Finite Group Databasebeta

← #402367

Subgroups — #402367

Order 512.

1164 conjugacy classes of subgroups.

The subgroup lattice has 516 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#13817C211yesmaximal, characteristic
5#11373C211yesmaximal, characteristic
6#11322C211yesmaximal, characteristic
7#11227C211yesmaximal, characteristic
8#11077C212yesmaximal
9#11050C212yesmaximal
10#10908C212yesmaximal
11#10849C212yesmaximal
12C22×C4×Q8C2211yescharacteristic
13C22×#106C2211yescharacteristic
14C22×C4⋊C8C2212yes—
15C22×C4⋊C8C2211yescharacteristic
16C22×#103C2211yescharacteristic
17C22×#103C2212yes—
18C22×#103C2211yescharacteristic
19C2×#398—21no—
20C2×#398—21no—
21C2×#391C2212yes—
22C2×#389C2211yescharacteristic
23C2×#384C2211yescharacteristic
24C2×#384C2212yes—
25C2×C4×C4⋊C4C2212yes—
26#1865—24no—
27#1803—24no—
28C2×#340C2212yes—
29C2×#340C2211yescharacteristic
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2212yes—
35C2×#336C2211yescharacteristic
36#1444—22no—
37#1436—22no—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40#1434—21no—
41C4×#95—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2311yescharacteristic
45C23×C8C2312yes—
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×C42—22no—
64C22×C42C2311yescharacteristic
65C22×C42C2312yes—
66C2×#106—22no—
67C2×#106—24no—
68C2×C4⋊C8—22no—
69C2×C4⋊C8—24no—
70C2×C4⋊C8—42no—
71C2×C4⋊C8—42no—
72C2×C4⋊C8—42no—
73C2×#103—22no—
74C2×#103—22no—
75C2×#103—22no—
76C2×#103—24no—
77C2×#103—22no—
78C2×#103—42no—
79C2×#103—42no—
80C2×#103—42no—
81#398—44no—
82#398—44no—
83#391—24no—
84#391Q818yes—
85#389—22no—
86#389—22no—
87#384—24no—
88#384—22no—
89#384—22no—
90#384—42no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—42no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95D411yescharacteristic
102C2×#95D412yes—
103C2×#95D411yescharacteristic
104#340—24no—
105#340—24no—
106#340—22no—
107#340—42no—
108#340—42no—
109#340—42no—
110#336—22no—
111#336—24no—
112C22×Q8—21no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—21no—
116C22×Q8—21no—
117C22×Q8—22no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8C2×D412yes—
121C22×Q8C2×Q814yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—22no—
126C23×C4—22no—
127C23×C4—21no—
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D412yes—
132C23×C4C2411yescharacteristic
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—21no—
136C22×C8—22no—
137C22×C8—21no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—21no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—21no—
149C22×C8#4112yes—
150C4×Q8—28no—
151C4×Q8—44no—
152C4×Q8—48no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4—81no—
190C2×C4⋊C4—81no—
191C2×C4⋊C4—82no—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×Q814yes—
194C2×C4⋊C4#4112yes—
195C2×C4⋊C4#4114yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—24no—
203C2×C42—44no—
204C2×C42—44no—
205C2×C42—44no—
206C2×C42—82no—
207C2×C42C2×D412yes—
208C2×C42C2×Q814yes—
209C2×C42#4112yes—
210C2×C42#4114yes—
211#106—44no—
212C4⋊C8—44no—
213C4⋊C8—48no—
214#103—28no—
215#103—44no—
216#103—48no—
217#95—28no—
218#95—28no—
219#95—22no—
220#95—24no—
221#95—44no—
222#95—44no—
223#95—42no—
224#95—44no—
225#95—42no—
226#95—81no—
227#95SD1614yes—
228C24C22×D411yescharacteristic
229C2×Q8—22no—
230C2×Q8—24no—
231C2×Q8—22no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—24no—
236C2×Q8—24no—
237C2×Q8—24no—
238C2×Q8—24no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C4⋊Q814yes—
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—24no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4#12112yes—
300C22×C4#12112yes—
301C22×C4C22⋊Q814yes—
302C22×C4C22⋊Q814yes—
303C22×C4C2×SD1612yes—
304C22×C4C2×SD1614yes—
305C22×C4AGL(1,ℤ/8)12yes—
306C22×C4#13714yes—
307C22×C4C22×D411yescharacteristic
308C22×C4C22×Q812yes—
309C22×C4C2×#4112yes—
310C22×C4C2×#4111yescharacteristic
311C22×C4C2×#4111yescharacteristic
312C22×C4C2×#4112yes—
313C22×C4C2×#4111yescharacteristic
314C22×C4H(5,𝔽2)12yes—
315C22×C4H(5,𝔽2)11yescharacteristic
316C22×C4H(5,𝔽2)11yescharacteristic
317C2×C8—22no—
318C2×C8—24no—
319C2×C8—41no—
320C2×C8—42no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—42no—
324C2×C8—41no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—24no—
339C4⋊C4—24no—
340C4⋊C4—48no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—42no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—42no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—88no—
353C4⋊C4—84no—
354C4⋊C4—88no—
355C4⋊C4—84no—
356C4⋊C4—84no—
357C4⋊C4#12314yes—
358C42—22no—
359C42—24no—
360C42—22no—
361C42—24no—
362C42—24no—
363C42—24no—
364C42—24no—
365C42—48no—
366C42—88no—
367C23C2×#12111yescharacteristic
368C23C2×C22⋊Q812yes—
369C23#54612yes—
370C23#54611yescharacteristic
371C23#55011yescharacteristic
372C23C22×SD1611yescharacteristic
373C23C2×AGL(1,ℤ/8)11yescharacteristic
374C23C2×#13712yes—
375C23#57611yescharacteristic
376C23#57711yescharacteristic
377C23#57812yes—
378Q8—24no—
379Q8—24no—
380Q8—44no—
381Q8—42no—
382Q8—42no—
383Q8—44no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—81no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—81no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4#46014yes—
443C2×C4#47518yes—
444C2×C4C2×#12311yescharacteristic
445C2×C4#52511yescharacteristic
446C2×C4#52912yes—
447C2×C4#52912yes—
448C2×C4C2×C4⋊Q811yescharacteristic
449C2×C4#53211yescharacteristic
450C2×C4#53312yes—
451C2×C4#53411yescharacteristic
452C2×C4#53511yescharacteristic
453C2×C4#53812yes—
454C2×C4#54012yes—
455C2×C4#55112yes—
456C2×C4#55311yescharacteristic
457C2×C4#55412yes—
458C2×C4#55412yes—
459C2×C4#55412yes—
460C2×C4#55412yes—
461C2×C4#55511yescharacteristic
462C8—42no—
463C8—81no—
464C8—82no—
465C22#241211yescharacteristic
466C22#241411yescharacteristic
467C22#245012yes—
468C22#245412yes—
469C22#285711yescharacteristic
470C22C2×#46011yescharacteristic
471C22#303911yescharacteristic
472C22#304411yescharacteristic
473C22#304511yescharacteristic
474C22C2×#47512yes—
475C22#307912yes—
476C22#308212yes—
477C22#308312yes—
478C22#329511yescharacteristic
479C22#329812yes—
480C22#330812yes—
481C22#331212yes—
482C22#331412yes—
483C22#332411yescharacteristic
484C22#333112yes—
485C22#339211yescharacteristic
486C22#339812yes—
487C22#339911yescharacteristic
488C4—28no—
489C4—24no—
490C4—44no—
491C4—42no—
492C4—44no—
493C4—44no—
494C4—82no—
495C4—84no—
496C4—162no—
497C4—161no—
498C4#239511yescharacteristic
499C4#250211yescharacteristic
500C4#252212yes—
501C4#257412yes—
502C4#258311yescharacteristic
503C4#266111yescharacteristic
504C2#1484011yescharacteristic
505C2#2452811yescharacteristic
506C2#2454811yescharacteristic
507C2#2462811yescharacteristic
508C2#2464811yescharacteristic
509C2#2641212yes—
510C2#2643112yes—
511C2#2652812yes—
512C2#2654212yes—
513C2#3319611yescharacteristic
514C2#3320611yescharacteristic
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
#138172
#113732
#113222
#112272
#110772
#110502
#109082
#108492