Finite Group Databasebeta

← #474364

Subgroups — #474364

Order 512.

800 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14348C211yesmaximal, characteristic
2#14276C211yesmaximal, characteristic
3#11373C211yesmaximal, characteristic
4#11371C211yesmaximal, characteristic
5#11358C212yesmaximal
6#11358C211yesmaximal, characteristic
7#11358C211yesmaximal, characteristic
8#11293C212yesmaximal
9#11292C212yesmaximal
10#11267C212yesmaximal
11#10796C211yesmaximal, characteristic
12C2×#389C2211yescharacteristic
13C2×#389C2211yescharacteristic
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#382C2211yescharacteristic
17C2×#382C2211yescharacteristic
18C2×#376C2211yescharacteristic
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2212yes—
31#1442—22no—
32#1442—22no—
33#1441—22no—
34#1441—22no—
35C4⋊#95C2212yes—
36C4⋊#95C2212yes—
37C4⋊#95C2211yescharacteristic
38C4⋊#95C2211yescharacteristic
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2311yescharacteristic
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54#389—42no—
55#389—42no—
56#384—22no—
57#384—22no—
58#384—22no—
59#384—22no—
60#382—24no—
61#382—22no—
62#382—22no—
63#376—24no—
64C2×#95—22no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95D412yes—
75C2×#95D412yes—
76#340—24no—
77#340—24no—
78#340—42no—
79#340—42no—
80#340—42no—
81#340—42no—
82#340—42no—
83#340—42no—
84#336—24no—
85#336—22no—
86#336—22no—
87#336—42no—
88C23×C4—21no—
89C23×C4—21no—
90C23×C4—22no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—22no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×D412yes—
97C23×C4C2×D412yes—
98C23×C4C2411yescharacteristic
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
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—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—28no—
140C2×C4⋊C4—42no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4—44no—
143C2×C4⋊C4—82no—
144C2×C4⋊C4—82no—
145C2×C4⋊C4—82no—
146C2×C4⋊C4—82no—
147C2×C4⋊C4—82no—
148C2×C4⋊C4—82no—
149C2×C4⋊C4#4112yes—
150C2×C4⋊C4#4112yes—
151C2×C42—22no—
152C2×C42—21no—
153C2×C42—21no—
154C2×C42—22no—
155C2×C42—22no—
156C2×C42—22no—
157C2×C42—21no—
158C2×C42—22no—
159C2×C42—21no—
160C2×C42#4114yes—
161C2×C42#4112yes—
162C2×C42#4112yes—
163#95—24no—
164#95—24no—
165#95—42no—
166#95—42no—
167#95—44no—
168#95—44no—
169#95—82no—
170#95—82no—
171#95—82no—
172#95—82no—
173#95—82no—
174#95—82no—
175C24C22×D411yescharacteristic
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
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#12314yes—
233C22×C4#12414yes—
234C22×C4C2×#4111yescharacteristic
235C22×C4C2×#4111yescharacteristic
236C22×C4C2×#4112yes—
237C22×C4C2×#4111yescharacteristic
238C22×C4C2×#4111yescharacteristic
239C22×C4H(5,𝔽2)12yes—
240C22×C4H(5,𝔽2)11yescharacteristic
241C22×C42−1+412yes—
242C22×C42−1+412yes—
243C22×C42−1+411yescharacteristic
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—88no—
275C4⋊C4—88no—
276C4⋊C4—84no—
277C4⋊C4—84no—
278C42—24no—
279C42—24no—
280C42—24no—
281C42—24no—
282C42—42no—
283C42—42no—
284C23C2×#12311yescharacteristic
285C23#52511yescharacteristic
286C23C2×#12411yescharacteristic
287C23#53511yescharacteristic
288C23#53611yescharacteristic
289C23#53611yescharacteristic
290C23#53711yescharacteristic
291C23#57612yes—
292C23#57712yes—
293C23#57712yes—
294C23#57812yes—
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4#53912yes—
354C2×C4#53912yes—
355C2×C4#54012yes—
356C2×C4#54212yes—
357C2×C4#54212yes—
358C2×C4#54212yes—
359C2×C4#55212yes—
360C2×C4#55212yes—
361C2×C4#55212yes—
362C2×C4#55212yes—
363C2×C4#55611yescharacteristic
364C2×C4#55611yescharacteristic
365C2×C4#55911yescharacteristic
366C2×C4#55911yescharacteristic
367C2×C4#56312yes—
368C2×C4#56412yes—
369C8—82no—
370C8—82no—
371C22#248411yescharacteristic
372C22#250311yescharacteristic
373C22#259211yescharacteristic
374C22#262411yescharacteristic
375C22#263311yescharacteristic
376C22#264011yescharacteristic
377C22#282211yescharacteristic
378C22#309812yes—
379C22#309912yes—
380C22#311812yes—
381C22#312112yes—
382C22#313612yes—
383C22#313712yes—
384C22#322011yescharacteristic
385C22#322111yescharacteristic
386C22#322211yescharacteristic
387C22#322311yescharacteristic
388C22#324112yes—
389C22#324112yes—
390C22#324212yes—
391C22#324212yes—
392C22#326212yes—
393C22#326312yes—
394C4—44no—
395C4—44no—
396C4—82no—
397C4—82no—
398C4—81no—
399C4—81no—
400C4—162no—
401C4—162no—
402C4—161no—
403C4—161no—
404C4#276712yes—
405C4#276712yes—
406C4#277312yes—
407C4#277312yes—
408C2#1696111yescharacteristic
409C2#2762312yes—
410C2#2797012yes—
411C2#2936212yes—
412C2#2993111yescharacteristic
413C2#2993211yescharacteristic
414C2#3008411yescharacteristic
415C2#3008611yescharacteristic
416C2#3020911yescharacteristic
417C2#3021011yescharacteristic
418C2#3285512yes—
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
#143482
#142762
#113732
#113712
#113582
#112932
#112922
#112672
#107962