Finite Group Databasebeta

← #241178

Subgroups — #241178

Order 512.

906 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35181C211yesmaximal, characteristic
2#21359C211yesmaximal, characteristic
3#21358C211yesmaximal, characteristic
4#14150C211yesmaximal, characteristic
5#10572C214yesmaximal
6#10571C214yesmaximal
7#8026C211yesmaximal, characteristic
8#8026C211yesmaximal, characteristic
9#7908C211yesmaximal, characteristic
10C2×#431C2211yescharacteristic
11C2×#431C2211yescharacteristic
12#2851—22no—
13#2646C2214yes—
14#2571—21no—
15#2571—21no—
16#2570—22no—
17#2570—22no—
18#2552—21no—
19#2552—21no—
20#2317—21no—
21#2317—21no—
22C2×#389—21no—
23#2285C2211yescharacteristic
24#2285C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28#1948—21no—
29#1948—21no—
30#1947—21no—
31#1947—21no—
32#1853C2212yes—
33#1853C2212yes—
34#1852C2212yes—
35#1852C2212yes—
36C4×#107—22no—
37C4×#106—22no—
38#1444C2212yes—
39#1442C2212yes—
40#1436—22no—
41C4⋊#95—21no—
42#1294C2214yes—
43#1294C2214yes—
44#1280C2214yes—
45C2×#125—22no—
46C2×#117—21no—
47C2×#117—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C4⋊C4C2311yescharacteristic
54C22×C42—21no—
55C22×C42D412yes—
56C22×C42C2311yescharacteristic
57#431—22no—
58#431—22no—
59#431Q814yes—
60#431Q814yes—
61C2×#107—22no—
62C2×#107—22no—
63C2×#106—22no—
64C2×#106—22no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C22⋊C8C2312yes—
68C2×C22⋊C8C2312yes—
69C2×C4×C8—21no—
70C2×C4×C8—21no—
71#400—24no—
72#400—24no—
73#398—24no—
74#398—24no—
75#389—22no—
76#389—22no—
77#389—22no—
78#389—22no—
79#389—22no—
80#389—22no—
81#389—44no—
82#387—24no—
83#387—24no—
84#385—24no—
85#385—24no—
86#384—22no—
87#384—22no—
88#384D411yescharacteristic
89#384D411yescharacteristic
90#384D411yescharacteristic
91#384D411yescharacteristic
92#382—22no—
93#382—22no—
94#382—22no—
95#382—21no—
96#382—21no—
97#382—22no—
98#382Q814yes—
99#380—21no—
100#380—21no—
101#380C2312yes—
102#380C2312yes—
103C4×C4⋊C4—21no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C4×C4⋊C4—21no—
108C4×C4⋊C4—21no—
109C4×C4⋊C4—21no—
110C4×C4⋊C4—21no—
111C4×C4⋊C4—21no—
112C4×C4⋊C4—21no—
113C4×C4⋊C4D412yes—
114C4×C4⋊C4D412yes—
115C2×#95—21no—
116C2×#95—22no—
117C2×#95—21no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95C2312yes—
121C2×#95C2312yes—
122#340—22no—
123#340—22no—
124#340—22no—
125#340—22no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4C2×D412yes—
130C23×C4C2×D412yes—
131C23×C4C2×D411yescharacteristic
132C23×C4C2×D411yescharacteristic
133C23×C4C2411yescharacteristic
134C22×C8—22no—
135C22×C8—22no—
136#125—84no—
137#117—42no—
138#117—42no—
139#117—42no—
140#117—42no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—82no—
173C2×C4⋊C4C2×D412yes—
174C2×C4⋊C4C2×D412yes—
175C2×C4⋊C4C2×D412yes—
176C2×C4⋊C4C2×D412yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—41no—
184C2×C42—41no—
185C2×C42—42no—
186C2×C42—42no—
187C2×C42—82no—
188C2×C42C2×D411yescharacteristic
189C2×C42C2×D411yescharacteristic
190C2×C42C2×D411yescharacteristic
191C2×C42C2×D411yescharacteristic
192C2×C42C2×Q812yes—
193C2×C42C2×Q812yes—
194C2×C42C2×Q812yes—
195C2×C42#4112yes—
196#107—44no—
197#107—44no—
198#106—44no—
199#106—44no—
200C4⋊C8—24no—
201C4⋊C8—24no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8C2×Q814yes—
205C22⋊C8C2×Q814yes—
206C4×C8—24no—
207C4×C8—24no—
208#95—24no—
209#95—24no—
210#95—24no—
211#95—24no—
212#95—22no—
213#95—22no—
214#95—24no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—44no—
221#95—44no—
222#95—41no—
223#95—41no—
224#95—82no—
225#95C2×Q814yes—
226C24C22×D411yescharacteristic
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4#12011yescharacteristic
267C22×C4#12011yescharacteristic
268C22×C4#12011yescharacteristic
269C22×C4#12011yescharacteristic
270C22×C4C22⋊Q812yes—
271C22×C4C22⋊Q812yes—
272C22×C4C4⋊Q812yes—
273C22×C4C4⋊Q812yes—
274C22×C4#13512yes—
275C22×C4#13512yes—
276C22×C4AGL(1,ℤ/8)12yes—
277C22×C4#13712yes—
278C22×C4C22×D411yescharacteristic
279C22×C4C22×D411yescharacteristic
280C22×C4C22×Q811yescharacteristic
281C22×C4C22×Q811yescharacteristic
282C22×C4C22×Q811yescharacteristic
283C22×C4C2×#4111yescharacteristic
284C2×C8—24no—
285C2×C8—24no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—48no—
315C4⋊C4—84no—
316C4⋊C4—84no—
317C4⋊C4—84no—
318C4⋊C4—84no—
319C4⋊C4—88no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C42—44no—
325C42—44no—
326C42—44no—
327C42—82no—
328C42—82no—
329C42—82no—
330C42C22⋊Q812yes—
331C42C22⋊Q812yes—
332C42C22⋊Q812yes—
333C42C22⋊Q812yes—
334C42C4⋊Q812yes—
335C42C4⋊Q812yes—
336C42C4⋊Q812yes—
337C42C4⋊Q812yes—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23C2×#12011yescharacteristic
343C23C2×C22⋊Q811yescharacteristic
344C23C2×C4⋊Q811yescharacteristic
345C23C2×#13511yescharacteristic
346C23C2×#13511yescharacteristic
347C23C2×AGL(1,ℤ/8)11yescharacteristic
348C23C2×#13711yescharacteristic
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
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—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4#39512yes—
407C2×C4#39512yes—
408C2×C4#39512yes—
409C2×C4#39512yes—
410C2×C4#44912yes—
411C2×C4#44912yes—
412C2×C4#45212yes—
413C2×C4#45212yes—
414C2×C4#47814yes—
415C2×C4#47914yes—
416C2×C4#49914yes—
417C2×C4#50114yes—
418C2×C4C2×C22⋊Q811yescharacteristic
419C2×C4C2×C22⋊Q811yescharacteristic
420C2×C4C2×C4⋊Q811yescharacteristic
421C2×C4C2×C4⋊Q811yescharacteristic
422C8—44no—
423C8—44no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22C2×#39511yescharacteristic
437C22C2×#44911yescharacteristic
438C22C2×#45211yescharacteristic
439C22#301911yescharacteristic
440C22#302011yescharacteristic
441C22#302511yescharacteristic
442C22#302511yescharacteristic
443C22C2×#47811yescharacteristic
444C22C2×#47911yescharacteristic
445C22C2×#49911yescharacteristic
446C22C2×#50111yescharacteristic
447C4—22no—
448C4—22no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—84no—
454C4—82no—
455C4—82no—
456C4—82no—
457C4—82no—
458C4—82no—
459C4—82no—
460C4—82no—
461C4—82no—
462C4#205914yes—
463C4#205914yes—
464C2—21no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2#1821411yescharacteristic
469C2#1821511yescharacteristic
470C2#1822211yescharacteristic
471C2#1822311yescharacteristic
472C2C2×#205911yescharacteristic
473C2#2356111yescharacteristic
474C2#2356411yescharacteristic
subgroupG/H
center, socleC23C2×#120
commutator, Frattini, cosocleC23×C4C24
prime radicalC24C22×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ 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
#351812
#213592
#213582
#141502
#105722
#105712
#80262
#79082