Finite Group Databasebeta

← #470790

Subgroups — #470790

Order 512.

908 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2095C211yesmaximal, characteristic
2C2×#2074C211yesmaximal, characteristic
3#14348C211yesmaximal, characteristic
4#14261C211yesmaximal, characteristic
5#11373C211yesmaximal, characteristic
6#11358C211yesmaximal, characteristic
7#11232C212yesmaximal
8#11219C212yesmaximal
9#11190C212yesmaximal
10#11077C212yesmaximal
11#10833C211yesmaximal, characteristic
12C22×#107C2212yes—
13C22×C4⋊C8C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C2×#391C2211yescharacteristic
17C2×#391C2211yescharacteristic
18C2×#391C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21C2×#382C2211yescharacteristic
22C2×#376C2211yescharacteristic
23#2095—24no—
24#2074—24no—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2211yescharacteristic
31C2×#336C2211yescharacteristic
32C2×#336C2212yes—
33#1443—22no—
34#1442—22no—
35#1442—22no—
36#1442—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C23×Q8C2311yescharacteristic
42C23×C8C2312yes—
43C23×C8C2312yes—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C2×#107—24no—
55C2×#107—24no—
56C2×#107—42no—
57C2×C4⋊C8—24no—
58C2×C4⋊C8—24no—
59C2×C4⋊C8—42no—
60C2×#103—24no—
61C2×#103—24no—
62C2×#103—24no—
63C2×#103—42no—
64C2×#103—42no—
65C2×#103—42no—
66#391—22no—
67#391—24no—
68#391—42no—
69#391D414yes—
70#389—42no—
71#384—22no—
72#384—22no—
73#382—22no—
74#382—22no—
75#376—24no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95—21no—
79C2×#95—22no—
80C2×#95—21no—
81C2×#95—21no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—22no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95D412yes—
89C2×#95D412yes—
90#340—24no—
91#340—42no—
92#340—42no—
93#340—42no—
94#340—42no—
95#336—22no—
96#336—22no—
97#336—42no—
98C22×Q8—21no—
99C22×Q8—22no—
100C22×Q8—22no—
101C22×Q8—22no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—22no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8C2×D412yes—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4—22no—
111C23×C4—21no—
112C23×C4—22no—
113C23×C4—21no—
114C23×C4C2×D411yescharacteristic
115C23×C4C2×D411yescharacteristic
116C23×C4C2×D412yes—
117C23×C4C2×D412yes—
118C23×C4C2411yescharacteristic
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8#4114yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
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—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4C2×D412yes—
162C2×C42—22no—
163C2×C42—22no—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42—21no—
167C2×C42—22no—
168C2×C42—21no—
169C2×C42—22no—
170C2×C42—21no—
171C2×C42C2×D412yes—
172C2×C42#4112yes—
173C2×C42#4114yes—
174#107—48no—
175C4⋊C8—48no—
176#103—48no—
177#103—48no—
178#95—28no—
179#95—24no—
180#95—24no—
181#95—42no—
182#95—42no—
183#95—42no—
184#95—44no—
185#95—44no—
186#95—82no—
187#95—82no—
188#95—82no—
189#95—82no—
190#95—82no—
191#95—82no—
192C24C22×D411yescharacteristic
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—24no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×Q8—42no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—42no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4#12114yes—
268C22×C4#12314yes—
269C22×C4C22×D411yescharacteristic
270C22×C4C2×#4112yes—
271C22×C4C2×#4112yes—
272C22×C4C2×#4111yescharacteristic
273C22×C4H(5,𝔽2)11yescharacteristic
274C22×C4H(5,𝔽2)11yescharacteristic
275C22×C4H(5,𝔽2)12yes—
276C22×C42−1+411yescharacteristic
277C22×C42−1+411yescharacteristic
278C22×C42−1+412yes—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C4⋊C4—24no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—88no—
308C4⋊C4—84no—
309C42—24no—
310C42—24no—
311C42—24no—
312C42—24no—
313C42—42no—
314C42—42no—
315C23C2×#12111yescharacteristic
316C23C2×#12311yescharacteristic
317C23#53211yescharacteristic
318C23#53511yescharacteristic
319C23#53611yescharacteristic
320C23#53711yescharacteristic
321C23#53711yescharacteristic
322C23#57612yes—
323C23#57712yes—
324C23#57812yes—
325C23#57812yes—
326Q8—44no—
327Q8—44no—
328Q8—82no—
329Q8—82no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4#53511yescharacteristic
391C2×C4#53611yescharacteristic
392C2×C4#53912yes—
393C2×C4#54012yes—
394C2×C4#54112yes—
395C2×C4#54212yes—
396C2×C4#54211yescharacteristic
397C2×C4#54211yescharacteristic
398C2×C4#54612yes—
399C2×C4#54712yes—
400C2×C4#55112yes—
401C2×C4#55212yes—
402C2×C4#55212yes—
403C2×C4#55912yes—
404C2×C4#56212yes—
405C2×C4#56312yes—
406C8—44no—
407C8—82no—
408C22#248611yescharacteristic
409C22#249811yescharacteristic
410C22#254411yescharacteristic
411C22#262011yescharacteristic
412C22#262411yescharacteristic
413C22#266411yescharacteristic
414C22#282011yescharacteristic
415C22#304412yes—
416C22#304512yes—
417C22#309712yes—
418C22#309812yes—
419C22#317712yes—
420C22#317912yes—
421C22#322011yescharacteristic
422C22#322111yescharacteristic
423C22#322311yescharacteristic
424C22#322311yescharacteristic
425C22#324212yes—
426C22#324312yes—
427C22#325812yes—
428C22#325812yes—
429C22#326212yes—
430C22#326212yes—
431C4—44no—
432C4—44no—
433C4—82no—
434C4—82no—
435C4—81no—
436C4—81no—
437C4—161no—
438C4—162no—
439C4—162no—
440C4—161no—
441C4#269812yes—
442C4#270612yes—
443C4#275412yes—
444C4#277312yes—
445C2#1670111yescharacteristic
446C2#2765612yes—
447C2#2787212yes—
448C2#2862511yescharacteristic
449C2#2863011yescharacteristic
450C2#2984012yes—
451C2#2993111yescharacteristic
452C2#2993411yescharacteristic
453C2#3039112yes—
454C2#3282911yescharacteristic
455C2#3283211yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#20952
C2×#20742
#143482
#142612
#113732
#113582
#112322
#112192
#111902
#110772
#108332