Finite Group Databasebeta

← #475961

Subgroups — #475961

Order 512.

884 conjugacy classes of subgroups.

The subgroup lattice has 469 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2101C212yesmaximal
2#14277C211yesmaximal, characteristic
3#14277C211yesmaximal, characteristic
4#11358C212yesmaximal
5#11267C212yesmaximal
6#11228C212yesmaximal
7#11227C212yesmaximal
8#11207C212yesmaximal
9#10833C211yesmaximal, characteristic
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C2×#389C2212yes—
13C2×#389C2212yes—
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#382C2211yescharacteristic
17C2×#382C2211yescharacteristic
18C2×#376C2211yescharacteristic
19#2101—28no—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#336C2212yes—
29C2×#336C2212yes—
30#1444—21no—
31#1444—21no—
32#1444—21no—
33#1444—21no—
34#1442—21no—
35#1442—21no—
36#1442—21no—
37#1442—21no—
38C4⋊#95C2212yes—
39C4⋊#95C2212yes—
40C23×C8C2312yes—
41C23×C8C2312yes—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C22×C42C2311yescharacteristic
55C2×C4⋊C8—22no—
56C2×C4⋊C8—22no—
57C2×C4⋊C8—41no—
58C2×C4⋊C8—41no—
59C2×C4⋊C8—41no—
60C2×C4⋊C8—41no—
61#389—24no—
62#389—24no—
63#389—24no—
64#389—24no—
65#384—41no—
66#384—41no—
67#384—41no—
68#384—41no—
69#382—22no—
70#382—22no—
71#382D414yes—
72#382Q814yes—
73#376—41no—
74#376—41no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—21no—
78C2×#95—21no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95D411yescharacteristic
86C2×#95D411yescharacteristic
87C2×#95D411yescharacteristic
88C2×#95D411yescharacteristic
89#340—24no—
90#340—24no—
91#340—24no—
92#340—24no—
93#340—42no—
94#340—42no—
95#340—42no—
96#340—42no—
97#336—24no—
98#336—24no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4—22no—
102C23×C4—22no—
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4C2411yescharacteristic
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
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—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4—42no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4—44no—
151C2×C4⋊C4—44no—
152C2×C4⋊C4—82no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4—82no—
155C2×C4⋊C4—82no—
156C2×C4⋊C4—82no—
157C2×C4⋊C4—82no—
158C2×C4⋊C4—82no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4C2×D414yes—
161C2×C4⋊C4C2×Q814yes—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42C2×D412yes—
175C2×C42C2×Q812yes—
176C2×C42#4112yes—
177C2×C42#4112yes—
178C2×C42#4112yes—
179C2×C42#4112yes—
180C4⋊C8—44no—
181C4⋊C8—44no—
182#95—24no—
183#95—24no—
184#95—24no—
185#95—24no—
186#95—41no—
187#95—41no—
188#95—41no—
189#95—41no—
190#95—44no—
191#95—44no—
192#95—82no—
193#95—82no—
194#95—82no—
195#95—82no—
196C24C22×D411yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
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—24no—
222C22×C4—24no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4#12112yes—
250C22×C4#12112yes—
251C22×C4C22⋊Q812yes—
252C22×C4C22⋊Q812yes—
253C22×C4#12412yes—
254C22×C4#12412yes—
255C22×C4C22×D411yescharacteristic
256C22×C4C22×Q811yescharacteristic
257C22×C4C2×#4111yescharacteristic
258C22×C4C2×#4111yescharacteristic
259C22×C4C2×#4111yescharacteristic
260C22×C4C2×#4111yescharacteristic
261C22×C4H(5,𝔽2)11yescharacteristic
262C22×C4H(5,𝔽2)11yescharacteristic
263C22×C4H(5,𝔽2)11yescharacteristic
264C22×C42−1+411yescharacteristic
265C22×C42−1+411yescharacteristic
266C22×C42−1+411yescharacteristic
267C22×C42−1+411yescharacteristic
268C22×C42−1+411yescharacteristic
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—88no—
300C4⋊C4—88no—
301C4⋊C4—84no—
302C4⋊C4—84no—
303C4⋊C4—84no—
304C4⋊C4—84no—
305C42—22no—
306C42—22no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C23C2×#12111yescharacteristic
318C23C2×C22⋊Q811yescharacteristic
319C23C2×#12411yescharacteristic
320C23#53411yescharacteristic
321C23#53611yescharacteristic
322C23#53611yescharacteristic
323C23#53711yescharacteristic
324C23#57612yes—
325C23#57712yes—
326C23#57712yes—
327C23#57812yes—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
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#53711yescharacteristic
387C2×C4#53711yescharacteristic
388C2×C4#53811yescharacteristic
389C2×C4#53811yescharacteristic
390C2×C4#53911yescharacteristic
391C2×C4#53911yescharacteristic
392C2×C4#53911yescharacteristic
393C2×C4#53911yescharacteristic
394C2×C4#53911yescharacteristic
395C2×C4#53911yescharacteristic
396C2×C4#54411yescharacteristic
397C2×C4#54411yescharacteristic
398C2×C4#54711yescharacteristic
399C2×C4#54711yescharacteristic
400C2×C4D4×Q811yescharacteristic
401C2×C4#55011yescharacteristic
402C2×C4#55411yescharacteristic
403C2×C4#55611yescharacteristic
404C2×C4#55611yescharacteristic
405C2×C4#55611yescharacteristic
406C2×C4#55611yescharacteristic
407C2×C4#55611yescharacteristic
408C2×C4#55711yescharacteristic
409C2×C4#55711yescharacteristic
410C2×C4#56311yescharacteristic
411C2×C4#56311yescharacteristic
412C2×C4#56411yescharacteristic
413C2×C4#56411yescharacteristic
414C8—82no—
415C8—82no—
416C22#253811yescharacteristic
417C22#254711yescharacteristic
418C22#256811yescharacteristic
419C22#261811yescharacteristic
420C22#262711yescharacteristic
421C22#263911yescharacteristic
422C22#282211yescharacteristic
423C22#304512yes—
424C22#304612yes—
425C22#308312yes—
426C22#308412yes—
427C22#313612yes—
428C22#313712yes—
429C22#319911yescharacteristic
430C22#320011yescharacteristic
431C22#320011yescharacteristic
432C22#320211yescharacteristic
433C22#324112yes—
434C22#324212yes—
435C22#324312yes—
436C22#324412yes—
437C22#325712yes—
438C22#325812yes—
439C4—42no—
440C4—42no—
441C4—42no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—84no—
446C4—84no—
447C4—162no—
448C4—162no—
449C4#272611yescharacteristic
450C4#272611yescharacteristic
451C4#272711yescharacteristic
452C4#272711yescharacteristic
453C4#280511yescharacteristic
454C4#280511yescharacteristic
455C4#281011yescharacteristic
456C4#281011yescharacteristic
457C2#1707411yescharacteristic
458C2#2829312yes—
459C2#2873012yes—
460C2#2922812yes—
461C2#2976511yescharacteristic
462C2#2976611yescharacteristic
463C2#2997611yescharacteristic
464C2#2997711yescharacteristic
465C2#3019211yescharacteristic
466C2#3019311yescharacteristic
467C2#3285412yes—
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×#21012
#142772
#113582
#112672
#112282
#112272
#112072
#108332