yes—
300C22×C4C22×D411yescharacteristic
301C22×C4C2×#4112yes—
302C22×C4C2×#4111yescharacteristic
303C22×C4C2×#4111yescharacteristic
304C22×C4C2×#4111yescharacteristic
305C22×C4H(5,𝔽2)12yes—
306C22×C4H(5,𝔽2)11yescharacteristic
307C22×C4H(5,𝔽2)11yescharacteristic
308C22×C42−1+412yes—
309C22×C42−1+412yes—
310C2×C8—22no—
311C2×C8—24no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—41no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—48no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—88no—
347C4⋊C4—84no—
348C4⋊C4—88no—
349C4⋊C4—84no—
350C4⋊C4—84no—
351C42—22no—
352C42—22no—
353C42—24no—
354C42—48no—
355C42—42no—
356C42—42no—
357C42—42no—
358C42—42no—
359C23C2×#12111yescharacteristic
360C23#53612yes—
361C23#54612yes—
362C23#54611yescharacteristic
363C23#55011yescharacteristic
364C23C22×SD1611yescharacteristic
365C23C2×AGL(1,ℤ/8)11yescharacteristic
366C23C2×#13712yes—
367C23#57611yescharacteristic
368C23#57711yescharacteristic
369C23#57812yes—
370Q8—24no—
371Q8—24no—
372Q8—42no—
373Q8—42no—
374Q8—44no—
375Q8—44no—
376C2×C4—22no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—82no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—81no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4#46014yes—
436C2×C4C2×#12311yescharacteristic
437C2×C4#52511yescharacteristic
438C2×C4#53411yescharacteristic
439C2×C4#53511yescharacteristic
440C2×C4#53611yescharacteristic
441C2×C4#53611yescharacteristic
442C2×C4#53912yes—
443C2×C4#53912yes—
444C2×C4#53912yes—
445C2×C4#54112yes—
446C2×C4#54212yes—
447C2×C4#55112yes—
448C2×C4#55212yes—
449C2×C4#55212yes—
450C2×C4#55311yescharacteristic
451C2×C4#55511yescharacteristic
452C2×C4#56212yes—
453C2×C4#56212yes—
454C8—42no—
455C8—82no—
456C8—81no—
457C22#241211yescharacteristic
458C22#241411yescharacteristic
459C22#262111yescharacteristic
460C22#268712yes—
461C22#269412yes—
462C22C2×#46011yescharacteristic
463C22#303911yescharacteristic
464C22#304411yescharacteristic
465C22#304511yescharacteristic
466C22#322912yes—
467C22#323912yes—
468C22#324212yes—
469C22#324312yes—
470C22#329511yescharacteristic
471C22#329812yes—
472C22#330812yes—
473C22#331212yes—
474C22#331612yes—
475C22#332411yescharacteristic
476C22#333312yes—
477C22#339211yescharacteristic
478C22#339812yes—
479C22#339911yescharacteristic
480C4—24no—
481C4—44no—
482C4—44no—
483C4—44no—
484C4—42no—
485C4—82no—
486C4—82no—
487C4—162no—
488C4—162no—
489C4—161no—
490C4#248411yescharacteristic
491C4#262311yescharacteristic
492C4#263811yescharacteristic
493C4#273912yes—
494C4#274412yes—
495C4#281611yescharacteristic
496C2#1639311yescharacteristic
497C2#2452811yescharacteristic
498C2#2454611yescharacteristic
499C2#2462811yescharacteristic
500C2#2464811yescharacteristic
501C2#2986611yescharacteristic
502C2#2987511yescharacteristic
503C2#3135412yes—
504C2#3138012yes—
505C2#3157212yes—
506C2#3159212yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ 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×#18652
C2×#18032
#151452
#139312
#113732
#113572
#112572
#112552
#112272
#111902
#110502