Finite Group Databasebeta

← #453781

Subgroups — #453781

Order 512.

844 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14041C212yesmaximal
2#11346C211yesmaximal, characteristic
3#11328C211yesmaximal, characteristic
4#11316C212yesmaximal
5#11315C212yesmaximal
6#11292C212yesmaximal
7#11256C211yesmaximal, characteristic
8#10907C212yesmaximal
9#10907C212yesmaximal
10C22×#107C2211yescharacteristic
11C22×#107C2211yescharacteristic
12C2×#389C2212yes—
13C2×C4×C4⋊C4C2212yes—
14C2×C4×C4⋊C4C2211yescharacteristic
15C2×#340C2212yes—
16C2×#340C2212yes—
17C2×#340C2212yes—
18C2×#340C2211yescharacteristic
19C2×#340C2212yes—
20C2×#340C2211yescharacteristic
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#336C2212yes—
24C2×#336C2212yes—
25C2×#336C2211yescharacteristic
26C2×#336C2211yescharacteristic
27#1445—22no—
28#1442—22no—
29#1436—22no—
30#1436—22no—
31C4⋊#95C2212yes—
32C4⋊#95C2212yes—
33C4⋊#95C2212yes—
34C4⋊#95C2212yes—
35C23×C8C2312yes—
36C23×C8C2311yescharacteristic
37C23×C8C2311yescharacteristic
38C22×C4⋊C4—22no—
39C22×C4⋊C4D411yescharacteristic
40C22×C4⋊C4D411yescharacteristic
41C22×C4⋊C4C2312yes—
42C22×C4⋊C4C2312yes—
43C22×C4⋊C4C2312yes—
44C22×C4⋊C4C2312yes—
45C22×C42—22no—
46C22×C42C2312yes—
47C22×C42C2311yescharacteristic
48C2×#107—24no—
49C2×#107—24no—
50C2×#107—41no—
51C2×#107—41no—
52#389—24no—
53#389—24no—
54C4×C4⋊C4—41no—
55C4×C4⋊C4—41no—
56C4×C4⋊C4—42no—
57C4×C4⋊C4—42no—
58C2×#95—22no—
59C2×#95—22no—
60C2×#95—22no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95—22no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95D412yes—
69#340—22no—
70#340—22no—
71#340—24no—
72#340—24no—
73#340—24no—
74#340—24no—
75#340—24no—
76#340—42no—
77#336—24no—
78#336—24no—
79#336—41no—
80#336—41no—
81C23×C4—22no—
82C23×C4—22no—
83C23×C4—22no—
84C23×C4—22no—
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D412yes—
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D412yes—
89C23×C4C2411yescharacteristic
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—22no—
99C22×C8—22no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8#4112yes—
106C22×C8#4112yes—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—24no—
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—28no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—82no—
135C2×C4⋊C4—82no—
136C2×C4⋊C4#4114yes—
137C2×C4⋊C4#4114yes—
138C2×C4⋊C4#4114yes—
139C2×C42—22no—
140C2×C42—22no—
141C2×C42—22no—
142C2×C42—22no—
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—22no—
149C2×C42—44no—
150C2×C42—82no—
151C2×C42—82no—
152#107—44no—
153#107—44no—
154#95—28no—
155#95—42no—
156#95—44no—
157#95—44no—
158#95—44no—
159#95—44no—
160#95—82no—
161#95—82no—
162#95—82no—
163#95—82no—
164#95—82no—
165C24C22×D411yescharacteristic
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—24no—
177C22×C4—24no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4#13512yes—
217C22×C4#13714yes—
218C22×C4C2×#4112yes—
219C22×C4C2×#4111yescharacteristic
220C22×C4C2×#4111yescharacteristic
221C22×C4C2×#4112yes—
222C22×C4C2×#4112yes—
223C22×C4H(5,𝔽2)11yescharacteristic
224C22×C4H(5,𝔽2)11yescharacteristic
225C22×C42−1+411yescharacteristic
226C22×C42−1+412yes—
227C22×C42−1+411yescharacteristic
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—24no—
248C4⋊C4—24no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—44no—
252C4⋊C4—44no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—88no—
264C42—42no—
265C42—42no—
266C42—41no—
267C42—42no—
268C42—41no—
269C42—42no—
270C42—42no—
271C42—88no—
272C23#52512yes—
273C23#53411yescharacteristic
274C23#54711yescharacteristic
275C23#54711yescharacteristic
276C23#54812yes—
277C23C2×#13511yescharacteristic
278C23C2×#13712yes—
279C23#57511yescharacteristic
280C23#57611yescharacteristic
281C23#57612yes—
282C23#57811yescharacteristic
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—82no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4#52912yes—
336C2×C4#52912yes—
337C2×C4#53912yes—
338C2×C4#53911yescharacteristic
339C2×C4#53911yescharacteristic
340C2×C4#54112yes—
341C2×C4#54112yes—
342C2×C4#55111yescharacteristic
343C2×C4#55111yescharacteristic
344C2×C4#55212yes—
345C2×C4#55212yes—
346C2×C4#55312yes—
347C2×C4#55612yes—
348C2×C4#55612yes—
349C2×C4#55911yescharacteristic
350C2×C4#55911yescharacteristic
351C2×C4#56311yescharacteristic
352C2×C4#56311yescharacteristic
353C8—42no—
354C8—42no—
355C8—82no—
356C22#246912yes—
357C22#247512yes—
358C22#260011yescharacteristic
359C22#272411yescharacteristic
360C22#272811yescharacteristic
361C22#310812yes—
362C22#311612yes—
363C22#312212yes—
364C22#312412yes—
365C22#319111yescharacteristic
366C22#319511yescharacteristic
367C22#319911yescharacteristic
368C22#320311yescharacteristic
369C22#334111yescharacteristic
370C22#334211yescharacteristic
371C22#334612yes—
372C22#334612yes—
373C22#335211yescharacteristic
374C22#335511yescharacteristic
375C22#336112yes—
376C22#337012yes—
377C22#337412yes—
378C22#337512yes—
379C4—44no—
380C4—42no—
381C4—84no—
382C4—82no—
383C4—81no—
384C4—84no—
385C4—84no—
386C4—162no—
387C4#251711yescharacteristic
388C4#252311yescharacteristic
389C4#259612yes—
390C4#277612yes—
391C4#278911yescharacteristic
392C4#279411yescharacteristic
393C2#1611511yescharacteristic
394C2#2713312yes—
395C2#2715212yes—
396C2#2736112yes—
397C2#2738812yes—
398C2#2941611yescharacteristic
399C2#2942211yescharacteristic
400C2#3246211yescharacteristic
401C2#3246711yescharacteristic
402C2#3254511yescharacteristic
403C2#3256311yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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
#140412
#113462
#113282
#113162
#113152
#112922
#112562
#109072