Finite Group Databasebeta

← #474789

Subgroups — #474789

Order 512.

836 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14277C211yesmaximal, characteristic
2#14277C211yesmaximal, characteristic
3#11372C212yesmaximal
4#11293C212yesmaximal
5#11292C212yesmaximal
6#11267C212yesmaximal
7#11208C212yesmaximal
8#11207C212yesmaximal
9#10796C211yesmaximal, characteristic
10C2×#389C2212yes—
11C2×#389C2212yes—
12C2×#384C2211yescharacteristic
13C2×#384C2211yescharacteristic
14C2×#382C2211yescharacteristic
15C2×#382C2211yescharacteristic
16C2×#376C2211yescharacteristic
17C2×#340C2212yes—
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#336C2212yes—
26C2×#336C2212yes—
27C2×#336C2211yescharacteristic
28C2×#336C2211yescharacteristic
29#1444—21no—
30#1444—21no—
31#1444—21no—
32#1444—21no—
33#1442—21no—
34#1442—21no—
35#1442—21no—
36#1442—21no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4C2312yes—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54#389—24no—
55#389—24no—
56#389—42no—
57#389—42no—
58#384—41no—
59#384—41no—
60#384—41no—
61#384—41no—
62#382—24no—
63#382—22no—
64#382Q814yes—
65#376—41no—
66#376—41no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—22no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95D411yescharacteristic
78C2×#95D411yescharacteristic
79C2×#95D411yescharacteristic
80C2×#95D411yescharacteristic
81#340—24no—
82#340—24no—
83#340—42no—
84#340—42no—
85#340—42no—
86#340—42no—
87#340—42no—
88#340—42no—
89#336—24no—
90#336—24no—
91#336—41no—
92#336—41no—
93C23×C4—22no—
94C23×C4—22no—
95C23×C4—22no—
96C23×C4—22no—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2411yescharacteristic
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—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C2×C4⋊C4—22no—
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—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—42no—
141C2×C4⋊C4—42no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—44no—
145C2×C4⋊C4—44no—
146C2×C4⋊C4—82no—
147C2×C4⋊C4—82no—
148C2×C4⋊C4—82no—
149C2×C4⋊C4—82no—
150C2×C4⋊C4—82no—
151C2×C4⋊C4—82no—
152C2×C4⋊C4—82no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4C2×Q814yes—
155C2×C4⋊C4#4114yes—
156C2×C42—22no—
157C2×C42—21no—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—22no—
166C2×C42—22no—
167C2×C42C2×Q812yes—
168C2×C42#4112yes—
169C2×C42#4114yes—
170#95—24no—
171#95—24no—
172#95—24no—
173#95—24no—
174#95—41no—
175#95—41no—
176#95—41no—
177#95—41no—
178#95—44no—
179#95—44no—
180#95—82no—
181#95—82no—
182#95—82no—
183#95—82no—
184C24C22×D411yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—24no—
202C22×C4—24no—
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—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
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—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4C22⋊Q812yes—
240C22×C4C22⋊Q812yes—
241C22×C4#12412yes—
242C22×C4#12412yes—
243C22×C4C22×Q811yescharacteristic
244C22×C4C2×#4112yes—
245C22×C4C2×#4111yescharacteristic
246C22×C4C2×#4112yes—
247C22×C4H(5,𝔽2)12yes—
248C22×C4H(5,𝔽2)11yescharacteristic
249C22×C4H(5,𝔽2)11yescharacteristic
250C22×C42−1+411yescharacteristic
251C22×C42−1+411yescharacteristic
252C22×C42−1+412yes—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—88no—
284C4⋊C4—84no—
285C4⋊C4—84no—
286C4⋊C4—84no—
287C4⋊C4—84no—
288C4⋊C4—88no—
289C42—22no—
290C42—22no—
291C42—22no—
292C42—22no—
293C42—24no—
294C42—24no—
295C42—42no—
296C42—42no—
297C23C2×C22⋊Q811yescharacteristic
298C23#52511yescharacteristic
299C23C2×#12411yescharacteristic
300C23#53411yescharacteristic
301C23#53511yescharacteristic
302C23#53611yescharacteristic
303C23#53611yescharacteristic
304C23#57612yes—
305C23#57712yes—
306C23#57712yes—
307C23#57812yes—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4#53911yescharacteristic
367C2×C4#53911yescharacteristic
368C2×C4#53912yes—
369C2×C4#53912yes—
370C2×C4#54112yes—
371C2×C4#54112yes—
372C2×C4#54411yescharacteristic
373C2×C4#54411yescharacteristic
374C2×C4#55312yes—
375C2×C4#55312yes—
376C2×C4#55412yes—
377C2×C4#55512yes—
378C2×C4#55612yes—
379C2×C4#55712yes—
380C2×C4#56212yes—
381C2×C4#56212yes—
382C8—82no—
383C8—82no—
384C22#256311yescharacteristic
385C22#258111yescharacteristic
386C22#259111yescharacteristic
387C22#262711yescharacteristic
388C22#263311yescharacteristic
389C22#264211yescharacteristic
390C22#281611yescharacteristic
391C22#308312yes—
392C22#308412yes—
393C22#311912yes—
394C22#312012yes—
395C22#313612yes—
396C22#313712yes—
397C22#319911yescharacteristic
398C22#320011yescharacteristic
399C22#320011yescharacteristic
400C22#320211yescharacteristic
401C22#322412yes—
402C22#322512yes—
403C22#324112yes—
404C22#324212yes—
405C22#324312yes—
406C22#324412yes—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—42no—
411C4—81no—
412C4—81no—
413C4—84no—
414C4—84no—
415C4—162no—
416C4—162no—
417C4#278312yes—
418C4#278312yes—
419C4#280212yes—
420C4#280212yes—
421C2#1700811yescharacteristic
422C2#2915112yes—
423C2#2928512yes—
424C2#2934311yescharacteristic
425C2#2934411yescharacteristic
426C2#2997611yescharacteristic
427C2#2997711yescharacteristic
428C2#3008812yes—
429C2#3023212yes—
430C2#3277911yescharacteristic
431C2#3278011yescharacteristic
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
#142772
#113722
#112932
#112922
#112672
#112082
#112072
#107962